The UBV Color Evolution of Classical Novae. III. Time-stretched Color–Magnitude Diagram of Novae in Outburst

First, we need to know the intrinsic color and time-stretching factor f_s in order to analyze a particular nova light curve. The procedure is summarized as follows:

• 1.  
  Calculate the intrinsic colors of (B − V)₀ and (U − B)₀ as

  $$\begin{eqnarray}&&{\left(B-V\right)}_{0}=(B-V)-E(B-V)\end{eqnarray} \tag{ 2 }$$

  and

  $$\begin{eqnarray}&&{\left(U-B\right)}_{0}=(U-B)-0.64E(B-V),\end{eqnarray} \tag{ 3 }$$

  where the factor of 0.64 is taken from Rieke & Lebofsky (1985). The color excess E(B − V) is taken from the literature, if available.
• 2.  
  Determine the time-stretching factor f_s of a target nova from a comparison with a template nova in the light/color curves (see, e.g., Figure 19). We adopt the template nova as one of LV Vul, V1500 Cyg, V1668 Cyg, or V1974 Cyg, which has a well-determined distance modulus μ_V ≡ (m − M)_V and extinction E(B − V). We use LV Vul as the template nova unless otherwise specified. The time-scaling factor f_s is measured against the timescale of LV Vul. In the light/color curves, we stretch/squeeze the timescale of the target nova (horizontal shift in a logarithmic timescale) and also shift the magnitude in the vertical direction. The light curve of the target nova overlaps the template nova by stretching horizontally (in the time direction) by a factor of f_s, and by shifting vertically by ΔV, we estimate the distance modulus of the target nova,

  $$\begin{eqnarray}&&\begin{array}{l}{\left(m-M\right)}_{V,\mathrm{target}}\\ \quad =\,{\left({\left(m-M\right)}_{V}+{\rm{\Delta }}V\right)}_{\mathrm{template}}-2.5\mathrm{log}{f}_{{\rm{s}}}.\end{array}\end{eqnarray} \tag{ 4 }$$

  Hachisu & Kato (2010) called this the time-stretching method. We usually increase/decrease the horizontal shift by a step of δ(Δlog t) = δ(log f_s) = 0.01 and the vertical shift by a step of δ(ΔV) = 0.1 mag, and determine the best one by eye. The model light curves obey the universal decline law. This phase corresponds to the optically thick wind phase before the nebular phase started. In fact, many novae show a good agreement with the model light curve in the optically thick phase. Moreover, we find that the V light curve of a target nova often shows a good agreement with that of a template nova even in the nebular (optically thin) phase. In such a case, we use all the phases to determine the time-scaling factor (see, e.g., Figure 2).
• 3.  
  Determine the WD mass and absolute brightness from the comparison with model light curves calculated by Hachisu & Kato (2010, 2015, 2016a). These light curves are obtained for various WD masses and chemical compositions. The distance modulus in the V band, (m − M)_V, is determined independently of step 2.
• 4.  
  Steps 2 and 3 above are independent methods. Thus, good agreement of the two (m − M)_V confirms our method. We obtain the distance d to the target nova from the relation

  $$\begin{eqnarray}&&{\left(m-M\right)}_{V}=3.1E(B-V)+5\mathrm{log}(d/10\,\mathrm{pc}),\end{eqnarray} \tag{ 5 }$$

  where the factor R_V = A_V/E(B − V) = 3.1 is the ratio of total to selective extinction (e.g., Rieke & Lebofsky 1985).
• 5.  
  We apply the same time-stretching method to the U, B, I_C, and K_s bands, if they are available, that is,

  $$\begin{eqnarray}\begin{array}{rcl}{\left(m-M\right)}_{U,\mathrm{target}} & = & \left({\left(m-M\right)}_{U}\right.\\ & & +{\left.{\rm{\Delta }}U-2.5\mathrm{log}{f}_{{\rm{s}}}\right)}_{\mathrm{template}},\end{array}\end{eqnarray} \tag{ 6 }$$

  $$\begin{eqnarray}\begin{array}{rcl}{\left(m-M\right)}_{B,\mathrm{target}} & = & \left({\left(m-M\right)}_{B}\right.\\ & & +\,{\left.{\rm{\Delta }}B-2.5\mathrm{log}{f}_{{\rm{s}}}\right)}_{\mathrm{template}},\end{array}\end{eqnarray} \tag{ 7 }$$

  $$\begin{eqnarray}\begin{array}{rcl}{\left(m-M\right)}_{I,\mathrm{target}} & = & \left({\left(m-M\right)}_{I}\right.\\ & & +\,{\left.{\rm{\Delta }}{I}_{{\rm{C}}}-2.5\mathrm{log}{f}_{{\rm{s}}}\right)}_{\mathrm{template}},\end{array}\end{eqnarray} \tag{ 8 }$$

  $$\begin{eqnarray}\begin{array}{rcl}{\left(m-M\right)}_{K,\mathrm{target}} & = & \left({\left(m-M\right)}_{K}\right.\\ & & +\,{\left.{\rm{\Delta }}{K}_{{\rm{s}}}-2.5\mathrm{log}{f}_{{\rm{s}}}\right)}_{\mathrm{template}},\end{array}\end{eqnarray} \tag{ 9 }$$

  where the time-scaling factor f_s is unique and the same as that in Equation (4). Thus, we independently obtain the five distance moduli in the U, B, V, I_C, and K_s bands (for example, Figure 18). Then, we obtain the relation between the distance d and color excess E(B − V) for the target nova where we use the relations

  $$\begin{eqnarray}&&{\left(m-M\right)}_{U}=4.75E(B-V)+5\mathrm{log}(d/10\,\mathrm{pc}),\end{eqnarray} \tag{ 10 }$$

  $$\begin{eqnarray}&&{\left(m-M\right)}_{B}=4.1E(B-V)+5\mathrm{log}(d/10\,\mathrm{pc}),\end{eqnarray} \tag{ 11 }$$

  $$\begin{eqnarray}&&{\left(m-M\right)}_{I}=1.5E(B-V)+5\mathrm{log}(d/10\,\mathrm{pc}),\end{eqnarray} \tag{ 12 }$$

  $$\begin{eqnarray}&&{\left(m-M\right)}_{K}=0.35E(B-V)+5\mathrm{log}(d/10\,\mathrm{pc}),\end{eqnarray} \tag{ 13 }$$

  and A_U/E(B − V) = 4.75, A_B/E(B − V) = 4.1, A_I/E(B − V) = 1.5, and A_K/E(B − V) = 0.35 are taken from Rieke & Lebofsky (1985). We plot these relations given by Equations (10), (11), (5), (12), and (13) in the reddening−distance plane. If these lines cross at the same point, this point gives correct values of reddening E(B − V) and distance d (for example, Figure 7(a)).
• 6.  
  Using E(B − V), (m − M)_V, and f_s obtained in the above procedures, we plot the (B − V)₀–M_V color–magnitude diagram and the (B − V)₀–(M_V − 2.5 log f_s) time-stretched color–magnitude diagram of the target nova (for example, Figures 8 and 9, respectively). We derive the relation

  $$\begin{eqnarray}\begin{array}{rcl}{\left(m-M^{\prime} \right)}_{V,\mathrm{target}} & \equiv & {\left({m}_{V}-({M}_{V}-2.5\mathrm{log}{f}_{{\rm{s}}})\right)}_{\mathrm{target}}\\ & = & {\left({\left(m-M\right)}_{V}+{\rm{\Delta }}V\right)}_{\mathrm{template}}\end{array}\end{eqnarray} \tag{ 14 }$$

  from Equations (1) and (4).
• 7.  
  If the track of the target nova overlaps with the LV Vul (or V1500 Cyg, V1668 Cyg, V1974 Cyg) template track in the time-stretched color–magnitude diagram, we regard our set of f_s, E(B − V), (m − M)_V, and distance d to be reasonable.

In what follows, we use LV Vul, V1500 Cyg, V1668 Cyg, and V1974 Cyg as template novae, because their distances and extinctions have been well determined. Figure 1 shows the distance–reddening relations toward the four template novae, (a) LV Vul, (b) V1500 Cyg, (c) V1668 Cyg, and (d) V1974 Cyg. We have already analyzed them in our previous papers (e.g., Hachisu & Kato 2016a, 2016b), but here we reanalyze them because new distance–reddening relations have recently become available (e.g., Chen et al. 2019; Green et al. 2018). To summarize, we use five results: (1) Marshall et al. (2006) published a three-dimensional (3D) extinction map of our Galaxy. The range is −1000 ≤ l ≤ 1000 and −100 ≤ b ≤ +100, and the resolution of the grids is Δl = 025 and Δb = 025, where (l, b) are the galactic coordinates. (2) Sale et al. (2014) presented a 3D reddening map in the region of 30° ≤ l < 215° and $| b| \lt 5^\circ$. Their data are based on the INT Photometric H-Alpha Survey photometry. (3) Green et al. (2015) published a 3D reddening map with a wider range of three quarters of the sky and with much finer grids of 34–137, the distance resolution of which is 25%. The data of the distance–reddening relation were recently revised by Green et al. (2018). (4) Özdörmez et al. (2016) obtained distance–reddening relations toward 46 novae based on the unique position of the red clump giants in the color–magnitude diagram. Recently, Özdörmez et al. (2018) added the data of recent novae. (5) Chen et al. (2019) presented 3D interstellar dust reddening maps of the galactic plane in three colors, E(G − K_s), E(G_BP − G_RP), and E(H − K_s). We use the conversion of E(B − V) = 0.75E(G_BP − G_RP) from Chen et al. (2019). The maps have a spatial angular resolution of 6 arcmin and covers the galactic longitude 0° < l < 360° and latitude $| b| \lt 10^\circ$. The maps are constructed from parallax estimates from Gaia Data Release 2 (Gaia DR2) combined with the photometry from Gaia DR2 and the infrared photometry from the 2MASS and WISE surveys.

Zoom In Zoom Out Reset image size

These five 3D dust maps often show large discrepancies (see, e.g., Figure 1(a)). The 3D dust maps essentially give an averaged value of a relatively broad region and thus, the pinpoint reddening could be different from it, because the resolutions of these dust maps are considerably larger than those of molecular cloud structures observed in the interstellar medium. For example, Figure 1(a) shows a large discrepancy among the various relations. The orange line (Green et al. 2018) is quite consistent with our values, i.e., the crossing point of (m − M)_V = 11.85 (blue line) and E(B − V) = 0.60 (vertical solid red line). This will be discussed in detail in Section 2.3.1.

Here, we re-examine the four template novae LV Vul, V1500 Cyg, V1668 Cyg, and V1974 Cyg with the new distance–reddening relations (Green et al. 2018; Chen et al. 2019) and fix the distances and extinctions for later use.

2.3.1. LV Vul 1968#1

The reddening toward LV Vul was estimated by Fernie (1969) to be E(B − V) = 0.6 ± 0.2 from the color excesses of 14 B stars near the line of sight. Tempesti (1972) obtained E(B − V) = 0.55 from the color at optical maximum; i.e., E(B − V) = (B − V)_max − (B − V)_0,max = 0.9–0.35 = 0.55. He adopted (B − V)_0,max = +0.35 (Schmidt 1957) instead of (B − V)_0,max = +0.23 (van den Bergh & Younger 1987). Hachisu & Kato (2014) obtained E(B − V) = 0.60 ± 0.05 by fitting with the typical color–color evolution track of nova outbursts. Slavin et al. (1995) obtained the distance toward LV Vul to be d = 0.92 ± 0.08 kpc using a nebular expansion parallax method.

Figure 2 shows the (a) V and (b) B light curves of LV Vul as well as YY Dor (2004) and LMC N 2009a. The LV Vul data are the same as those in Figure 4 of Paper II. The light curves of YY Dor and LMC N 2009a are time-stretched against those of LV Vul. These two novae are analyzed by Hachisu & Kato (2018b), and the various properties are summarized in their Tables 1–3. They determined the time-scaling factors of YY Dor and LMC N 2009a against LV Vul, which are plotted in Figure 2. In this case, we shift up/down the YY Dor and LMC N 2009a light curves in a step of δ(ΔV) = 0.1 mag (or δ(ΔB) = 0.1 mag) and find the best fit by eye. We use all parts of the light curve if they overlap each other. If not, we use only the part of the optically thick wind phase before the nebular (or dust blackout) phase started. Fortunately, the three light curves of LV Vul, YY Dor, and LMC N 2009a broadly overlap each other even during the nebular phase as shown in Figure 2.

Zoom In Zoom Out Reset image size

YY Dor and LMC N 2009a belong to the Large Magellanic Cloud (LMC) and their distances are well constrained. We adopt μ_0,LMC = 18.493 ± 0.048 (Pietrzyński et al. 2011). The reddening toward YY Dor is assumed to be E(B − V) = 0.12, which is the typical reddening toward the LMC (Imara & Blitz 2007). The distance modulus in the V band is (m − M)_V = μ₀ + A_V = 18.49 + 3.1 × 0.12 = 18.86 toward the LMC novae. Applying the obtained f_s and ΔV to Equation (4), we have the relation

$$\begin{eqnarray}&&\begin{array}{l}{\left(m-M\right)}_{V,\mathrm{LV}\mathrm{Vul}}\\ \quad =\,{\left({\left(m-M\right)}_{V}+{\rm{\Delta }}V\right)}_{\mathrm{YY}\mathrm{Dor}}-2.5\mathrm{log}3.16\\ \quad =\,18.86-5.75\pm 0.2-1.25=11.86\pm 0.2\\ \quad =\,{\left({\left(m-M\right)}_{V}+{\rm{\Delta }}V\right)}_{\mathrm{LMCN}2009{\rm{a}}}-2.5\mathrm{log}2.0\\ \quad =\,18.86-6.25\pm 0.2-0.75=11.86\pm 0.2.\end{array}\end{eqnarray} \tag{ 15 }$$

Thus, we obtain (m − M)_V = 11.86 ± 0.1 for LV Vul, which is consistent with our previous results of (m − M)_V = 11.85 ± 0.1 (Hachisu & Kato 2018b).

In the same way, we obtain ΔB from Figure 2(b). Using this ΔB and f_s, we obtain

$$\begin{eqnarray}&&\begin{array}{l}{\left(m-M\right)}_{B,\mathrm{LV}\mathrm{Vul}}\\ \quad =\,{\left({\left(m-M\right)}_{B}+{\rm{\Delta }}B\right)}_{\mathrm{YY}\mathrm{Dor}}-2.5\mathrm{log}3.16\\ \quad =\,18.98-5.3\pm 0.2-1.25=12.43\pm 0.2\\ \quad =\,{\left({\left(m-M\right)}_{B}+{\rm{\Delta }}B\right)}_{\mathrm{LMCN}2009{\rm{a}}}-2.5\mathrm{log}2.0\\ \quad =\,18.98-5.8\pm 0.2-0.75=12.43\pm 0.2\end{array}\end{eqnarray} \tag{ 16 }$$

from Equation (7). Here, we adopt (m − M)_B = 18.49 + 4.1 × 0.12 = 18.98 for the LMC novae. Thus, we obtain (m − M)_B = 12.43 ± 0.1 for LV Vul.

We determine the stretching factor f_s by horizontally shifting the light and color curves. Its step is δlog f_s = 0.01 as explained in Section 2.1. Usually, we use three BVI_C light curves and the (B − V)₀ color curve to overlap them with those of the template novae against a unique f_s. The error in log f_s depends on how well these light/color curves overlap. Typically, we have 0.03–0.05 for the error in log f_s. This error is not independent but propagates to the error of the vertical fit ΔV. We estimate the typical total error of (ΔV − 2.5 log f_s) = (±0.2) + (±0.1). In the case of LV Vul, log f_s is rather well determined against YY Dor and LMC N 2009a, that is, the error of (log f_s) = ±0.02 (see Section 5.1 of Hachisu & Kato 2018b). Therefore, the total error is about (ΔV − 2.5 log f_s) = (±0.2) + (±0.05). In what follows, we include the error in the f_s determination in the error in the vertical fit ΔV, because the vertical fit always reflects the error in the f_s determination.

We plot these two distance–reddening relations of Equations (5) and (11) in Figure 1(a) by the thin solid blue and magenta lines, respectively. The crossing point of the blue, magenta, orange, and vertical red lines, i.e., d = 1.0 kpc and E(B − V) = 0.60, is in reasonable agreement with d = 0.92 ± 0.08 kpc (Slavin et al. 1995) and E(B − V) = 0.60 ± 0.05 (Hachisu & Kato 2014, 2016b). Thus, we confirm that the distance modulus in the V band is (m − M)_V = 11.85 ± 0.1, the reddening is E(B − V) = 0.60 ± 0.05, and the distance is d = 1.0 ± 0.2 kpc. These values are listed in Table 1.

Table 1.  Extinctions, Distance Moduli, and Distances for Selected Novae

Object	Outburst	E(B − V)	(m − M)V	d	log fsa	(m − M')V	References
	(year)			(kpc)
CI Aql	2000	1.0	15.7	3.3	−0.22	15.15	3
V1419 Aql	1993	0.52	15.0	4.7	+0.15	15.35	4
V679 Car	2008	0.69	16.1	6.2	+0.0	16.1	4
V705 Cas	1993	0.45	13.45	2.6	+0.45	14.55	4
V1065 Cen	2007	0.45	15.0	5.3	+0.0	15.0	2
V1369 Cen	2013	0.11	10.25	0.96	+0.17	10.65	4
IV Cep	1971	0.65	14.5	3.1	+0.0	14.5	2
T CrB	1946	0.056	10.1	0.96	−1.32	13.4	3
V407 Cyg	2010	1.0	16.1	3.9	−0.37	15.2	3
V1500 Cyg	1975	0.45	12.3	1.5	−0.22	11.75	1
V1668 Cyg	1978	0.30	14.6	5.4	+0.0	14.6	1
V1974 Cyg	1992	0.30	12.2	1.8	+0.03	12.3	1
V2362 Cyg	2006	0.60	15.4	5.1	+0.25	16.05	4
V2468 Cyg	2008	0.65	16.2	6.9	+0.38	17.15	4
V2491 Cyg	2008	0.45	17.4	15.9	−0.34	16.55	4
YY Dor	2010	0.12	18.9	50.0	−0.72	17.1	3
V446 Her	1960	0.40	11.95	1.38	+0.0	11.95	4
V533 Her	1963	0.038	10.65	1.28	+0.08	10.85	4
V838 Her	1991	0.53	13.7	2.6	−1.22	10.65	3
V959 Mon	2012	0.38	13.15	2.5	+0.14	13.5	2
RS Oph	2006	0.65	12.8	1.4	−1.02	10.25	3
V2615 Oph	2007	0.90	15.95	4.3	+0.20	16.45	4
V574 Pup	2004	0.45	15.0	5.3	+0.10	15.25	4
U Sco	2010	0.26	16.3	12.6	−1.32	13.0	3
V745 Sco	2014	0.70	16.6	7.8	−1.32	13.3	3
V1534 Sco	2014	0.93	17.6	8.8	−1.22	14.55	3
V496 Sct	2009	0.45	13.7	2.9	+0.30	14.45	4
V5114 Sgr	2004	0.47	16.65	10.9	−0.12	16.35	4
V5666 Sgr	2014	0.50	15.4	5.8	+0.25	16.0	4
V382 Vel	1999	0.25	11.5	1.4	−0.29	10.75	4
LV Vul	1968	0.60	11.85	1.0	+0.0	11.85	1,2,4
PW Vul	1984	0.57	13.0	1.8	+0.35	13.85	4
LMC N 2009a	2014	0.12	18.9	50.0	−0.52	17.6	3
LMC N 2012a	2012	0.12	18.9	50.0	−1.22	15.85	3
LMC N 2013	2013	0.12	18.9	50.0	−0.42	17.85	3
SMCN 2016	2016	0.08	16.8	20.4	−0.72	15.0	3
M31N 2008-12a	2015	0.30	24.8	780	−1.32	21.5	3

Note.

^af_s is the timescale against LV Vul.

References. 1. Hachisu & Kato (2016b), 2. Hachisu & Kato (2018a), 3. Hachisu & Kato (2018b), 4. present paper.

Download table as:  ASCIITypeset image

2.3.2. V1500 Cyg 1975

The distance to V1500 Cyg has been discussed by many authors. Young et al. (1976) estimated the distance to be 1.4 ± 0.1 kpc for E(B − V) = 0.45 (Tomkin et al. 1976) from the distance–reddening law toward the nova (depicted by the filled red circles in Figure 1(b)). We add Marshall et al.'s (2006) relations for four directions close to V1500 Cyg, that is, (l, b) = (8975, 000) (red open squares), (9000, 000) (green filled squares), (8975, −025) (blue asterisks), and (9000, −025) (magenta open circles). We further add the relations of Green et al. (2015, 2018), Sale et al. (2014), Özdörmez et al. (2016), and Chen et al. (2019). Green et al.'s and Sale et al.'s relations (black and green lines) give d = 1.5 kpc for E(B − V) = 0.45.

A firm upper limit to the apparent distance modulus was obtained to be (m − M)_V ≤ 12.5 by Ando & Yamashita (1976) from the galactic rotational velocities of interstellar H and K absorption lines. The nebular expansion parallax method also gives an estimate of the distance. Becker & Duerbeck (1980) first imaged an expanding nebula (025 yr⁻¹) of V1500 Cyg and estimated a distance of 1350 pc from the expansion velocity of v_exp = 1600 km s⁻¹. However, Wade et al. (1991) resolved an expanding nebula and obtained a much lower expansion rate of 016 yr⁻¹; they estimated the distance to be 1.56 kpc, with a much smaller expansion velocity of v_exp = 1180 km s⁻¹ (Cohen 1985). Slavin et al. (1995) obtained a similar expanding angular velocity of the nebula (016 yr⁻¹) and obtained a distance of 1550 pc from v_exp = 1180 km s⁻¹. Therefore, the distance is reasonably determined to be d = 1.5 ± 0.1 kpc from the nebular expansion parallax method.

Hachisu & Kato (2014) obtained (m − M)_V = 12.3 for V1500 Cyg using the time-stretching method together with the light curves of GK Per and V603 Aql (see Figure 40 and Equation (A1) of Paper I). We plot (m − M)_V = 12.3 (blue solid line) and E(B − V) = 0.45 (vertical red solid line) in Figure 1(b). The crossing point of these two lines is consistent with the distance–reddening relations of Green et al. (2015, 2018), Sale et al. (2014), Özdörmez et al. (2016), and Chen et al. (2019), except Marshall et al. (2006). Thus, we confirm d = 1.5 ± 0.1 kpc, E(B − V) = 0.45 ± 0.05, and (m − M)_V = 12.3 ± 0.1. The time-scaling factor of V1500 Cyg is determined to be f_s = 0.60 against LV Vul. We list these values in Table 1.

We check the distance moduli of V1500 Cyg with the LMC novae, YY Dor and LMC N 2009a, based on the time-stretching method. Figure 3 shows the BVI light curves of V1500 Cyg as well as YY Dor and LMC N 2009a. Here we use the I-band data of V1500 Cyg because no I_C data are available. We apply Equation (7) for the B band to Figure 3(a) and obtain

$$\begin{eqnarray}&&\begin{array}{l}{\left(m-M\right)}_{B,{\rm{V}}1500\mathrm{Cyg}}\\ \quad =\,{\left({\left(m-M\right)}_{B}+{\rm{\Delta }}B\right)}_{\mathrm{YY}\mathrm{Dor}}-2.5\mathrm{log}3.2\\ \quad =\,18.98-5.0\pm 0.2-1.25=12.73\pm 0.2\\ \quad =\,{\left({\left(m-M\right)}_{B}+{\rm{\Delta }}B\right)}_{\mathrm{LMC}{\rm{N}}2009{\rm{a}}}-2.5\mathrm{log}2.0\\ \quad =\,18.98-5.5\pm 0.2-0.75=12.73\pm 0.2,\end{array}\end{eqnarray} \tag{ 17 }$$

where we adopt (m − M)_B = 18.49 + 4.1 × 0.12 = 18.98 for the LMC novae. Thus, we obtain (m − M)_B,V1500 Cyg = 12.73 ± 0.1.

Zoom In Zoom Out Reset image size

For the V light curves in Figure 3(b), we similarly obtain

$$\begin{eqnarray}&&\begin{array}{l}{\left(m-M\right)}_{V,{\rm{V}}1500\mathrm{Cyg}}\\ \quad =\,{\left({\left(m-M\right)}_{V}+{\rm{\Delta }}V\right)}_{\mathrm{YY}\mathrm{Dor}}-2.5\mathrm{log}3.2\\ \quad =\,18.86-5.3\pm 0.2-1.25=12.31\pm 0.2\\ \quad =\,{\left({\left(m-M\right)}_{V}+{\rm{\Delta }}V\right)}_{\mathrm{LMC}{\rm{N}}2009{\rm{a}}}-2.5\mathrm{log}2.0\\ \quad =\,18.86-5.8\pm 0.2-0.75=12.31\pm 0.2,\end{array}\end{eqnarray} \tag{ 18 }$$

where we adopt (m − M)_V = 18.49 + 3.1 × 0.12 = 18.86 for the LMC novae. Thus, we obtain (m − M)_V,V1500 Cyg = 12.31 ± 0.1.

We apply Equation (8) to Figure 3(c) and obtain

$$\begin{eqnarray}&&\begin{array}{l}{\left(m-M\right)}_{I,{\rm{V}}1500\mathrm{Cyg}}\\ \quad =\,{\left({\left(m-M\right)}_{I}+{\rm{\Delta }}{I}_{C}\right)}_{\mathrm{YY}\mathrm{Dor}}-2.5\mathrm{log}3.2\\ \quad =\,18.66-5.85\pm 0.3-1.25=11.56\pm 0.3\\ \quad =\,{\left({\left(m-M\right)}_{I}+{\rm{\Delta }}{I}_{C}\right)}_{\mathrm{LMC}{\rm{N}}2009{\rm{a}}}-2.5\mathrm{log}2.0\\ \quad =\,18.66-6.35\pm 0.3-0.75=11.56\pm 0.3,\end{array}\end{eqnarray} \tag{ 19 }$$

where we adopt (m − M)_I = 18.49 + 1.5 × 0.12 = 18.66 for the LMC novae. Thus, we obtain (m − M)_I,V1500 Cyg = 11.56 ± 0.2.

We plot three distance moduli in the B, V, and I_C bands in Figure 1(b) by the magenta, blue, and cyan lines, that is, (m − M)_B = 12.73, (m − M)_V = 12.31, and (m − M)_I = 11.56, together with Equations (11), (5), and (12), respectively. These three lines cross at d = 1.5 kpc and E(B − V) = 0.45. This crossing point is an independent confirmation of the distance and reddening.

2.3.3. V1668 Cyg 1978

Figure 4 shows the UBV light curves of V1668 Cyg and LV Vul. The timescale of V1668 Cyg is the same as that LV Vul, that is, f_s = 1.0 against LV Vul. If the chemical composition of V1668 Cyg is similar to that of LV Vul, both WD masses should be similar. The peak of V1668 Cyg is slightly brighter than that of LV Vul. In general, the peak brightness depends mainly on the WD mass and initial envelope mass. The peak magnitude is brighter for the more massive ignition mass even if the WD masses are the same. Such a tendency was discussed in detail in Hachisu & Kato (2010; see their Figure 2 for the physical explanation). The initial envelope mass, that is, the ignition mass, is closely related to the mass accretion rate on the WD. The larger the mass accretion rate, the smaller the ignition mass (see, e.g., Figure 3 of Kato et al. 2014). We suppose that the mass accretion rate is smaller in V1668 Cyg than in LV Vul even if the two WD masses are similar.

Zoom In Zoom Out Reset image size

These two nova light curves overlap well except for the peak brightnesses. The distance moduli of LV Vul are well determined in Section 2.3.1, so the distance moduli of V1668 Cyg are calculated to be (m − M)_U = 12.84 + 2.25 ± 0.1 = 15.1 ± 0.1, (m − M)_B = 12.45 + 2.45 ± 0.1 = 14.9 ± 0.1, and (m − M)_V = 11.85 + 2.75 ± 0.1 = 14.6 ± 0.1 from the time-stretching method. These three distance moduli cross at d = 5.4 kpc and E(B − V) = 0.30 in the distance–reddening plane of Figure 1(c).

Hachisu & Kato (2006, 2016a) calculated free–free emission model light curves based on the optically thick wind model (Kato & Hachisu 1994) for various WD masses and chemical compositions and fitted their free–free emission model light curves with the V and y light curves of V1668 Cyg. They further fitted their blackbody emission UV 1455 Å model light curves with the International Ultraviolet Explore (IUE) UV 1455 Å observation, and estimated the WD mass. This is a narrowband (1445–1465 Å) flux that represents well the continuum UV fluxes of novae (Cassatella et al. 2002).

Assuming the chemical composition of CO nova 3 for V1668 Cyg, Hachisu & Kato (2016a) obtained the best-fit model of 0.98 M_☉ WD with both the V and UV 1455 Å light curves. (Such model light-curve fittings are also plotted in Figure 23 in Appendix A.2.) We plot the distance–reddening relation of (m − M)_V = 14.6 ± 0.1 (thick solid blue line flanked by two thin blue lines in Figure 1(c)) and another distance–reddening relation of the UV 1455 Å fit (thick solid magenta line flanked by two thin solid magenta lines) of

$$\begin{eqnarray}&&\begin{array}{l}2.5\mathrm{log}{F}_{1455}^{\mathrm{mod}}-2.5\mathrm{log}{F}_{1455}^{\mathrm{obs}}\\ \quad =\,5\mathrm{log}\left(\displaystyle \frac{d}{10\mathrm{kpc}}\right)+8.3\times E(B-V),\end{array}\end{eqnarray} \tag{ 20 }$$

where ${F}_{1455}^{\mathrm{mod}}$ is the model flux at the distance of 10 kpc and ${F}_{1455}^{\mathrm{obs}}$ the observed flux. Here we assume an absorption of A_λ = 8.3 × E(B − V) at λ = 1455 Å (Seaton 1979).

We further plot other distance–reddening relations toward V1668 Cyg in Figure 1(c): Slovak & Vogt (1979; filled red circles), Marshall et al. (2006), Green et al. (2015, 2018), and Chen et al. (2019). Marshall et al.'s are for four nearby directions: (l, b) = (9075, −675) (red open squares), (9100, −675) (green filled squares), (9075, −700) (blue asterisks), and (9100, −700) (magenta open circles). These trends/lines broadly cross at d = 5.4 ± 0.5 kpc and E(B − V) = 0.30 ± 0.05 except that of Chen et al. (2019). The extinction almost saturates at the distance of d ≳ 3 kpc as shown in Figure 1(c). This is consistent with the galactic 2D dust absorption map of E(B − V) = 0.29 ± 0.02 in the direction toward V1668 Cyg at the NASA/IPAC Infrared Science Archive,³ which is calculated on the basis of data from Schlafly & Finkbeiner (2011). Thus, we confirm E(B − V) = 0.30 ± 0.05.

2.3.4. V1974 Cyg 1992

We obtain the reddening and distance from the time-stretching method. We plot the UBV light curves of V1974 Cyg together with those of LV Vul and V1668 Cyg in Figure 5. The UBV light curves overlap well until the nebular phase started on Day ∼60. We use only part of the optically thick wind (or optically thick ejecta) phase, which is represented by the decline trend F_ν ∝ t^−1.75 (Hachisu & Kato 2006). The time-scaling factor of f_s = 1.07 against LV Vul is well determined from the fitting of the UV 1455 Å light curve between V1668 Cyg and V1974 Cyg (see, e.g., Figure 39(a) in Appendix B.6).

Zoom In Zoom Out Reset image size

We apply Equation (6) for the U band to Figure 5(a) and obtain

$$\begin{eqnarray}&&\begin{array}{l}{\left(m-M\right)}_{U,{\rm{V}}1974\mathrm{Cyg}}\\ \quad =\,{\left({\left(m-M\right)}_{U}+{\rm{\Delta }}U\right)}_{\mathrm{LV}\mathrm{Vul}}-2.5\mathrm{log}1.07\\ \quad =\,12.85-0.1\pm 0.2-0.08=12.67\pm 0.2\\ \quad =\,{\left({\left(m-M\right)}_{U}+{\rm{\Delta }}U\right)}_{{\rm{V}}1668\mathrm{Cyg}}-2.5\mathrm{log}1.07\\ \quad =\,15.1-2.3\pm 0.2-0.08=12.72\pm 0.2,\end{array}\end{eqnarray} \tag{ 21 }$$

where we adopt (m − M)_{U,LV Vul} = 11.85 + (4.75 − 3.1) × 0.60 = 12.85, and (m − M)_U,V1668 Cyg = 14.6 + (4.75 − 3.1) × 0.30 = 15.10. Thus, we obtain (m − M)_U,V1974 Cyg = 12.7 ± 0.1. For the B light curves in Figure 5(b), we similarly obtain

$$\begin{eqnarray}&&\begin{array}{l}{\left(m-M\right)}_{B,{\rm{V}}1974\mathrm{Cyg}}\\ \quad =\,{\left({\left(m-M\right)}_{B}+{\rm{\Delta }}B\right)}_{\mathrm{LV}\mathrm{Vul}}-2.5\mathrm{log}1.07\\ \quad =\,12.45+0.1\pm 0.2-0.08=12.47\pm 0.2\\ \quad =\,{\left({\left(m-M\right)}_{B}+{\rm{\Delta }}B\right)}_{{\rm{V}}1668\mathrm{Cyg}}-2.5\mathrm{log}1.07\\ \quad =\,14.9-2.3\pm 0.2-0.08=12.52\pm 0.2,\end{array}\end{eqnarray} \tag{ 22 }$$

where we adopt (m − M)_B,LV Vul = 11.85 + 1.0 × 0.6 = 12.45 and (m − M)_B,V1668 Cyg = 14.6 + 1.0 × 0.3 = 14.9. Thus, we obtain (m − M)_B,V1974 Cyg = 12.5 ± 0.1. We apply Equation (4) to Figure 5(c) and obtain

$$\begin{eqnarray}&&\begin{array}{l}{\left(m-M\right)}_{V,{\rm{V}}1974\mathrm{Cyg}}\\ \quad =\,{\left({\left(m-M\right)}_{V}+{\rm{\Delta }}V\right)}_{\mathrm{LV}\mathrm{Vul}}-2.5\mathrm{log}1.07\\ \quad =\,11.85+0.4\pm 0.2-0.08=12.17\pm 0.2\\ \quad =\,{\left({\left(m-M\right)}_{V}+{\rm{\Delta }}V\right)}_{{\rm{V}}1668\mathrm{Cyg}}-2.5\mathrm{log}1.07\\ \quad =\,14.6-2.3\pm 0.2-0.08=12.22\pm 0.2.\end{array}\end{eqnarray} \tag{ 23 }$$

Thus, we obtain (m − M)_V,V1974 Cyg = 12.2 ± 0.1. These three distance moduli, that is, (m − M)_U = 12.7, (m − M)_B = 12.5, and (m − M)_V = 12.2 together with Equations (10), (11), and (5), cross at d = 1.8 kpc and E(B − V) = 0.30 as shown in Figure 1(d).

Hachisu & Kato (2016a) modeled the V, UV 1455 Å, and supersoft X-ray light curves and fitted a 0.98 M_☉ WD model with the observed V, UV 1455 Å, and X-ray fluxes assuming the chemical composition of CO nova 3 (see, e.g., Figure 33(a) for such a model light-curve fit). The supersoft X-ray flux was calculated assuming that the photospheric emission is approximated by blackbody emission in the supersoft X-ray band. The V model light curve gives a distance modulus in the V band of (m − M)_V = 12.2 (blue line) as shown in Figure 1(d), while the UV 1455 Å light-curve fit gives the relation shown by the magenta line.

These two lines (blue and magenta) cross at d ≈ 1.8 kpc and E(B − V) ≈ 0.29 as shown in Figure 1(d). The figure also depicts other distance–reddening relations toward V1974 Cyg, whose galactic coordinates are (l, b) = (891338, 78193). The four sets of data points with error bars correspond to the distance–reddening relations in four directions close to V1974 Cyg: (l, b) = (8900,775) (red open squares), (8925, 775) (green filled squares), (8900, 800) (blue asterisks), and (8925, 800) (magenta open circles), the data for which are taken from Marshall et al. (2006). We also add distance–reddening relations given by Green et al. (2015, 2018; black/orange lines, respectively), Özdörmez et al. (2016; open cyan-blue diamonds with error bars), and Chen et al. (2019; cyan-blue line). The orange line is consistent with the crossing point at d ≈ 1.8 kpc and E(B − V) ≈ 0.30.

Chochol et al. (1997) estimated the distance to V1974 Cyg as d = 1.77 ± 0.11 kpc using a nebular expansion parallax method. This distance is consistent with our value of d = 1.8 ± 0.1 kpc. The reddening was also estimated by many researchers. For example, Austin et al. (1996) obtained the reddening toward V1974 Cyg mainly on the basis of the UV and optical line ratios for days 200 through 500, i.e., E(B − V) = 0.3 ± 0.1. The NASA/IPAC galactic 2D dust absorption map gives E(B − V) = 0.35 ± 0.01 in the direction toward V1974 Cyg. This slightly larger value of reddening indicates that the reddening toward V1974 Cyg does not saturate yet at the distance of 1.8 kpc, as shown in Figure 1(d). These are all consistent with our estimates, that is, (m − M)_V = 12.2 ± 0.1, d = 1.8 ± 0.1 kpc, and E(B − V) = 0.3 ± 0.05. These values are listed in Table 1.

Hachisu & Kato (2016b) proposed six template tracks of novae with well-determined distance modulus in the V-band (m − M)_V and color excess E(B − V). They dubbed them the V1500 Cyg, V1668 Cyg, V1974 Cyg, LV Vul, FH Ser, and PU Vul tracks as shown in Figure 6(a). Here, we adopt E(B − V) = 0.60 and (m − M)_V = 11.85 for LV Vul from Section 2.3.1, E(B − V) = 0.45 and (m − M)_V = 12.3 for V1500 Cyg from Section 2.3.2, E(B − V) = 0.30 and (m − M)_V = 14.6 for V1668 Cyg from Section 2.3.3, E(B − V) = 0.30 and (m − M)_V = 12.2 for V1974 Cyg from Section 2.3.4, E(B − V) = 0.60 and (m − M)_V = 11.7 for FH Ser, and E(B − V) = 0.30 and (m − M)_V = 14.3 for PU Vul both from Hachisu & Kato (2016b). They categorized 40 novae into one of these six subgroups, depending on their similarity on the (B − V)₀–M_V diagram.

Zoom In Zoom Out Reset image size

The LV Vul and V1974 Cyg tracks split into two branches just after the nebular phase started. As already discussed in our previous papers (see, e.g., Figure 10 and Section 3.3 of Hachisu & Kato 2014), strong emission lines such as [O iii] contribute to the blue edge of the V filter. A small difference in the V-filter response function makes a large difference in the V magnitude and results in a large difference in the B − V color. This is the reason why the track splits into two (or three or even four) branches among various observatories.

In the present work, we propose the (B − V)₀–(M_V − 2.5 log f_s) diagram, that is, Figure 6(b). In this new color–magnitude diagram, the above six nova tracks are shifted up or down. Here, we show the above six tracks of V1500 Cyg, V1974 Cyg, V1668 Cyg, LV Vul, FH Ser, and PU Vul, adopting (m − M')_V = 11.75 for V1500 Cyg, (m − M')_V = 12.3 for V1974 Cyg, (m − M')_V = 11.85 for LV Vul. (m − M')_V = 14.6 for V1668 Cyg, (m − M')_V = 12.45 for FH Ser, and (m − M')_V = 16.4 for PU Vul.

The tracks of V1500 Cyg and V1974 Cyg are different from each other in the early phase but almost overlap in the middle part of the tracks. They turn from toward the blue to toward the red at a similar place, that is, the turning corner. Therefore, we regard V1974 Cyg to belong to the V1500 Cyg type in the time-stretched color–magnitude diagram.

Also, the V1668 Cyg track almost follows the template track of LV Vul. Thus, these two template tracks can be merged into the same group. The track of FH Ser is close to that of V1668 Cyg and LV Vul. The track of PU Vul is close to that of V1500 Cyg. Thus, the six tracks seem to closely converge into one of the two groups, LV Vul/V1668 Cyg or V1500 Cyg/V1974 Cyg, in the time-stretched color–magnitude diagram.

The main difference between them is that the V1668 Cyg/LV Vul group novae evolve almost straight down along (B − V)₀ ∼ −0.03 during (M_V − 2.5 log f_s) = −7 and −4, while the V1500 Cyg/V1974 Cyg group novae evolve blueward up to (B − V)₀ ∼ −0.5 during (M_V − 2.5 log f_s) = −5 and −3. This tendency is clear, e.g., in the case of V2362 Cyg (Figure 13(d)).

We obtain the distance and reddening toward V574 Pup based on the time-stretching method. Figure 7(a) shows four distance moduli in the B, V, I_C, and K_s bands with the thin solid magenta, blue, cyan, and cyan-blue lines, that is, (m − M)_B = 15.43, (m − M)_V = 15.0, (m − M)_I = 14.22, and (m − M)_K = 13.68, respectively, which are obtained in Appendix A.1, together with Equations (11), (5), (12), and (13). These four lines cross at d = 5.3 kpc and E(B − V) = 0.45. Thus, we obtain the reddening toward V574 Pup, E(B − V) = 0.45 ± 0.05; the distance of V574 Pup, d = 5.3 ± 0.5 kpc; and the time-scaling factor, f_s = 1.26 against LV Vul. The distance modulus in the V band is (m − M)_V = 15.0 ± 0.1. These values are listed in Table 1.

Zoom In Zoom Out Reset image size

We further check our estimates of the distance modulus in the V-band (m − M)_V = 15.0 ± 0.1 and extinction E(B − V) = 0.45 ± 0.05. Figure 7(a) shows the distance–reddening relations toward V574 Pup, whose galactic coordinates are (l, b) = (2425695, −19933). The thick solid black/orange lines denote the distance–reddening relations given by Green et al. (2015, 2018), respectively. The open cyan-blue diamonds with error bars are taken from Özdörmez et al. (2016). The thick solid cyan-blue line denotes the result of Chen et al. (2019). These four distance–reddening relations based on the dust map are consistent with each other until d ≲ 5 kpc.

Green et al.'s black/orange lines are roughly consistent with our results of d = 5.3 ± 0.5 kpc and E(B − V) = 0.45 ± 0.05. The NASA/IPAC galactic 2D dust absorption map gives E(B − V) = 0.60 ± 0.02 toward V574 Pup, which is slightly larger than our value of E(B − V) = 0.45 ± 0.05. This is because the reddening increases further beyond the position of V574 Pup as shown in Figure 7(a).

Using E(B − V) = 0.45 and (m − M)_V = 15.0, we plot the color–magnitude diagram of V574 Pup in Figure 8(a). We add tracks of V1500 Cyg (solid green line), LV Vul (solid orange line), and V1974 Cyg (solid magenta line) for comparison. The data of V574 Pup are scattered in the early phase owing to its oscillatory behavior but close to that of V1974 Cyg (solid magenta line). Therefore, V574 Pup belongs to the V1974 Cyg type in the (B − V)₀–M_V color–magnitude diagram. The track in the early oscillatory phase shows a circular movement similar to that of V705 Cas as shown in Figure 37(b) of Paper II.

Zoom In Zoom Out Reset image size

In Figure 9(a), adopting E(B − V) = 0.45 and (m − M')_V = 15.25 in Equation (29), we obtain the time-stretched color–magnitude diagram of V574 Pup. "(m − M')_V = 15.25(−0.25)" in the figure means that (m − M')_V = 15.25 and (m − M)_V = 15.25 − 0.25 = 15.0.

Zoom In Zoom Out Reset image size

We note the starting epoch of the nebular phase in Figures 8(a) and 9(a). The nebular phase could be identified by the first clear appearance of the nebular emission lines [O iii] or [Ne iii], which are stronger than permitted lines. The nebular phase of V574 Pup started at m_V ∼ 12 from the spectra of the Small Medium Aperture Telescope System (SMARTS) database⁴ (Walter et al. 2012), which is denoted by the large open cyan square in Figures 8(a) and 9(a). After the onset of the nebular phase, the track turns to the right (red). This is because the strong emission lines of [O iii] contribute to the blue edge of the V filter, and its large contribution makes the B − V color redder.

Ness et al. (2007) discussed that the SSS phase started between 2005 May and July. This epoch corresponds to m_V ∼ 13.2 and denoted by "SSS on" in Figures 8(a) and 9(a). The (B − V)₀ color seems to keep a constant value of ∼0.0 during the SSS phase, as shown in Figure 19(b).

In Figure 9(a), the track of V574 Pup almost follows those of V1500 Cyg and V1974 Cyg except for the early oscillation phase. Thus, we conclude that V574 Pup belongs to the V1500 Cyg/V1974 Cyg type in the time-stretched color–magnitude diagram.

Kato & Hachisu (1994) calculated evolutions of nova outbursts based on the optically thick wind theory. Their numerical models provide various physical quantities such as the photospheric temperature, radius, velocity, and wind mass-loss rate of a nova hydrogen-rich envelope (mass of M_env) for a specified WD mass (M_WD) and chemical composition of the envelope. Hachisu & Kato (2015) calculated the absolute V-magnitude light curves based on Kato & Hachisu's envelope models. Their model V light curve is composed of photospheric emission and free–free emission. The photospheric emission is approximated by blackbody emission at the photosphere, while the free–free emission is calculated from the photospheric radius, velocity, and wind mass-loss rate (Hachisu & Kato 2015). Fitting the absolute V magnitudes (M_V) of model light curve with the observed apparent V magnitudes (m_V), we are able to specify the (m − M)_V (and even M_WD) for the nova. Such results are presented in Hachisu & Kato (2015, 2016a, 2018a, 2018b).

Hachisu & Kato (2010) estimated the WD mass of V574 Pup to be 1.05 M_☉. In Figure 19(a), we plot the 1.05 M_☉ WD model (solid black line for V magnitudes and solid red line for soft X-ray fluxes) with the chemical composition of Ne nova 3 (Hachisu & Kato 2016a). We use the absolute V magnitudes of the 1.05 M_☉ WD model calculated in Hachisu & Kato (2016a). We add a 0.98 M_☉ WD model (solid green lines both for V and soft X-rays) with the chemical composition of CO nova 3 (Hachisu & Kato 2016a) for comparison, the timescale of which is stretched by a factor of f_s = 1.17. The absolute V light curve of the 1.05 M_☉ WD model reasonably follows the observed apparent V light curves of V574 Pup for (m − M)_V = 15.0. In these models, the optically thick winds stop at the open black circle (at the right edge of the solid black line).

The model supersoft X-ray light curve also shows a good fit to the X-ray observation, i.e., the turn-on and turn-off times. The X-ray data are the same as those of Hachisu & Kato (2010). Thus, the 1.05 M_☉ WD model is consistent with the X-ray data. We list the WD mass of V574 Pup in Table 2.

We plot three distance moduli in the B, V, and I_C bands in Figure 7(b) by the magenta, blue, and cyan lines, that is, (m − M)_B = 16.8, (m − M)_V = 16.1, and (m − M)_I = 15.0 in Appendix A.2 together with Equations (11), (5), and (12), respectively. These three lines cross at d = 6.2 kpc and E(B − V) = 0.69. Thus, we obtain the reddening toward V679 Car, E(B − V) = 0.69 ± 0.05; the distance of V574 Pup, d = 6.2 ± 0.7 kpc; and the time-scaling factor, f_s = 1.0 against LV Vul. The distance modulus in the V band is (m − M)_V = 16.1 ± 0.1. These values are listed in Table 1.

We check the distance and reddening toward V679 Car, the galactic coordinates of which are (l, b) = (2914697, −05479), on the basis of dust extinction maps calculated by Marshall et al. (2006) and Chen et al. (2019). Figure 7(b) shows the relations given by Marshall et al. (2006): (l, b) = (29125, −050) by open red squares, (29150, −050) by filled green squares, (29125, −075) by blue asterisks, and (29150, −075) by open magenta circles. The filled green squares of Marshall et al. (2006) are the closest direction toward V679 Car among the four nearby directions. The solid cyan-blue line denotes the relation given by Chen et al. (2019). Neither Green et al.'s (2015, 2018) nor Özdörmez et al.'s (2016) data are available toward this direction. The three relations of (m − M)_B = 16.8 (magenta line), (m − M)_V = 16.1 (blue line), and (m − M)_I = 15.0 (cyan line) cross at d = 6.2 kpc and E(B − V) = 0.69. This crossing point is significantly different from the closest relation (filled green squares) given by Marshall et al. (2006). However, Chen et al.'s relation (solid cyan-blue line) seems to show a possible agreement with our crossing point, although the data end at d = 4.5 kpc.

This large discrepancy can be understood as follows: Marshall et al.'s 3D dust map gives an averaged value of a relatively broad region, and thus a pinpoint reddening toward the nova could be different from the values of the 3D dust maps, because the resolution of the dust map is considerably larger than that of molecular cloud structures observed in the interstellar medium. For example, Marshall et al.'s 3D dust map gave a significantly different value for the reddening of LV Vul as shown in Figure 1(a).

The V light-curve and (B − V)₀ color-curve shapes of V679 Car are similar to those of LV Vul and V1668 Cyg as shown in Figures 22 and 23. This suggests that the color–magnitude diagram of V679 Car is also similar to them. Adopting E(B − V) = 0.69 and (m − M)_V = 16.1, we plot the color–magnitude track in Figure 8(b) together with V1500 Cyg (solid green line) and LV Vul (solid orange line). The SMARTS spectra of V679 Car show that the nebular phase started between JD 2454845.71 (UT 2009 January 14.21) and JD 2454860.67 (UT 2009 January 29.17), corresponding to m_V = 12.45 and B − V = 0.40, which is denoted by the large open red square in Figure 8(b). The start of the nebular phase usually corresponds to the turning point from toward blue to toward red (from toward left to toward right) as already discussed in Section 3. The track of V679 Car is broadly located on the track of LV Vul (orange line), although the (B − V)₀ colors of the early phase are rather scattered and slightly bluer than those of LV Vul. After this turning point, the track of V679 Car follows that of LV Vul. We conclude that V679 Car belongs to the LV Vul type in the color–magnitude diagram (Paper II).

Adopting E(B − V) = 0.69 and (m − M')_V = 16.1 from Equation (35), we plot the time-stretched color–magnitude diagram of V679 Car in Figure 9(b). The (B − V)₀ intrinsic color is not affected by time stretch (see Hachisu & Kato 2018a). Because f_s = 1.0, the time-stretched color–magnitude track is the same as in Figure 8(b), but the track of V1500 Cyg is shifted down. The overlap of the track to the LV Vul track supports our values of E(B − V) = 0.69 and (m − M')_V = 16.1, that is, f_s = 1.0, E(B − V) = 0.69 ± 0.05, (m − M)_V = 16.1 ± 0.1, and d = 6.2 ± 0.7 kpc. We list our results in Table 1.

Figure 23(a) shows the model light curve of a 0.98 M_☉ WD (solid red lines) with the envelope chemical composition of CO Nova 3 (Hachisu & Kato 2016a). Taking the distance modulus in the V band of (m − M)_V = 16.1, we reasonably fit the model absolute V light curve with the observed apparent V magnitudes of V679 Car. Thus, our obtained value of (m − M)_V = 16.1 is consistent with the model light curve. We also add the 0.98 M_☉ WD model (solid green lines) with the same envelope chemical composition of CO nova 3 but with a slightly larger initial envelope mass, assuming (m − M)_V = 14.6 for V1668 Cyg. This model fits with the V and UV 1455 Å light curves of V1668 Cyg as already discussed in our previous paper (Hachisu & Kato 2016a).

Our model light curve of the 0.98 M_☉ WD predicts the SSS phase between day 250 and day 600 as shown in Figure 23(a). V679 Car was observed by Swift eight times, but no SSS phase was detected (Schwarz et al. 2011). The epochs of the Swift observations are indicated by the downward magenta arrows. The second and third arrows almost overlap. We expect to detect supersoft X-rays at the last one or two. Non-detection may be owing to a large extinction toward V679 Car, as large as E(B − V) = 0.69, corresponding to N_H = 8.3 × 10²¹E(B − V) = 0.6 × 10²² cm⁻² (Liszt 2014)—or see also Figure 3 in Schwarz et al. (2011)—and a relatively large distance of 6.2 kpc.

We obtain the distance and reddening toward the nova using the time-stretching method. We plot four distance moduli in the B, V, I_C, and K_s bands in Figure 7(c), which are obtained in Appendix A.3. These four (magenta, blue, cyan, cyan-blue) lines cross at the distance of 0.96 kpc and the reddening of E(B − V) = 0.11. Thus, we obtain the distance d = 0.96 ± 0.1 kpc, the reddening E(B − V) = 0.11 ± 0.03, and the time-scaling factor f_s = 1.48 against LV Vul.

Izzo et al. (2013) obtained an extinction of E(B − V) = 0.11 ± 0.08 from the relation given by Poznanski et al. (2012) or E(B − V) = 0.14 from the relation given by Munari & Zwitter (1997), both between the widths of the Na i D doublet and the extinction. Shore et al. (2014) obtained the extinction of E(B − V) ∼ 0.1 using UV interstellar spectra. They also estimated the distance of d ∼ 2.4 kpc by comparing the UV fluxes with those of V339 Del. As already mentioned, Mason et al. (2018) obtained the reddening of E(B − V) = 0.15 from the Na i D2 λ5890 interstellar absorption line and the best-fit neutral hydrogen column density derived from the model of interstellar Lyα absorption.

We further examine the reddening and distance based on various distance–reddening relations. Figure 7(c) shows the distance–reddening relations toward V1369 Cen, whose galactic coordinates are (l, b) = (3109816, +27274). We plot Marshall et al.'s (2006) relations (l, b) = (31075, +250) by open red squares, (31100, +250) by filled green squares, (31075, +275) by blue asterisks, and (31100, +275) by open magenta circles. The open magenta circles are the closest direction among the four nearby directions. Green et al.'s or Özdörmez et al.'s data are not available. We add the relation (cyan-blue line) given by Chen et al. (2019), which is consistent with our crossing point of E(B − V) = 0.11 and d = 0.96 kpc. Although Marshall et al.'s relations do not reach E(B − V) ≲ 0.2, it seems that its trend of linear extension toward E(B − V) = 0.11 is roughly consistent with our crossing point at d = 0.96 ± 0.1 kpc and E(B − V) = 0.11 ± 0.03.

Adopting E(B − V) = 0.11 and (m − M)_V = 10.25, we plot the color–magnitude diagram of V1369 Cen in Figure 8(c). We also plot the tracks of V1500 Cyg (solid green line), LV Vul (solid orange line), and V496 Sct (filled cyan triangles). The data of V496 Sct are the same as those in Figures 72(b) and 73 of Paper II. The track of V1369 Cen and V496 Sct almost follow that of LV Vul in the early phase until the dust-shell formation, which is denoted by the large open blue square. After that, the track of V1369 Cen lies under the track of LV Vul.

Figure 9(c) shows the time-stretched color–magnitude diagram of V1369 Cen. We adopt E(B − V) = 0.11 and (m − M')_V = 10.65 from Equation (37). Now, the track of V1369 Cen and V496 Sct almost follow that of LV Vul. Thus, we conclude that V1369 Cen belongs to the LV Vul type in the time-stretched color–magnitude diagram. This overlapping of the V1369 Cen track to that of LV Vul suggests that our adopted values of E(B − V) = 0.11, f_s = 1.48, and (m − M')_V = 10.65 are reasonable.

Figure 27(a) shows the model absolute V light curve of a 0.90 M_☉ WD (thick solid red line) with the envelope chemical composition of CO Nova 3 (Hachisu & Kato 2016a). Here, we assume (m − M)_V = 10.25. The chemical composition of V1369 Cen ejecta is not known, so we assume CO Nova 3 because V1369 Cen showed an optically thin dust blackout similar to V1668 Cyg, the chemical composition of which is represented roughly by CO Nova 3 (Hachisu & Kato 2006, 2016a).

In free–free emission-dominant spectra, optical and near-infrared (NIR), i.e., B, V, and I_C, light curves should have the same shape (see, e.g., Hachisu & Kato 2006). The V1369 Cen data show such a property in the middle phase of the light curves and are in good agreement with the model light curve. The observed B and V magnitudes departed from the theoretical light curve at t ≳ 100 days because of the strong contributions of emission lines to the B and V bands in the nebular phase (see Paper I). This model light curve again confirms our result of (m − M)_V = 10.25. The WD mass is around 0.9 M_☉.

Our 0.90 M_☉ WD model also predicts an SSS phase from Day 340 until Day 960 (thin solid red line in Figure 27(a)). Page et al. (2014) reported an X-ray spectrum on UT 2014 March 8 (JD 2456724.5). This epoch (Day ∼100) corresponds to the deepest dust blackout (see Figure 24) and is much earlier than the X-ray turn-on time in our model. Mason et al. (2018) presented the X-ray count rates of V1369 Cen obtained with Swift. We plot the X-ray data taken from the Swift Web site⁵ (Evans et al. 2009) in Figure 27(a). The blue pluses represent the hard X-ray (1.5–10 kev) and the magenta crosses denote the soft X-ray (0.3–1.5 keV) components. No clear supersoft X-rays were detected until Day 370. We may conclude that the X-rays detected on Day ∼100 are not from the WD surface but have a shock origin.

For the reddening toward V446 Her, Hachisu & Kato (2014) obtained the arithmetic average of the values in the literature to be E(B − V) = 0.41 ± 0.15. Recently, Özdörmez et al. (2016) proposed another average of E(B − V) = 0.37 ± 0.04 including the result of Selvelli & Gilmozzi (2013), E(B − V) = 0.38 ± 0.04, from the archival 2200 Å feature. See Paper II and Özdörmez et al. (2016) for a summary of other estimates on the distance and reddening. In the present paper, we adopt E(B − V) = 0.40 ± 0.05 after Hachisu & Kato (2014). We obtain the distance of d = 1.38 ± 0.2 kpc from Equation (5), E(B − V) = 0.40 ± 0.05, f_s = 1.0 against LV Vul, and (m − M)_V = 11.95 ± 0.1 in Appendix B.1.

Figure 10(a) shows the various distance–reddening relations toward V446 Her, the galactic coordinates of which are (l, b) = (454092, +47075). The vertical solid red line denotes the reddening of E(B − V) = 0.40. The solid blue line denotes the distance modulus in the V band, i.e., (m − M)_V = 11.95 and Equation (5). These two lines cross at E(B − V) = 0.40 and d = 1.38 kpc. We further plot Marshall et al.'s (2006) relations in four directions close to the direction of V446 Her: that toward (l, b) = (4525, 450) is denoted by open red squares, (4550, 450) by filled green squares, (4525, 475) by blue asterisks, and (4550, 475) by open magenta circles. The closest direction in the galactic coordinates is that of the open magenta circles among the four nearby directions. The solid black/orange lines denote the distance–reddening relations given by Green et al. (2015, 2018), respectively. The solid green line represents the relation given by Sale et al. (2014). The open cyan diamonds depict the relation of Özdörmez et al. (2016). The cyan-blue line represents the relation given by Chen et al. (2019). Our crossing point at E(B − V) = 0.40 and d = 1.38 kpc is consistent with Marshall et al.'s (open magenta circles) and Green et al.'s (solid black/orange lines) relations. Our crossing point is also consistent with the distance–reddening relation given by Özdörmez et al. (2016). Cohen (1985) obtained the distance to V446 Her using the expansion parallax method to be d = (v_exp × t)/r_shell = (1235 km s⁻¹ × 24 yr)/45 = 1.35 kpc. Our value of d = 1.38 ± 0.2 kpc is consistent with Cohen's value. Thus, we confirm again that our obtained values of (m − M)_V = 11.95 ± 0.1, E(B − V) = 0.40 ± 0.05, and d = 1.38 ± 0.2 kpc are reasonable.

Zoom In Zoom Out Reset image size

Adopting E(B − V) = 0.40 and (m − M')_V = 11.95 in Equation (51), we obtain the time-stretched color–magnitude diagram of V446 Her in Figure 11(a). The track of V446 Her is just on the LV Vul track (solid orange line). Therefore, V446 Her belongs to the LV Vul type. This overlapping with the LV Vul track supports our values of E(B − V) = 0.40 and (m − M')_V = 11.95, that is, f_s = 1.0, E(B − V) = 0.40 ± 0.05, (m − M)_V = 11.95 ± 0.1, and d = 1.38 ± 0.2 kpc. We list our results in Table 1.

Zoom In Zoom Out Reset image size

Taking (m − M)_V = 11.95 for V446 Her, we add a 0.98 M_☉ WD model (solid red line) with the chemical composition of CO nova 3 (Hachisu & Kato 2016a) in Figure 32(a). The model absolute V light curve reasonably fits with the observed apparent V light curve of V446 Her. This confirms that the distance modulus of (m − M)_V = 11.95 is reasonable. In the same figure, we depict another 0.98 M_☉ WD model with (m − M)_V = 14.6 for V1668 Cyg (solid black lines). The difference between these two models represents the difference in the initial hydrogen-rich envelope mass; the initial envelope mass M_env,0 of the solid red line is slightly smaller than that of the solid black line.

V533 Her was studied in Paper II on the (B − V)₀–M_V diagram, but we here examine it on the time-stretched color–magnitude diagram. Hachisu & Kato (2016b) took E(B − V) = 0.038 ± 0.002 from the NASA/IPAC galactic absorption map. We adopt their value of E(B − V) = 0.038. We determine the distance modulus in the V band to be (m − M)_V = 10.65 ± 0.1 together with f_s = 1.20 against LV Vul in Appendix B.2, and plot it with the solid blue line in Figure 10(b). The vertical solid red line is the color excess of E(B − V) = 0.038. These two lines cross at d = 1.28 kpc (and E(B − V) = 0.038). Thus, we obtain the distance of d = 1.28 ± 0.2 kpc.

Figure 10(b) also shows a few distance–reddening relations toward V533 Her, the galactic coordinates of which are (l, b) = (691887, +242733). None of Marshall et al.'s, Sale et al.'s, Özdörmez et al.'s, and Chen et al.'s relations is available. The solid black/orange lines denote the distance–reddening relations given by Green et al. (2015, 2018), respectively. Our crossing point is broadly consistent with Green et al.'s distance–reddening relations.

Adopting E(B − V) = 0.038 and (m − M')_V = 10.85 in Equation (53), we obtain the time-stretched color–magnitude diagram of V533 Her in Figure 11(b). We also add the template tracks of LV Vul (thick solid orange lines), V1500 Cyg (thick solid green line), and V1974 Cyg (solid magenta lines). The V533 Her track broadly follows the middle part of the V1974 Cyg tracks at least until the onset of the nebular phase (see also Figures 33(a) and (b)). We regard V533 Her to belong to the V1500 Cyg type in the time-stretched color–magnitude diagram. This supports our values of (m − M')_V = 10.85 and E(B − V) = 0.038, that is, (m − M)_V = 10.65 ± 0.1, E(B − V) = 0.038 ± 0.01, and f_s = 1.20. Our results are listed in Table 1.

We again discuss the effect of different responses in the color filters. The color–magnitude track of V533 Her bifurcates at the onset of the nebular phase around UT 1963 April 19 (Chincarini & Rosino 1964), i.e., at m_V = 7.2, denoted by the large open blue square in Figure 11(b). We plot four color–magnitude data taken from Kreiner et al. (1966), Shen et al. (1964), van Genderen (1963), and Chincarini (1964), from upper to lower (or from right to left), and one of the three major branches immediately turns to the right. After the onset of the nebular phase, strong emission lines [O iii] began to contribute to the blue edge of the V filter. The response of each V filter is different from each other at the blue edge, and this difference makes a significant difference in the V magnitude. This effect can be clearly seen in Figures 3–5 of Kreiner et al. (1966), in which the V magnitude started to branch off after UT 1963 April 10 while the B magnitude did not do so among the various observers.

We check our obtained value of (m − M)_V = 10.65 by fitting with our model V light curve in Figure 33(a). We add a 1.03 M_☉ WD model (solid red line) with the chemical composition of Ne nova 2 (Hachisu & Kato 2010). Taking (m − M)_V = 10.65 for V533 Her, the absolute model V light curve reproduces the observed apparent V light curve of V533 Her (filled red circles). This confirms that the distance modulus of (m − M)_V = 10.65 is reasonable.

PW Vul was examined in Paper II on the (B − V)₀–M_V diagram. Here, we re-examine it on the time-stretched color–magnitude diagram. In Appendix B.3, we obtain (m − M)_V = 13.0 ± 0.2 together with f_s = 2.24 against LV Vul based on the time-stretching method. Taking (m − M)_V = 13.0 for PW Vul, we plot a 0.83 M_☉ WD model (solid red line) with the chemical composition of CO nova 4 (Hachisu & Kato 2015) in Figure 34(a). The model absolute V light curve reasonably fits with the observed apparent V light curve of PW Vul after t > 60 days. This confirms that the distance modulus of (m − M)_V = 13.0 is reasonable.

We also fit our UV 1455 Å light-curve model of the 0.83 M_☉ WD with the observation as shown in Figure 34(a). We obtain ${F}_{1455}^{\mathrm{mod}}=15$ and ${F}_{1455}^{\mathrm{obs}}=6$ in units of 10⁻¹² erg cm⁻² s⁻¹ Å⁻¹ at the upper bound of Figure 34(a). With these values, we plot the distance–reddening relation of Equation (20) in Figure 10(c) by the solid magenta line. The solid blue line of (m − M)_V = 13.0 and this magenta line cross at d = 1.8 kpc and E(B − V) = 0.57. These light-curve fittings are essentially the same as in our previous work (Hachisu & Kato 2015). Thus, we obtain the distance of d = 1.8 ± 0.2 kpc from Equation (5), E(B − V) = 0.57 ± 0.05, and (m − M)_V = 13.0 ± 0.2. This distance estimate is consistent with the distance estimated by Downes & Duerbeck (2000), d = 1.8 ± 0.05 kpc, with the nebular expansion parallax method. We list the results in Table 1.

For comparison, in Figure 34(a), we depict a 0.98 M_☉ WD model (solid blue lines) with the chemical composition of CO nova 3 (Hachisu & Kato 2015), assuming that (m − M)_V = 14.6 for V1668 Cyg. With the same stretching factor of f_s = 2.24, both the V and UV 1455 Å light curves almost overlap between PW Vul and V1668 Cyg. This confirms that the optical light curves and UV 1455 Å light curves follow the same time-scaling law as already explained in Section 1.

We check the distance and reddening based on various distance–reddening relations. Hachisu & Kato (2015) obtained E(B − V) = 0.55 ± 0.05 from the fitting in the color–color diagram (Paper I), being consistent with the crossing point mentioned above. Figure 10(c) shows various distance–reddening relations toward PW Vul, the galactic coordinates of which are (l, b) = (610983, +51967). We plot the constraint of d = 1.8 ± 0.05 kpc by Downes & Duerbeck (2000; solid horizontal black lines). We further add other distance–reddening relations toward PW Vul. The vertical solid red line is E(B − V) = 0.57. We plot the distance–reddening relations (solid black/orange lines) given by Green et al. (2015, 2018), respectively. We also plot the four distance–reddening relations of Marshall et al. (2006): that toward (l, b) = (6100, +500) is denoted by open red squares, (6125, +500) by filled green squares, (6100, +525) by blue asterisks, and (6125, +525) by open magenta circles, each with error bars. The closest direction in the galactic coordinates is that of blue asterisks. The open cyan-blue diamonds represent the relation given by Özdörmez et al. (2016). Our crossing point at d = 1.8 kpc and E(B − V) = 0.57 is ΔE(B − V) = 0.15 mag larger than the trends of Marshall et al.'s blue asterisks data. To summarize, our set of d = 1.8 kpc and E(B − V) = 0.57 is not consistent with all of the 3D dust maps given by Marshall et al. (2006), Özdörmez et al. (2016), Green et al. (2015, 2018), and Chen et al. (2019). This is the first and only the case where our crossing point is largely different from that in several 3D dust maps. We discuss the reason for such a large discrepancy below.

The 3D dust maps basically give an averaged value of a relatively broad region, so the pinpoint reddening could be different from the values of the 3D dust maps. The pinpoint estimate of the reddening toward PW Vul indicates E(B − V) = 0.55 ± 0.05, as already discussed in Hachisu & Kato (2015). For example, Andreä et al. (1991) obtained E(B − V) = 0.58 ± 0.06 from the He ii λ1640/λ4686 ratio and E(B − V) = 0.55 ± 0.1 from the interstellar absorption feature at 2200 Å for the reddening toward PW Vul. Saizar et al. (1991) reported E(B − V) = 0.60 ± 0.06 from the He ii λ1640/λ4686 ratio. Hachisu & Kato (2014) estimated the reddening to be E(B − V) = 0.55 ± 0.05 from the color–color diagram fit of PW Vul. As for the distance to PW Vul, Downes & Duerbeck (2000) obtained d = 1.8 ± 0.05 kpc with the nebular expansion parallax method. These pinpoint constraints are all consistent with our crossing point of E(B − V) = 0.57 ± 0.05, (m − M)_V = 13.0 ± 0.2, and d = 1.8 ± 0.2 kpc.

We further obtain the distance moduli of the UBVI bands and check their crossing points in the distance–reddening plane. We obtain (m − M)_U = 13.92, (m − M)_B = 13.55, and (m − M)_V = 13.0 (and (m − M)_I = 12.12) in Appendix B.3, and plot them in Figure 10(c) with the thin solid green, cyan, thick solid blue (and thin solid blue-magenta) lines, respectively. These lines cross at E(B − V) = 0.57 and d = 1.8 kpc, confirming again our results.

Adopting E(B − V) = 0.57 and (m − M')_V = 13.85 in Equation (55), we obtain the time-stretched color–magnitude diagram of PW Vul in Figure 11(c). Here, we plot the data taken from Noskova et al. (1985), Kolotilov & Noskova (1986), and Robb & Scarfe (1995). PW Vul follows the V1500 Cyg track except for the very early phase. Therefore, PW Vul belongs to the V1500 Cyg type in the time-stretched color–magnitude diagram. This overlapping to the V1500 Cyg track supports our estimates of E(B − V) = 0.57 and (m − M')_V = 13.85, that is, f_s = 2.24, E(B − V) = 0.57 ± 0.05, (m − M)_V = 13.0 ± 0.2, and d = 1.8 ± 0.2 kpc. We list our results in Table 1.

V1419 Aql was examined in Paper II on the (B − V)₀–M_V diagram. Here, we re-examine it on the time-stretched color–magnitude diagram. We determine the distance modulus in the V band to be (m − M)_V = 15.0 ± 0.2 together with f_s = 1.41 against LV Vul in Appendix B.4. For the reddening toward V1419 Aql, Hachisu & Kato (2014, 2016b) obtained E(B − V) = 0.50 ± 0.05 from the fitting in the color–color diagram (Paper I). On the other hand, the NASA/IPAC galactic 2D dust absorption map gives E(B − V) = 0.55 ± 0.01 in the direction toward V1419 Aql. See Hachisu & Kato (2014, 2016b) and Özdörmez et al. (2016) for a summary of other estimates on the extinction and distance of V1419 Aql. We adopt the arithmetic mean of these two values, i.e., E(B − V) = 0.52 ± 0.05 in the present paper. Then, we obtain the distance of d = 4.7 ± 0.5 kpc from Equation (5).

We check the distance and reddening toward V1419 Aql, the galactic coordinates of which are (l, b) = (368110, −41000), based on the various distance–reddening relations in Figure 10(d). The solid blue line denotes the distance modulus of (m − M)_V = 15.0 and Equation (5). The vertical solid red line is E(B − V) = 0.52. These two lines cross at d = 4.7 kpc (and E(B − V) = 0.52). We add the distance–reddening relations (solid black/orange lines) given by Green et al. (2015, 2018), respectively. We also plot four distance–reddening relations of Marshall et al. (2006): that toward (l, b) = (3675, −400) is denoted by open red squares, (3700, −400) by filled green squares, (3675, −425) by blue asterisks, and (3700, −425) by open magenta circles, each with error bars. The closest direction is that of open red squares. The solid green line is the relation given by Sale et al. (2014). The open cyan-blue diamonds with error bars show the relation given by Özdörmez et al. (2016). The solid cyan-blue line is the relation given by Chen et al. (2019). Our set of E(B − V) = 0.52 and d = 4.7 kpc is broadly consistent with the distance–reddening relations of Marshall et al. (2006), Sale et al. (2014), Green et al. (2018), and Özdörmez et al. (2016). Thus, we confirm that our adopted values of E(B − V) = 0.52 ± 0.05, (m − M)_V = 15.0 ± 0.2, and d = 4.7 ± 0.5 kpc are reasonable. We list our results in Table 1.

Adopting E(B − V) = 0.52 and (m − M')_V = 15.35 in Equation (63), we obtain the time-stretched color–magnitude diagram of V1419 Aql in Figure 11(d). Here, we plot the data taken from Munari et al. (1994a) and IAU Circular Nos. 5794, 5802, 5807, and 5829. The track of V1419 Aql is considerably affected by dust formation, the start of which is denoted by the large magenta square. We regard V1419 Aql belongs to the LV Vul type because the V1419 Aql track follows part of the V1668 Cyg track (blue lines) until the dust blackout starts. For comparison, we also plot the V1065 Cen track (filled blue triangles) that shows a similar shallow dust blackout (see Figures 4 and 6 of Hachisu & Kato 2018a). The track of V1065 Cen almost follows the lower branch of LV Vul, while the track of V1419 Aql is not clear owing to dust blackout.

Finally, we plot a 0.90 M_☉ WD model with the chemical composition of CO nova 3 (Hachisu & Kato 2016a) with the solid red lines in Figure 37(a). The V model light curve reasonably fits with the V light curve of V1419 Aql during log t (days) = 1.0–1.5. This confirms our value of (m − M)_V = 15.0.

V705 Cas was examined in Paper II, but we re-examine it on the time-stretched color–magnitude diagram. For the reddening toward V705 Cas, we adopt E(B − V) = 0.45 ± 0.05 after Hachisu & Kato (2014). We do not repeat the discussion. Papers I and II give a summary of the distance and reddening toward V705 Cas, (l, b) = (1136595, −40959). We obtain the time-scaling factor of f_s = 2.8 against LV Vul and the distance of d = 2.6 ± 0.3 kpc from Equation (5), E(B − V) = 0.45 ± 0.05, and (m − M)_V = 13.45 ± 0.2 in Appendix B.5. Using the expansion parallax method, Eyres et al. (1996) and Diaz et al. (2001) obtained d = 2.5 kpc and d = 2.9 ± 0.4 kpc, respectively. These distances are all consistent with our value of d = 2.6 ± 0.3 kpc. We list our results in Table 1.

Next, we discuss the model light-curve fitting. We obtain (m − M)_V = 13.45 based on the time-stretching method in Appendix B.5. Assuming that (m − M)_V = 13.45, we plot a 0.78 M_☉ WD model (solid magenta lines) with the chemical composition of CO nova 4 (Hachisu & Kato 2015) in Figure 38(a). The model absolute V and UV 1455 Å light curves of the 0.78 M_☉ WD reasonably fit with the observed apparent V and UV 1455 Å light curves of V705 Cas. This model light-curve fitting is essentially the same as Figure 15 of Hachisu & Kato (2015), and we again confirm that the distance modulus of (m − M)_V = 13.45 is reasonable for V705 Cas. In the same figure, we add a 0.83 M_☉ WD model (solid blue lines) with the same chemical composition of CO nova 4, assuming that (m − M)_V = 13.0 for PW Vul.

We reanalyze the distance and reddening toward V705 Cas based on various distance–reddening relations in Figure 12(a). The solid blue line shows (m − M)_V = 13.45 and Equation (5). The solid magenta line is the UV 1455 Å fit of our 0.78 M_☉ WD model. The UV 1455 Å light-curve fit gives the relation of Equation (20) together with ${F}_{1455}^{\mathrm{obs}}=6.0$ and ${F}_{1455}^{\mathrm{mod}}=12.5$ in units of 10⁻¹² erg cm⁻² s⁻¹ Å⁻¹ at the upper bound of Figure 38(a). We also plot the relations given by Green et al. (2015, 2018) with the solid black/orange lines, respectively. No data of Marshall et al. (2006) are available in this direction. The solid green line represent the relation given by Sale et al. (2014). The open cyan-blue diamonds with error bars denote the relation given by Özdörmez et al. (2016). The solid cyan-blue line denotes the relation given by Chen et al. (2019). The blue, magenta, and red lines cross at E(B − V) = 0.45 and d = 2.6 kpc. This crossing point is also consistent with the distance–reddening relation given by Green et al. (2015, black line), Sale et al. (2014, green line), and Özdörmez et al. (2016, cyan-blue diamonds).

Zoom In Zoom Out Reset image size

Adopting E(B − V) = 0.45 and (m − M')_V = 14.55 in Equation (65), we obtain the time-stretched color–magnitude diagram of V705 Cas in Figure 13(a). Here, we plot the data taken from Munari et al. (1994b), Hric et al. (1998), and IAU Circular Nos. 5905, 5912, 5914, 5920, 5928, 5929, 5945, and 5957. The track of V705 Cas is also affected by dust formation as denoted by the large black square. We also plot the V1065 Cen track (see Figures 4 and 6 of Hachisu & Kato 2018a) in Figure 13(a). V1065 Cen shows a similar dust blackout to V705 Cas but the depth of its dust blackout is much shallower (see Figure 51) than that of V705 Cas. The V1065 Cen track comes back soon after the dust blackout and follows again the LV Vul track, so that V1065 Cen belongs to the LV Vul type in the time-stretched color–magnitude diagram. We regard V705 Cas to also belong to the LV Vul type because the V705 Cas track almost follows that of LV Vul and V1065 Cen until the dust blackout starts. The early pulse (oscillation) in the V light curve makes a loop in the color–magnitude diagram. This kind of loop was also seen in multiple-peak novae like V723 Cas and V5558 Sgr as discussed by Hachisu & Kato (2016b). We list our results in Table 1.

Zoom In Zoom Out Reset image size

V382 Vel was also studied in Paper II on the (B − V)₀–M_V diagram. In this subsection, we examine it on the (B − V)₀–(M_V − 2.5 log f_s) diagram. For the reddening toward V382 Vel, (l, b) = (2841674, +57715), Steiner et al. (1999) obtained E(B − V) = A_V/3.1 = 0.8/3.1 = 0.26 from an equivalent width of 0.024 nm of the interstellar Ca ii K line. Orio et al. (2002) obtained the hydrogen column density toward V382 Vel to be N_H ∼ 2 × 10²¹ cm⁻² from X-ray spectrum fittings. This value can be converted with E(B − V) = N_H/4.8 × 10²¹ ∼ 0.4 (Bohlin et al. 1978), E(B − V) = N_H/5.8 × 10²¹ ∼ 0.34 (Güver & Özel 2009), and E(B − V) = N_H/6.8 × 10²¹ ∼ 0.3 (Liszt 2014). On the other hand, della Valle et al. (2002) obtained E(B − V) = 0.05 from various line ratios and E(B − V) = 0.09 from Na i D interstellar absorption features. Shore et al. (2003) obtained E(B − V) = 0.20 from the resemblance of IUE spectra to those of V1974 Cyg. Shore et al. (2003) and Ness et al. (2005) obtained N_H = 1.2 × 10²¹ cm⁻², corresponding to E(B − V) = N_H/4.8 × 10²¹ = 0.25, E(B − V) = N_H/5.8 × 10²¹ = 0.21, and E(B − V) = N_H/6.8 × 10²¹ = 0.18. Hachisu & Kato (2014) obtained E(B − V) = 0.15 ± 0.05 by fitting the color–color track of V382 Vel with the general track of novae. To summarize, there are two estimates, E(B − V) = 0.1 ± 0.05 and E(B − V) = 0.25 ± 0.05.

We obtain three distance moduli of B, V, and I_C bands in Appendix B.6 based on the time-stretching method. We plot these distance moduli in Figure 12(b) with the magenta, blue, and cyan lines, that is, (m − M)_B = 11.7, (m − M)_V = 11.48, and (m − M)_I = 11.09, together with Equations (11), (5), and (12). These three lines broadly cross at d = 1.4 kpc and E(B − V) = 0.25. Thus, we obtain the time-scaling factor f_s = 0.51 against LV Vul, the reddening toward V382 Vel, E(B − V) = 0.25 ± 0.05, and the distance to V382 Vel, d = 1.4 ± 0.2 kpc. The distance modulus in the V band is (m − M)_V = 11.5 ± 0.2. These values are listed in Table 1.

Adopting E(B − V) = 0.25 and (m − M')_V = 10.75 in Equation (67), we plot the time-stretched color–magnitude diagram of V382 Vel in Figure 13(b). The nebular phase had started at least by the end of 1999 June, i.e., ∼40 days after optical maximum (della Valle et al. 2002). We plot this phase (M_V = m_V − (m − M)_V ≈ 7.09 − 11.5 = −4.41) with the large open red square in Figure 13(b). The track of V382 Vel follows the V1500 Cyg/V1974 Cyg tracks at least until the nebular phase started. Thus, we regard V382 Vel to belong to the V1500 Cyg type in the time-stretched color–magnitude diagram. This overlapping with the tracks of V1500 Cyg/V1974 Cyg supports our values of E(B − V) = 0.25 and (m − M')_V = 10.75, that is, E(B − V) = 0.25 ± 0.05, (m − M)_V = 11.5 ± 0.2, f_s = 0.51, and d = 1.4 ± 0.2 kpc.

Taking (m − M)_V = 11.5 for V382 Vel, we plot the V model light curve (total flux of free–free plus photospheric emission; solid red line) of a 1.23 M_☉ WD with the envelope chemical composition of Ne nova 2 (Hachisu & Kato 2010, 2016a) in Figure 39(a). The model V light curve reasonably reproduces the observation (filled red circles). This model light-curve fitting gives the same result as Figure 27 of Hachisu & Kato (2016a). Thus, we again confirm that the distance modulus of (m − M)_V = 11.5 ± 0.2 is reasonable.

We further examine the distance and reddening toward V382 Vel, (l, b) = (2841674, +57715), based on various distance–reddening relations in Figure 12(b). We plot four sets of distance–reddening relation calculated by Marshall et al. (2006): that toward (l, b) = (28400, +575) is denoted by open red squares, (28425, +575) by filled green squares, (28400, +600) by blue asterisks, and (28425, +600) by open magenta circles. The filled green squares are the closest direction among the four nearby directions. The open cyan-blue diamonds with error bars denote the relation given by Özdörmez et al. (2016). The solid cyan-blue line denotes the relation given by Chen et al. (2019). The vertical solid red line is the color excess of E(B − V) = 0.25. Our crossing point at d = 1.4 kpc and E(B − V) = 0.25 is broadly consistent with Marshall et al.'s and Özdörmez et al.'s relations within error bars.

The distance toward V382 Vel was recently estimated by Tomov et al. (2015) to be d = (v_exp × t)/r_shell = (1800 ± 100 km s⁻¹ × 12 yr)/(60 ± 025) ≈ 0.8 ± 0.1 kpc with the expansion parallax method. This value is much smaller than our estimate of d = 1.4 ± 0.2 kpc. However, the distance obtained with the expansion parallax method depends largely on the assumed velocity, v_exp. If we adopt other velocities estimated in the early outburst phase v_exp ∼ 3500 km s⁻¹ (e.g., della Valle et al. 2002) or v_exp ∼ 2900 km s⁻¹ (e.g., Ness et al. 2005), we obtain larger distances such as d ∼ 1.5 kpc or d ∼ 1.2 kpc, respectively.

V5114 Sgr was studied in Paper II on the (B − V)₀–M_V diagram. In this subsection, we re-examine it but on the (B − V)₀–(M_V − 2.5 log f_s) diagram. We obtain three distance moduli in the U, B, and V bands in Appendix B.7. We plot these three distance moduli in Figure 12(c) with the magenta, cyan, and blue lines, that is, (m − M)_U = 17.45, (m − M)_B = 17.15, and (m − M)_V = 16.65, together with Equations (10), (11), and (5), respectively. These three lines do not exactly but broadly cross at d = 10.9 kpc and E(B − V) = 0.47. Thus, we obtain the time-scaling factor of f_s = 0.76 against LV Vul, the reddening of E(B − V) = 0.47 ± 0.05, and the distance of d = 10.9 ± 1 kpc. These values are listed in Table 1.

Various reddening estimates were summarized in Paper II, and their arithmetic mean was calculated to be E(B − V) = 0.51 ± 0.09. The NASA/IPAC galactic dust absorption map gives E(B − V) = 0.49 ± 0.02 in the direction toward V5114 Sgr. Hachisu & Kato (2014) derived the reddening of E(B − V) = 0.45 ± 0.05 on the basis of the general track of the color–color evolution of novae. These are all consistent with our new value of E(B − V) = 0.47 ± 0.05.

Next, we reanalyze the distance and reddening toward V5114 Sgr, (l, b) = (39429, −63121), based on the various distance–reddening relations in Figure 12(c). The vertical solid red line is E(B − V) = 0.47. We plot four distance–reddening relations of Marshall et al. (2006): that toward (l, b) = (375, −650) is denoted by open red squares, (400, −650) by filled green squares, (375, −625) by blue asterisks, and (400, −625) by open magenta circles, each with error bars. The closest direction in the galactic coordinates is that of open magenta circles. The black/orange lines are the relations given by Green et al. (2015, 2018), respectively. The cyan-blue line is the relation given by Chen et al. (2019). We further add the 3D reddening map given by Schultheis et al. (2014). We plot four of Schuletheis et al.'s distance–reddening relations toward near the direction of V5114 Sgr, (l, b) = (39, −64), (39, −63), (40, −64), and (40, −63), with the very thin solid cyan lines. The lines show zigzag patterns in this case, although the reddening must increase monotonically with the distance. In this sense, Schuletheis et al.'s distance–reddening relation may not be appropriate in the middle part of the lines. Our set of E(B − V) = 0.47 and d = 10.9 kpc is consistent with the trend of Marshall et al.'s data (open magenta circles), although ΔE(B − V) ∼ 0.05–0.1 mag smaller than Green et al.'s.

Adopting E(B − V) = 0.47 and (m − M')_V = 16.35 in Equation (72), we obtain the time-stretched color–magnitude diagram of V5114 Sgr in Figure 13(c). Here, we plot the data taken from Ederoclite et al. (2006), IAU Circular Nos. 8306 and 8310, and SMARTS. V5114 Sgr follows those of V1500 Cyg/V1974 Cyg. Therefore, we regard V5114 Sgr to belong to the V1500 Cyg type in the time-stretched color–magnitude diagram. This overlapping supports our estimates of E(B − V) = 0.47 and (m − M')_V = 16.35, that is, f_s = 0.76, E(B − V) = 0.47 ± 0.05, (m − M)_V = 16.65 ± 0.1, and d = 10.9 ± 1 kpc. We list our results in Table 1.

Taking (m − M)_V = 16.65 for V5114 Sgr, we plot the V model light curve (solid red line) of a 1.15 M_☉ WD with the envelope chemical composition of Ne nova 2 (Hachisu & Kato 2010, 2016a) in Figure 41(a). The model V light curve reasonably reproduces the observation (filled red circles). This again confirms that the distance modulus of (m − M)_V = 16.65 ± 0.1 is reasonable.

V2362 Cyg was also studied in Paper II. Here, we re-examine it on the (B − V)₀–(M_V − 2.5 log f_s) diagram. V2362 Cyg shows a prominent secondary maximum (e.g., Kimeswenger et al. 2008; Munari et al. 2008b; see Figure 43). The origin of the secondary maximum was discussed by Hachisu & Kato (2009).

The color excess of V2362 Cyg was estimated by various authors (see Section 3.22 of Paper II). We adopt E(B − V) = 0.60 ± 0.05 after Hachisu & Kato (Paper II). Then, the time-scaling factor is obtained to be f_s = 1.78 against LV Vul, and the distance is d = 5.1 ± 0.5 kpc from Equation (5) together with (m − M)_V = 15.4 ± 0.2 in Appendix B.8.

Adopting E(B − V) = 0.60 and (m − M')_V = 16.05 from Equation (77), we plot the time-stretched color–magnitude diagram of V2362 Cyg in Figure 13(d). We also add the template tracks of LV Vul (thick solid orange line) and V1500 Cyg (thick solid green line). We further add another track of V1500 Cyg (thick solid cyan line), which is shifted toward the red by Δ(B − V) = 0.20 mag.

V2362 Cyg shows an interesting evolution in the color–magnitude diagram. V2362 Cyg goes down along the LV Vul track (orange line) or the redshifted V1500 Cyg track (cyan line) just after the optical maximum. In the secondary maximum phase, it goes up along the original track of V1500 Cyg (solid green line) as denoted by the open blue circles, and then goes down along the same V1500 Cyg track (solid green line) as denoted by the filled magenta circles with black outlines. After the onset of the nebular phase, the track turns to the right and follows again the upper LV Vul track (orange line) or the redshifted V1500 Cyg track (cyan line).

These two distinct tracks are hints to resolve why the two types of V1500 Cyg and LV Vul tracks are clearly separated in the time-stretched color–magnitude diagram. Munari et al. (2008b, p. 155) wrote that "the emission spectrum at second maximum was quite different from that at first maximum, reflecting the much higher temperature of the underlying continuum. At second maximum, Fe ii emission lines were not seen and were replaced by N ii, N iii, O ii, [O i], and He i." The strong emission lines (He ii/N iii as well as Balmer lines such as Hγ, Hδ, H) contribute to the B band and make B − V blue in the secondary maximum phase. Thus, the difference in the (B − V)₀ color is real rather than the difference in the V-filter response. We can conclude that the two tracks reflect the difference in the ionization state which originates from the temperature difference of the underlying continuum. We call the redder location the LV Vul type and the bluer location the V1500 Cyg type. The separation is Δ(B − V)₀ ∼ 0.2 mag. The overlapping of these tracks of V2362 Cyg with the two template novae, LV Vul and V1500 Cyg, supports our values of (m − M')_V = 16.05 and E(B − V) = 0.60, that is, f_s = 1.78, E(B − V) = 0.60 ± 0.05, (m − M)_V = 15.4 ± 0.2, and d = 5.1 ± 0.5 kpc. We list our results in Table 1.

We re-examine the distance–reddening relation toward V2362 Cyg, (l, b) = (873724, −23574), based on several distance–reddening relations in Figure 12(d). The solid blue line denotes the distance–reddening relation of Equation (5) together with (m − M)_V = 15.4. The vertical solid red line is the color excess of V2362 Cyg estimated in Paper II. These two lines cross at d = 5.1 kpc (and E(B − V) = 0.60). We plot four sets of distance–reddening relations calculated by Marshall et al. (2006): that toward (l, b) = (8725, −225) is denoted by open red squares, (8750, −225) by filled green squares, (8725, −250) by blue asterisks, and (8750, −250) by open magenta circles. The open red squares are the closest direction toward V2362 Cyg among the four nearby directions. The solid black/orange lines denote the distance–reddening relations given by Green et al. (2015, 2018), respectively. The solid green line represent the relation given by Sale et al. (2014) and the open cyan-blue diamonds with error bars indicate the relation given by Özdörmez et al. (2016). The solid cyan-blue line is the relation given by Chen et al. (2019). Our crossing point at d = 5.1 kpc and E(B − V) = 0.60 is roughly consistent with Marshall et al.'s (open red squares) and Green et al.'s (solid black/orange lines) relations, although the reddenings given by Sale et al. (2014) and Özdörmez et al. (2016) slightly deviate from the crossing point. Thus, we confirm again that our estimated values of (m − M)_V = 15.4 ± 0.2, E(B − V) = 0.60 ± 0.05, and d = 5.1 ± 0.5 kpc are reasonable.

V2615 Oph was also studied in Paper II on the (B − V)₀–M_V diagram. In this subsection, we re-examine it on the (B − V)₀–(M_V − 2.5 log f_s) diagram.

We obtain three distance moduli in the B, V, and I_C bands in Appendix B.9. We plot these three distance moduli in Figure 14(a) with the thin solid magenta, blue, and cyan lines. These three lines cross at d = 4.3 kpc and E(B − V) = 0.90. Therefore, we adopt E(B − V) = 0.90 ± 0.05. See Paper II for other estimates of the reddening and distance. Thus, we obtain the time-scaling factor of f_s = 1.58 against LV Vul and the distance of d = 4.3 ± 0.4 kpc, E(B − V) = 0.90 ± 0.05, and (m − M)_V = 15.95 ± 0.2.

Zoom In Zoom Out Reset image size

We reanalyze the distance and reddening toward V2615 Oph, (l, b) = (41475, +33015), based on various distance–reddening relations in Figure 14(a). We plot four distance–reddening relations of Marshall et al. (2006): that toward (l, b) = (400, +325) is denoted by open red squares, (425, +325) by filled green squares, (400, +350) by blue asterisks, and (425, +350) by open magenta circles, each with error bars. The direction toward V2615 Oph is between those of open red squares and filled green squares. We add the distance–reddening relations (solid black/orange lines) given by Green et al. (2015, 2018), respectively. We further add four distance–reddening relations (very thin solid cyan lines) given by Schultheis et al. (2014). The open cyan-blue diamonds are the relation given by Özdörmez et al. (2016). The cyan-blue line represents the relation given by Chen et al. (2019): one is toward (415, +325) and the other is toward (415, +335). Our crossing point at E(B − V) = 0.90 and d = 4.3 kpc is consistent with the both trends of Marshall et al. and Green et al. The NASA/IPAC galactic 2D dust absorption map gives E(B − V) = 0.87 ± 0.02 toward V2615 Oph, consistent with our value of E(B − V) = 0.90 ± 0.05. We list our results in Table 1.

Adopting E(B − V) = 0.90 and (m − M')_V = 16.45 in Equation (79), we obtain the time-stretched color–magnitude diagram of V2615 Oph in Figure 15(a). Here, we show the time-stretched track of V1065 Cen by the filled cyan triangles. The track of V2615 Oph is similar to that of V1065 Cen until the dust blackout. It broadly follows the LV Vul track. Therefore, V2615 Oph belongs to the LV Vul type in the time-stretched color–magnitude diagram. This overlapping supports our estimates of E(B − V) = 0.90 and (m − M')_V = 16.45, that is, f_s = 1.58, E(B − V) = 0.90 ± 0.05, (m − M)_V = 15.95 ± 0.2, and d = 4.3 ± 0.4 kpc.

Zoom In Zoom Out Reset image size

Taking (m − M)_V = 15.95 for V2615 Oph, we plot the V model light curve (solid red line) of a 0.90 M_☉ WD with the envelope chemical composition of CO nova 3 (Hachisu & Kato 2016a) in Figure 44(a). The model V light curve reasonably reproduces the observation (filled red circles). This confirms that the distance modulus of (m − M)_V = 15.95 ± 0.2 is reasonable.

V2468 Cyg was studied in Paper II. Here, we re-examine it on the (B − V)₀–(M_V − 2.5 log f_s) diagram.

We obtain three distance moduli in the B, V, and I_C bands in Appendix B.10. We plot these three distance moduli in Figure 14(b) by the thin solid magenta, blue, and cyan lines. These three lines cross at d = 6.9 kpc and E(B − V) = 0.65. We adopt f_s = 2.4 against LV Vul, E(B − V) = 0.65 ± 0.05, and (m − M)_V = 16.2 ± 0.2. The previous values in Paper II are E(B − V) = 0.75 ± 0.05, (m − M)_V = 15.6 ± 0.2, and d = 4.5 ± 0.5 kpc, which are smaller than our new values. The main difference is the improvement in the time-scaling factor. See the discussion in Paper II for a summary of other estimates of the reddening and distance toward V2468 Cyg.

Figure 14(b) also shows several distance–reddening relations toward V2468 Cyg, (l, b) = (668084, +02455). We plot four distance–reddening relations of Marshall et al. (2006): that toward (l, b) = (6675, +000) is denoted by open red squares, (6700, +000) by filled green squares, (6675, +025) by blue asterisks, and (6700, +025) by open magenta circles, each with error bars. The closest direction in the galactic coordinates is that of blue asterisks. We add the distance–reddening relations (solid black/orange lines) given by Green et al. (2015, 2018), respectively. The solid green line represents the relation given by Sale et al. (2014), and the open cyan-blue diamonds with error bars are given by Özdörmez et al. (2016). The cyan-blue line represents the relation given by Chen et al. (2019). Our crossing point at E(B − V) = 0.65 and d = 6.9 kpc is consistent with the distance–reddening relation given by Özdörmez et al. Thus, we confirm that our set of E(B − V) = 0.65 ± 0.05 and d = 6.9 ± 0.8 kpc is reasonable. We list our results in Table 1.

Adopting E(B − V) = 0.65 and (m − M')_V = 17.15 in Equation (84), we obtain the time-stretched color–magnitude diagram of V2468 Cyg in Figure 15(b). Here, we plot the data of V2468 Cyg taken from the American Association of Variable Star Observers (AAVSO). Although the color data are rather scattered, V2468 Cyg broadly follows the V1500 Cyg track. Therefore, V2468 Cyg belongs to the V1500 Cyg type. This overlapping supports our estimates of E(B − V) = 0.65 and (m − M')_V = 17.15, that is, f_s = 2.4, E(B − V) = 0.65 ± 0.05, (m − M)_V = 16.2 ± 0.2, and d = 6.9 ± 0.8 kpc.

Taking (m − M)_V = 16.2 for V2468 Cyg, we plot the V model light curve (solid red line) of a 0.85 M_☉ WD with the envelope chemical composition of CO nova 4 (Hachisu & Kato 2015) in Figure 46(a). The model V light curve reasonably reproduces the upper bound of observation (filled red circles) during log t (days) ∼ 1–2. This suggests that the distance modulus of (m − M)_V = 16.2 ± 0.2 is reasonable.

V2491 Cyg was studied in Paper II on the (B − V)₀–M_V diagram. In this subsection, we re-examine it on the (B − V)₀–(M_V − 2.5 log f_s) diagram. V2491 Cyg showed a small secondary maximum (e.g., Hachisu & Kato 2009). This nova is also characterized by the detection of pre-outburst X-ray emission (Ibarra & Kuulkers 2008; Ibarra et al. 2008). Hachisu & Kato (2016b) adopted E(B − V) = 0.23 after Munari et al. (2011) while we here adopt a different value of E(B − V) = 0.45. These two values are significantly different, so we explained the reason below.

Figure 14(c) plots three distance moduli in the B, V, and I_C bands obtained from the time-stretching method in Appendix B.11 with the magenta, blue, and cyan lines, that is, (m − M)_B = 17.83, (m − M)_V = 17.41, and (m − M)_I = 16.62 together with Equations (11), (5), and (12). These three lines broadly cross at d = 15.9 kpc and E(B − V) = 0.45.

Figure 14(c) also shows several distance–reddening relations toward V2491 Cyg, (l, b) = (672287, +43532). We plot the distance–reddening relations given by Marshall et al. (2006): that toward (l, b) = (6700, 425) is denoted by open red squares, (6725, 425) by filled green squares, (6700, 450) by blue asterisks, and (6725, 450) by open magenta circles. The closest direction in galactic coordinates is that denoted by the filled green squares. The solid green line represents the relation given by Sale et al. (2014), black/orange lines by Green et al. (2015, 2018). The open cyan-blue diamonds with error bars denote the relation given by Özdörmez et al. (2016), and the solid cyan-blue line represents the relation given by Chen et al. (2019).

Marshall et al.'s distance–reddening relations (green squares and blue asterisks) match the smaller value of E(B − V) = 0.23 ± 0.01. On the other hand, Green et al.'s and Sale et al.'s relations are consistent with the larger value of E(B − V) = 0.45 ± 0.05, which is consistent with our new estimate of E(B − V) = 0.45 ± 0.05.

The reddening toward V2491 Cyg was obtained by Lynch et al. (2008b) to be E(B − V) = 0.3 from O i lines, which was revised by Rudy et al. (2008b) to be E(B − V) = 0.43 from the O i lines at 0.84 and 1.13 μm. Munari et al. (2011) obtained E(B − V) = 0.23 ± 0.01 from an average of E(B − V) = 0.24 from Na i 5889.953 line profiles, E(B − V) = (B − V)_max − (B − V)_0,max = 0.46 − (0.23 ± 0.06) = 0.23 ± 0.06, and E(B − V) = (B − V)_t2 − (B − V)_0,t2 = 0.20 − (−0.02 ± 0.04) =  0.22 ± 0.04, from the intrinsic colors at maximum and t₂ time (van den Bergh & Younger 1987). The distance modulus and distance to V2491 Cyg were estimated by Munari et al. (2011) as (m − M)_V = m_V,max − M_V,max = 7.45 − (−9.06) = 16.51 from the MMRD relation (Cohen 1988) together with t₂ = 4.8 days, and then derived the distance of d = 14 kpc. On the other hand, the NASA/IPAC Galactic 2D dust absorption map gives E(B − V) = 0.48 ± 0.03 in the direction toward V2491 Cyg. To summarize, there are two estimates of the reddening, i.e., E(B − V) = 0.23 ± 0.01 and E(B − V) = 0.43 ± 0.05. Our value is consistent with the larger one. We here adopt E(B − V) = 0.45 ± 0.05 and d = 15.9 ± 2 kpc. The distance modulus in the V band is (m − M)_V = 17.4 ± 0.2. These values are listed in Table 1.

Using E(B − V) = 0.45 and (m − M')_V = 16.55 from Equation (89), we plot the time-stretched color–magnitude diagram of V2491 Cyg in Figure 15(c). We add the template tracks of LV Vul (thick solid orange line), V1500 Cyg (thick solid green line), and V1974 Cyg (solid magenta line). We also add the V1500 Cyg track shifted toward the blue by Δ(B − V) = −0.25 (thick solid cyan line). V2491 Cyg approximately follows the blueshifted V1500 Cyg track (cyan line) except during the tiny secondary maximum. The track turns to the right after the onset of the nebular phase (Paper II). This redward excursion is due to the large contribution of the strong emission lines [O iii] to the V magnitude as already discussed in the previous subsections.

Munari et al. (2011) suggested the low metallicity of [Fe/H] = −0.25 for V2491 Cyg. This subsolar metallicity is roughly consistent with −0.5 < [Fe/H] < −0.3 at the galactocentric distance (∼14 kpc) of V2491 Cyg. Hachisu & Kato (2018b) clarified that the color–magnitude tracks of LMC novae are located at the side bluer than those of galactic novae by Δ(B − V) = −0.3. For example, the color–magnitude track of YY Dor overlaps with the V1668 Cyg track shifted by Δ(B − V) = −0.3. They supposed that this blueshift is caused by the lower metallicity of LMC stars, [Fe/H] = −0.55 (see, e.g., Piatti & Geisler 2013). The LMC N 2009a track is in good agreement with the 0.2 mag blueshifted V1500 Cyg and 0.15 mag blueshifted U Sco tracks (Hachisu & Kato 2018b). This bluer feature of the LMC N 2009a track is also due to the lower metallicity. The blueshifted nature of the V2491 Cyg track is consistent with the nature of LMC novae (Hachisu & Kato 2018b).

It should be noted that the empirical relations proposed by van den Bergh & Younger (1987), i.e., (B − V)₀ = 0.23 ± 0.06 at maximum and (B − V)₀ = −0.02 ± 0.04 at t₂, are not applicable to novae of subsolar metallicity as clearly shown in Figure 15(c). This is one of the reasons why Munari et al. (2011) obtained the smaller reddening of E(B − V) = 0.23 ± 0.01.

Munari et al. (2011) obtained the abundance of ejecta to be X = 0.573, Y = 0.287, and Z = 0.140 by mass weight, with those of individual elements being X_N = 0.074, X_O = 0.049, and X_Ne = 0.015 (see also Tarasova 2014b for another abundance estimate). This abundance is close to that of Ne nova 2 (Hachisu & Kato 2010). Taking (m − M)_V = 17.4 for V2491 Cyg, we plot the V model light curve of 1.35 M_☉ (solid red lines) and 1.30 M_☉ (solid green lines) WDs with the envelope chemical composition of Ne nova 2 in Figure 48(a). The model V light curve reasonably reproduces the observation (filled red circles) except during the secondary maximum. This suggests that the distance modulus of (m − M)_V = 17.4 ± 0.2 is reasonable.

Our model light-curve fitting suggests that the WD mass is approximately 1.35 M_☉. The WD mass of RS Oph has been estimated to be ∼1.35 M_☉ by Hachisu et al. (2006, 2007) and Hachisu & Kato (2018b). It is interesting to compare the V (or y) and supersoft X-ray light curves of these two novae (Figure 16). The starting time of the SSS phases are almost the same between the two novae while the duration of the SSS phase is rather different and much longer in the recurrent nova RS Oph than in the classical nova V2491 Cyg.

Zoom In Zoom Out Reset image size

V496 Sct was studied in Paper II on the (B − V)₀–M_V diagram. In this subsection, we re-examine it on the (B − V)₀–(M_V − 2.5 log f_s) diagram.

We obtain the distance moduli of the BVI_C bands in Appendix B.12 and plot them with the magenta, blue, and cyan lines, i.e., (m − M)_B = 14.15, (m − M)_V = 13.71, and (m − M)_I = 13.02, in Figure 14(d). These three lines broadly cross each other at d = 2.9 kpc and E(B − V) = 0.45. Thus, we determine the distance and reddening to be d = 2.9 ± 0.3 kpc and E(B − V) = 0.45 ± 0.05. The distance modulus in the V band is (m − M)_V = 13.7 ± 0.2.

Hachisu & Kato (2016b) obtained E(B − V) = 0.50 ± 0.05 by assuming that the intrinsic B − V color curve of V496 Sct is the same as that of FH Ser and NQ Vul. See Paper II for a summary of the other estimates of the reddening. We reanalyze the distance and reddening toward V496 Sct, (l, b) = (252838, −17678), based on various distance–reddening relations in Figure 14(d). We plot four distance–reddening relations of Marshall et al. (2006): that toward (l, b) = (2525, −175) is denoted by open red squares, (2550, −175) by filled green squares, (2525, −200) by blue asterisks, and (2550, −200) by open magenta circles, each with error bars. The closest direction in galactic coordinates is that of open red squares. We add the distance–reddening relations (solid black/orange lines) given by Green et al. (2015, 2018), respectively. The open cyan-blue diamonds with error bars represent the relation given by Özdörmez et al. (2016). The solid cyan-blue line denotes the relation given by Chen et al. (2019). Our set of d = 2.9 kpc and E(B − V) = 0.45 is consistent with the trends of Marshall et al., Green et al., Özdörmez et al, and Chen et al. Our results are listed in Table 1.

Adopting E(B − V) = 0.45 and (m − M')_V = 14.45 in Equation (94), we obtain the time-stretched color–magnitude diagram of V496 Sct in Figure 15(d). Here, we plot the data taken from Raj et al. (2012) and SMARTS (Walter et al. 2012). V496 Sct follows the LV Vul track until the dust blackout. Note that, even after the dust blackout, V496 Sct returns and follows the LV Vul track again (upper branch after the onset of nebular phase). Therefore, V496 Sct belongs to the LV Vul type in the time-stretched color–magnitude diagram. This overlapping supports our estimates of E(B − V) = 0.45 and (m − M')_V = 14.45, that is, f_s = 2.0, E(B − V) = 0.45 ± 0.05, (m − M)_V = 13.7 ± 0.2, and d = 2.9 ± 0.3 kpc.

Taking (m − M)_V = 13.7 for V496 Sct, we plot the model V light curve (solid red line) of a 0.85 M_☉ WD with the envelope chemical composition of CO nova 3 (Hachisu & Kato 2016a) in Figure 50(a). The model V light curve reasonably reproduces the observation (filled red circles). This confirms that the distance modulus of (m − M)_V = 13.7 ± 0.2 is reasonable.

Recently, Schaefer (2018, his Table 1) listed distances of 64 novae from Gaia DR2. Among them, seven novae dubbed as having a "very well observed light curve (<30% error)" coincide with our analyzed novae in Table 1. These distances are compared with the present results (Gaia DR2) as follows: CI Aql, 3.3 kpc (3.19 kpc); V705 Cas, 2.6 kpc (2.16 kpc); V1974 Cyg, 1.8 kpc (1.63 kpc); V446 Her, 1.38 kpc (1.36 kpc); V533 Her, 1.28 kpc (1.20 kpc); V382 Vel, 1.4 kpc (1.80 kpc); and PW Vul, 1.8 kpc (2.42 kpc). These values are in good agreement within each error box.

Figure 17 shows (a) the V light curve and (b) (B − V)₀ color curve of V574 Pup on a linear timescale. We deredden the color with E(B − V) = 0.45 as obtained in Section 3.1. The BV data are taken from the SMARTS database (Walter et al. 2012), AAVSO, and the VSOLJ. The B − V data of AAVSO (open blue circles) are systematically bluer by 0.2 mag compared with the other two colors of SMARTS and VSOLJ, so we shift them toward the red by 0.2 mag in Figure 17(b). Such differences come from the slightly different responses of the V filters at different observatories (see, e.g., the discussion in Hachisu & Kato 2006). The horizontal solid red line indicates the B − V color of optically thick free–free emission, i.e., (B − V)₀ = −0.03 (see Paper I). The typical error of SMARTS BVRI data is about 0.001 mag, which is much smaller than the size of each symbol. The error in the AAVSO and VSOLJ data is not reported.

Zoom In Zoom Out Reset image size

Figure 18 shows the (a) B, (b) V, (c) I_C, and (d) K_s light curves of V574 Pup together with YY Dor and LMC N 2009a. Here, we assume that V574 Pup outbursted on JD 2453326.0 (Day 0). Hachisu & Kato (2018b) have already analyzed YY Dor and LMC N 2009a and their various properties are summarized in their Tables 1–3. We increase/decrease the horizontal shift by a step of δ(Δlog t) = δlog f_s = 0.01 and the vertical shift by a step of δ(ΔV) = 0.1 mag, and determine the best overlapping one by eye. As mentioned in Section 1, the model light curves obey the universal decline law. This phase corresponds to the optically thick wind phase before the nebular phase started. Therefore, we should use only the optically thick phase. However, we usually use all of the phases if they overlap each other even after the nebular phase in order to determine the time-scaling factor accurately as much as possible. If not, we use only the part of optically thick wind phase before the nebular (or dust blackout) phase started. It should be noted that the time-scaling factor of f_s is common among these four band light curves. In the case of Figure 18, the four band light curves overlap each other well even after the nebular phase has started. For the B band, we apply Equation (7) to Figure 18(a) and obtain

$$\begin{eqnarray}&&\begin{array}{l}{\left(m-M\right)}_{B,{\rm{V}}574\mathrm{Pup}}\\ \quad =\,{\left({\left(m-M\right)}_{B}+{\rm{\Delta }}B\right)}_{\mathrm{YY}\mathrm{Dor}}-2.5\mathrm{log}6.6\\ \quad =\,18.98-1.5\pm 0.2-2.05=15.43\pm 0.2\\ \quad =\,{\left({\left(m-M\right)}_{B}+{\rm{\Delta }}B\right)}_{\mathrm{LMC}{\rm{N}}2009{\rm{a}}}-2.5\mathrm{log}4.2\\ \quad =\,18.98-2.0\pm 0.2-1.55=15.43\pm 0.2,\end{array}\end{eqnarray} \tag{ 24 }$$

where we adopt (m − M)_B = 18.49 + 4.1 × 0.12 = 18.98 for the LMC novae. Thus, we obtain (m − M)_B,V574 Pup = 15.43 ± 0.1.

Zoom In Zoom Out Reset image size

For the V light curves in Figure 18(b), we similarly obtain

$$\begin{eqnarray}&&\begin{array}{l}{\left(m-M\right)}_{V,{\rm{V}}574\mathrm{Pup}}\\ \quad =\,{\left({\left(m-M\right)}_{V}+{\rm{\Delta }}V\right)}_{\mathrm{YY}\mathrm{Dor}}-2.5\mathrm{log}6.6\\ \quad =\,18.86-1.8\pm 0.2-2.05=15.01\pm 0.2\\ \quad =\,{\left({\left(m-M\right)}_{V}+{\rm{\Delta }}V\right)}_{\mathrm{LMC}{\rm{N}}2009{\rm{a}}}-2.5\mathrm{log}4.2\\ \quad =\,18.86-2.3\pm 0.2-1.55=15.01\pm 0.2,\end{array}\end{eqnarray} \tag{ 25 }$$

where we adopt (m − M)_V = 18.49 + 3.1 × 0.12 = 18.86 for the LMC novae. Thus, we obtain (m − M)_V,V574 Pup = 15.0 ± 0.1.

We apply Equation (8) for the I_C band to Figure 18(c) and obtain

$$\begin{eqnarray}&&\begin{array}{l}{\left(m-M\right)}_{I,{\rm{V}}574\mathrm{Pup}}\\ \quad =\,{\left({\left(m-M\right)}_{I}+{\rm{\Delta }}{I}_{C}\right)}_{\mathrm{YY}\mathrm{Dor}}-2.5\mathrm{log}6.6\\ \quad =\,18.67-2.4\pm 0.3-2.05=14.22\pm 0.3\\ \quad =\,{\left({\left(m-M\right)}_{I}+{\rm{\Delta }}{I}_{C}\right)}_{\mathrm{LMC}{\rm{N}}2009{\rm{a}}}-2.5\mathrm{log}4.2\\ \quad =\,18.67-2.9\pm 0.3-1.55=14.22\pm 0.3,\end{array}\end{eqnarray} \tag{ 26 }$$

(m − M)_I = 18.49 + 1.5 × 0.12 = 18.67 for the LMC novae. Thus, we obtain (m − M)_I,V574 Pup = 14.22 ± 0.2.

For the K_s light curves in Figure 18(d), we apply Equation (9) and obtain

$$\begin{eqnarray}&&\begin{array}{l}{\left(m-M\right)}_{K,{\rm{V}}574\mathrm{Pup}}\\ \quad =\,{\left({\left(m-M\right)}_{K}+{\rm{\Delta }}{K}_{s}\right)}_{\mathrm{YY}\mathrm{Dor}}-2.5\mathrm{log}6.6\\ \quad =\,18.53-2.8\pm 0.4-2.05=13.68\pm 0.4\\ \quad =\,{\left({\left(m-M\right)}_{K}+{\rm{\Delta }}{K}_{s}\right)}_{\mathrm{LMC}{\rm{N}}2009{\rm{a}}}-2.5\mathrm{log}4.2\\ \quad =\,18.53-3.3\pm 0.4-1.55=13.68\pm 0.4,\end{array}\end{eqnarray} \tag{ 27 }$$

(m − M)_K,YY Dor = 18.49 + 0.35 × 0.12 = 18.53 for the LMC novae. Thus, we obtain (m − M)_K,V574 Pup = 13.68 ± 0.2.

Figure 19 shows the V light curve and (B − V)₀ color curve of V574 Pup on a logarithmic timescale in comparison with V1974 Cyg. The V1974 Cyg data are taken from Figure 38 of Paper II. We add visual magnitudes (small red dots) of V574 Pup, which are taken from AAVSO. The V light curves of these two novae do not exactly but broadly overlap each other. Note that there are two different values of the V1974 Cyg V magnitudes in the nebular phase. This is because the response of each V filter is different between these two observations. We set the V light curve of V574 Pup to overlap with the lower (fainter) branch of the V1974 Cyg light curves. We also take into account the (B − V)₀ color evolution in Figure 19(b) to determine the horizontal shift of Δlog t = log f_s. We set log f_s to overlap the two (B − V)₀ color evolution as much as possible.

Zoom In Zoom Out Reset image size

Applying the obtained f_s and ΔV to Equation (4), we have the relation

$$\begin{eqnarray}&&\begin{array}{l}{\left(m-M\right)}_{V,{\rm{V}}574\mathrm{Pup}}\\ \quad =\,{\left({\left(m-M\right)}_{V}+{\rm{\Delta }}V\right)}_{{\rm{V}}1974\mathrm{Cyg}}-2.5\mathrm{log}1.17\\ \quad =\,12.2+3.0\pm 0.2-0.175=15.025\pm 0.3,\end{array}\end{eqnarray} \tag{ 28 }$$

where we adopt (m − M)_V,V1974 Cyg = 12.2 in Section 2.3.4. Thus, we obtain f_s = 1.07 × 1.17 = 1.26 against LV Vul (see Table 1) and (m − M)_V = 15.0 ± 0.3 for V574 Pup.

Using (m − M)_V = 15.0 ± 0.3 and f_s = 1.26, we have the relation

$$\begin{eqnarray}&&\begin{array}{l}{\left(m-M^{\prime} \right)}_{V,{\rm{V}}574\mathrm{Pup}}\\ \quad \equiv \,{\left({m}_{V}-({M}_{V}-2.5\mathrm{log}{f}_{{\rm{s}}})\right)}_{{\rm{V}}574\mathrm{Pup}}\\ \quad =\,{\left({\left(m-M\right)}_{V}+2.5\mathrm{log}{f}_{{\rm{s}}}\right)}_{{\rm{V}}574\mathrm{Pup}}\\ \quad =\,15.0\pm 0.3+2.5\times 0.10=15.25\pm 0.3.\end{array}\end{eqnarray} \tag{ 29 }$$

Figure 20 shows the (a) V and (b) (B − V)₀ evolutions of V679 Car on a linear timescale. The BV data are taken from AAVSO (open blue circles), VSOLJ (filled green stars), and SMARTS (filled red circles). Here, (B − V)₀ are dereddened with E(B − V) = 0.69 as obtained in Section 4.1, but the B − V data of VSOLJ (filled green stars) are systematically shifted toward the red by 0.25 mag to overlap them with the other color data. The typical error of SMARTS BVRI data is about 0.003 mag, which is much smaller than the size of each symbol. The error in the AAVSO and VSOLJ data is not reported.

Zoom In Zoom Out Reset image size

Figure 21 shows the B, V, and I_C light curves of V679 Car together with those of the LMC novae YY Dor and LMC N 2009a. Here, we assume that the V679 Car outburst started on JD 2454794.5 (Day 0). As in Figure 21(c), the I_C light curve of V679 Car overlaps with those of YY Dor and LMC N 2009a only in the first 60 days because of the different contributions of line emission in the nebular phase. Thus, we use only the V light curves that overlap for a longer period to determine the time-scaling factor f_s.

Zoom In Zoom Out Reset image size

We apply Equation (7) for the B band to Figure 21(a) and obtain

$$\begin{eqnarray}&&\begin{array}{l}{\left(m-M\right)}_{B,{\rm{V}}679\mathrm{Car}}\\ \quad =\,{\left({\left(m-M\right)}_{B}+{\rm{\Delta }}B\right)}_{\mathrm{YY}\mathrm{Dor}}-2.5\mathrm{log}5.2\\ \quad =\,18.98-0.4\pm 0.2-1.8=16.78\pm 0.2\\ \quad =\,{\left({\left(m-M\right)}_{B}+{\rm{\Delta }}B\right)}_{\mathrm{LMC}{\rm{N}}2009{\rm{a}}}-2.5\mathrm{log}3.3\\ \quad =\,18.98-0.9\pm 0.2-1.3=16.78\pm 0.2.\end{array}\end{eqnarray} \tag{ 30 }$$

Thus, we obtain (m − M)_B,V679 Car = 16.78 ± 0.1.

For the V light curves in Figure 21(b), we similarly obtain

$$\begin{eqnarray}&&\begin{array}{l}{\left(m-M\right)}_{V,{\rm{V}}679\mathrm{Car}}\\ \quad =\,{\left({\left(m-M\right)}_{V}+{\rm{\Delta }}V\right)}_{\mathrm{YY}\mathrm{Dor}}-2.5\mathrm{log}5.2\\ \quad =\,18.86-1.0\pm 0.2-1.8=16.06\pm 0.2\\ \quad =\,{\left({\left(m-M\right)}_{V}+{\rm{\Delta }}V\right)}_{\mathrm{LMC}{\rm{N}}2009{\rm{a}}}-2.5\mathrm{log}3.3\\ \quad =\,18.86-1.5\pm 0.2-1.3=16.06\pm 0.2.\end{array}\end{eqnarray} \tag{ 31 }$$

Thus, we obtain (m − M)_V,V679 Car = 16.06 ± 0.1.

We apply Equation (8) to Figure 21(c) and obtain

$$\begin{eqnarray}&&\begin{array}{l}{\left(m-M\right)}_{I,{\rm{V}}679\mathrm{Car}}\\ \quad =\,\,{\left({\left(m-M\right)}_{I}+{\rm{\Delta }}{I}_{C}\right)}_{\mathrm{YY}\mathrm{Dor}}-2.5\mathrm{log}5.2\\ \quad =\,18.67-1.9\pm 0.3-1.8=14.97\pm 0.3\\ \quad =\,{\left({\left(m-M\right)}_{I}+{\rm{\Delta }}{I}_{C}\right)}_{\mathrm{LMC}{\rm{N}}2009{\rm{a}}}-2.5\mathrm{log}3.3\\ \quad =\,18.67-2.4\pm 0.3-1.3=14.97\pm 0.3.\end{array}\end{eqnarray} \tag{ 32 }$$

Thus, we obtain (m − M)_I,V679 Car = 14.97 ± 0.2.

Figure 22 shows the comparison with the galactic novae LV Vul and V1668 Cyg in the (a) B and (b) V light curves. Note that we do not time-stretch these two novae because their timescales are almost the same as those of V679 Car.

Zoom In Zoom Out Reset image size

Applying Equation (7) for the B band to Figure 22(a), we have the relation

$$\begin{eqnarray}&&\begin{array}{l}{\left(m-M\right)}_{B,{\rm{V}}679\mathrm{Car}}\\ \quad =\,{\left({\left(m-M\right)}_{B}+{\rm{\Delta }}B\right)}_{\mathrm{LV}\mathrm{Vul}}-2.5\mathrm{log}1.0\\ \quad =\,12.45+4.3\pm 0.2+0.0=16.75\pm 0.2\\ \quad =\,{\left({\left(m-M\right)}_{B}+{\rm{\Delta }}B\right)}_{{\rm{V}}1668\mathrm{Cyg}}-2.5\mathrm{log}1.0\\ \quad =\,14.9+1.9\pm 0.2+0.0=16.8\pm 0.2.\end{array}\end{eqnarray} \tag{ 33 }$$

Thus, we obtain (m − M)_B,V679 Car = 16.78 ± 0.2, being consistent with Equation (30).

Applying Equation (4) to Figure 22(b), we have the relation

$$\begin{eqnarray}&&\begin{array}{l}{\left(m-M\right)}_{V,{\rm{V}}679\mathrm{Car}}\\ \quad =\,{\left(m-M\right)}_{V,\mathrm{LV}\mathrm{Vul}}+{\rm{\Delta }}V-2.5\mathrm{log}1.0\\ \quad =\,11.85+4.2\pm 0.2+0.0=16.05\pm 0.2\\ \quad =\,{\left(m-M\right)}_{V,{\rm{V}}1668\mathrm{Cyg}}+{\rm{\Delta }}V-2.5\mathrm{log}1.0\\ \quad =\,14.6+1.5\pm 0.2+0.0=16.1\pm 0.2.\end{array}\end{eqnarray} \tag{ 34 }$$

Thus, we obtain f_s = 1.0 against LV Vul and (m − M)_V = 16.08 ± 0.1 for V679 Car, again being consistent with Equation (31). Thus, we confirm that both the time-stretching methods for the galactic novae and LMC novae give the same results for the B and V bands of V679 Car.

Figure 23 shows the same V light curve as in Figure 22(b), but also shows the color evolution. We confirm that we do not need to stretch the light/color curves because its timescale is almost the same as that of LV Vul and V1668 Cyg. We shift the V light curves of LV Vul by 4.2 mag and V1668 Cyg by 1.5 mag downward in order to overlap these V light curves.

Zoom In Zoom Out Reset image size

The (B − V)₀ color evolution in Figure 23(b) is also used to constrain the horizontal shift of Δlog t = log f_s = 0.0. The (B − V)₀ color evolution of LV Vul splits into two branches just after the nebular phase started as shown in Figure 23(b). This is because each response function of the V filters is slightly different from each other between these two observations. We set the (B − V)₀ color evolution of V679 Car to overlap with the lower branch of LV Vul in Figure 23(b). The time-scaling factor of f_s = 1.0 gives a good match between the two (B − V)₀ color curves.

From Equations (1), (4), and (34), we have the relation

$$\begin{eqnarray}\begin{array}{rcl}{\left(m-M^{\prime} \right)}_{V,{\rm{V}}679\mathrm{Car}} & \equiv & {\left({m}_{V}-({M}_{V}-2.5\mathrm{log}{f}_{{\rm{s}}})\right)}_{{\rm{V}}679\mathrm{Car}}\\ & = & {\left({\left(m-M\right)}_{V}+{\rm{\Delta }}V\right)}_{\mathrm{LV}\mathrm{Vul}}\\ & = & 11.85+4.2\pm 0.2=16.05\pm 0.2.\end{array}\end{eqnarray} \tag{ 35 }$$

Figure 24 shows the (a) V light curves and (b) (B − V)₀ color curves of V1369 Cen, where (B − V)₀ are dereddened with E(B − V) = 0.11 as obtained in Section 5. The V data of AAVSO (blue open circles), VSOLJ (filled green stars), and SMARTS (filled red circles) are very similar to each other.

Zoom In Zoom Out Reset image size

Figure 25 shows the light/color curves of V1369 Cen as well as those of LV Vul and V496 Sct on a logarithmic timescale. Here we assume that the nova outbursted on JD 2456627.5 (Day 0). We add a straight solid black line labeled "t⁻³" that indicates the homologously expanding ejecta, i.e., free expansion, after the optically thick winds stop (see, e.g., Woodward et al. 1997; Hachisu & Kato 2006). Both the V1369 Cen and V496 Sct light curves have wavy structures in the early phase, but we overlap these three novae light/color curves as much as possible. In the middle phase, both V1369 Cen and V496 Sct show a sharp and shallow dip due to dust blackout. In the later nebular phase, the V light curves of V1369 Cen and V496 Sct well overlap the upper branch of LV Vul. The V light curve of LV Vul splits into two branches in the nebular phase due to the different responses of their V filters as discussed in Paper II. This is because strong [O iii] lines contribute to the blue edge of the V filter in the nebular phase, and small differences among the response functions of V filters lead to large differences in the V magnitudes. The (B − V)₀ color curves of LV Vul also splits into two branches for log t ≳ 2.0, that is, in the nebular phase. The V light curve of V1369 Cen follows V496 Sct and the upper branch of LV Vul, while the (B − V)₀ color curve of V1369 Cen follows V496 Sct and the lower branch of LV Vul.

Zoom In Zoom Out Reset image size

Applying Equation (4) to Figure 25, we have the relation

$$\begin{eqnarray}&&\begin{array}{l}{\left(m-M\right)}_{V,{\rm{V}}1369\mathrm{Cen}}\\ \quad =\,{\left(m-M+{\rm{\Delta }}V\right)}_{V,\mathrm{LV}\mathrm{Vul}}-2.5\mathrm{log}1.48\\ \quad =\,11.85-1.2\pm 0.2-0.425=10.23\pm 0.2\\ \quad =\,{\left(m-M+{\rm{\Delta }}V\right)}_{V,{\rm{V}}496\mathrm{Sct}}-2.5\mathrm{log}0.74\\ \quad =\,13.7-3.8\pm 0.2+0.325=10.23\pm 0.2.\end{array}\end{eqnarray} \tag{ 36 }$$

Thus, we obtain f_s = 1.48 against LV Vul and (m − M)_V = 10.23 ± 0.2 for V1369 Cen. These values are summarized in Table 1

From Equations (1), (4), and (36), we have the relation

$$\begin{eqnarray}&&\begin{array}{l}{\left(m-M^{\prime} \right)}_{V,{\rm{V}}1369\mathrm{Cen}}\\ \quad \equiv \,{\left({m}_{V}-({M}_{V}-2.5\mathrm{log}{f}_{{\rm{s}}})\right)}_{{\rm{V}}1369\mathrm{Cen}}\\ \quad =\,{\left({\left(m-M\right)}_{V}+{\rm{\Delta }}V\right)}_{\mathrm{LV}\mathrm{Vul}}\\ \quad =\,11.85-1.2\pm 0.2=10.65\pm 0.2.\end{array}\end{eqnarray} \tag{ 37 }$$

We further compare with other novae having similar light curves to V1369 Cen, i.e., V496 Sct and V5666 Sgr. Figure 26 shows the time-stretched light curves of the B, V, I_C, and K_s bands. The light curves well overlap except for the K_s band. Applying Equation (7) for the B band to Figure 26(a), we have the relation

$$\begin{eqnarray}&&\begin{array}{l}{\left(m-M\right)}_{B,{\rm{V}}1369\mathrm{Cen}}\\ \quad =\,{\left({\left(m-M\right)}_{B}+{\rm{\Delta }}B\right)}_{{\rm{V}}496\mathrm{Sct}}-2.5\mathrm{log}0.74\\ \quad =\,14.15-4.1\pm 0.2+0.325=10.38\pm 0.2,\end{array}\end{eqnarray} \tag{ 38 }$$

where we adopt (m − M)_B,V496 Sct = 13.7 + 1.0 × 0.45 = 14.15 from Section 7.12. Thus, we obtain (m − M)_B = 10.38 ± 0.2 for V1369 Cen. We obtain d = 0.97 ± 0.1 kpc from Equation (11) together with E(B − V) = 0.11 and (m − M)_B = 10.38 ± 0.2. We plot this relation of (m − M)_B = 10.38 with the solid magenta line in Figure 7(c).

Zoom In Zoom Out Reset image size

Applying Equation (4) to Figure 26(b), we have the relation

$$\begin{eqnarray}&&\begin{array}{l}{\left(m-M\right)}_{V,{\rm{V}}1369\mathrm{Cen}}\\ \quad =\,{\left({\left(m-M\right)}_{V}+{\rm{\Delta }}V\right)}_{{\rm{V}}496\mathrm{Sct}}-2.5\mathrm{log}0.74\\ \quad =\,13.7-3.8\pm 0.2+0.325=10.23\pm 0.2,\end{array}\end{eqnarray} \tag{ 39 }$$

where we adopt (m − M)_V,V496 Sct = 13.7 from Section 7.12. Thus, we obtain (m − M)_V = 10.23 ± 0.2 for V1369 Cen. We obtain d = 0.95 ± 0.1 kpc from Equation (5) together with E(B − V) = 0.11. We plot this relation of (m − M)_V = 10.23 with the solid blue line in Figure 7(c).

From the I_C band data in Figure 26(a), we obtain

$$\begin{eqnarray}&&\begin{array}{l}{\left(m-M\right)}_{I,{\rm{V}}1369\mathrm{Cen}}\\ \quad =\,{\left({\left(m-M\right)}_{I}+{\rm{\Delta }}{I}_{C}\right)}_{{\rm{V}}496\mathrm{Sct}}-2.5\mathrm{log}0.74\\ \quad =\,12.98-3.2\pm 0.2+0.325=10.11\pm 0.2,\end{array}\end{eqnarray} \tag{ 40 }$$

where we adopt (m − M)_I,V496 Sct = 13.7 − 1.6 × 0.45 = 12.98. Thus, we obtain (m − M)_I,V574 Pup = 10.11 ± 0.2. We obtain d = 0.97 ± 0.1 kpc from Equation (12) together with E(B − V) = 0.11. We plot this relation of (m − M)_I = 10.11 with the solid cyan line in Figure 7(c).

V1369 Cen and V496 Sct showed a shallow dust blackout around 100 days (log t ∼ 2.0) after the outbursts (Figure 26). Correspondingly, the K_s light curves are enhanced above the line of universal decline law (F_ν ∝ t^−1.75), as shown in Figure 26(d). In such a case, we do not use this part for overlapping. In the later phase, however, the decline trend of V1369 Cen becomes similar to that of V496 Sct and V5666 Sgr. We, thus, try to overlap as much as possible in the later phase. Applying Equation (9) for the K_s band, we obtain

$$\begin{eqnarray}&&\begin{array}{l}{\left(m-M\right)}_{K,{\rm{V}}1369\mathrm{Cen}}\\ \quad =\,{\left({\left(m-M\right)}_{K}+{\rm{\Delta }}{K}_{{\rm{s}}}\right)}_{{\rm{V}}496\mathrm{Sct}}-2.5\mathrm{log}0.74\\ \quad =\,12.46-2.8\pm 0.3+0.325=9.99\pm 0.3,\end{array}\end{eqnarray} \tag{ 41 }$$

where we adopt (m − M)_K,V496 Sct = 13.7 − 2.75 × 0.45 = 12.46. Thus, we obtain (m − M)_{K,V1369 Cen} = 9.99 ± 0.3. The distance is determined to be d = 0.98 ± 0.3 kpc from Equation (13) together with E(B − V) = 0.11. This distance is consistent with those determined from the B, V, and I_C bands. We plot this relation of (m − M)_K = 9.99 with the solid cyan-blue line in Figure 7(c).

Figure 27 shows the comparison with V1668 Cyg, one of the well-studied novae. The timescale of V1668 Cyg is stretched with f_s = 1.48, and the V magnitude difference is ΔV = −3.9. From the time-stretching method, we have the relation

$$\begin{eqnarray}&&\begin{array}{l}{\left(m-M\right)}_{V,{\rm{V}}1369\mathrm{Cen}}\\ \quad =\,{\left(m-M+{\rm{\Delta }}V\right)}_{V,{\rm{V}}1668\mathrm{Cyg}}-2.5\mathrm{log}1.48\\ \quad =\,14.6-3.9\pm 0.2-0.43=10.27\pm 0.2,\end{array}\end{eqnarray} \tag{ 42 }$$

where we adopt (m − M)_V,V1668 Cyg = 14.6 from Section 2.3.3. Thus, we again confirm that f_s = 1.48 against LV Vul and (m − M)_V = 10.27 ± 0.2. To summarize, we adopt (m − M)_V = 10.25 ± 0.1 from various estimates based on the time-stretching method.

Zoom In Zoom Out Reset image size

Figure 28 shows (a) the V and visual light and (b) (B − V)₀ color curves of V5666 Sgr. The V and visual data of AAVSO (blue open circles and magenta dots) and V data of VSOLJ (filled green stars) are systematically shifted downward by 0.3 mag and 0.2 mag, respectively, to overlap them with the SMARTS data (filled red circles). Here, (B − V)₀ are dereddened with E(B − V) = 0.50 as obtained in Section 6. The B − V data of AAVSO (blue open circles) and VSOLJ (filled green stars) are systematically shifted upward by 0.03 mag and 0.02 mag, respectively, to overlap them with the SMARTS data (filled red circles).

Zoom In Zoom Out Reset image size

Figure 29 shows (a) the V light curves of V5666 Sgr, LV Vul, V496 Sct, and V1369 Cen, and (b) their (B − V)₀ color curves on logarithmic timescales. Here we assume that the V5666 Sgr outbursted on JD 2456681.0 (Day 0). Figure 29 compares V5666 Sgr with similar V light-curve novae, V496 Sct and V1369 Cen, in addition to LV Vul. We stretch the timescales of LV Vul, V496 Sct, and V1369 Cen by 1.78, 0.89, and 1.20, respectively, against V5666 Sgr to overlap them with the V5666 Sgr V light and (B − V)₀ color curves. From the time-stretching method, we have the relation

$$\begin{eqnarray}&&\begin{array}{l}{\left(m-M\right)}_{V,{\rm{V}}5666\mathrm{Sgr}}\\ \quad =\,{\left(m-M+{\rm{\Delta }}V\right)}_{V,\mathrm{LV}\mathrm{Vul}}-2.5\mathrm{log}1.78\\ \quad =\,11.85+4.2\pm 0.2-0.63=15.42\pm 0.2\\ \quad =\,{\left(m-M+{\rm{\Delta }}V\right)}_{V,{\rm{V}}496\mathrm{Sct}}-2.5\mathrm{log}0.89\\ \quad =\,13.7+1.6\pm 0.2+0.13=15.43\pm 0.2\\ \quad =\,{\left(m-M+{\rm{\Delta }}V\right)}_{V,{\rm{V}}1369\mathrm{Cen}}-2.5\mathrm{log}1.20\\ \quad =\,10.25+5.3\pm 0.2-0.20=15.35\pm 0.2.\end{array}\end{eqnarray} \tag{ 43 }$$

Thus, we obtained (m − M)_V,V5666 Sgr = 15.4 ± 0.1.

Zoom In Zoom Out Reset image size

From Equations (1), (4), and (43), we have the relation

$$\begin{eqnarray}&&\begin{array}{l}{\left(m-M^{\prime} \right)}_{V,{\rm{V}}5666\mathrm{Sgr}}\\ \quad \equiv \,{\left({m}_{V}-({M}_{V}-2.5\mathrm{log}{f}_{{\rm{s}}})\right)}_{{\rm{V}}5666\mathrm{Sgr}}\\ \quad =\,{\left({\left(m-M\right)}_{V}+{\rm{\Delta }}V\right)}_{\mathrm{LV}\mathrm{Vul}}\\ \quad =\,11.85+4.2\pm 0.2=16.05\pm 0.2.\end{array}\end{eqnarray} \tag{ 44 }$$

We further compare the V5666 Sgr light curves with other novae having similar light curves, V1369 Cen and V496 Sct. Figure 30 shows the same time-stretched light curves of the B, V, I_C, and K_s bands as in Figure 26. Applying Equation (7) for the B band to Figure 30(a), we have the relation

$$\begin{eqnarray}&&\begin{array}{l}{\left(m-M\right)}_{B,{\rm{V}}5666\mathrm{Sgr}}\\ \quad =\,{\left({\left(m-M\right)}_{B}+{\rm{\Delta }}B\right)}_{{\rm{V}}496\mathrm{Sct}}-2.5\mathrm{log}0.89\\ \quad =\,14.15+1.6\pm 0.2+0.125=15.88\pm 0.2\\ \quad =\,{\left({\left(m-M\right)}_{B}+{\rm{\Delta }}B\right)}_{{\rm{V}}1369\mathrm{Cen}}-2.5\mathrm{log}1.2\\ \quad =\,10.36+5.7\pm 0.2-0.20=15.86\pm 0.2,\end{array}\end{eqnarray} \tag{ 45 }$$

where we adopt (m − M)_B,V496 Sct = 13.7 + 1.0 × 0.45 = 14.15 from Section 7.12 and (m − M)_B,V1369 Cen = 10.25 + 1.0 × 0.11 = 10.36 from Section 5. Thus, we obtain (m − M)_B = 15.87 ± 0.1 for V5666 Sgr. We obtain d = 5.8 ± 0.6 kpc from Equation (11) together with E(B − V) = 0.50 and (m − M)_B = 15.87 ± 0.1. We plot this relation of (m − M)_B = 15.87 with the solid magenta line in Figure 7(d).

Zoom In Zoom Out Reset image size

Applying Equation (4) to Figure 30(b), we have the relation

$$\begin{eqnarray}&&\begin{array}{l}{\left(m-M\right)}_{V,{\rm{V}}5666\mathrm{Sgr}}\\ \quad =\,{\left({\left(m-M\right)}_{V}+{\rm{\Delta }}V\right)}_{{\rm{V}}496\mathrm{Sct}}-2.5\mathrm{log}0.89\\ \quad =\,13.7+1.6\pm 0.2+0.125=15.4\pm 0.2\\ \quad =\,{\left({\left(m-M\right)}_{V}+{\rm{\Delta }}V\right)}_{{\rm{V}}1369\mathrm{Cen}}-2.5\mathrm{log}1.2\\ \quad =\,10.25+5.3\pm 0.2-0.20=15.35\pm 0.2,\end{array}\end{eqnarray} \tag{ 46 }$$

where we adopt (m − M)_V,V496 Sct = 13.7 from Section 7.12 and (m − M)_V,V1369 Cen = 10.25 from Section 5. Thus, we obtain (m − M)_V = 15.38 ± 0.1 for V5666 Sgr. We obtain d = 5.8 ± 0.6 kpc from Equation (5) together with E(B − V) = 0.50 ± 0.05 and (m − M)_V = 15.38 ± 0.1. We plot this relation of (m − M)_V = 15.38 with the solid blue line in Figure 7(d).

From the I_C band data in Figure 30(c), we obtain

$$\begin{eqnarray}&&\begin{array}{l}{\left(m-M\right)}_{I,{\rm{V}}5666\mathrm{Sgr}}\\ \quad =\,{\left({\left(m-M\right)}_{I}+{\rm{\Delta }}{I}_{C}\right)}_{{\rm{V}}496\mathrm{Sct}}-2.5\mathrm{log}0.89\\ \quad =\,12.98+1.5\pm 0.2+0.125=14.61\pm 0.2\\ \quad =\,{\left({\left(m-M\right)}_{I}+{\rm{\Delta }}{I}_{C}\right)}_{{\rm{V}}1369\mathrm{Cen}}-2.5\mathrm{log}1.2\\ \quad =\,10.07+4.7\pm 0.2-0.20=14.57\pm 0.2,\end{array}\end{eqnarray} \tag{ 47 }$$

where we adopt (m − M)_I,V496 Sct = 13.7 − 1.6 × 0.45 = 12.98 and (m − M)_I,V1369 Cen = 10.25 − 1.6 × 0.11 = 10.07. Thus, we obtain (m − M)_I,V5666 Sgr = 14.59 ± 0.1. We obtain d = 5.9 ± 0.6 kpc from Equation (12) together with E(B − V) = 0.50 ± 0.05 and (m − M)_I = 14.59 ± 0.1. We plot this relation of (m − M)_I = 14.59 with the solid cyan line in Figure 7(d).

We try to overlap the K_s light curves as much as possible in the later phase of Figure 30(d). Applying Equation (9) for the K_s band, we obtain

$$\begin{eqnarray}&&\begin{array}{l}{\left(m-M\right)}_{K,{\rm{V}}5666\mathrm{Sgr}}\\ \quad =\,{\left({\left(m-M\right)}_{K}+{\rm{\Delta }}{K}_{{\rm{s}}}\right)}_{{\rm{V}}496\mathrm{Sct}}-2.5\mathrm{log}0.89\\ \quad =\,12.46+1.5\pm 0.3+0.125=14.09\pm 0.3\\ \quad =\,{\left({\left(m-M\right)}_{K}+{\rm{\Delta }}{K}_{{\rm{s}}}\right)}_{{\rm{V}}1369\mathrm{Cen}}-2.5\mathrm{log}1.2\\ \quad =\,9.95+4.3\pm 0.3-0.20=14.05\pm 0.3,\end{array}\end{eqnarray} \tag{ 48 }$$

where we adopt (m − M)_K,V496 Sct = 13.7 − 2.75 × 0.45 = 12.46 and (m − M)_K,V1369 Cen = 10.25 − 2.75 × 0.11 = 9.95. Thus, we obtain (m − M)_K,V5666 Sgr = 14.07 ± 0.2. We obtain d = 6.0 ± 0.6 kpc from Equation (13) together with E(B − V) = 0.50 ± 0.05 and (m − M)_K = 14.07 ± 0.2. We plot this relation of (m − M)_K = 14.07 with the solid cyan-blue line in Figure 7(d).

Figure 31 also shows another comparison with LV Vul and V1668 Cyg. The light/color curves of LV Vul and V1668 Cyg are stretched by a factor of 1.78, so we obtain

$$\begin{eqnarray}&&\begin{array}{l}{\left(m-M\right)}_{V,{\rm{V}}5666\mathrm{Sgr}}\\ \quad =\,{\left(m-M+{\rm{\Delta }}V\right)}_{V,\mathrm{LV}\mathrm{Vul}}-2.5\mathrm{log}1.78\\ \quad =\,11.85+4.2\pm 0.2-0.63=15.42\pm 0.2\\ \quad =\,{\left(m-M+{\rm{\Delta }}V\right)}_{V,{\rm{V}}1668\mathrm{Cyg}}-2.5\mathrm{log}1.78\\ \quad =\,14.6+1.4\pm 0.2-0.63=15.37\pm 0.2\end{array}\end{eqnarray} \tag{ 49 }$$

from our time-stretching method. Thus, we again confirm (m − M)_V,V5666 Sgr = 15.4 ± 0.2.

Zoom In Zoom Out Reset image size

Figure 32 shows the light/color curves of V446 Her on a logarithmic timescale as well as LV Vul and V1668 Cyg. We overlap the light/color curves of these three novae as much as possible. Based on the time-stretching method, we have the relation

$$\begin{eqnarray}&&\begin{array}{l}{\left(m-M\right)}_{V,{\rm{V}}446\mathrm{Her}}\\ \quad =\,{\left(m-M+{\rm{\Delta }}V\right)}_{V,\mathrm{LV}\mathrm{Vul}}-2.5\mathrm{log}1.0\\ \quad =\,11.85+0.1\pm 0.2+0.0=11.95\pm 0.2\\ \quad =\,{\left(m-M+{\rm{\Delta }}V\right)}_{V,{\rm{V}}1668\mathrm{Cyg}}-2.5\mathrm{log}1.0\\ \quad =\,14.6-2.6\pm 0.2+0.0=12.0\pm 0.2.\end{array}\end{eqnarray} \tag{ 50 }$$

Thus, we obtain f_s = 1.0 and (m − M)_V = 11.95 ± 0.1 for V446 Her. The new distance modulus is slightly larger than the previous value of (m − M)_V = 11.7 ± 0.1 (Paper II). This difference comes from the improved values of f_s and ΔV. From Equations (14) and (50), we have the relation

$$\begin{eqnarray}&&\begin{array}{l}{\left(m-M^{\prime} \right)}_{V,{\rm{V}}446\mathrm{Her}}\\ \quad \equiv \,{\left({m}_{V}-({M}_{V}-2.5\mathrm{log}{f}_{{\rm{s}}})\right)}_{{\rm{V}}446\mathrm{Her}}\\ \quad =\,{\left(m-M+{\rm{\Delta }}V\right)}_{V,\mathrm{LV}\mathrm{Vul}}\\ \quad =\,11.85+0.1\pm 0.2=11.95\pm 0.2.\end{array}\end{eqnarray} \tag{ 51 }$$

Zoom In Zoom Out Reset image size

We obtain f_s and (m − M)_V with the time-stretching method as in Figure 33, which shows the V light curve as well as the dereddened (B − V)₀ and (U − B)₀ color curves. We add the light/color curves of LV Vul and V1974 Cyg and overlap these light/color curves as much as possible. Applying the time-stretching method of Equation (4) to Figure 33(a), we have the relation

$$\begin{eqnarray}&&\begin{array}{l}{\left(m-M\right)}_{V,{\rm{V}}533\mathrm{Her}}\\ \quad =\,{\left({\left(m-M\right)}_{V}+{\rm{\Delta }}V\right)}_{\mathrm{LV}\mathrm{Vul}}-2.5\mathrm{log}1.20\\ \quad =\,11.85-1.0\pm 0.3-0.20=10.65\pm 0.3\\ \quad =\,{\left({\left(m-M\right)}_{V}+{\rm{\Delta }}V\right)}_{{\rm{V}}1974\mathrm{Cyg}}-2.5\mathrm{log}1.15\\ \quad =\,12.2-1.4\pm 0.3-0.15=10.65\pm 0.3.\end{array}\end{eqnarray} \tag{ 52 }$$

The new result of (m − M)_V = 10.65 ± 0.2 is almost the same as the previous result of (m − M)_V = 10.8 ± 0.2 (Paper II), but slightly improves the time-scaling factors of f_s and vertical fit of ΔV. We obtain f_s = 1.20 against the template LV Vul. The distance is calculated to be d = 1.28 kpc from Equation (5) together with (m − M)_V = 10.65 and E(B − V) = 0.038. This value is almost the same as what Hachisu & Kato (2016b) concluded from various results in the literature.

Zoom In Zoom Out Reset image size

From Equations (14) and (52), we have the relation

$$\begin{eqnarray}&&\begin{array}{l}{\left(m-M^{\prime} \right)}_{V,{\rm{V}}533\mathrm{Her}}\\ \quad \equiv \,{\left({m}_{V}-({M}_{V}-2.5\mathrm{log}{f}_{{\rm{s}}})\right)}_{{\rm{V}}533\mathrm{Her}}\\ \quad =\,{\left({\left(m-M\right)}_{V}+{\rm{\Delta }}V\right)}_{\mathrm{LV}\mathrm{Vul}}\\ \quad =\,11.85-1.0\pm 0.3=10.85\pm 0.3.\end{array}\end{eqnarray} \tag{ 53 }$$

Figure 34 shows the light/color curves of PW Vul on a logarithmic timescale as well as LV Vul, V1500 Cyg, and V1668 Cyg. We deredden the colors of PW Vul with E(B − V) = 0.57 as obtained in Section 7.3. In this figure, we regard the V light curve of PW Vul to oscillate between the V light curves of V1668 Cyg and V1500 Cyg during log t (days) ∼ 1.4–2.1. Based on the time-stretching method, we have the relation

$$\begin{eqnarray}&&\begin{array}{l}{\left(m-M\right)}_{V,\mathrm{PW}\mathrm{Vul}}\\ \quad =\,{\left(m-M+{\rm{\Delta }}V\right)}_{V,\mathrm{LV}\mathrm{Vul}}-2.5\mathrm{log}2.24\\ \quad =\,11.85+2.0\pm 0.3-0.88=12.97\pm 0.3\\ \quad =\,{\left(m-M+{\rm{\Delta }}V\right)}_{V,{\rm{V}}1668\mathrm{Cyg}}-2.5\mathrm{log}2.24\\ \quad =\,14.6-0.7\pm 0.3-0.88=13.02\pm 0.3\\ \quad =\,{\left(m-M+{\rm{\Delta }}V\right)}_{V,{\rm{V}}1500\mathrm{Cyg}}-2.5\mathrm{log}3.7\\ \quad =\,12.3+2.1\pm 0.3-1.43=12.97\pm 0.3.\end{array}\end{eqnarray} \tag{ 54 }$$

Thus, we obtain f_s = 2.24 against the template nova LV Vul and confirm the previous result of (m − M)_V = 13.0 ± 0.2 for PW Vul (Hachisu & Kato 2015, 2016b). From Equations (14) and (54), we have the relation

$$\begin{eqnarray}&&\begin{array}{l}{\left(m-M^{\prime} \right)}_{V,\mathrm{PW}\mathrm{Vul}}\\ \quad \equiv \,{\left({m}_{V}-({M}_{V}-2.5\mathrm{log}{f}_{{\rm{s}}})\right)}_{\mathrm{PW}\mathrm{Vul}}\\ \quad =\,{\left(m-M+{\rm{\Delta }}V\right)}_{V,\mathrm{LV}\mathrm{Vul}}\\ \quad =\,11.85+2.0\pm 0.3=13.85\pm 0.3.\end{array}\end{eqnarray} \tag{ 55 }$$

Zoom In Zoom Out Reset image size

We further obtain the distance moduli of the BVI_C bands and examine the distance and reddening toward PW Vul. Figure 35 shows the three band light curves of PW Vul as well as V679 Car, YY Dor, and LMC N 2009a. For the B band, we apply Equation (7) to Figure 35(a) and obtain

$$\begin{eqnarray}&&\begin{array}{l}{\left(m-M\right)}_{B,\mathrm{PW}\mathrm{Vul}}\\ \quad =\,{\left({\left(m-M\right)}_{B}+{\rm{\Delta }}B\right)}_{\mathrm{YY}\mathrm{Dor}}-2.5\mathrm{log}11.7\\ \quad =\,18.98-2.8\pm 0.2-2.67=13.51\pm 0.2\\ \quad =\,{\left({\left(m-M\right)}_{B}+{\rm{\Delta }}B\right)}_{\mathrm{LMC}{\rm{N}}2009{\rm{a}}}-2.5\mathrm{log}7.4\\ \quad =\,18.98-3.3\pm 0.2-2.17=13.51\pm 0.2\\ \quad =\,{\left({\left(m-M\right)}_{B}+{\rm{\Delta }}B\right)}_{{\rm{V}}679\mathrm{Car}}-2.5\mathrm{log}2.24\\ \quad =\,16.79-2.4\pm 0.2-0.87=13.52\pm 0.2,\end{array}\end{eqnarray} \tag{ 56 }$$

where we adopt (m − M)_B,V679 Car = 16.1 + 1.0 × 0.69 = 16.79. Thus, we obtain (m − M)_B,PW Vul = 13.52 ± 0.1.

Zoom In Zoom Out Reset image size

For the V light curves in Figure 35(b), we similarly obtain

$$\begin{eqnarray}&&\begin{array}{l}{\left(m-M\right)}_{V,\mathrm{PW}\mathrm{Vul}}\\ \quad =\,{\left({\left(m-M\right)}_{V}+{\rm{\Delta }}V\right)}_{\mathrm{YY}\mathrm{Dor}}-2.5\mathrm{log}11.7\\ \quad =\,18.86-3.2\pm 0.2-2.67=12.99\pm 0.2\\ \quad =\,{\left({\left(m-M\right)}_{V}+{\rm{\Delta }}V\right)}_{\mathrm{LMC}{\rm{N}}2009{\rm{a}}}-2.5\mathrm{log}7.4\\ \quad =\,18.86-3.7\pm 0.2-2.17=12.99\pm 0.2\\ \quad =\,{\left({\left(m-M\right)}_{V}+{\rm{\Delta }}V\right)}_{{\rm{V}}679\mathrm{Car}}-2.5\mathrm{log}2.24\\ \quad =\,16.1-2.2\pm 0.2-0.87=13.03\pm 0.2,\end{array}\end{eqnarray} \tag{ 57 }$$

where we adopt (m − M)_V,V679 Car = 16.1 in Section 4. Thus, we obtain (m − M)_V,PW Vul = 13.0 ± 0.1.

Applying Equation (8) for the I_C band to Figure 35(c), we obtain

$$\begin{eqnarray}&&\begin{array}{l}{\left(m-M\right)}_{I,\mathrm{PW}\mathrm{Vul}}\\ \quad =\,{\left({\left(m-M\right)}_{I}+{\rm{\Delta }}{I}_{C}\right)}_{\mathrm{YY}\mathrm{Dor}}-2.5\mathrm{log}11.7\\ \quad =\,18.67-3.9\pm 0.3-2.67=12.1\pm 0.3\\ \quad =\,{\left({\left(m-M\right)}_{I}+{\rm{\Delta }}{I}_{C}\right)}_{\mathrm{LMC}{\rm{N}}2009{\rm{a}}}-2.5\mathrm{log}7.4\\ \quad =\,18.67-4.4\pm 0.3-2.17=12.1\pm 0.3\\ \quad =\,{\left({\left(m-M\right)}_{I}+{\rm{\Delta }}{I}_{C}\right)}_{{\rm{V}}679\mathrm{Car}}-2.5\mathrm{log}2.24\\ \quad =\,15.0-2.0\pm 0.3-0.87=12.13\pm 0.3,\end{array}\end{eqnarray} \tag{ 58 }$$

where we adopt (m − M)_I,V679 Car = 16.1 − 1.6 × 0.69 = 15.0. However, we should not use this result because no I_C but only I data of PW Vul are available (Robb & Scarfe 1995), and the I light curve of PW Vul (filled blue circles) does not accurately follow the other I_C data, which follow the universal decline law as shown in Figure 35(c).

We also plot the U, B, and V light curves of PW Vul together with those of LV Vul, V1668 Cyg, and V5114 Sgr in Figure 36. We apply Equation (6) for the U band to Figure 36(a) and obtain

$$\begin{eqnarray}&&\begin{array}{l}{\left(m-M\right)}_{U,\mathrm{PW}\mathrm{Vul}}\\ \quad =\,{\left({\left(m-M\right)}_{U}+{\rm{\Delta }}U\right)}_{\mathrm{LV}\mathrm{Vul}}-2.5\mathrm{log}2.24\\ \quad =\,12.85+1.9\pm 0.2-0.87=13.88\pm 0.2\\ \quad =\,{\left({\left(m-M\right)}_{U}+{\rm{\Delta }}U\right)}_{{\rm{V}}1668\mathrm{Cyg}}-2.5\mathrm{log}2.24\\ \quad =\,15.1-0.3\pm 0.2-0.87=13.93\pm 0.2\\ \quad =\,{\left({\left(m-M\right)}_{U}+{\rm{\Delta }}U\right)}_{{\rm{V}}5114\mathrm{Sgr}}-2.5\mathrm{log}2.95\\ \quad =\,17.43-2.3\pm 0.2-1.17=13.96\pm 0.2,\end{array}\end{eqnarray} \tag{ 59 }$$

where we adopt (m − M)_U,LV Vul = 11.85 + (4.75 − 3.1) × 0.60 = 12.85, (m − M)_U,V1668 Cyg = 14.6 + (4.75 − 3.1) × 0.30 = 15.10, and (m − M)_U,V5114 Sgr = 16.65 + (4.75 − 3.1) × 0.47 = 17.43. Thus, we obtain (m − M)_U,PW Vul = 13.92 ± 0.2. For the B light curves in Figure 36(b), we similarly obtain

$$\begin{eqnarray}&&\begin{array}{l}{\left(m-M\right)}_{B,\mathrm{PW}\mathrm{Vul}}\\ \quad =\,{\left({\left(m-M\right)}_{B}+{\rm{\Delta }}B\right)}_{\mathrm{LV}\mathrm{Vul}}-2.5\mathrm{log}2.24\\ \quad =\,12.45+2.0\pm 0.2-0.87=13.58\pm 0.2\\ \quad =\,{\left({\left(m-M\right)}_{B}+{\rm{\Delta }}B\right)}_{{\rm{V}}1668\mathrm{Cyg}}-2.5\mathrm{log}2.24\\ \quad =\,14.9-0.5\pm 0.2-0.87=13.53\pm 0.2\\ \quad =\,{\left({\left(m-M\right)}_{B}+{\rm{\Delta }}B\right)}_{{\rm{V}}5114\mathrm{Sgr}}-2.5\mathrm{log}2.95\\ \quad =\,17.12-2.4\pm 0.2-1.17=13.55\pm 0.2,\end{array}\end{eqnarray} \tag{ 60 }$$

where we adopt (m − M)_B,LV Vul = 11.85 + 1.0 × 0.6 = 12.45, (m − M)_B,V1668 Cyg = 14.6 + 1.0 × 0.3 = 14.9, and (m − M)_B,V5114 Sgr = 16.65 + 1.0 × 0.47 = 17.12. Thus, we obtain (m − M)_B,PW Vul = 13.55 ± 0.2. We apply Equation (4) to Figure 36(c) and obtain

$$\begin{eqnarray}&&\begin{array}{l}{\left(m-M\right)}_{V,\mathrm{PW}\mathrm{Vul}}\\ \quad =\,{\left({\left(m-M\right)}_{V}+{\rm{\Delta }}V\right)}_{\mathrm{LV}\mathrm{Vul}}-2.5\mathrm{log}2.24\\ \quad =\,11.85+2.0\pm 0.2-0.87=12.98\pm 0.2\\ \quad =\,{\left({\left(m-M\right)}_{V}+{\rm{\Delta }}V\right)}_{{\rm{V}}1668\mathrm{Cyg}}-2.5\mathrm{log}2.24\\ \quad =\,14.6-0.7\pm 0.2-0.87=13.03\pm 0.2\\ \quad =\,{\left({\left(m-M\right)}_{V}+{\rm{\Delta }}V\right)}_{{\rm{V}}5114\mathrm{Sgr}}-2.5\mathrm{log}2.95\\ \quad =\,16.65-2.5\pm 0.2-1.17=12.98\pm 0.2.\end{array}\end{eqnarray} \tag{ 61 }$$

Thus, we obtain (m − M)_V,PW Vul = 13.0 ± 0.1. This result is essentially the same as that in Equations (54) and (57).

Zoom In Zoom Out Reset image size

We plot these four distance moduli of the U, B, V, and I_C bands in Figure 10(c) by the thin solid green, cyan, and thick solid blue, and thin solid blue-magenta lines, that is, (m − M)_U = 13.92, (m − M)_B = 13.55, and (m − M)_V = 13.0 and (m − M)_I = 12.12, respectively. These four lines cross at d = 1.8 kpc and E(B − V) = 0.57.

Figure 37 shows the light/color curves of V1419 Aql as well as those of LV Vul and V1668 Cyg. We regard the V light curve of V1419 Aql to follow V1668 Cyg and the upper branch of LV Vul during log t (days) ∼ 1.0–1.4. Based on the time-stretching method, we have the relation

$$\begin{eqnarray}&&\begin{array}{l}{\left(m-M\right)}_{V,{\rm{V}}1419\mathrm{Aql}}\\ \quad =\,{\left(m-M+{\rm{\Delta }}V\right)}_{V,\mathrm{LV}\mathrm{Vul}}-2.5\mathrm{log}1.41\\ \quad =\,11.85+3.5\pm 0.3-0.38=14.97\pm 0.3\\ \quad =\,{\left(m-M+{\rm{\Delta }}V\right)}_{V,{\rm{V}}1668\mathrm{Cyg}}-2.5\mathrm{log}1.41\\ \quad =\,14.6+0.8\pm 0.3-0.38=15.02\pm 0.3.\end{array}\end{eqnarray} \tag{ 62 }$$

Thus, we obtain f_s = 1.41 against the template nova LV Vul and (m − M)_V = 15.0 ± 0.2. The new value is slightly larger than the previous estimate of (m − M)_V = 14.6 ± 0.1 by Hachisu & Kato (2016b), because the time-scaling factor f_s and ΔV are improved. From Equations (14) and (62), we have the relation

$$\begin{eqnarray}&&\begin{array}{l}{\left(m-M^{\prime} \right)}_{V,{\rm{V}}1419\mathrm{Aql}}\\ \quad \equiv \,{\left({m}_{V}-({M}_{V}-2.5\mathrm{log}{f}_{{\rm{s}}})\right)}_{{\rm{V}}1419\mathrm{Aql}}\\ \quad =\,{\left(m-M+{\rm{\Delta }}V\right)}_{V,\mathrm{LV}\mathrm{Vul}}\\ \quad =\,11.85+3.5\pm 0.3=15.35\pm 0.3.\end{array}\end{eqnarray} \tag{ 63 }$$

Zoom In Zoom Out Reset image size

Figure 38 shows the light/color curves of V705 Cas as well as those of LV Vul and PW Vul. We deredden the colors of V705 Cas with E(B − V) = 0.45 as obtained in Section 7.5. Based on the time-stretching method, we have the relation

$$\begin{eqnarray}&&\begin{array}{l}{\left(m-M\right)}_{V,{\rm{V}}705\mathrm{Cas}}\\ \quad =\,{\left(m-M+{\rm{\Delta }}V\right)}_{V,\mathrm{LV}\mathrm{Vul}}-2.5\mathrm{log}2.8\\ \quad =\,11.85+2.7\pm 0.3-1.13=13.42\pm 0.3\\ \quad =\,{\left(m-M+{\rm{\Delta }}V\right)}_{V,\mathrm{PW}\mathrm{Vul}}-2.5\mathrm{log}1.26\\ \quad =\,13.0+0.7\pm 0.3-0.25=13.45\pm 0.3.\end{array}\end{eqnarray} \tag{ 64 }$$

Thus, we obtain f_s = 2.8 against the template nova LV Vul and (m − M)_V = 13.45 ± 0.2. This value is consistent with the previous value of (m − M)_V = 13.4 ± 0.1 estimated by Hachisu & Kato (2015). From Equations (14) and (64), we have the relation

$$\begin{eqnarray}&&\begin{array}{l}{\left(m-M^{\prime} \right)}_{V,{\rm{V}}705\mathrm{Cas}}\\ \quad \equiv \,{\left({m}_{V}-({M}_{V}-2.5\mathrm{log}{f}_{{\rm{s}}})\right)}_{{\rm{V}}705\mathrm{Cas}}\\ \quad =\,{\left(m-M+{\rm{\Delta }}V\right)}_{V,\mathrm{LV}\mathrm{Vul}}\\ \quad =\,11.85+2.7\pm 0.3=14.55\pm 0.3.\end{array}\end{eqnarray} \tag{ 65 }$$

Zoom In Zoom Out Reset image size

Figure 39 shows the light/color curves of V382 Vel as well as those of LV Vul, V1668 Cyg, and V1974 Cyg. The data of V382 Vel are the same as those in Figures 1 and 27 of Paper II. We add a straight solid black line labeled "t⁻³" that indicates the homologously expanding ejecta, i.e., free expansion after the optically thick winds stop (see, e.g., Woodward et al. 1997; Hachisu & Kato 2006). The V light curves of these four novae roughly overlap each other except for the very early phase of LV Vul. Based on the time-stretching method, we have the relation

$$\begin{eqnarray}&&\begin{array}{l}{\left(m-M\right)}_{V,{\rm{V}}382\mathrm{Vel}}\\ \quad =\,{\left(m-M+{\rm{\Delta }}V\right)}_{V,\mathrm{LV}\mathrm{Vul}}-2.5\mathrm{log}0.51\\ \quad =\,11.85-1.1\pm 0.3+0.73=11.48\pm 0.3\\ \quad =\,{\left(m-M+{\rm{\Delta }}V\right)}_{V,{\rm{V}}1668\mathrm{Cyg}}-2.5\mathrm{log}0.51\\ \quad =\,14.6-3.8\pm 0.3+0.73=11.53\pm 0.3\\ \quad =\,{\left(m-M+{\rm{\Delta }}V\right)}_{V,{\rm{V}}1974\mathrm{Cyg}}-2.5\mathrm{log}0.54\\ \quad =\,12.2-1.4\pm 0.3+0.68=11.48\pm 0.3.\end{array}\end{eqnarray} \tag{ 66 }$$

Thus, we obtain f_s = 0.51 against the template nova LV Vul and (m − M)_V = 11.5 ± 0.2. The result of (m − M)_V = 11.5 ± 0.2 is the same as (m − M)_V = 11.5 ± 0.2 in a previous work (Hachisu & Kato 2016a). From Equations (14) and (66), we have the relation

$$\begin{eqnarray}&&\begin{array}{l}{\left(m-M^{\prime} \right)}_{V,{\rm{V}}382\mathrm{Vel}}\\ \quad \equiv \,{\left({m}_{V}-({M}_{V}-2.5\mathrm{log}{f}_{{\rm{s}}})\right)}_{{\rm{V}}382\mathrm{Vel}}\\ \quad =\,{\left({\left(m-M\right)}_{V}+{\rm{\Delta }}V\right)}_{\mathrm{LV}\mathrm{Vul}}\\ \quad =\,11.85-1.1\pm 0.3=10.75\pm 0.3.\end{array}\end{eqnarray} \tag{ 67 }$$

Zoom In Zoom Out Reset image size

We obtain the reddening and distance from the time-stretching method. We plot the B, V, and I_C light curves of V382 Vel together with those of the LMC novae YY Dor and LMC N 2009a in Figure 40. We apply Equation (7) for the B band to Figure 40(a) and obtain

$$\begin{eqnarray}&&\begin{array}{l}{\left(m-M\right)}_{B,{\rm{V}}382\mathrm{Vel}}\\ \quad =\,{\left({\left(m-M\right)}_{B}+{\rm{\Delta }}B\right)}_{\mathrm{YY}\mathrm{Dor}}-2.5\mathrm{log}2.7\\ \quad =\,18.98-6.2\pm 0.3-1.08=11.7\pm 0.3\\ \quad =\,{\left({\left(m-M\right)}_{B}+{\rm{\Delta }}B\right)}_{\mathrm{LMC}{\rm{N}}2009{\rm{a}}}-2.5\mathrm{log}1.7\\ \quad =\,18.98-6.7\pm 0.3-0.58=11.7\pm 0.3.\end{array}\end{eqnarray} \tag{ 68 }$$

Thus, we obtain (m − M)_B,V382 Vel = 11.7 ± 0.2. For the V light curves in Figure 40(b), we similarly obtain

$$\begin{eqnarray}&&\begin{array}{l}{\left(m-M\right)}_{V,{\rm{V}}382\mathrm{Vel}}\\ \quad =\,{\left({\left(m-M\right)}_{V}+{\rm{\Delta }}V\right)}_{\mathrm{YY}\mathrm{Dor}}-2.5\mathrm{log}2.7\\ \quad =\,18.86-6.3\pm 0.3-1.08=11.48\pm 0.3\\ \quad =\,{\left({\left(m-M\right)}_{V}+{\rm{\Delta }}V\right)}_{\mathrm{LMC}{\rm{N}}2009{\rm{a}}}-2.5\mathrm{log}1.7\\ \quad =\,18.86-6.8\pm 0.3-0.58=11.48\pm 0.3.\end{array}\end{eqnarray} \tag{ 69 }$$

Thus, we obtain (m − M)_V,V382 Vel = 11.48 ± 0.2. We apply Equation (8) for the I_C band to Figure 40(c) and obtain

$$\begin{eqnarray}&&\begin{array}{l}{\left(m-M\right)}_{I,{\rm{V}}382\mathrm{Vel}}\\ \quad =\,{\left({\left(m-M\right)}_{I}+{\rm{\Delta }}{I}_{C}\right)}_{\mathrm{YY}\mathrm{Dor}}-2.5\mathrm{log}2.7\\ \quad =\,18.67-6.5\pm 0.3-1.08=11.09\pm 0.3\\ \quad =\,{\left({\left(m-M\right)}_{I}+{\rm{\Delta }}{I}_{C}\right)}_{\mathrm{LMC}{\rm{N}}2009{\rm{a}}}-2.5\mathrm{log}1.7\\ \quad =\,18.67-7.0\pm 0.3-0.58=11.09\pm 0.3.\end{array}\end{eqnarray} \tag{ 70 }$$

Thus, we obtain (m − M)_I,V382 Vel = 11.09 ± 0.2.

Zoom In Zoom Out Reset image size

Figure 41 shows the light/color curves of V5114 Sgr as well as LV Vul and V1668 Cyg. We regard the V light curve of V5114 Sgr to follow that of V1668 Cyg and LV Vul. Based on the time-stretching method, we have the relation

$$\begin{eqnarray}&&\begin{array}{l}{\left(m-M\right)}_{V,{\rm{V}}5114\mathrm{Sgr}}\\ \quad =\,{\left(m-M+{\rm{\Delta }}V\right)}_{V,\mathrm{LV}\mathrm{Vul}}-2.5\mathrm{log}0.76\\ \quad =\,11.85+4.5\pm 0.2+0.30=16.65\pm 0.2\\ \quad =\,{\left(m-M+{\rm{\Delta }}V\right)}_{V,{\rm{V}}1668\mathrm{Cyg}}-2.5\mathrm{log}0.76\\ \quad =\,14.6+1.75\pm 0.2+0.30=16.65\pm 0.2.\end{array}\end{eqnarray} \tag{ 71 }$$

Thus, we obtain f_s = 0.76 against the template nova LV Vul and (m − M)_V = 16.65 ± 0.1. This value is slightly larger than the previous value of (m − M)_V = 16.5 ± 0.1 estimated by Hachisu & Kato (2016b). From Equations (14) and (71), we have the relation

$$\begin{eqnarray}&&\begin{array}{l}{\left(m-M^{\prime} \right)}_{V,{\rm{V}}5114\mathrm{Sgr}}\\ \quad \equiv \,{\left({m}_{V}-({M}_{V}-2.5\mathrm{log}{f}_{{\rm{s}}})\right)}_{{\rm{V}}5114\mathrm{Sgr}}\\ \quad =\,{\left(m-M+{\rm{\Delta }}V\right)}_{V,\mathrm{LV}\mathrm{Vul}}\\ \quad =\,11.85+4.5\pm 0.2=16.35\pm 0.2.\end{array}\end{eqnarray} \tag{ 72 }$$

Zoom In Zoom Out Reset image size

We obtain the reddening and distance from the time-stretching method. We plot the U, B, and V light curves of V5114 Sgr together with those of LV Vul and V1668 Cyg in Figure 42. We apply Equation (6) for the U band to Figure 42(a) and obtain

$$\begin{eqnarray}&&\begin{array}{l}{\left(m-M\right)}_{U,{\rm{V}}5114\mathrm{Sgr}}\\ \quad =\,{\left({\left(m-M\right)}_{U}+{\rm{\Delta }}U\right)}_{\mathrm{LV}\mathrm{Vul}}-2.5\mathrm{log}0.76\\ \quad =\,12.85+4.3\pm 0.2+0.30=17.45\pm 0.2\\ \quad =\,{\left({\left(m-M\right)}_{U}+{\rm{\Delta }}U\right)}_{{\rm{V}}1668\mathrm{Cyg}}-2.5\mathrm{log}0.76\\ \quad =\,15.1+2.05\pm 0.2+0.30=17.45\pm 0.2,\end{array}\end{eqnarray} \tag{ 73 }$$

where we adopt (m − M)_U,LV Vul = 11.85 + (4.75 − 3.1) × 0.60 = 12.85, and (m − M)_U,V1668 Cyg = 14.6 + (4.75 − 3.1) × 0.30 = 15.10. Thus, we obtain (m − M)_U,V5114 Sgr = 17.45 ± 0.2. For the B light curves in Figure 42(b), we similarly obtain

$$\begin{eqnarray}&&\begin{array}{l}{\left(m-M\right)}_{B,{\rm{V}}5114\mathrm{Sgr}}\\ \quad =\,{\left({\left(m-M\right)}_{B}+{\rm{\Delta }}B\right)}_{\mathrm{LV}\mathrm{Vul}}-2.5\mathrm{log}0.76\\ \quad =\,12.45+4.4\pm 0.2+0.30=17.15\pm 0.2\\ \quad =\,{\left({\left(m-M\right)}_{B}+{\rm{\Delta }}B\right)}_{\mathrm{LMC}{\rm{N}}2009{\rm{a}}}-2.5\mathrm{log}0.76\\ \quad =\,14.9+1.95\pm 0.2+0.30=17.15\pm 0.2,\end{array}\end{eqnarray} \tag{ 74 }$$

where we adopt (m − M)_B,LV Vul = 11.85 + 1.0 × 0.6 = 12.45 and (m − M)_B,V1668 Cyg = 14.6 + 1.0 × 0.3 = 14.9. Thus, we obtain (m − M)_B,V5114 Sgr = 17.15 ± 0.2. We apply Equation (4) to Figure 42(c) and obtain

$$\begin{eqnarray}&&\begin{array}{l}{\left(m-M\right)}_{V,{\rm{V}}5114\mathrm{Sgr}}\\ \quad =\,{\left({\left(m-M\right)}_{V}+{\rm{\Delta }}V\right)}_{\mathrm{LV}\mathrm{Vul}}-2.5\mathrm{log}0.76\\ \quad =\,11.85+4.5\pm 0.2+0.30=16.65\pm 0.2\\ \quad =\,{\left({\left(m-M\right)}_{V}+{\rm{\Delta }}V\right)}_{{\rm{V}}1668\mathrm{Cyg}}-2.5\mathrm{log}0.76\\ \quad =\,14.6+1.75\pm 0.2+0.30=16.65\pm 0.2.\end{array}\end{eqnarray} \tag{ 75 }$$

Thus, we obtain (m − M)_V,V5114 Sgr = 16.65 ± 0.2. This result is essentially the same as that in Equation (71). We plot these three distance moduli of the U, B, and V bands in Figure 12(c) with the magenta, cyan, and blue lines, that is, (m − M)_U = 17.45, (m − M)_B = 17.15, and (m − M)_V = 16.65, together with Equations (10), (11), and (5), respectively. These three lines cross at d = 10.9 kpc and E(B − V) = 0.47.

Zoom In Zoom Out Reset image size

Figure 43 shows the light/color curves of V2362 Cyg on a logarithmic timescale as well as LV Vul and V1500 Cyg. We regard the V light curve of V2362 Cyg to follow that of V1500 Cyg. Based on the time-stretching method, we have the relation

$$\begin{eqnarray}&&\begin{array}{l}{\left(m-M\right)}_{V,{\rm{V}}2362\mathrm{Cyg}}\\ \quad =\,{\left(m-M+{\rm{\Delta }}V\right)}_{V,\mathrm{LV}\mathrm{Vul}}-2.5\mathrm{log}1.78\\ \quad =\,11.85+4.2\pm 0.3-0.63=15.42\pm 0.3\\ \quad =\,{\left(m-M+{\rm{\Delta }}V\right)}_{V,{\rm{V}}1500\mathrm{Cyg}}-2.5\mathrm{log}2.95\\ \quad =\,12.3+4.3\pm 0.2-1.18=15.42\pm 0.2.\end{array}\end{eqnarray} \tag{ 76 }$$

Thus, we obtain f_s = 1.78 against the template nova LV Vul and (m − M)_V = 15.4 ± 0.2.

Zoom In Zoom Out Reset image size

This new distance modulus in the V band is smaller than the previous value of (m − M)_V = 15.9 ± 0.1 in Paper II, because we improved both the time-scaling factor of f_s and the vertical fit of ΔV. The LV Vul upper branch in the time-stretched color–magnitude diagram corresponds to the redder (lower) branch after the onset of the nebular phase in the (B − V)₀ color curves of Figure 43(b). We regard the V2362 Cyg color curves to overlap with this redder branch of LV Vul in the (B − V)₀ color curve. Thus, we have more carefully determined the time-scaling factor of f_s here than in our previous work (Paper II).

From Equations (14) and (76), we obtain the relation

$$\begin{eqnarray}&&\begin{array}{l}{\left(m-M^{\prime} \right)}_{V,{\rm{V}}2362\mathrm{Cyg}}\\ \quad \equiv \,{\left({m}_{V}-({M}_{V}-2.5\mathrm{log}{f}_{{\rm{s}}})\right)}_{{\rm{V}}2362\mathrm{Cyg}}\\ \quad =\,{\left(m-M+{\rm{\Delta }}V\right)}_{V,\mathrm{LV}\mathrm{Vul}}\\ \quad =\,11.85+4.2\pm 0.3=16.05\pm 0.3.\end{array}\end{eqnarray} \tag{ 77 }$$

Figure 44 shows the light/color curves of V2615 Oph as well as those of LV Vul and V1419 Aql. The colors of V2615 Oph are dereddened with E(B − V) = 0.90 as obtained in Section 7.9. The BV light curve data of this nova were obtained by Munari et al. (2008a). However, their B − V data show systematic differences among three observatories, "a," "b," and "c" (see their Figure 1). So, we shift the B − V data of group "a" (filled red circles in Figure 15(a)) bluer by 0.15 mag. The B − V data of group "b" and "c" (filled blue circles in Figure 15(a)) are not shifted. As a result, the B − V data of these three groups broadly overlap each other in Figures 44(b) and 15(a). We also add the V data taken from SMARTS (Walter et al. 2012). Based on the time-stretching method, we have the relation

$$\begin{eqnarray}&&\begin{array}{l}{\left(m-M\right)}_{V,{\rm{V}}2615\mathrm{Oph}}\\ \quad =\,{\left(m-M+{\rm{\Delta }}V\right)}_{V,\mathrm{LV}\mathrm{Vul}}-2.5\mathrm{log}1.58\\ \quad =\,11.85+4.6\pm 0.2-0.50=15.95\pm 0.2\\ \quad =\,{\left(m-M+{\rm{\Delta }}V\right)}_{V,{\rm{V}}1419\mathrm{Aql}}-2.5\mathrm{log}1.12\\ \quad =\,15.0+1.1\pm 0.2-0.13=15.97\pm 0.2.\end{array}\end{eqnarray} \tag{ 78 }$$

Thus, we obtain f_s = 1.58 against the template nova LV Vul and (m − M)_V = 15.95 ± 0.2. This value is smaller than the previous estimate of (m − M)_V = 16.5 ± 0.1 (Paper II). This is due not only to our careful (B − V)₀ fitting that improves the time-scaling factor of f_s but also to the revised vertical V fit to the LV Vul light curve. From Equations (14) and (78), we have the relation

$$\begin{eqnarray}&&\begin{array}{l}{\left(m-M^{\prime} \right)}_{V,{\rm{V}}2615\mathrm{Oph}}\\ \quad \equiv \,{\left({m}_{V}-({M}_{V}+2.5\mathrm{log}{f}_{s})\right)}_{{\rm{V}}2615\mathrm{Oph}}\\ \quad =\,{\left(m-M+{\rm{\Delta }}V\right)}_{V,\mathrm{LV}\mathrm{Vul}}\\ \quad =\,11.85+4.6\pm 0.2=16.45\pm 0.2.\end{array}\end{eqnarray} \tag{ 79 }$$

Zoom In Zoom Out Reset image size

We obtain the reddening and distance from the time-stretching method. We plot the B, V, and I_C light curves of V2615 Oph together with those of V1368 Cen, V834 Car, and the LMC novae, YY Dor and LMC N 2009a, in Figure 45 on a logarithmic timescale. We apply Equation (7) for the B band to Figure 45(a) and obtain

$$\begin{eqnarray}&&\begin{array}{l}{\left(m-M\right)}_{B,{\rm{V}}2615\mathrm{Oph}}\\ \quad =\,{\left({\left(m-M\right)}_{B}+{\rm{\Delta }}B\right)}_{{\rm{V}}1368\mathrm{Cen}}-2.5\mathrm{log}0.66\\ \quad =\,18.53-2.1\pm 0.4+0.45=16.88\pm 0.3\\ \quad =\,{\left({\left(m-M\right)}_{B}+{\rm{\Delta }}B\right)}_{{\rm{V}}834\mathrm{Car}}-2.5\mathrm{log}2.5\\ \quad =\,17.75+0.1\pm 0.4-0.97=16.88\pm 0.3\\ \quad =\,{\left({\left(m-M\right)}_{B}+{\rm{\Delta }}B\right)}_{\mathrm{YY}\mathrm{Dor}}-2.5\mathrm{log}8.3\\ \quad =\,18.98+0.2\pm 0.4-2.3=16.88\pm 0.3\\ \quad =\,{\left({\left(m-M\right)}_{B}+{\rm{\Delta }}B\right)}_{\mathrm{LMC}{\rm{N}}2009{\rm{a}}}-2.5\mathrm{log}5.2\\ \quad =\,18.98-0.3\pm 0.4-1.8=16.88\pm 0.3,\end{array}\end{eqnarray} \tag{ 80 }$$

where we adopt (m − M)_B,V1368 Cen = 17.6 + 0.93 = 18.53 and (m − M)_B,V834 Car = 17.25 + 0.50 = 17.75 from Hachisu & Kato (2019). Thus, we obtain (m − M)_B,V2615 Oph = 16.88 ± 0.2. For the V light curves in Figure 45(b), we similarly obtain

$$\begin{eqnarray}&&\begin{array}{l}{\left(m-M\right)}_{V,{\rm{V}}2615\mathrm{Oph}}\\ \quad =\,{\left({\left(m-M\right)}_{V}+{\rm{\Delta }}V\right)}_{{\rm{V}}1368\mathrm{Cen}}-2.5\mathrm{log}0.66\\ \quad =\,17.6-2.1\pm 0.3+0.45=15.95\pm 0.3\\ \quad =\,{\left({\left(m-M\right)}_{V}+{\rm{\Delta }}V\right)}_{{\rm{V}}834\mathrm{Car}}-2.5\mathrm{log}2.5\\ \quad =\,17.25-0.3\pm 0.3-0.97=15.98\pm 0.3\\ \quad =\,{\left({\left(m-M\right)}_{V}+{\rm{\Delta }}V\right)}_{\mathrm{YY}\mathrm{Dor}}-2.5\mathrm{log}8.3\\ \quad =\,18.86-0.6\pm 0.3-2.3=15.96\pm 0.3\\ \quad =\,{\left({\left(m-M\right)}_{V}+{\rm{\Delta }}V\right)}_{\mathrm{LMC}{\rm{N}}2009{\rm{a}}}-2.5\mathrm{log}5.2\\ \quad =\,18.86-1.1\pm 0.3-1.8=15.96\pm 0.3,\end{array}\end{eqnarray} \tag{ 81 }$$

where we adopt (m − M)_V,V1368 Cen = 17.6 and (m − M)_V,V834 Car = 17.25 from Hachisu & Kato (2019). Thus, we obtain (m − M)_V,V2615 Oph = 15.96 ± 0.2, which is consistent with Equation (78). We apply Equation (8) for the I_C band to Figure 45(c) and obtain

$$\begin{eqnarray}&&\begin{array}{l}{\left(m-M\right)}_{I,{\rm{V}}2615\mathrm{Oph}}\\ \quad =\,{\left({\left(m-M\right)}_{I}+{\rm{\Delta }}{I}_{C}\right)}_{{\rm{V}}1368\mathrm{Cen}}-2.5\mathrm{log}0.66\\ \quad =\,16.11-2.0\pm 0.5+0.45=14.56\pm 0.3\\ \quad =\,{\left({\left(m-M\right)}_{I}+{\rm{\Delta }}{I}_{C}\right)}_{{\rm{V}}834\mathrm{Car}}-2.5\mathrm{log}2.5\\ \quad =\,16.45-0.9\pm 0.5-0.97=14.58\pm 0.3\\ \quad =\,{\left({\left(m-M\right)}_{I}+{\rm{\Delta }}{I}_{C}\right)}_{\mathrm{YY}\mathrm{Dor}}-2.5\mathrm{log}8.3\\ \quad =\,18.67-1.8\pm 0.5-2.3=14.57\pm 0.3\\ \quad =\,{\left({\left(m-M\right)}_{I}+{\rm{\Delta }}{I}_{C}\right)}_{\mathrm{LMC}{\rm{N}}2009{\rm{a}}}-2.5\mathrm{log}5.2\\ \quad =\,18.67-2.3\pm 0.5-1.8=14.57\pm 0.3,\end{array}\end{eqnarray} \tag{ 82 }$$

where we adopt (m − M)_I,V1368 Cen = 17.6 − 1.6 × 0.93 = 16.11 and (m − M)_I,V834 Car = 17.25 − 1.6 × 0.50 = 16.45 from Hachisu & Kato (2019). Thus, we obtain (m − M)_I,V2615 Oph = 14.57 ± 0.2. We plot these three distance moduli in Figure 14(a) by the thin solid magenta, blue, and cyan lines. These three lines cross at d = 4.3 kpc and E(B − V) = 0.90.

Zoom In Zoom Out Reset image size

Figure 46 shows the light/color curves of V2468 Cyg as well as those of LV Vul and V1500 Cyg. The (B − V)₀ color is dereddened with E(B − V) = 0.65 as obtained in Section 7.10. We regard the early phase of the V2468 Cyg V light curve to be superbright like V1500 Cyg and then to oscillate between LV Vul and V1500 Cyg in the phase of log t (days) = 1.0–2.0. The spectra of V1500 Cyg during the superbright phase (until Day ∼5 and above the model V light curve of the red line) are approximated with a blackbody (Gallagher & Ney 1976; Ennis et al. 1977). After the superbright phase ended, the spectrum of V1500 Cyg changed to be that of free–free emission, so that V magnitudes are fitted with our model light curve (solid red line). Our time-stretching method is applicable to the part of the free–free emission-dominated phase of optical light curves.

Zoom In Zoom Out Reset image size

Based on the time-stretching method, we have the relation

$$\begin{eqnarray}&&\begin{array}{l}{\left(m-M\right)}_{V,{\rm{V}}2468\mathrm{Cyg}}\\ \quad =\,{\left(m-M+{\rm{\Delta }}V\right)}_{V,\mathrm{LV}\mathrm{Vul}}-2.5\mathrm{log}2.4\\ \quad =\,11.85+5.3\pm 0.3-0.95=16.2\pm 0.3\\ \quad =\,{\left(m-M+{\rm{\Delta }}V\right)}_{V,{\rm{V}}1500\mathrm{Cyg}}-2.5\mathrm{log}4.0\\ \quad =\,12.3+5.4\pm 0.3-1.5=16.2\pm 0.3.\end{array}\end{eqnarray} \tag{ 83 }$$

Thus, we obtain f_s = 2.4 against the template nova LV Vul and (m − M)_V = 16.2 ± 0.2. The newly obtained value is larger than the previous value of (m − M)_V = 15.6 ± 0.1 estimated in Paper II because we improved the time-scaling factor f_s and the vertical ΔV fit. From Equations (14) and (83), we have the relation

$$\begin{eqnarray}&&\begin{array}{l}{\left(m-M^{\prime} \right)}_{V,{\rm{V}}2468\mathrm{Cyg}}\\ \quad \equiv \,{\left({m}_{V}-({M}_{V}-2.5\mathrm{log}{f}_{s})\right)}_{{\rm{V}}2468\mathrm{Cyg}}\\ \quad =\,{\left(m-M+{\rm{\Delta }}V\right)}_{V,\mathrm{LV}\mathrm{Vul}}\\ \quad =\,11.85+5.3\pm 0.3=17.15\pm 0.3.\end{array}\end{eqnarray} \tag{ 84 }$$

We obtain the reddening and distance from the time-stretching method. We plot the B, V, and I_C light curves of V2468 Cyg together with those of V1535 Sco, V834 Car, and the LMC novae, YY Dor and LMC N 2009a, in Figure 47 on a logarithmic timescale. We apply Equation (7) for the B band to Figure 47(a) and obtain

$$\begin{eqnarray}&&\begin{array}{l}{\left(m-M\right)}_{B,{\rm{V}}2468\mathrm{Cyg}}\\ \quad =\,{\left({\left(m-M\right)}_{B}+{\rm{\Delta }}B\right)}_{{\rm{V}}1535\mathrm{Sco}}-2.5\mathrm{log}1.0\\ \quad =\,19.08-2.2\pm 0.4-0.0=16.88\pm 0.3\\ \quad =\,{\left({\left(m-M\right)}_{B}+{\rm{\Delta }}B\right)}_{{\rm{V}}834\mathrm{Car}}-2.5\mathrm{log}3.7\\ \quad =\,17.75+0.5\pm 0.4-1.42=16.83\pm 0.3\\ \quad =\,{\left({\left(m-M\right)}_{B}+{\rm{\Delta }}B\right)}_{\mathrm{YY}\mathrm{Dor}}-2.5\mathrm{log}12.6\\ \quad =\,18.98+0.6\pm 0.4-2.75=16.83\pm 0.3\\ \quad =\,{\left({\left(m-M\right)}_{B}+{\rm{\Delta }}B\right)}_{\mathrm{LMC}{\rm{N}}2009{\rm{a}}}-2.5\mathrm{log}7.9\\ \quad =\,18.98+0.1\pm 0.4-2.25=16.83\pm 0.3,\end{array}\end{eqnarray} \tag{ 85 }$$

where we adopt (m − M)_B,V1535 Sco = 18.3 + 0.78 = 19.08 and (m − M)_B,V834 Car = 17.25 + 0.50 = 17.75 from Hachisu & Kato (2019). Thus, we obtain (m − M)_B,V2468 Cyg = 16.85 ± 0.2. For the V light curves in Figure 47(b), we similarly obtain

$$\begin{eqnarray}&&\begin{array}{l}{\left(m-M\right)}_{V,{\rm{V}}2468\mathrm{Cyg}}\\ \quad =\,{\left({\left(m-M\right)}_{V}+{\rm{\Delta }}V\right)}_{{\rm{V}}1535\mathrm{Sco}}-2.5\mathrm{log}1.0\\ \quad =\,18.3-2.1\pm 0.3-0.0=16.2\pm 0.3\\ \quad =\,{\left({\left(m-M\right)}_{V}+{\rm{\Delta }}V\right)}_{{\rm{V}}834\mathrm{Car}}-2.5\mathrm{log}3.7\\ \quad =\,17.25+0.4\pm 0.3-1.42=16.23\pm 0.3\\ \quad =\,{\left({\left(m-M\right)}_{V}+{\rm{\Delta }}V\right)}_{\mathrm{YY}\mathrm{Dor}}-2.5\mathrm{log}12.6\\ \quad =\,18.86+0.1\pm 0.3-2.75=16.21\pm 0.3\\ \quad =\,{\left({\left(m-M\right)}_{V}+{\rm{\Delta }}V\right)}_{\mathrm{LMC}{\rm{N}}2009{\rm{a}}}-2.5\mathrm{log}7.9\\ \quad =\,18.86-0.4\pm 0.3-2.25=16.21\pm 0.3,\end{array}\end{eqnarray} \tag{ 86 }$$

where we adopt (m − M)_V,V1535 Sco = 18.3 and (m − M)_V,V834 Car = 17.25 from Hachisu & Kato (2019). Thus, we obtain (m − M)_V,V2468 Cyg = 16.21 ± 0.2, consistent with Equation (83). We apply Equation (8) for the I_C band to Figure 47(c) and obtain

$$\begin{eqnarray}&&\begin{array}{l}{\left(m-M\right)}_{I,{\rm{V}}2468\mathrm{Cyg}}\\ \quad =\,{\left({\left(m-M\right)}_{I}+{\rm{\Delta }}{I}_{C}\right)}_{{\rm{V}}1535\mathrm{Sco}}-2.5\mathrm{log}1.0\\ \quad =\,17.05-1.9\pm 0.5-0.0=15.15\pm 0.3\\ \quad =\,{\left({\left(m-M\right)}_{I}+{\rm{\Delta }}{I}_{C}\right)}_{{\rm{V}}834\mathrm{Car}}-2.5\mathrm{log}3.7\\ \quad =\,16.45+0.1\pm 0.5-1.42=15.13\pm 0.3\\ \quad =\,{\left({\left(m-M\right)}_{I}+{\rm{\Delta }}{I}_{C}\right)}_{\mathrm{YY}\mathrm{Dor}}-2.5\mathrm{log}12.6\\ \quad =\,18.67-0.8\pm 0.5-2.75=15.12\pm 0.3\\ \quad =\,{\left({\left(m-M\right)}_{I}+{\rm{\Delta }}{I}_{C}\right)}_{\mathrm{LMC}{\rm{N}}2009{\rm{a}}}-2.5\mathrm{log}7.9\\ \quad =\,18.67-1.3\pm 0.5-2.25=15.12\pm 0.3,\end{array}\end{eqnarray} \tag{ 87 }$$

where we adopt (m − M)_I,V1535 Sco = 18.3 − 1.6 × 0.78 = 17.05 and (m − M)_I,V834 Car = 17.25 − 1.6 × 0.50 = 16.45 from Hachisu & Kato (2019). Thus, we obtain (m − M)_I,V2468 Cyg = 15.13 ± 0.2.

Zoom In Zoom Out Reset image size

Figure 48 shows the light/color curves of V2491 Cyg as well as those of LV Vul and V1500 Cyg. Based on the time-stretching method, we have the relation

$$\begin{eqnarray}&&\begin{array}{l}{\left(m-M\right)}_{V,{\rm{V}}2491\mathrm{Cyg}}\\ \quad =\,{\left(m-M+{\rm{\Delta }}V\right)}_{V,\mathrm{LV}\mathrm{Vul}}-2.5\mathrm{log}0.46\\ \quad =\,11.85+4.7\pm 0.4+0.85=17.4\pm 0.4\\ \quad =\,{\left(m-M+{\rm{\Delta }}V\right)}_{V,{\rm{V}}1500\mathrm{Cyg}}-2.5\mathrm{log}0.76\\ \quad =\,12.3+4.8\pm 0.4+0.30=17.4\pm 0.4.\end{array}\end{eqnarray} \tag{ 88 }$$

Thus, we obtain f_s = 0.46 against the template nova LV Vul and (m − M)_V = 17.4 ± 0.3. The new distance modulus in the V band is larger than the previous value of (m − M)_V = 16.5 ± 0.1 (Paper II). This is because the reddening is revised to be E(B − V) = 0.45, and the time-scaling factor is improved to be f_s = 0.46. We carefully redetermine the time-scaling factor by fitting the (B − V)₀ color curve of V2491 Cyg (filled red circles) with that of LV Vul (filled cyan stars) and V1500 Cyg (open blue circles) as shown in Figure 48(b). From Equations (14) and (88), we obtain

$$\begin{eqnarray}&&\begin{array}{l}{\left(m-M^{\prime} \right)}_{V,{\rm{V}}2491\mathrm{Cyg}}\\ \quad \equiv \,{\left({m}_{V}-({M}_{V}-2.5\mathrm{log}{f}_{{\rm{s}}})\right)}_{{\rm{V}}2491\mathrm{Cyg}}\\ \quad =\,{\left(m-M+{\rm{\Delta }}V\right)}_{V,\mathrm{LV}\mathrm{Vul}}\\ \quad =\,11.85+4.7\pm 0.4=16.55\pm 0.4.\end{array}\end{eqnarray} \tag{ 89 }$$

Zoom In Zoom Out Reset image size

We obtain the reddening and distance from the time-stretching method. We plot the B, V, and I_C light curves of V2491 Cyg together with those of the LMC novae YY Dor and LMC N 2009a in Figure 49 on a logarithmic timescale. We apply Equation (7) for the B band to Figure 49(a) and obtain

$$\begin{eqnarray}&&\begin{array}{l}{\left(m-M\right)}_{B,{\rm{V}}2491\mathrm{Cyg}}\\ \quad =\,{\left({\left(m-M\right)}_{B}+{\rm{\Delta }}B\right)}_{\mathrm{YY}\mathrm{Dor}}-2.5\mathrm{log}2.4\\ \quad =\,18.98-0.2\pm 0.4-0.95=17.83\pm 0.4\\ \quad =\,{\left({\left(m-M\right)}_{B}+{\rm{\Delta }}B\right)}_{\mathrm{LMC}{\rm{N}}2009{\rm{a}}}-2.5\mathrm{log}1.51\\ \quad =\,18.98-0.7\pm 0.4-0.45=17.83\pm 0.4.\end{array}\end{eqnarray} \tag{ 90 }$$

Thus, we obtain (m − M)_B,V2491 Cyg = 17.83 ± 0.3. For the V light curves in Figure 49(b), we similarly obtain

$$\begin{eqnarray}&&\begin{array}{l}{\left(m-M\right)}_{V,{\rm{V}}2491\mathrm{Cyg}}\\ \quad =\,{\left({\left(m-M\right)}_{V}+{\rm{\Delta }}V\right)}_{\mathrm{YY}\mathrm{Dor}}-2.5\mathrm{log}2.4\\ \quad =\,18.86-0.5\pm 0.3-0.95=17.41\pm 0.3\\ \quad =\,{\left({\left(m-M\right)}_{V}+{\rm{\Delta }}V\right)}_{\mathrm{LMC}{\rm{N}}2009{\rm{a}}}-2.5\mathrm{log}1.51\\ \quad =\,18.86-1.0\pm 0.3-0.45=17.41\pm 0.3.\end{array}\end{eqnarray} \tag{ 91 }$$

Thus, we obtain (m − M)_V,V2491 Cyg = 17.41 ± 0.2. We apply Equation (8) for the I_C band to Figure 49(c) and obtain

$$\begin{eqnarray}&&\begin{array}{l}{\left(m-M\right)}_{I,{\rm{V}}2491\mathrm{Cyg}}\\ \quad =\,{\left({\left(m-M\right)}_{I}+{\rm{\Delta }}{I}_{C}\right)}_{\mathrm{YY}\mathrm{Dor}}-2.5\mathrm{log}2.4\\ \quad =\,18.67-1.1\pm 0.5-0.95=16.62\pm 0.5\\ \quad =\,{\left({\left(m-M\right)}_{I}+{\rm{\Delta }}{I}_{C}\right)}_{\mathrm{LMC}{\rm{N}}2009{\rm{a}}}-2.5\mathrm{log}1.51\\ \quad =\,18.67-1.6\pm 0.5-0.45=16.62\pm 0.5.\end{array}\end{eqnarray} \tag{ 92 }$$

Thus, we obtain (m − M)_I,V2491 Cyg = 16.62 ± 0.3.

Zoom In Zoom Out Reset image size

We plot these three distance moduli of the B, V, and I_C bands in Figure 14(c) with the magenta, blue, and cyan lines, that is, (m − M)_B = 17.83, (m − M)_V = 17.41, and (m − M)_I = 16.62, together with Equations (11), (5), and (12). These three lines broadly cross at d = 15.9 kpc and E(B − V) = 0.45.

Figure 50 shows the light/color curves of V496 Sct as well as those of LV Vul and V1668 Cyg. In the early phase, the V light curve of V496 Sct overlaps that of LV Vul. In the middle phase, V496 Sct shows a sharp and shallow dip, due to dust blackout. In the later nebular phase, V496 Sct overlaps well with the upper branch of LV Vul, where the V light curve of LV Vul splits into two branches in the nebular phase due to the different responses of their V filters as discussed in Paper II. This is because strong [O iii] lines contribute to the blue edge of the V-band filter in the nebular phase, and small differences among the response functions of V filters lead to large differences in the V magnitudes. The (B − V)₀ color curves of LV Vul also splits into two branches for log t ≳ 2.0, that is, in the nebular phase. The lower branch of LV Vul in the (B − V)₀ color curve is close to that of V496 Sct. We regard the V light curve of V496 Sct to follow that of V1668 Cyg and the upper branch of LV Vul, and the (B − V)₀ color curve of V496 Sct to follow the lower branch of LV Vul.

Zoom In Zoom Out Reset image size

Based on the time-stretching method, we have the relation

$$\begin{eqnarray}&&\begin{array}{l}{\left(m-M\right)}_{V,{\rm{V}}496\mathrm{Sct}}\\ \quad =\,{\left(m-M+{\rm{\Delta }}V\right)}_{V,\mathrm{LV}\mathrm{Vul}}-2.5\mathrm{log}2.0\\ \quad =\,11.85+2.6\pm 0.3-0.75=13.7\pm 0.3\\ \quad =\,{\left(m-M+{\rm{\Delta }}V\right)}_{V,{\rm{V}}1668\mathrm{Cyg}}-2.5\mathrm{log}2.0\\ \quad =\,14.6-0.1\pm 0.3-0.75=13.75\pm 0.3.\end{array}\end{eqnarray} \tag{ 93 }$$

Thus, we obtain f_s = 2.0 against the template nova LV Vul and (m − M)_V = 13.7 ± 0.2. The new value is much smaller than the previous estimate of (m − M)_V = 14.4 ± 0.1 (Paper II). This is because we improved the time-scaling factor f_s and the vertical V light curve fitting. From Equations (14) and (93), we have the relation

$$\begin{eqnarray}&&\begin{array}{l}{\left(m-M^{\prime} \right)}_{V,{\rm{V}}496\mathrm{Sct}}\\ \quad \equiv \,{\left({m}_{V}-({M}_{V}-2.5\mathrm{log}{f}_{s})\right)}_{{\rm{V}}496\mathrm{Sct}}\\ \quad =\,{\left(m-M+{\rm{\Delta }}V\right)}_{V,\mathrm{LV}\mathrm{Vul}}\\ \quad =\,11.85+2.6\pm 0.3=14.45\pm 0.3.\end{array}\end{eqnarray} \tag{ 94 }$$

Figure 51 shows the light/color curves of V496 Sct as well as those of LV Vul and V1065 Cen. The light/color curves of V1065 Cen show different paths of V496 Sct. We regard the V light curve of V1065 Cen to follow the lower branch of LV Vul and the (B − V)₀ color curve to evolve along the upper branch of LV Vul in the nebular phase (t > 100 days). For V1065 Cen, Hachisu & Kato (2018a) derived (m − M)_V = 15.0 ± 0.2 and E(B − V) = 0.45 ± 0.05 (and f_s = 1.0 against LV Vul) as summarized in Table 1. Applying Equation (4) to Figure 51, we have the relation