Morpho-kinematic Modeling of the Expanding Ejecta of the Extremely Slow Nova V1280 Scorpii

A classical nova is caused by a thermonuclear runaway on the surface of a white dwarf (WD) following the accretion of hydrogen-rich material from a nondegenerate stellar companion in a close binary system (e.g., Warner 2003; Bode & Evans 2008; Chomiuk et al. 2020; Della Valle & Izzo 2020). Thermal and kinetic energies of the accreted gas material are powered by radiation from the nuclear burning, and the envelope greatly expands, increasing its brightness rapidly. When the photospheric radius of the nova ejecta is greater than the binary separation, a common envelope is formed in which the ejected matter interacts with the secondary star. After the optical peak, the optical luminosity of a nova declines exponentially due to continuous nuclear fusion on the WD surface at a quasi-steady rate. As most of the accreted material is released by the optically thick wind, the nuclear burning terminates, and then eventually the WD returns to its quiet state. Such evolution of nova outbursts has been accepted as a standard model (e.g., Prialnik 1986; Kato & Hachisu 1994).

A maximum magnitude versus rate of decline (MMRD) relation, which is an empirical relationship whereby a faster declining nova shows a brighter optical peak, is still in debate (e.g., Shara et al. 2017; Özdönmez et al. 2018; Schaefer 2018; Hachisu et al. 2020). On the theoretical side, however, Hachisu & Kato (2006) discovered a universal decline law of classical novae based on the free–free emission and the optically thick wind theory, which reproduced well the optical light curves of many observed novae, especially those showing a smooth decline in brightness (e.g., Hachisu & Kato 2010, 2016a, 2018, 2019a, 2019b). Their model successfully predicts essential parameters of novae such as the WD mass and the distance under the assumption of spherical symmetry. According to Hachisu et al. (2020), the maximum visual magnitude for specific novae, for example the S-types defined by Strope et al. (2010), can be derived if the ignition mass associated with the mass accretion rate is given. On the other hand, the optical luminosity of the nova emitting γ-ray radiation near the optical maximum is proposed to be contributed considerably by shock interactions between distinct fast and slow outflows (Chomiuk et al. 2014; Li et al. 2017; Aydi et al. 2020a, 2020b). It is suggested that the slow outflow is associated with the initial ejection concentrated in the equatorial plane and the fast flow is likely a radiation pressure-driven wind from the WD. The observations strongly suggest that their samples, and many novae, are multiphased and aspherical (see also, e.g., Gill & O'Brien 2000; Nelson et al. 2014). Thus, the mass ejection near maximum light, which is directly connected to the MMRD relation, is still poorly understood owing to the diversity of nova properties. Another parameter that is often not taken into account is the morphology of the ejecta. This should be a key to revealing the physical process of mass loss during the nova eruption and the diversity of novae.

The nova V1280 Scorpii (hereafter, V1280 Sco) was independently discovered by two Japanese amateur astronomers (Y. Nakamura and Y. Sakurai) on 2007 February 4.85 UT (defined as Δt = 0 days, MJD = 54,135.845) at the ninth visual magnitude (Yamaoka et al. 2007a), which was followed by a somewhat slow rise to its maximum brightness of V = 3.78 mag on February 16.19 (Munari et al. 2007). A low-dispersion optical spectrum obtained on February 5.87 (one day after the discovery) showed Balmer and Fe ii lines with P Cygni absorption profiles, and the object was confirmed as a classical nova (Naito & Narusawa 2007). Naito et al. (2012) reported the results of photometric and spectroscopic observations from pre-maximum to plateau phase (from 2007 February to 2011 April), concluding that V1280 Sco is an extremely slow nova that has an exceptionally long plateau spanning over 1000 days. V1280 Sco only entered the nebular phase about 50 months after eruption, which allowed Naito et al. (2012) to estimate the mass of the WD as less than ∼0.6 M_☉.

V1280 Sco can be considered to be one of the most important novae because it has multifaceted properties associated with the long-standing nova mysteries such as multiple variations near the maximum, dust formation, and the clumpiness of the ejecta (e.g., Hounsell et al. 2010; Sadakane et al. 2010; Chesneau et al. 2012). Using high-time-resolution data obtained by the Solar Mass Ejection Imager (SMEI) on board the Coriolis satellite, Hounsell et al. (2010) revealed that this nova experiences some short episodes (each timescale is less than one day) of rebrightening with amplitude of ∼1 mag near the peak (also see Figure 7). Dust formation around V1280 Sco was reported to occur 11 days after the maximum (Chesneau et al. 2008) and has been investigated by various instruments in mid- and near-infrared wavelengths (e.g., Das et al. 2008; Chesneau et al. 2008, 2012; Sakon et al. 2016). The presence of a dusty hourglass-shaped bipolar (or elongated) nebula around V1280 Sco was revealed based on high-spatial-resolution observations using the Very Large Telescope (Chesneau et al. 2012) and the Gemini South telescope (Sakon et al. 2016) between 2009 and 2012. Multiple absorption lines likely originating from clumpy gas clouds (ejected shells) were observed in high-dispersion spectra obtained with the 8.2 m Subaru telescope (Sadakane et al. 2010; Naito et al. 2013). Such multiple components of Na i D, Ca ii H and K, and metastable He i* were detected at least until 2012 (five years after the eruption), which stands in contrast to observable lifetimes (2–8 weeks) of the transient heavy element absorption (THEA) systems (e.g., Sc ii, Ti ii, Cr ii, Fe ii) referred to in Williams et al. (2008) and the radioactive isotope of beryllium ⁷Be ii (Tajitsu et al. 2015, 2016). Rosenbush (2020), furthermore, highlighted its uniqueness in that V1280 Sco is the only nova that has been at an unusually high and stable level of brightness for more than 10 years after the recovery from the dust extinction.

To seek clues to the cause of these nova phenomena, we investigate the morphology of V1280 Sco using [O iii] and [N ii] forbidden lines in this paper. In Section 2 our observational data are presented, while in Section 3 we discuss our modeling techniques and associated assumption. Section 4 shows our model fits to the observed line profiles. We discuss our results in Section 5 and finally present the conclusions in Section 6.

High-dispersion spectroscopic observations of V1280 Sco were conducted with the High Dispersion Spectrograph (HDS; Noguchi et al. 2002) attached to the 8.2 m Subaru telescope from 2009 to 2019. This observation period corresponds to the long plateau phase spanning over 10 years shown in Figure 1, where the V-mag data from 2012 to 2019 are obtained by the Kamogata/Kiso/Kyoto Wide-field Survey (KWS) ¹⁷ (a total of 785 data points) and our photometric observations using the 1.6 m Pirka telescope with Multi-Spectral Imager (MSI; Watanabe et al. 2012) at Nayoro Observatory of Hokkaido University (a total of 10 data points), following the data obtained at Osaka Kyoiku University (OKU) from 2007 to 2011 published in Naito et al. (2012).

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Table 1 provides a journal of spectroscopic observations. We obtained 29 spectra under nine configurations (different wavelength ranges) of the spectrograph, which covered the wavelength region from 3030 Å to 8890 Å in total. A typical resolving power is R ∼ 60,000 at Hα, while the slit width is 0.3 mm (corresponding to 06 on the sky). Each position angle (PA) of the slit was not controlled with an image rotator during the exposure. Figure 2 shows, for example, the Subaru/HDS slit position on 2012 February 24 (Δt = 1846 days), overlaid on the mid-infrared image taken on 2012 June 6 (Δt = 1949 days) using the Gemini South telescope with T-ReCS (also see Section 5.1).

Data reduction was carried out using the iraf ¹⁸ software package in the standard manner. Wavelength calibration was performed using the Th–Ar comparison spectrum obtained during each observation. All spectra were converted to the heliocentric scale. Reddening correction is not performed.

Figure 3 shows the evolution of [O iii] λλ4959, 5007 and [N ii] λ5755 forbidden lines and the Hβ recombination line using the selected spectra (see remarks in Table 1). The appearances of [O iii] λλ4959, 5007 and [N ii] λ5755 are shown as thick horizontal lines in Figure 1, while dashed lines show the period when each appearance is not confirmed due to missing spectral data. V1280 Sco had taken a very long time (∼50 months) to enter the nebular phase, according to a clear detection of both [O iii] λ4959 and λ5007. There appeared to be P Cygni-like absorptions on Hβ lines from 2009 to 2011. The nova continues to generate the wind (∼2100 km s⁻¹) caused by the hydrogen burning for at least about 4500 days until 2019.

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Optical images of resolved nova remnants show that nova shells tend to be clumpy and have a myriad of structures (e.g., Hutchings 1972; Solf 1983; Gill & O'Brien 2000; Harman & O'Brien 2003; Santamaría et al. 2020). A correlation appears to exist between the speed class of the nova and the degree of shaping, suggesting the slower the nova, the more prolate the nebular remnant (Slavin et al. 1995). An interpretation is given by Lloyd et al. (1997) in which the effects of the interaction of the ejecta during a common envelope phase vary among novae of different speed classes, which are associated with the different timescales of the slow and fast wind phases. Here, we aim to disentangle the morphology of V1280 Sco as an extremely slow nova by means of morpho-kinematic studies of the [O iii] and [N ii] line profiles.

In order to disentangle the 3D geometry and kinematic structure of V1280 Sco we used shape ¹⁹ (Steffen et al. 2011), a morpho-kinematic modeling and reconstruction tool for astrophysical objects, which has yielded various results for nova shells (e.g., Ribeiro et al. 2009, 2011, 2013a, 2013b; Munari et al. 2011; Harvey et al. 2018; Pavana et al. 2020; Santamaría et al. 2022). shape is particularly suited to studying expanding nova shells that show [O iii] and [N ii] forbidden lines such as V1280 Sco because it has been developed for modeling optically thin environments (e.g., planetary nebulae).

We modeled our observations assuming a bipolar geometry, where we varied the inclination angles, maximum expansion velocities, and squeezes. A total of 72,800 synthetic spectra made with different parameter combinations of morphologies, inclination angles (where an inclination i = 90° corresponds to the orbital plane being edge-on) from 0° to 90° (in steps of 1°), and maximum expansion velocities (${V}_{\exp }$) from 100 to 8000 km s⁻¹ (in steps of 100 km s⁻¹) that are assumed to take place in a Hubble flow where material furthest from the binary system is moving fastest. We then flux-matched the synthetic and observed spectra by χ² minimization analysis. Additionally we introduced two new parameters: (i) the ratio of [O iii] λ4959 to λ5007 to take into account the difference in the effect of interstellar reddening between [O iii] λ4959 and [O iii] λ5007, and (ii) a shift velocity to correct the Doppler effect due to relative motion between the object and observer. The assumed bipolar structure is based on the previous study for Nova Mon 2012 (V959 Mon), where the simplest morphology of [O iii] λλ4959, 5007 is found to be that of a bipolar structure (Ribeiro et al. 2013b). Forbidden lines such as [O iii] and [N ii] come from the outer regions, which tend to be broadly symmetric profiles and trace well the expansion velocity and geometry of the ejecta, whereas Balmer lines come from the whole of the ionized ejecta, a part of which suffers some absorption causing asymmetry represented by a P Cygni profile. As noted in Section 2, the line profiles of [O iii] and [N ii] are quite different from that of Hβ, which suggests that these origins are also different.

The full parameter space for inclination, maximum expansion velocity, degree of shaping (squeeze from 0.1 to 1.0 in steps of 0.1, defined below), [O iii] λ5007/λ4959 ratio (from 3.0 to 3.8 in steps of 0.1, only for analyses of [O iii] lines), and shift velocity (from 50 km s⁻¹ to 100 km s⁻¹ in steps of 5 km s⁻¹) was explored to retrieve the synthetic emission line spectrum to compare with the observed spectra to determine χ². The squeeze (a modifier within shape) compresses or expands a structure as a function of position along the symmetry axis (in this case the major axis). We use the fractional amount by which the object is compressed to the squeeze axis (in this case the minor axis). The squeeze (denoted squ as a parameter) is defined as

$$\begin{eqnarray}&&{squ}=1-\displaystyle \frac{a}{b},\end{eqnarray} \tag{ 1 }$$

where a and b are the semiminor and semimajor axes, respectively, of the ejected shell measured from the center of the binary system (Figure 4).

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The results of exploring the full parameter space for [O iii] and [N ii] profiles are shown in Table 2, where the best-fit parameter values for the maximum expansion velocity, inclination angle, and squeeze along with their respective χ²/degree of freedom (dof) (or reduced χ²) and the P-value are given. The errors are determined assuming a reduced χ² greater than 1σ. The observed spectra and the model spectra for each of the inclinations, velocities, and squeezes were compared to find the best fit via a χ² test for [O iii] and [N ii] emission lines (top of Figures 5 and 6, respectively). We derive the best-fitting expansion velocity, inclination, and squeeze as ${V}_{\exp }={2100}_{-100}^{+100}$ km s⁻¹, $i={80}_{-3}^{+1}$ deg, and ${squ}={1.0}_{-0.1}^{+0.0}$ for [O iii] λλ4959, 5007 on 2012 February 24 (Figure 5, bottom), and ${V}_{\exp }={1600}_{-100}^{+100}$ km s⁻¹, $i={81}_{-4}^{+2}$ deg, and ${squ}={1.0}_{-0.1}^{+0.0}$ for [N ii] λ5755 on 2011 June 12 (Figure 6, bottom), respectively.

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Table 2. The Best-fit Parameter Values for [O iii] λλ4959, 5007 and [N ii] λ5755 Analyses

Date	MJD	${V}_{\exp }$	Inclination	Squeeze	[O iii] λ5007/λ4959	Shift Velocity	χ2/dof	P-value
		(km s−1)	(deg)		Ratio	(km s−1)
[O iii] λλ4959, 5007
2011-07-24	55,766.275	${1900}_{-0}^{+0}$	${78}_{-0}^{+0}$	${1.0}_{-0.0}^{+0.0}$	3.2	65	0.77946	0.9779
2011-08-06	55,779.239	${2000}_{-0}^{+0}$	${77}_{-0}^{+1}$	${0.9}_{-0.0}^{+0.0}$	3.7	100	0.80622	0.9593
2011-09-30	55,834.236	${2200}_{-0}^{+0}$	${81}_{-1}^{+0}$	${1.0}_{-0.0}^{+0.0}$	3.5	50	1.0003	0.4836
2012-02-24	55,981.645	${2100}_{-100}^{+100}$	${80}_{-3}^{+1}$	${1.0}_{-0.1}^{+0.0}$	3.8	90	0.62846	0.9999
2012-03-20	56,006.612	${2200}_{-100}^{+0}$	${81}_{-1}^{+0}$	${1.0}_{-0.0}^{+0.0}$	3.8	50	0.72668	0.9948
2012-03-20	56,006.635	${2100}_{-100}^{+0}$	${81}_{-1}^{+2}$	${1.0}_{-0.0}^{+0.0}$	3.7	50	0.72446	0.9951
2012-06-30	56,108.328	${2200}_{-100}^{+0}$	${83}_{-2}^{+1}$	${1.0}_{-0.0}^{+0.0}$	3.8	50	0.95245	0.6451
2012-07-04	56,112.419	${2200}_{-0}^{+0}$	${81}_{-0}^{+0}$	${1.0}_{-0.0}^{+0.0}$	3.8	50	0.71391	0.9965
2013-03-27	56,378.571	${2100}_{-0}^{+300}$	${81}_{-3}^{+3}$	${0.8}_{-0.0}^{+0.2}$	3.8	50	0.69979	0.9977
2013-07-01	56,474.379	${2000}_{-0}^{+100}$	${81}_{-2}^{+0}$	${0.8}_{-0.0}^{+0.1}$	3.8	85	0.97178	0.5809
2018-05-18	58,256.461	${1900}_{-100}^{+100}$	${81}_{-2}^{+1}$	${1.0}_{-0.0}^{+0.0}$	3.6	100	0.71925	0.9954
[N ii] λ5755
2009-05-09	54,960.517	${1600}_{-700}^{+300}$	${82}_{-22}^{+5}$	${1.0}_{-0.6}^{+0.0}$		50	1.0157	0.4426
2009-06-15	54,997.525	${1500}_{-500}^{+400}$	${80}_{-23}^{+6}$	${0.8}_{-0.4}^{+0.2}$		50	1.1388	0.2308
2009-06-16	54,998.492	${2000}_{-600}^{+200}$	${79}_{-15}^{+5}$	${0.9}_{-0.4}^{+0.1}$		50	1.0031	0.4696
2009-06-16	54,998.510	${1900}_{-200}^{+200}$	${79}_{-4}^{+2}$	${0.9}_{-0.1}^{+0.1}$		50	0.77003	0.9178
2009-07-04	55,016.452	${1800}_{-0}^{+100}$	${80}_{-1}^{+2}$	${0.9}_{-0.0}^{+0.1}$		50	0.7724	0.9118
2009-07-06	55,018.389	${1800}_{-200}^{+100}$	${81}_{-3}^{+1}$	${1.0}_{-0.2}^{+0.0}$		50	0.73702	0.9417
2010-07-01	55,378.405	${1700}_{-100}^{+200}$	${81}_{-4}^{+2}$	${1.0}_{-0.1}^{+0.0}$		50	0.74756	0.9293
2011-03-17	55,637.644	${1800}_{-100}^{+0}$	${79}_{-1}^{+2}$	${1.0}_{-0.0}^{+0.0}$		60	0.89937	0.7037
2011-06-12	55,724.440	${1600}_{-100}^{+100}$	${81}_{-4}^{+2}$	${1.0}_{-0.1}^{+0.0}$		50	0.47080	0.9999
2011-07-24	55,766.275	${1500}_{-0}^{+100}$	${83}_{-2}^{+1}$	${1.0}_{-0.0}^{+0.0}$		60	0.54222	0.9981
2011-08-06	55,779.239	${1600}_{-100}^{+0}$	${83}_{-2}^{+1}$	${1.0}_{-0.0}^{+0.0}$		50	0.87737	0.7346
2011-09-30	55,834.236	${1700}_{-0}^{+0}$	${83}_{-2}^{+1}$	${1.0}_{-0.0}^{+0.0}$		50	0.87234	0.7587
2012-01-13	55,939.679	${1600}_{-100}^{+0}$	${83}_{-4}^{+1}$	${1.0}_{-0.1}^{+0.0}$		100	0.54133	0.9986
2012-02-24	55,981.645	${1600}_{-700}^{+100}$	${83}_{-40}^{+1}$	${1.0}_{-0.2}^{+0.0}$		65	1.1818	0.1583
2012-03-20	56,006.612	${1600}_{-0}^{+100}$	${83}_{-3}^{+0}$	${1.0}_{-0.0}^{+0.0}$		50	0.68317	0.9754
2012-07-04	56,112.419	${1600}_{-100}^{+0}$	${81}_{-4}^{+3}$	${1.0}_{-0.1}^{+0.0}$		50	0.58529	0.9970
2013-03-27	56,378.571	${1800}_{-200}^{+100}$	${85}_{-5}^{+2}$	${1.0}_{-0.1}^{+0.0}$		50	0.54641	0.9988
2013-07-01	56,474.379	${1600}_{-800}^{+100}$	${83}_{-47}^{+7}$	${1.0}_{-0.8}^{+0.0}$		50	0.97773	0.5195

Note. The errors are given for reduced χ² greater than 1σ.

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Table 2 shows that the best-fit model spectra for each profile are those with high values of inclination and squeeze, replicating well the general features of observed spectra. It should be kept in mind here that in all cases, such best-fit spectra would not fully replicate the observed spectra because an observed spectrum includes lines from other elements and/or components originating in different regions, which are not taken into account in the modeling (see bottom of Figure 5 for example). As also shown in Figure 3, the contributions from the residuals can change relatively along with the strength of [O iii] and [N ii] lines. This effect appears as errors in fitting parameters, especially for earlier and later observations of [N ii] λ5755 when the line strength is relatively weak. On the whole, the inclinations and squeezes derived from [O iii] analyses are consistent within the errors with those from using [N ii], while expansion velocities seem to be significantly different between them. This is likely associated with the difference of ionization region between [O iii] and [N ii], that is, [N ii] λ5755 with a higher excitation energy (∼4.05 eV) comes from a more inner region than [O iii] λλ4959, 5007 with a lower excitation energy (∼2.51 eV) when assuming a Hubble flow. Accordingly, the fact that we derive very similar parameters using the two forbidden lines of [O iii] and [N ii] makes the results more robust. It is noteworthy that the spectra in each phase are well reproduced by an inclination angle of ∼80° and a squeeze of ∼1.0.

5.1. Infrared Images and Optical Morphology

High-spatial-resolution observations performed using the Very Large Telescope with VISIR from 2009 to 2011 (Chesneau et al. 2012) and using the Gemini South telescope with T-ReCS from 2010 to 2012 (Sakon et al. 2016, also see Figure 2) revealed a bipolar-shaped (or elongated) dusty nebula round V1280 Sco (see Figure 7 for the observation dates). Chesneau et al. (2012) suggested that the mass loss was dominantly polar. Besides, Naito et al. (2013) described the structure of the ejected shell as on the left of Figure 8, where the inclination angle was supposed to be low. Their picture was based on the presence of the dusty bipolar nebula and multiple absorbing gases (Na i D, Ca ii H and K, and metastable He i*), the velocity range of which is from −650 to −900 km s⁻¹, moving along the line of sight detected by the Subaru telescope with HDS. Whereas, as shown in Section 4, [O iii] and [N ii] forbidden line regions (${V}_{\exp }=1600\text{-}2100$ km s⁻¹, fast outflow) are expanded/elongated with an inclination angle of ∼80°, that is, almost orthogonal to the line of sight. These findings enable us to improve the drawing of V1280 Sco as on the right of Figure 8, where the inclination angle is high (edge-on) and the ejecta consist of an equatorial torus (ring) and a bipolar outflow. Within the slower component of the ejecta, the density is often enhanced toward the equatorial plane. This equatorial torus may shape the faster component of the ejecta into a bipolar morphology (e.g., Sokoloski et al. 2016). This idea is consistent with the radio or optical direct imaging studies of some novae such as V959 Mon (γ-ray nova, Linford et al. 2015; Healy et al. 2017), T Pyx (recurrent nova, Chesneau et al. 2011; Sokoloski et al. 2016), and HR Del (slow nova, Harman & O'Brien 2003; Moraes & Diaz 2009), which reveal that the ejecta from novae appear to consist of two main components: a slow, dense outflow and a fast outflow or wind.

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5.2. Eruption Scenario

5.3. Distance and Peak Luminosity

The distance to V1280 Sco was estimated in various approaches. Hounsell et al. (2010) estimated the distance to be d = 630 ± 100 pc, where they obtained the peak luminosity (L_⋆) as

$$\begin{eqnarray}&&{L}_{\star }=2.4\times {10}^{4}{\left(\displaystyle \frac{{t}_{{\rm{c}}}}{24\,\mathrm{days}}\right)}^{2}{\left(\displaystyle \frac{{v}_{\mathrm{ej}}}{600\,\mathrm{km}\,{{\rm{s}}}^{-1}}\right)}^{2}{\left(\displaystyle \frac{{T}_{{\rm{c}}}}{1200\,{\rm{K}}}\right)}^{4}{L}_{\odot },\end{eqnarray} \tag{ 2 }$$

by measuring the condensation time (t_c = 24 days) of dust grains from SMEI data (see Figure 7), assuming that the condensation temperature (T_c) was 1200 K and the ejection velocity (v_ej) was 600 km s⁻¹, and then compared it with the maximum light ${m}_{V}^{\max }=4$, taking the interstellar extinction A_V = 1.2 ± 0.3. On the other hand, Chesneau et al. (2008) and Naito et al. (2012) derived d = 1.6 ± 0.4 kpc and d = 1.1 ± 0.5 kpc from the expansion parallax of a dusty shell assuming the velocity is 500 km s⁻¹ and 350 km s⁻¹, respectively, where the difference depends on taking account of the direction of flow and velocity field of the dusty ejecta; for example the morphology can change from a torus-dominant geometry to a bipolar-shaped one as suggested for V339 Del (Kawakita et al. 2019). Furthermore, Hachisu & Kato (2016b) obtained the distance as 0.96 kpc by examining the UBV color evolution based on their model of a universal decline law, which is consistent with our estimation of 1.1 kpc. Here we attempt to estimate the distance by using Equation (2) in a similar way to Hounsell et al. (2010). When we adopt 350 ± 160 km s⁻¹ instead of 600 km s⁻¹ as the ejection velocity (v_ej), and assume that the magnitude at the pre-maximum halt (∼6.3 mag; ∼2.5 mag larger than the maximum) corresponds to its Eddington luminosity for a ∼0.6 M_☉ WD (Hachisu & Kato 2004), a distance of 1.06 ± 0.49 kpc is derived. Hence, we may conclude that the mass of the WD in the V1280 Sco system is low (∼0.6 M_☉) and its distance is ∼1.1 kpc, and the peak magnitude is ∼2.5 mag super-Eddington.

The MMRD relationship is frequently used to estimate distances to Galactic novae, especially for statistical studies, while this is not completely explained in theory. Recently, Hachisu et al. (2020) have clarified the physics of MMRD points by considering the mass accretion rate onto the WD along with the optically thick wind theory, and concluded that the MMRD relation cannot be a precise distance indicator of individual nova due to its inevitable scatter. The scatter may be contributed from the novae with their luminosities powered by shock interactions correspondingly. Slow novae tend to bring the interaction between ejecta as shown in V1280 Sco, which can cause the deviation from the MMRD relation. For measurement of the distance to a nova, Schaefer (2018) recommends, in order of accuracy, (1) using the Gaia parallax and (2) using the catalog of Özdönmez et al. (2016) where distances are calculated using their specific reddening–distance relations. Özdönmez et al. (2016) provided the calculated distance for V1280 Sco as 1.4 ± 0.9 kpc, which is in good agreement with our estimation within uncertainties. According to Gaia Early Data Release 3, ²⁰ however, the parallax corresponding to ${3.64}_{-0.24}^{+0.27}$ kpc is given, whereas it is substantially larger than any previous estimation. If the Gaia value is adopted, the maximum absolute magnitude of V1280 Sco is estimated to be ${M}_{V}=-{10.23}_{-0.14}^{+0.13}$, which is much brighter than a typical slow nova (e.g., Selvelli & Gilmozzi 2019). More observations in future are needed to determine the distance to V1280 Sco and to discuss the differences in the estimated distance among them.

5.4. V1280 Sco and Other Novae with Morpho-kinematic Modeling

Morpho-kinematic modeling provides information on the expansion velocity, inclination angle, and morphology of the ejected shell following a nova outburst. The technique has been applied to novae whose resolved images and/or spectroscopic line profiles are observed. Simultaneous resolved imaging and complementary spectroscopic observations disentangle the morphology and kinematics of the ejecta. While resolved images have the advantage that they reveal a myriad of structures, they are not obtained until the ejecta expand enough to be resolved. This means that the information on morphology of the ejecta in the early outburst phase tends not to be available. On the other hand, spectroscopic observations allow us to constrain the model, including the change of the morphology, from the early phase to later stages. However, it is difficult to model the ejecta without the aid of imaging for the case where spectral line profiles are composed of multiple and complex components.

Table 3 shows examples of novae with morpho-kinematic modeling with shape. In this paper we modeled V1280 Sco over ∼1500 days after outburst as a bipolar structure of forbidden lines of [O iii] λλ4959, 5007 and [N ii] λ5755, along with an equatorial torus (ring) based on the high-resolution image of a dusty nebula with the Gemini South/T-ReCS and the detection of multiple absorption lines along the line of sight. Another most successful work, where the interplay between resolved imaging and ground-based spectroscopic observations played a great role, was performed for RS Oph (Ribeiro et al. 2009). Hubble Space Telescope (HST) ACS/HRC narrowband (F502N filter) imaging and ground-based spectroscopic observations ([O iii] λ5007 line profile) of RS Oph at 155 days after outburst drew the shape of ejecta as bipolar composed of an outer dumbbell and an inner hourglass structures. However, the shape can be constructed in only one phase even though such a high-quality data set is used. Actually, according to Ribeiro et al. (2009), the [O iii] λ5007 line of RS Oph has changed from narrow to wide, suggesting that narrow emission lines do not originate from the expanding remnant alone but arise from the ionized wind of the red giant (companion star) ahead of the forward shock. It is harder to draw firm conclusions unless there is simultaneous imaging and spectroscopy. In that respect, V1280 Sco has the potential to be observed with simultaneous spatially resolved imaging and high-dispersion spectroscopy in the near future due to its extremely slow evolution, which may make it possible to provide new findings on the evolution of morphological and spectral profiles as well as their correlation. This expectation is based on the fact that V1280 Sco shows the following similar results to novae V959 Mon and V5668 Sgr (Ribeiro et al. 2013b; Harvey et al. 2018).

Table 3. Examples of Novae with Morpho-kinematic Modeling with shape

Name (Outburst Year)	Morphology	i (deg)	Δta	Analyzed Line (s)	Imaging b	Ref.
V1280 Sco (2007)	Bipolar structure (and equatorial torus/ring)	${81}_{-4}^{+2}$	+1589 days	[N ii] λ5755	(Gemini-S)	1
	Bipolar structure (and equatorial torus/ring)	${80}_{-3}^{+1}$	+1846 days	[O iii] λλ4959, 5007	(Gemini-S)	1
T Aur (1891)	A peanut-shaped shell	75 ± 2	+125.0 yr	Hα (position–velocity)	NOT c	2
DQ Her (1934)	A prolate ellipsoid	87 ± 2	+82.4 yr	Hα (position–velocity)	NOT c	2
HR Del (1967)	A prolate ellipsoid with an equatorial component	37 ± 3	+53.1 yr	Hα (position–velocity)	NOT c	2
QU Vul (1984)	A spherical shape		+35.6 yr	Hα (position–velocity)	NOT c	2
RS Oph (2006)	Dumbbell structure with an hourglass overdensity	${39}_{-10}^{+1}$	+155 days	[O iii] λ5007	HST	3
V2491 Cyg (2008)	Polar blobs and an equatorial ring	${83}_{-12}^{+3}$	+108 days	Hα + [N ii] λλ6548, 6584		4
V2672 Oph (2009)	Prolate system with polar blobs and an equatorial ring	0 ± 6	+8.33 days	Hα		5
KT Eri (2009)	Dumbbell structure	${58}_{-7}^{+6}$	+ 42.29 days	Hα		6
V959 Mon (2012)	Bipolar structure (and equatorial ring)	82 ± 6	+130 days	[O iii] λλ4959, 5007	(HST)	7, 8
V5668 Sgr (2015)	An equatorial disk	85	+822 days	[O iii] λ4363	(HST, Keck)	9, 10
	An equatorial waist and polar cones	85	+822 days	[O iii] λλ4959, 5007	(HST, Keck)	9, 10
V906 Car (2018)	Asymmetric bipolar structure	53 ± 1.55	+21 days	Hα		11
	Asymmetric bipolar structure	60 ± 1.75	+21 days	O i λ8446		11
	Asymmetric bipolar ellipsoidal-like structure	50 ± 1.25	+96 days	[N ii] λ5755		11
	Asymmetric bipolar structure along with equatorial rings	50 ± 1.95	+316 days	Hα		11
	Asymmetric bipolar and triangular polar ends	35 ± 1.65	+316 days	He i λ5876		11

Notes.

^a Days or years after outburst defined in each reference for which data were used to analyze the inclination angle. ^b Telescopes used for high-resolution imaging observations. The parentheses indicate that the references for the morpho-kinematic modeling and the high-resolution imaging are different. ^c The 2.56 m Nordic Optical Telescope (NOT) at the Roque de los Muchachos Observatory (ORM, La Palma, Spain).

References. (1) Sakon et al. (2016); (2) Santamaría et al. (2022); (3) Ribeiro et al. (2009); (4) Ribeiro et al. (2011); (5) Munari et al. (2011); (6) Ribeiro et al. (2013a); (7) Ribeiro et al. (2013b); (8) Sokoloski et al. (2016); (9) Harvey et al. (2018); (10) Takeda et al. (2022); (11) Pavana et al. (2020).

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Despite the different properties of V1280 Sco (dust nova, long plateau) and V959 Mon (γ-ray nova, smooth decline), they are modeled alike as a bipolar structure with i = ∼80° using [O iii] λλ4959, 5007 profiles on 1846 days and on 130 days after outburst, respectively. Note that the images of V959 Mon were obtained with HST and the WFC3 camera (F657N and F502N filters) in 2014 and 2015, which correspond to approximately 2.5 and 3.5 yr after outburst, where the F657N filter traces mainly dense gas of Hα while the F502N filter traces more diffuse gas of [O iii] (Sokoloski et al. 2016). The 2014 HST images indicate that [O iii] emission appeared in a bipolar shape, which is roughly consistent with the morphology inferred by Ribeiro et al. (2013b), whereas a dense, edge-on equatorial torus was dominantly shown only in the F657N (Hα + [N ii]) filter. On the other hand, the 2015 HST images indicate that Hα and [O iii] emissions from the outer, fast flow had almost completely faded and the inner spherical [O iii] shell took on the appearance of two arcs. These changes can be reflected in the spectral feature naturally, so that such a spectral profile may be modeled as a bipolar structure and an equatorial ring as shown in V5668 Sgr. If this is the case for V1280 Sco, the [O iii] profile may change to be contributed from the emission that emanated from the equatorial torus as the system evolves (the density distribution and/or the ionization state changes). Furthermore, the high inclination angle (edge-on) of V1280 Sco may be used as a predictor for searches of eclipses or an accretion disk, which will then provide us further information on the system parameters, such as the orbital period and the white dwarf mass. In fact, an orbital period of 7.1 hr was observed as a preodic modulation by the rim of an accretion disk in V959 Mon (Page et al. 2013).

5.5. Observability of the [O iii] Direct Imaging

In this paper we studied the morphology of the expanding ejecta of the extremely slow nova V1280 Sco with a unique light curve. We compare synthetic line profile spectra to the observed spectra for [O iii] λλ4959, 5007 and [N ii] λ5755 emission lines in order to find the best-fit morphology, inclination angle, and maximum expansion velocity of the ejected shell. We derive the best-fitting expansion velocity, inclination, and squeeze as ${V}_{\exp }={2100}_{-100}^{+100}$ km s⁻¹, $i={80}_{-3}^{+1}$ deg, and ${squ}={1.0}_{-0.1}^{+0.0}$ using [O iii] line profiles, and ${V}_{\exp }={1600}_{-100}^{+100}$ km s⁻¹, $i={81}_{-4}^{+2}$ deg, and ${squ}={1.0}_{-0.1}^{+0.0}$ using the [N ii] λ5755 line profile, respectively. A high inclination angle is consistent with the observational results of showing multiple absorption lines originating from clumpy materials, which are likely to be produced in a dense and slow equatorially focused outflow. The observational fact that V1280 Sco showed three short episodes of brightening with amplitudes of ∼1 mag near the peak, a deep extinction due to dust formation ∼10 days after the maximum, and multiple intermediate-velocity clumpy components moving along the line of sight until several years after the peak, is consistent with an edge-on binary system if the internal shock model is adopted. We discuss the distance to V1280 Sco and suggest that the mass of the WD is low (∼0.6 M_☉) and its distance is ∼1.1 kpc, and the peak magnitude is ∼2.5 mag super-Eddington. Considering that V1280 Sco is an extremely slow nova, more observations in future could be conducted to investigate its nature. Increasing the sample size of novae for which morphology information is available will be helpful for addressing long-standing mysteries regarding nova outbursts such as the dominant energy source to power the optical light at the maximum, optical flares near the maximum, and dust formation.

This work is based on data collected at the Subaru Telescope, which is operated by the National Astronomical Observatory of Japan. The Pirka telescope is operated by Graduate School of Science, Hokkaido University, and is partially supported by the Optical and Near-Infrared Astronomy Inter-University Cooperation Program, MEXT, of Japan. This work (partially) has made use of data from the European Space Agency (ESA) mission Gaia (https://www.cosmos.esa.int/gaia), processed by the Gaia Data Processing and Analysis Consortium (DPAC, https://www.cosmos.esa.int/web/gaia/dpac/consortium). Funding for the DPAC has been provided by national institutions, in particular the institutions participating in the Gaia Multilateral Agreement. We are grateful to students at Osaka Kyoiku University for providing the photometric data that we used in this research. We thank Nayoro Observatory staff for their support. Thanks are also due to Izumi Hachisu and Mariko Kato for their useful comments. The publication of this work is financially supported by National Astronomical Observatory of Japan. V.A.R.M.R. acknowledges financial support from the South African Square Kilometre Array Project for the postdoctoral fellowship position at the University of Cape Town, the Radboud Excellence Initiative, the Fundação para a Ciência e a Tecnologia (FCT) in the form of an exploratory project of reference IF/00498/2015/CP1302/CT0001, FCT and the Ministério da Ciência, Tecnologia e Ensino Superior (MCTES) through national funds and when applicable co-funded EU funds under the project UIDB/EEA/50008/2020, and supported by Enabling Green E-science for the Square Kilometre Array Research Infrastructure (ENGAGE-SKA), POCI-01-0145-FEDER-022217, and PHOBOS, POCI-01-0145-FEDER-029932, funded by Programa Operacional Competitividade e Internacionalizaçã o (COMPETE 2020) and FCT, Portugal. H.N. and V.A.R.M.R. acknowledge financial support from the Global COE Program of Nagoya University "Quest for Fundamental Principles in the Universe (QFPU)" from JSPS and MEXT of Japan in the form of a visiting scholar fellowship.

Facilities: Subaru (HDS) - , Gemini:South (T-ReCS) - , Pirka:1.6m (MSI) - , Kamogata/Kiso/Kyoto Wide-field Survey - , Gaia -

Software: IRAF (Tody 1986), SHAPE (Steffen et al. 2011).