ASASSN-16oh: A Nova Outburst with No Mass Ejection—A New Type of Supersoft X-Ray Source in Old Populations

We plot the I magnitudes of ASASSN-16oh in Figure 1 (unfilled red circles), taken from the OGLE IV website (Mroz et al. 2016; Maccarone et al. 2019).

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For later use, we have estimated the V light curve from the I data and several V − I colors listed in Maccarone et al. (2019): V − I = 0.8 in quiescent phase, V − I = 0.36 on JD 2457657.7, V − I = 0.34 on JD 2457681.78, and V − I = 0.16 on JD 2457744.6. With a linear interpolation of these V − I data and assumed (start, end) of the outburst to be (200 days before, 100 days after) the I peak (JD 2457737.1), we recover the V magnitudes (filled blue circles) as shown in Figure 1. We assumed that the I brightness reaches a maximum on JD 2457737.1 from an interpolation of the other I data.

The characteristic property of the light curve is a slow rise, sharp peak followed by rapid decay. The brightness rises slowly in ∼200 days and declines fast in ∼100 days. These properties are unlike those of typical nova outbursts but rather similar to long orbital-period dwarf novae. For example, the dwarf nova outbursts of V1017 Sgr show a 90 day rise and 90 day decline with an almost symmetric light-curve shape. In contrast, a typical nova rises within a few days and decays much slowly over a timescale of years (see, e.g., Figure 1 of Hachisu & Kato 2015).

There are other common properties between ASASSN-16oh and the dwarf nova V1017 Sgr. The peak V brightness is ${M}_{V,\max }\sim -2.3$ in ASASSN-16oh, similar to ${M}_{V,\max }\sim -1.3$ in V1017 Sgr (Schaefer 2018). The quiescent brightnesses of both objects are also similar, that is, ${M}_{V,\min }\approx 2.1$ for ASASSN-16oh and ${M}_{V,\min }\approx 1.8$ for V1017 Sgr (Schaefer 2018). Thus, the light-curve shape of ASASSN-16oh may be explained as a long orbital-period dwarf nova.

Maccarone et al. (2019) presented the Southern African Large Telescope optical spectrum of ASASSN-16oh taken on UT 2016 December 16–24 (JD 2457738.5–245746.5), just after the I peak (JD 2457737.1). This spectrum shows no indication of mass loss, such as many broad emission lines or P-Cygni profiles usually seen in classical novae. Thus, if this is a classical nova phenomenon, it is a rare case in which no wind mass-loss occurs.

A distinct difference between ASASSN-16oh and dwarf novae is the supersoft X-ray detection. No SSS phase has ever been detected in dwarf novae while an SSS phase is frequently observed in classical novae (Schwarz et al. 2011). If ASASSN-16oh is a dwarf nova, this is the first case of supersoft X-ray detection (Maccarone et al. 2019).

Figure 1 also shows the X-ray count rates observed with Swift (0.3–10.0 keV: filled green squares outlined with a black line). It seems that the X-ray count rate reaches maximum slightly later than the I peak and decays with the I light curve.

The X-ray spectra are dominated by soft components. Maccarone et al. (2019) deduced a blackbody temperature of 900,000 K and a flux of ∼1 × 10³⁷ erg s⁻¹ from the Swift/XRT spectrum on UT 2016 December 15 (JD 2,457,737.5) at the distance of the SMC. From the Chandra/LETG spectrum taken on UT 2016 December 28 (JD 2,457,750.5), Maccarone et al. (2019) derived a blackbody temperature of 905,000 K, a luminosity of 6.7 × 10³⁶ erg s⁻¹, and the hydrogen column density of N_H = 3.4 × 10²⁰ cm⁻², and, for an atmosphere model of solar abundance, 750,000 K and N_H = 2.0 × 10²⁰ cm⁻². Hillman et al. (2019) reanalyzed the same Chandra spectrum obtained by Maccarone et al. (2019) with a metal-poor atmosphere model and obtained the effective temperature of 750,000 K, the bolometric luminosity of 4.3 × 10³⁶ erg s⁻¹, and the hydrogen column density of N_H = 2.3 × 10²⁰ cm⁻².

These temperatures are consistent with the surface temperatures of massive WDs in the SSS phase of classical novae (e.g., Kato 1997; Schwarz et al. 2011). Thus, a nuclear-burning origin seems to be a natural explanation for the X-rays.

Both Maccarone et al. (2019) and Hillman et al. (2019) obtained a similar column density of N_H = 2 × 10²⁰ cm⁻² that can be converted to E(B − V) = N_H/5.8 × 10²¹ ≈ 0.035 (Bohlin et al. 1978), E(B − V) = N_H/6.8 × 10²¹ ≈ 0.03 (Güver & Özel 2009), or E(B − V) = N_H/ 8.3 × 10²¹ ≈ 0.024 (Liszt 2014). In the present paper, we adopt A_V = 3.1E(B − V) = 0.1, ${(m-M)}_{V}=18.9+0.1\,=\,19.0$, and ${(m-M)}_{I}=18.95$.

Maccarone et al. (2019) obtained the unabsorbed X-ray luminosity to be ∼1 × 10³⁷ erg s⁻¹ from the Swift/XRT spectrum and to be 6.7 × 10³⁶ erg s⁻¹ from the Chandra/LETG spectrum. Hillman et al. (2019) obtained the unabsorbed X-ray flux to be 4.3 × 10³⁶ erg s⁻¹.

These luminosities are much lower than the Eddington luminosity ∼1 × 10³⁸ erg s⁻¹ for a 1.0 M_⊙ WD. If it is a classical nova outburst, the X-ray luminosity from the naked WD is close to the Eddington limit. Hillman et al. (2019) suggested that the low brightness is owing to occultation by the accretion disk rim as in the recurrent nova U Sco, although they did not include effects of the accretion disk in their V light-curve model. Orio et al. (2013) estimated the unabsorbed X-ray luminosity of U Sco in the SSS phase to be ∼7 × 10³⁶ erg s⁻¹ from the Chandra/HRC-S and LETG spectra. The surface of the WD is occulted by the disk rim and the X-rays come from Thomson scattering by expanded plasma around the WD. This X-ray luminosity is similar to that of ASASSN-16oh.

Figure 2 shows the color–magnitude diagram, (V − I)₀–M_I, of ASASSN-16oh around the peak of the outburst (t = −79.4, −55.3, and +7.5 days after the I peak). Here, (V − I)₀ is the intrinsic V − I color, which is calculated from the relation (V − I)₀ = (V − I) − 1.6E(B − V) (Rieke & Lebofsky 1985), and M_I is the absolute I magnitude.

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Figure 2 also shows the color–magnitude track of the recurrent nova U Sco in the 2010 outburst. We assume the distance modulus in the I band to be (m − M)_I = 15.9 and the reddening to be E(B − V) = 0.26 after Hachisu & Kato (2018). The UBVI_C data of U Sco are taken from Pagnotta et al. (2015). Except for the short period after the peak (${M}_{I}\lt -5$), the ${(V-I)}_{0}$ color of U Sco is almost constant, i.e., ${(V-I)}_{0}\sim 0.1-0.2$. U Sco has an irradiated accretion disk with the radius of ∼2.5 R_⊙ (Hachisu et al. 2000). U Sco entered a plateau phase in the V/I light curves when I > 14, that is, when ${M}_{I}\gtrsim -5$ as shown in Figure 2 of Pagnotta et al. (2015). This is because the V and I brightnesses are dominated by the irradiated accretion disk (Hachisu et al. 2000). This plateau phase corresponds almost to the SSS phase. The ${(V-I)}_{0}$ colors of ASASSN-16oh well overlap those of U Sco in its SSS phase (when ${M}_{I}\gtrsim -2$).

For comparison, we further add the track of a typical classical nova, V496 Sct. We assume the distance modulus in the I band to be ${(m-M)}_{I}=13.0$ and the reddening to be $E(B-V)=0.45$ after Hachisu & Kato (2019a). The BVI_C data of V496 Sct are taken from the archives of the Variable Star Observers League of Japan, the American Association of Variable Star Observers, the Small and Medium Aperture Telescope System (Walter et al. 2012), and Raj et al. (2012). The V and I light curves are plotted in Figure 52 of Hachisu & Kato (2019a) and the ${(V-I)}_{0}$–M_I color–magnitude diagram is presented in Hachisu & Kato (2019b). In usual classical novae, their optical spectra are dominated by free–free emission from optically thin ejecta. After the optical peak, the optical brightness monotonically decreases with time and its color goes toward the red, due mainly to the emission line effect in the I band such as the O i and Ca ii triplet. In the later phase (${M}_{I}\gt -4$), the nova enters the nebular phase, and strong emission lines such as [O iii] contribute to the V band. Then, the V − I color turns to the blue. No X-ray data of V496 Sct are available, but the nova should enter the SSS phase when it declined to M_I > 0 as shown in Figures 50 and 52 of Hachisu & Kato (2019a).

In general, classical novae are short orbital-period binaries of P_orb ∼  a few hours. They have an accretion disk with the radius of ∼0.5 R_⊙, the brightness of which is rather faint in the SSS phase. Even if the accretion disk survives after the nova outburst, it is deeply embedded in the ejecta. In the nebular phase, the accretion disk appears because the ejecta becomes optically thin, but it is too small to contribute to the luminosity and color.

In contrast, U Sco has a large accretion disk with the radius of ∼2.5 R_⊙ because the orbital period is P_orb = 1.23 days and its binary size (separation) is a ∼ 6–7 R_⊙ (Hachisu et al. 2000). Therefore, the irradiated disk substantially contributes to the V and I bands in the SSS phase (Hachisu et al. 2000). This is partly because the ejecta mass of U Sco is very small, and the nebular emission line effect is relatively small. These physical properties give rise to the color-evolution difference between U Sco and V496 Sct.

Because the (V − I)₀ color in the SSS phase is similar between ASASSN-16oh and U Sco, we expect that the V and I brightnesses of ASASSN-16oh originate from the irradiated accretion disk, like U Sco.

To further confirm the presence of an irradiated large accretion disk in ASASSN-16oh, we compare the absolute V magnitude with two other binaries that have a prominent irradiated accretion disk. One is the galactic recurrent nova U Sco and the other is the Large Magellanic Cloud (LMC) SSS RX J0513.9−6951.

2.6.1. U Sco

Figure 3(a) shows the light curve of U Sco in the 2010 outburst. We adopt the distance modulus in the V band to be (m − M)_V = 16.3 (Hachisu & Kato 2018). Around the optical peak, the brightness is dominated by the emission from the ejecta. As time goes on, the ejecta becomes optically thin and the continuum emission from the irradiated disk becomes dominant. In the SSS phase, the light curve shows a plateau because its brightness is dominated by the irradiated accretion disk. The disk keeps a constant brightness until the nuclear burning turns off around JD 2445,260.

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We add the absolute V magnitude, ${M}_{V}$, light curve of ASASSN-16oh to compare with that of U Sco. Here, the timescale of ASASSN-16oh is squeezed 5.5 times and the origin of time is shifted to match their supersoft X-ray peaks.

This figure demonstrates that the peak absolute magnitude M_V of ASASSN-16oh is roughly the same as that of U Sco in the SSS phase. We expect that a larger irradiated disk is brighter. Thus, a rough agreement of the absolute brightness indicates that the sizes of the accretion disks are comparable. The orbital period of U Sco is P_orb = 1.23 days (Schaefer & Ringwald 1995), and the disk size is ∼2.5 R_⊙ (Hachisu et al. 2000). This is broadly consistent with the orbital period (several days) of ASASSN-16oh suggested by Maccarone et al. (2019).

2.6.2. RX J0513.9−6951

Maccarone et al. (2019) obtained the spectral energy distribution (SED) of ASASSN-16oh from 2000 to 6000 Å that is well approximated by a power law of ${F}_{\lambda }\propto {\lambda }^{-2.33}$ as in Figure 4. Here, F_λ is the energy flux at the wavelength λ. For comparison, we added the continuum flux of the LMC SSS RX J0513.9−6951, which is taken from the spectrum observed with the International Ultraviolet Explore (IUE)/SWP and 2.2 m Max-Planck ESO telescope (Pakull et al. 1993). This spectrum shows a resemblance to ASASSN-16oh, suggesting that the binary is consistent with a nuclear-burning WD, irradiated accretion disk, and lobe-filling companion star like RX J0513.9−6951. We also add a model spectrum calculated by Popham & Di Stefano (1996) for LMC SSSs (thick solid black line). This model consists of a steady burning WD, irradiated accretion disk, and lobe-filling companion star. The total flux, which is the summation of these three components, well reproduces the ${F}_{\lambda }\propto {\lambda }^{-2.33}$ law. The irradiated accretion disk dominantly contributes to the total flux, whereas the irradiated secondary star contributes only to the optical region. The contribution from the WD photosphere is negligible. The agreement in the SED between RX J0513.9−6951 and ASASSN-16oh also suggests the presence of an irradiated accretion disk in ASASSN-16oh. We will discuss this point in more detail in Section 6.2.

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By definition, novae accompany strong and fast mass ejection (or strong and fast wind mass loss; see, e.g., Warner 1995). The optically thick winds are accelerated when the photospheric luminosity approaches the Eddington luminosity. Because the OPAL opacity has a prominent peak at $\mathrm{log}T$ (K) ∼ 5.2 owing to iron ionization (Iglesias & Rogers 1996), the optically thick winds are accelerated around this temperature region, i.e., deep inside the photosphere. The occurrence condition of winds was examined first by Kato (1985) for the old opacities and then by Kato & Hachisu (2009) and Kato et al. (2013) for the OPAL opacities (Iglesias & Rogers 1996). These works clarified that WDs do not emit optically thick winds in the following cases.

• 1.  
  In low-mass WDs, the wind acceleration is insufficient such that the wind velocity at the photosphere does not exceed the escape velocity there. The envelope simply expands and then shrinks without mass ejection. This occurs in low-mass WDs of ${M}_{\mathrm{WD}}\lt 0.5\mbox{--}0.6\,{M}_{\odot }$ for the metallicity of Z = 0.02 (Kato & Hachisu 2009). The galactic slow nova PU Vul corresponds to this case (Kato et al. 2011, 2012).
• 2.  
  When the mass-accretion rate is high and the ignition mass is very small, the envelope does not expand to reach $\mathrm{log}T$ (K) ∼ 5.2 at the photosphere. Winds are not accelerated (Kato & Hachisu 2009).
• 3.  
  In old population novae, the metallicity is very low so that the iron peak in the OPAL opacity is not high enough to accelerate winds (Kato et al. 2013).
• 4.  
  When the mass-accretion rate is higher than the stability line of steady hydrogen burning ${\dot{M}}_{\mathrm{acc}}\gt {\dot{M}}_{\mathrm{stable}}$, we can make a forced nova with no mass ejection by manipulating the stop/restart of mass accretion. This will be explained in Section 3.3.

Among a huge number of galactic novae (Z ∼ 0.02), only one (PU Vul) is known to be an object without optically thick winds. ASASSN-16oh is an SMC object and could be in a low-Z environment. With a lower Z, the wind acceleration is weaker because the lower iron abundance results in a smaller peak in the OPAL opacity. Kato et al. (2013) studied starts/ends of winds in various populations based on their steady-state approach. This approximation may not be good in the rising phase of strong nova outbursts. In this work, we study the occurrence of winds using a stellar evolution code (Kato et al. 2017b).

Our numerical code is the same as that described in Kato et al. (2017b). When the hydrogen-rich envelope of the WD expands after hydrogen ignites, wind mass loss often occurs. Henyey-type codes, widely used in stellar evolution calculation, have difficulties calculating extended stages of nova outbursts. This led many authors to assume some mass loss in their numerical codes to continue calculation, but these mass-loss rates are not based on reliable acceleration mechanism of nova winds (Kato et al. 2017a). Kato et al. (2017b) introduced how to obtain the mass-loss rate consistent with optically thick winds (Kato & Hachisu 1994). This method is to connect an interior structure with an outer wind solution and needs many iterations and human time until we obtain the final value of the mass-loss rate. In the present paper, we focus our calculation on no-mass-ejection novae. Therefore, without such an iteration process, we simply assume, if needed, a tentative mass-loss rate described by Equation (1) of Kato et al. (2017b).

We assume Population II composition for accreted matter, i.e., X = 0.75, Y = 0.249, and Z = 0.001, where X is hydrogen, Y is helium, and Z is the heavy element content in mass weight. This corresponds to a typical metallicity of the SMC ([Fe/H] = −1.25 ± 0.01; Cioni 2009).

The WD mass and mass-accretion rate of our models are plotted in Figure 5, which is the diagram of WD response for various WD masses and mass-accretion rates. Below the stability line of steady hydrogen burning (lower black line labeled ${\dot{M}}_{\mathrm{stable}}$), hydrogen-shell burning is unstable and the accreting WDs experience periodic shell flashes, i.e., nova outbursts. The equi-recurrence period of shell flashes is depicted by the cyan-blue lines, with the period beside each line. The crosses represent no-mass-ejection models, while the open circles depict models in which we assume mass loss; otherwise, our calculation does not converge.

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Above the stability line, the photospheric radius is larger for a larger mass-accretion rate. In the region to the left of the vertical blue line (M_WD ≲ 1.15 M_⊙), the envelope eventually expands to giant size without mass loss. The optically thick wind mass loss occurs only in the region above the upper horizontal black line and to the right of the vertical blue line, i.e., very massive WDs (M_WD ≳ 1.15 M_⊙) and high mass-accretion rates (${\dot{M}}_{\mathrm{acc}}\gtrsim 6\times {10}^{-7}{M}_{\odot }$ yr⁻¹).

Figure 6 shows the last four cycles of our three models. No mass ejection occurs in any of the models in this figure. The first two are close to but below the stability line, i.e., (a) M_WD = 1.0 M_⊙ with ${\dot{M}}_{\mathrm{acc}}=1.2\times {10}^{-7}{M}_{\odot }$ yr⁻¹ and (b) M_WD = 1.1 M_⊙ with ${\dot{M}}_{\mathrm{acc}}=1.5\times {10}^{-7}\,{M}_{\odot }$ yr⁻¹. The WD always accretes matter. The accretion rate is smaller than the nuclear-burning rate during the flash (${\dot{M}}_{\mathrm{acc}}\lt {\dot{M}}_{\mathrm{nuc}}$), then the envelope mass gradually decreases (${\dot{M}}_{\mathrm{env}}={\dot{M}}_{\mathrm{acc}}-{\dot{M}}_{\mathrm{nuc}}\lt 0$) to below the minimum envelope mass for hydrogen burning. Thus, hydrogen burning eventually ends. We call the novae that occur below the stability line "natural nova" to distinguish them from the "forced novae" that occur above the stability line (Hachisu et al. 2016).

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Figure 6(c) shows an example of a forced nova, i.e., M_WD = 1.3 M_⊙ with ${\dot{M}}_{\mathrm{acc}}=4.5\times {10}^{-7}\,{M}_{\odot }$ yr⁻¹, being located above the stability line. In this region, the nuclear-burning rate is balanced by the accretion rate (${\dot{M}}_{\mathrm{env}}={\dot{M}}_{\mathrm{acc}}-{\dot{M}}_{\mathrm{nuc}}=0$). The decrease in the envelope mass is supplied by the mass accretion. Thus, if we continue the mass accretion, hydrogen-shell burning will never end. If we stop the mass accretion, the envelope mass decreases by nuclear burning and the shell flash eventually ends. If we restart the mass accretion after some time later, we obtain the next shell flash. In this way, we have multicycle shell flashes. Figure 6(c) gives an example of the periodic change of the mass-accretion rate. If we stop/restart the mass accretion in our model calculation, we obtain successive shell flashes.

Figure 6 compares characteristic properties of these three models: the photospheric luminosity L_ph, photospheric temperature T_ph, and supersoft X-ray light curve L_X (0.3–1.0 keV) calculated from L_ph and T_ph, using a blackbody approximation. The photospheric temperature is shown only in the last cycle to avoid complicating the lines. As the photospheric temperature is always high ($\mathrm{log}{T}_{\mathrm{ph}}$ (K) > 5.4), most of photons are emitted in the far-UV and supersoft X-ray bands. As expected, they are all periodic SSSs.

We searched shell-flash models for no mass ejection. Below the stability line, i.e., in the natural novae, we found no-mass-ejection models only in low-mass WDs as shown in Figure 5. In more massive WDs (M_WD ≳ 1.1 M_⊙), shell flashes are stronger and mass ejection always occurs. The border between with/without mass ejection is about ${M}_{\mathrm{WD}}=1.0\mbox{--}1.1\,{M}_{\odot }$ as in Figure 5. This is consistent with the study of the occurrence condition of winds for metal-poor novae (Kato et al. 2013).

Far below the stability line, i.e., with lower mass-accretion rates, the shell flash becomes much stronger, and we have to assume large mass-loss rates during the outburst.

The SSS duration is longer in lower mass WDs. In the 1.0 and 1.1 M_⊙ WD models, the massive limit of no-mass-ejection models has the SSS duration much longer than 200 days, which is not consistent with the ASASSN-16oh observation (see Figure 6(c)). Thus, we conclude that there is no natural nova corresponding to ASASSN-16oh.

Above the stability line, i.e., in forced novae, the recurrence period can be controlled by manipulating the restarting time of accretion. If we delay the restarting time, the next outburst occurs later even if both the WD mass and mass-accretion rate are the same (Kato et al. 2014; Hachisu et al. 2016). The shell flash becomes stronger because the WD cools down during the delay.

As the recurrence period of forced novae can be controlled, we first search nova sequences for a short X-ray duration regardless of recurrence period. The outburst duration is shorter in more massive WDs. We found that a WD more massive than 1.32 M_⊙ can have an X-ray duration shorter than 200 days. In WDs more massive than 1.32 M_⊙, however, we have to assume mass loss to continue numerical calculation. Thus, the 1.32 M_⊙ WD is the upper mass limit in our calculation that fulfills a short X-ray duration (≲200 days) and no mass ejection. In the next subsection, we describe our 1.32 M_⊙ WD model in detail.

Table 1 summarizes the shell-flash properties of our five 1.32 M_⊙ models. It lists the WD mass (M_WD); metallicity (Z); mass-accretion rate (${\dot{M}}_{\mathrm{acc}}$); restarting time (t_restart) of accretion after previous shell flash occurs, i.e., the time from the epoch when the maximum nuclear luminosity is attained; whether or not numerical mass loss is adopted (yes or no); recurrence period (t_rec); maximum nuclear luminosity (${L}_{\mathrm{nuc}}^{\max }$); amount of accreted matter between two flashes (M_acc); mass retention efficiency, i.e., the ratio of the mass of ash helium and accreted matter (η); and the mean mass-increase rate of the WD (a CO core with a He layer; ${\dot{M}}_{\mathrm{CO}}$). The properties of Models A and D are almost the same because their mass-accretion rates are not that different. Also, Models B and E are similar. The maximum nuclear luminosity ${L}_{\mathrm{nuc}}^{\max }$ represents the flash strength. The flash is stronger for a smaller mass-accretion rate and a later restarting time of accretion.

Table 1.  Summary of Forced Nova Models

Model		MWD	Za	${\dot{M}}_{\mathrm{acc}}$	${t}_{\mathrm{restart}}$ b	Mass Loss	${t}_{\mathrm{rec}}$	${L}_{\mathrm{nuc}}^{\max }$	Macc	η	${\dot{M}}_{\mathrm{CO}}$
		(M⊙)		(${10}^{-7}{M}_{\odot }$ yr−1)	(yr)		(yr)	(${10}^{5}{L}_{\odot }$)	(${10}^{-7}{M}_{\odot }$)		(${10}^{-7}{M}_{\odot }$ yr−1)
A	...	1.32	0.001	5.0	0.55	no	1.1	1.2	2.9	1.0	2.6
B	...	1.32	0.001	5.0	2.6	yes	4.2	10	8.6	0.34	0.64
C	...	1.32	0.001	5.0	5.3	yes	7.3	13	9.5	0.26	0.35
D	...	1.32	0.001	5.2	0.53	no	1.0	1.0	2.7	1.0	2.6
E	...	1.32	0.001	5.2	2.8	yes	4.2	9.5	7.5	0.41	0.72
F	...	1.35	0.0001	5.0	0.58	no	1.1	0.85	2.7	1.0	2.4
G	...	1.35	0.0001	5.0	0.80	no	1.4	1.2	3.3	1.0	2.3
H	...	1.35	0.0001	5.0	1.5	yes	2.5	2.7	5.0	0.75	1.5

Notes.

^aX = 0.75, $Y=1.0-X-Z$. ^bRestarting time of mass accretion since the ${L}_{\mathrm{nuc}}$ peak.

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Figure 7(a) shows two models with no mass ejection, Models A (solid lines) and D (dotted lines). As the mass-accretion rates are almost the same, the light curves are very similar. The next outburst begins a bit later in the smaller mass-accretion model (Model A). The duration of the X-ray light curves are about 200 days in both models.

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Figure 7(b) shows Models B, C, and E, models with a later restarting time of mass-accretion. In these cases, the X-ray light curve decays faster than the models in panel (a). The recurrence period becomes longer, 4 yr in Models B and E, and 7 yr in Model C. In our calculation code, we cannot continue our calculation in the expanded stage unless we adopt a numerical mass-loss scheme, the rate of which is shown by the red line in the figure. As shown in Models B and C, we need to assume a larger mass-loss rate for a larger restarting time of mass accretion. This does not directly mean that the mass loss actually occurs because we did not adopt an iteration process to include realistic wind solutions as we did in Kato et al. (2017b). Even if real mass loss occurs, the acceleration is very weak in such a low-Z environment, and the wind velocity would be as small as ∼100 km s⁻¹ (Kato 1999), which is comparable with the FWHM of the He ii line in the optical spectra (Maccarone et al. 2019).

The wind durations of Models B, C, and E are 55–58 days as in Figure 7(b). The winds stopped 84–106 days before the optical detection of ASASSN-16oh. The wind velocity is as small as 100 km s⁻¹ or smaller, much smaller than the escape velocity. Therefore, the escaping matter would soon fall back to the equatorial plane and stay as circumbinary matter or merge into the accretion disk. We suppose that the escaping matter (wind) from the WD may not contribute to the He ii line at the detection of ASASSN-16oh.

Due to numerical difficulties, we did not calculate other models with similar parameters. We think that the 1.32 M_⊙ models are close to the one that is consistent with the observation of ASASSN-16oh.

We show the X-ray count rate of ASASSN-16oh in the decay phase of these theoretical light curves. In this fitting, we regarded the hydrogen-shell flash to have started 200 days before the X-ray detection. The WD was always bright in the X-ray band during this 200 days, but unfortunately, we had no chance of detection until a much later phase. We further assume that a massive mass inflow started shortly before the shell flash started. This mass inflow may be associated with a dwarf nova outburst. The dwarf nova outburst developed from inside to outside of the disk, which results in a slow rise of the V/I light curves. The V/I brightnesses could be brighter than normal dwarf nova outbursts because the disk is irradiated by the hot WD. Irrespective of whether a dwarf nova triggered the nova outburst or a nova outburst triggered a dwarf nova outburst, this picture roughly explains the observational properties of ASASSN-16oh discussed in Section 2.

We also calculated a similar model, but for a lower metallicity, i.e., Z = 0.0001, M_WD = 1.35 M_⊙, and ${\dot{M}}_{\mathrm{acc}}=5\times {10}^{-7}\,{M}_{\odot }$ yr⁻¹, with different restarting times of accretion. These model properties are listed in Table 1. Models F and G show no mass ejection, but Model H accompanies mass loss. They have very similar X-ray light curves to those in Figure 7.

The models except Model C show recurrence periods shorter than 6 yr. This does not match the observation of ASASSN-16oh, because at least a 6 yr quiescent phase is obvious prior to the outburst from the OGLE IV data (Maccarone et al. 2019).

To summarize, searching for a model having a short X-ray duration (<200 days), no mass- ejection, and long recurrence period (>6 yr), we find that the 1.32 M_⊙ WD (Z = 0.001) model is the closest one to the ASASSN-16oh observation.

The mass retention efficiency is η = 1.0 for no-mass-ejection models and η = 0.3–0.4 for mass-ejection models. After one cycle of hydrogen-shell flash, the ash helium accumulates on the CO core. This mass-increase rate of the CO core is listed in the last column of Table 1, with amounts as large as ${\dot{M}}_{\mathrm{CO}}\gt 2\times {10}^{-7}{M}_{\odot }$ yr⁻¹ for no-mass-ejection models.

It is instructive to show how shell flashes behave in the Hertzsprung–Russell (HR) diagram. Figure 8 shows shell-flash tracks in the HR diagram for the last cycle of our three models, 1.32 M_⊙ WD (black line), 1.1 M_⊙ WD (blue line), and 1.0 M_⊙ WD (red line). These models are already shown in Figures 7 (Model A), 6(b), and (a), respectively.

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As the shell flash proceeds, the WD starts from the bottom of the curve and brightens up and turns to the right in the HR diagram. The maximum expansion of the WD photosphere depends on the ignition mass. In these models, the ignition masses are very small so their envelopes do not extend beyond 0.1 R_⊙ (thin black line). This properties are already studied with hydrostatic approximation in Kato & Hachisu (2009) for Z = 0.02.

The thin orange line labeled as L_ph shows a sequence of hydrostatic solutions that represents a theoretical nova outburst on a 1.1 M_⊙ WD with a very large ignition mass of the hydrogen envelope. Here we assume that the chemical composition of the envelope is X = 0.75, Y = 0.249, and Z = 0.001 and the original WD radius underneath the hydrogen-rich envelope is $\mathrm{log}({R}_{\mathrm{WD}}/{R}_{\odot })=-2.104$ taken from the 1.1 M_⊙ model with the mass-accretion rate of ${\dot{M}}_{\mathrm{acc}}=1.5\times {10}^{-7}\,{M}_{\odot }$ yr⁻¹. It should be noted that the photospheric luminosity in the upper branch (horizontal part of the thin orange line) is almost the same as the Eddington luminosity.

The thick orange line labeled as M_V denotes the absolute V magnitudes corresponding to the sequence of the thin orange line. Here we have calculated the absolute V magnitude M_V from T_ph and L_ph with the blackbody approximation. The contributions from the accretion disk and companion star are not included. This figure is similar to Figure 15 of Iben (1982). Even if the L_ph is constant, the M_V is smaller (brighter) for a lower T_ph because of different bolometric corrections. In our models, the photospheric temperature does not decrease much ($\mathrm{log}{T}_{\mathrm{ph}}$ (K) > 5.4), so the V brightness is rather faint. For example, our 1.1 M_⊙ WD model (blue line) reaches the maximum at M_V = 3 as shown by the blue part on the lower orange line labeled M_V.

The inset shows the absolute V magnitudes of ASASSN-16oh. Its maximum brightness reaches M_V ∼ −2.3, which is much brighter than the naked WD. It is obvious that there is another source in the V/I brightnesses of ASASSN-16oh.

In the spreading layer model, the maximum luminosity is roughly estimated from gravitational energy release,

$$\begin{eqnarray}&&{L}^{\mathrm{acc}}=\displaystyle \frac{{{GM}}_{\mathrm{WD}}{\dot{M}}_{\mathrm{acc}}}{2{R}_{\mathrm{WD}}}.\end{eqnarray} \tag{ 1 }$$

For a 1.3 M_⊙ WD with ${\dot{M}}_{\mathrm{acc}}=3\times {10}^{-7}{M}_{\odot }$ yr⁻¹ and ${R}_{\mathrm{WD}}=3\times {10}^{8}\,\mathrm{cm}$, we have ${L}^{\mathrm{acc}}=5.2\times {10}^{36}$ erg s⁻¹. On the other hand, our 1.32 M_⊙ WD model in Figure 7 emits L_ph = 1.2 × 10³⁸ erg s⁻¹, 23 times larger than the spreading layer emission.

As introduced in Section 2, Maccarone et al. (2019) estimated the X-ray luminosity from the Chandra spectrum of ASASSN-16oh to be $6.7\times {10}^{36}$ erg s⁻¹. This value is consistent with the gravitational energy release from the spreading layer. Hillman et al. (2019) also obtained the unabsorbed X-ray flux to be $(4.3\mbox{--}6.4)\times {10}^{36}$ erg s⁻¹. They adopted a thermonuclear runaway model, which would emit an X-ray luminosity of about 10³⁸ erg s⁻¹, so they explained the observed small X-ray flux by occultation of the WD surface as in U Sco. We also assume the occultation of the WD surface by the inflated disk edge, that is, we cannot directly observe the WD emission but detect scattered photons which are much fewer than the original WD emission. It could occur if the binary inclination is high enough like in U Sco.

Maccarone et al. (2019) estimated the inclination angle of the binary from the span of the velocity variation in the He ii line (75 km s⁻¹). They assumed that the He ii line comes from the central part of the accretion disk. For a binary consisting of a 1.3 M_⊙ WD and 0.7 M_⊙ companion, they obtained the binary inclination from Keplerian law to be i = 12° for an orbital period of P_orb = 1 day, and i = 27° for P_orb = 10 days. This value should be replaced by i = 23° and i = 59°, respectively, because the authors misplaced the masses of the WD and donor in their calculation.

The above argument on the inclination angle of the binary should be modified if the He ii emission line is associated with the hot spot or irradiated companion. If the emitting region is close to the center of mass of the binary, the small line velocities are obtained even in a high inclination binary. Also the line velocity span may not always represent the radial velocity amplitude because of the sparse observation.

The accretion disk around a very hot WD may not be geometrically thin but could be inflated. The disk surface absorbs part of the supersoft X-ray flux from the WD to become hot and emit higher energy photons. This irradiation and reprocessing make the accretion disk inflated and brighter. Popham & Di Stefano (1996) assumed a ${\tan }^{-1}(z/\varpi )=15^\circ$ inflation in the UV–optical spectrum model for CAL 83 and RX J0513.9−6951. Schandl et al. (1997) adopted an inflated disk shape with angle up to ${\tan }^{-1}(z/\varpi )=24^\circ$ in the light-curve model of the LMC SSS CAL 87. Hachisu et al. (2000) adopted ${\tan }^{-1}(z/\varpi )=17^\circ$ at the edge of the disk in their light-curve model of the U Sco 1999 outburst. Here, z is the height of the disk surface from the equatorial plane and ϖ is the distance from the central WD.

The inclination angle of the binary could be one of the key parameters to distinguish the two models. If ASASSN-16oh is an eclipsing binary, it strongly supports the shell-flash model rather than the spreading layer model. If the binary is face on, the faint X-ray flux of ASASSN-16oh is consistent with the spreading layer model, while the shell-flash model needs some explanation for the faint X-ray flux. The present status indicates that the observational clues are not sufficient to draw a definite conclusion.

Figure 4 shows the SED of ASASSN-16oh (Maccarone et al. 2019). This spectrum resembles those of RX J0513.9−6951 taken by Pakull et al. (1993) in the optical high state. RX J0513.9−6951 is a binary consisting of a massive WD that undergoes steady hydrogen burning, an irradiated accretion disk, and an irradiated companion. Hachisu & Kato (2003) made light-curve models (solid magenta line in Figure 3(b)) in which the irradiated disk mainly contributes to the optical brightness. The resemblance with RX J0513.9−6951 indicates the presence of a bright irradiated accretion disk and companion in ASASSN-16oh.

Popham & Di Stefano (1996) calculated a composite spectrum for LMC persistent SSSs (thick solid black line in Figure 4). Their model binary consists of a hydrogen-burning WD of 1.2 M_⊙, irradiated accretion disk with a radius of 1.9 R_⊙, and Roche-lobe-filling 2 M_⊙ main-sequence companion. The orbital period is P_orb = 1 day. The inflated accretion disk (${\tan }^{-1}(z/\varpi )=15^\circ$ at its outer edge) is irradiated and brightened 19 times at λ = 1000 Å, and 4 times at λ = 6300 Å. As a result, the total flux, the summation of these three components, reproduces the ${F}_{\lambda }\propto {\lambda }^{-2.33}$ law. The WD does not contribute much in the UV/optical region, but the hydrogen-burning WD is necessarily because its large luminosity is the source of irradiation.

The composite spectrum by Popham and Di Stefano is fainter by ${\rm{\Delta }}\mathrm{log}{F}_{\lambda }\sim 0.3$ than that of observed ASASSN-16oh data. They assumed the WD luminosity of L_WD = 1.5 × 10³⁸ erg s⁻¹, which is comparable to our H-burning WD model (1.2 × 10³⁸ erg s⁻¹). If we assume that ASASSN-16oh is a binary of a 1.3 M_⊙ WD and a 0.7 M_⊙ companion with P_orb = 5 days, the binary separation a is ${((1.3+0.7)/(1.2+2))}^{1/3}\,{5}^{2/3}=2.5$ times larger than Popham and Di Stefano's model. If we scale up the binary size by a factor of 2.5, without changing the configuration, the irradiated area of the disk and companion become 2.5² = 6.25 times larger. This makes the flux increase by ${\rm{\Delta }}\mathrm{log}{F}_{\lambda }\sim \mathrm{log}6.25=+0.80$. If we adopt the binary inclination of 80°, instead of Popham and Di Stefano's 60°, then, the flux decrease owing to inclination is calculated to be $\mathrm{log}(\cos 80^\circ /\cos 60^\circ )=-0.46$. Then, the flux calculated by Popham and Di Stefano should be increased by 0.80–0.46 = 0.34 for our assumed binary. The resultant spectral energy distribution is very consistent with that of ASASSN-16oh obtained by Maccarone et al. (2019).

In the spreading layer model, the irradiation effect is small because the X-ray luminosity is small. The main contributor in the UV/optical range is the dwarf nova outburst. In general, the absolute flux of a dwarf nova is smaller than those shown in Figure 4 and the wavelength dependence was reported to be ${F}_{\lambda }\propto {\lambda }^{-{\rm{\Gamma }}}$, ${\rm{\Gamma }}\sim 1.5\mbox{--}2.3$ in the UV/optical range (e.g., Parikh et al. 2019).

In our shell-flash model, the X-ray flux begins to decrease when hydrogen burning almost dies out and the burning zone temperature gradually decreases. The speed of cooling depends on the WD mass; a more massive WD cools faster.

Figure 3(a) compares the light curves of ASASSN-16oh with those of U Sco in a normalized timescale. U Sco hosts a massive WD, 1.37 M_⊙ (Hachisu et al. 2000), more massive than our 1.32 M_⊙ for ASASSN-16oh, and then the cooling time is much shorter.

When the X-ray flux decreases with time, the irradiation effects decrease so that the UV/optical fluxes from the irradiated disk and companion also become faint. Thus, both the X-ray and optical fluxes decrease at the same time. In this way, our shell-flash model naturally explains the simultaneous behavior in the X-ray and optical fluxes along with those of U Sco as in Figure 3(a).

In the spreading layer model, the optical flux decreases when the dwarf nova outburst approaches its end. As the X-ray flux is closely related to the mass-accretion rate onto the WD, the expected X-ray count rate decreases with a decrease in the optical flux (e.g., Osaki 1996). It is, however, unknown whether a dwarf nova outburst could show a simultaneous decrease, like in U Sco, in both the X-ray and optical fluxes in the normalized timescale in Figure 3(a).

RS Oph is a recurrent nova that hosts a massive WD with high mass-accretion rate (1.35 M_⊙ and 1.2 × 10⁻⁷ M_⊙ yr⁻¹: Hachisu & Kato 2001; Hachisu et al. 2006). The WD mass and mass-accretion rate are more or less similar to those of ASASSN-16oh. If the X-ray emission of ASASSN-16oh is emitted from the optically thick spreading layer, we may expect supersoft X-rays in the quiescent phase of RS Oph.

Nelson et al. (2011) observed quiescent phase of RS Oph with the Chandra and XMM-Newton satellites, 537 and 744 days after the nova outburst. They analyzed the spectrum and obtained the maximum allowable blackbody temperature for an optically thick component of the spreading layer to be 0.034 keV (=3.9 × 10⁵ K). The upper limit of unabsorbed luminosity is ${(1.1\mbox{--}1.6)\times {10}^{35}(d/1.6\mathrm{kpc})}^{2}$ erg s⁻¹, where d is the distance to the star. This upper limit is smaller than those detected in ASASSN-16oh by a factor of 40.

The boundary layer between a WD and the inner edge of the accretion disk has been studied by various authors. (Popham & Narayan 1995; Piro & Bildsten 2004, and references therein.) If the mass-accretion rate is large, the boundary layer is geometrically thin, optically thick, and emits supersoft X-rays. When the accretion rate decreases, the boundary layer becomes optically thin, geometrically thick, and emits hard X-rays.

Popham & Narayan (1995) calculated the mass-accretion rate at this transition. For a 1.0 M_⊙ WD, the critical mass-accretion rate is $\mathrm{log}{\dot{M}}_{\mathrm{acc}}\,({M}_{\odot }$ yr⁻¹) = −6.12. This value depends on the model parameters, e.g., such as the WD rotation rate and viscosity parameter. They did not calculate for M_WD > 1.0 M_⊙, but from the tendency for a quick increase with the WD mass, the transition may occur at $\mathrm{log}\dot{M}\,({M}_{\odot }$ yr ${}^{-1})\sim -5$ for 1.3 M_⊙. Below this rate, the boundary layer is optically thin and would emit hard X-rays. A small accretion rate may be the reason why the supersoft X-ray component was not detected in the quiescent phase of RS Oph.

If the same argument is applied to ASASSN-16oh with an accretion rate of 3 × 10⁻⁷ M_⊙ yr⁻¹, the boundary layer should be optically thin and a hard X-ray component has to be expected during the outburst. However, there are no hard X-ray components in the spectrum (Maccarone et al. 2019). The possible reasons for the absence of hard X-rays are:

• (1)  
  A hot optically thin extended boundary layer was formed and emitted hard X-rays. However, the X-rays were occulted by the inflated disk edge and undetected, or its flux was too small to be detected.
• (2)  
  The mass accretion had already stopped before the period of observation.

The resemblance of the V − I color (Figure 2) and absolute magnitude M_V (Figure 3) indicates that ASASSN-16oh is a binary system consisting of a hydrogen-burning WD, irradiated accretion disk, and lobe-filling companion star. The spectral energy distribution F_λ ∝ λ^−2.33 (Figure 4) can be explained by the sum of contributions from an accretion disk and a companion star, which are irradiated by a WD in the luminous stage of a shell flash. Our shell-flash model is consistent with these three properties. We further show that the simultaneous declines in the X-ray and optical are also explained by our hydrogen-burning model (Section 6.3) and that our hydrogen-burning model is consistent with undetected hard X-ray flux even for the optically thin boundary layer case (Section 6.4).

ASASSN-16oh is an atypical dwarf nova in its slow rise/decay and large amplitude. It is very helpful to see if similarly shaped dwarf novae show similar color and brightness to ASASSN-16oh.

We examine the possibility of a dwarf nova outburst triggering a nova outburst.

An accreting WD will experience a nova outburst when the mass of the hydrogen-rich envelope reaches a critical value. Table 1 lists the amount of accreted matter to trigger hydrogen ignition. They are a few to several times 10⁻⁷ M_⊙. This ignition mass is smaller for a shorter recurrence period because the WD surface is hotter.

On the other hand, the mass-inflow rate onto the WD is estimated in several dwarf novae (Kimura et al. 2018). Among them, V364 Lib shows a relatively large mass-inflow rate of 1 × 10⁻⁷ M_⊙ yr⁻¹ (Kimura et al. 2018). This object has an orbital period of P_orb = 0.70 days, rising (decay) time of 10 (35) days, and small outburst amplitude of 1 mag. As ASASSN-16oh has a much larger outburst amplitude and longer orbital period, we may expect a larger mass-inflow rate. If we assume the mass-inflow rate of several times 10⁻⁷ M_⊙ yr⁻¹, the WD may accrete sufficient mass for hydrogen ignition. Our calculation assumed a periodic change of mass accretion, but in the real world, the mass inflow may occur irregularly. If WDs accrete sufficient mass through one or several times of mass-accretion events with a large mass-inflow rate, a weak shell flash may occur similarly to ASASSN-16oh.

Nova outbursts with high mass-accretion rates have been calculated by many authors (Prialnik & Kovetz 1995; Yaron et al. 2005; Idan et al. 2013; Hillman et al. 2015, 2019). Forced nova phenomena are studied in detail by Kato et al. (2014) and by Hachisu et al. (2016) in which they pointed out that forced novae are already calculated without recognizing it because they automatically switched on/off the mass accretion in their numerical codes. In the cases with very high mass-accretion rates, characteristic properties are similar to those in Figure 6, i.e., no mass ejection and a short quiescent phase comparable to the shell-flash duration.

The forced novae are still theoretical objects because no mechanism of switching on/off is identified. If the ASASSN-16oh outburst is a shell-flash phenomenon triggered by a dwarf nova, this is the first observational support for a forced nova.

In the forced novae, the mass-accretion rate is very high by its definition, so the shell flash could be weak. Thus, the mass retention efficiency of the WD is very high. Especially with no mass ejection, the mass retention efficiency of the WD is ∼100%. Such an object is a candidate of SN Ia progenitors. In this sense, ASASSN-16oh is a promising object.

Nova outbursts in various metallicities were systematically studied by Kato (1997, 1999) and by Kato et al. (2013). The optically thick winds, the main mechanism of mass loss during the nova outbursts, are accelerated owing to the prominent iron peak in the radiative opacity at $\mathrm{log}T$ (K) ∼ 5.2. For a lower metallicity, this Fe peak is small and almost disappears in Z ≲ 0.0004. In such a case, another peak due to He ionization ($\mathrm{log}T$ (K) ∼ 4.7, see Figure 4 of Kato et al. 2013 for opacities) works as the driving source.

Kato et al. (2013) showed that the Fe opacity peak works to drive the winds for a wide range of WD masses (${M}_{\mathrm{WD}}\gt 0.5\,{M}_{\odot }$) for Z = 0.02. For Z = 0.001, it works only in massive WDs (M_WD > 1.05 M_⊙) and the main driving source is replaced by the He opacity peak in less massive WDs. For Z ≤ 0.0004, only the He opacity peak works because the Fe peak disappears. The acceleration by the He opacity peak may be weak because its peak is small. Thus, we expect weak mass ejection or slow expansion. Observational counterparts of such phenomena are not identified yet, and then, it is not known if such a weak wind results in a nova outburst with efficient mass ejection from the binary.

Figure 10 shows the stability line and recurrence periods for the composition of X = 0.75 and Z = 0.0001. In the same figure, we added the results by Chen et al. (2019). The small red crosses denote flashes with no mass ejection, and the small open red circles are for those with mass loss. Their results are consistent with ours.

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This plot also shows their stability line (lower dotted line) and their expansion line above which the WD envelope increases (upper dotted line). These two lines are consistent with our ${\dot{M}}_{\mathrm{stable}}$ and 5 R_⊙ lines.

The stability line has been calculated by many authors (Nomoto et al. 2007; Ma et al. 2013; Wolf et al. 2013a, 2013b; Kato et al. 2014, for Z = 0.02), (and Chen et al. 2019, for Z = 0.0001). Our stability lines are lower than those of X = 0.7 and Z = 0.02 (Kato et al. 2014) by a factor of 0.8–0.9 (vertically lower by 0.05–0.1 dex) for X = 0.75 and Z = 0.001 in Figure 5, and by a factor of 0.6–0.8 (vertically lower by 0.1–0.2 dex) for X = 0.75 and Z = 0.0001 in Figure 10.

The stability line shows the minimum mass-accretion rate below which the hydrostatic envelope cannot keep the temperature high enough to support steady nuclear burning (point B in Figure 1 of Kato et al. 2014). For the same WD mass and accretion rate, the envelope mass is larger for a lower Z because of a difference in the opacity. Thus, the temperature at the bottom of the envelope is also high. This makes a difference in the stability line.

Figure 5 also shows the equi-recurrence period line. The recurrence period is shorter for massive WDs and higher mass-accretion rates.

The equi-recurrence period lines were obtained for the solar composition (X = 0.7 and Z = 0.02) by Kato et al. (2014) and by Hachisu et al. (2016). Our equi-recurrence period lines are systematically longer than their equi-period lines by a factor of ∼1.4 (shifted by 0.15 dex upward) in Figure 5 (for X = 0.75 and Z = 0.001) and by a factor of ∼1.8 (shifted by 0.25 dex upward) in Figure 10 (for X = 0.75 and Z = 0.0001).

For a lower Z, the ignition mass is larger because the lower opacity results in a lower blanket effect, and it takes more time until a hydrogen ignition occurs at the bottom of the accreted matter. Thus, for the same WD mass and mass-accretion rate, it takes a longer accretion time until the flash begins.