X-RAY FLASHES IN RECURRENT NOVAE: M31N 2008-12a AND THE IMPLICATIONS OF THE SWIFT NONDETECTION

We calculated recurrent nova models on 1.38 and 1.385 ${M}_{\odot }$ WDs accreting hydrogen-rich matter ($X=0.70,\,Y=0.28,$ and Z = 0.02 for hydrogen, helium, and heavy elements, respectively) with mass-accretion rates of $(1.4\mbox{--}2.5)\times {10}^{-7}\,{M}_{\odot }$ yr⁻¹, corresponding to recurrence periods from 1 to 0.5 yr (Darnley et al. 2015b; Henze et al. 2015a). We also calculated models for a 1.35 ${M}_{\odot }$ WD with 1.0 and 12 yr recurrence periods for comparison. Table 1 summarizes our models. The WD mass and mass-accretion rate are the given model parameters, and the other values, including recurrence periods, are calculated results.

Table 1.  Summary of Recurrent Nova Models

WD Mass	${\dot{M}}_{\mathrm{acc}}$	${t}_{\mathrm{rec}}$	${t}_{{\rm{X}} \mbox{-} \mathrm{flash}}$ a	${L}_{\mathrm{nuc}}^{\max }$	${T}_{\mathrm{nuc}}^{\max }$
(${M}_{\odot }$)	(${10}^{-7}{M}_{\odot }$ yr−1)	(yr)	(day)	(${10}^{6}{L}_{\odot }$)	(108 K)
1.385	2.0	0.54	0.90	2.3	1.74
1.385	1.4	0.97	0.59	5.1	1.84
1.38	2.5	0.47	1.4	1.5	1.66
1.38	1.6	0.95	0.78	3.9	1.77
1.35	2.6	1.0	2.5	1.5	1.54
1.35	0.5	12	0.37	29	1.89

Note.

^aDuration of the X-ray flash: ${L}_{{\rm{X}}}$(0.3–1.0 keV) $\gt \,{10}^{4}\,{L}_{\odot }$.

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We calculated several outburst cycles until the shell flashes reached a limit cycle. We used the same Henyey-type code as in Kato et al. (2014, 2015) and Hachisu et al. (2016) but adopted a thinner static boundary layer ($2$ $\times {10}^{-10}\,{M}_{\mathrm{WD}}$) for the outermost surface layer and smaller time steps and mass zones. These technical improvements enabled us to calculate the photospheric values much more accurately in the extended phase (after point B in Figure 1) until the optically thick wind begins to blow at $\mathrm{log}{T}_{\mathrm{ph}}$ (K) ∼ 5.5. The X-ray light curves are calculated from the photospheric luminosity ${L}_{\mathrm{ph}}$ and temperature ${T}_{\mathrm{ph}}$ assuming blackbody emission.

Our report here is focused on the very early phase of nova outbursts, i.e., the X-ray flash phase. The occurrence of the optically thick wind in our models is judged using the surface boundary condition BC1 listed in Table A1 of Kato & Hachisu (1994).

Figure 2 shows the energy budget in the very early phase of shell flashes on a $1.38\,{M}_{\odot }$ WD for two recurrence periods: ${P}_{\mathrm{rec}}=0.95\,\mathrm{yr}$ (${\dot{M}}_{\mathrm{acc}}=1.6\times {10}^{-7}\,{M}_{\odot }$ yr⁻¹; solid lines) and ${P}_{\mathrm{rec}}=0.47\,\mathrm{yr}$ (${\dot{M}}_{\mathrm{acc}}=2.5\times {10}^{-7}\,{M}_{\odot }$ yr⁻¹; dashed lines). The nuclear luminosity,

$$\begin{eqnarray}&&{L}_{\mathrm{nuc}}={\int }_{0}^{M}{\epsilon }_{n}{{dM}}_{r},\end{eqnarray} \tag{ 1 }$$

takes a maximum value of ${L}_{\mathrm{nuc}}^{\max }=3.9\times {10}^{6}\,{L}_{\odot }$ for the ${P}_{\mathrm{rec}}=0.95$ yr case and ${L}_{\mathrm{nuc}}^{\max }=1.5\times {10}^{6}\,{L}_{\odot }$ for the ${P}_{\mathrm{rec}}=0.47\,\mathrm{yr}$ case. Here ${\epsilon }_{n}$ is the energy generation rate per unit mass for hydrogen burning, M_r is the mass within the radius r, and M is the mass of the WD including the envelope mass. The maximum value is lower for the shorter recurrence period. A shorter recurrence period corresponds to a higher mass-accretion rate, and ignition starts at a smaller envelope mass because of heating by a larger gravitational energy release rate. We define the hydrogen-rich envelope mass as the mass above X = 0.1, i.e.,

$$\begin{eqnarray}&&{M}_{\mathrm{env}}={\int }_{X\gt 0.1}{{dM}}_{r},\end{eqnarray} \tag{ 2 }$$

and the ignition mass, ${M}_{\mathrm{ig}}$, as the hydrogen-rich envelope mass at the maximum nuclear energy release rate, i.e., ${M}_{\mathrm{ig}}={M}_{\mathrm{env}}$ (at ${L}_{\mathrm{nuc}}={L}_{\mathrm{nuc}}^{\max }$), because the envelope mass is increasing owing to mass accretion even after hydrogen ignites. The ignition mass is $2.0\times {10}^{-7}\,{M}_{\odot }$ for ${P}_{\mathrm{rec}}=0.95$ yr and $1.6\times {10}^{-7}\,{M}_{\odot }$ for ${P}_{\mathrm{rec}}=0.47\,\mathrm{yr}$. For a smaller envelope mass, the pressure at the bottom of the envelope is lower and therefore the maximum temperature is also lower. As a result, the maximum value of ${L}_{\mathrm{nuc}}^{\max }$ is lower for a shorter recurrence period.

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Although a high nuclear luminosity ($\sim {10}^{6}\,{L}_{\odot }$) is produced, most of the energy is absorbed by the burning shell, as indicated by the large negative values of the gravitational energy release rate, ${L}_{{\rm{G}}}$, which is defined by

$$\begin{eqnarray}&&{L}_{{\rm{G}}}={\int }_{0}^{M}{\epsilon }_{g}{{dM}}_{r}={\int }_{0}^{M}-T{\left(\displaystyle \frac{\partial s}{\partial t}\right)}_{{M}_{r}}{{dM}}_{r},\end{eqnarray} \tag{ 3 }$$

where ${\epsilon }_{g}$ is the gravitational energy release rate per unit mass, T is the temperature, and s is the entropy per unit mass (see, e.g., Kato et al. 2014; Hachisu et al. 2016).

As a result, the photospheric luminosity ${L}_{\mathrm{ph}}$ ($\approx {L}_{\mathrm{nuc}}-| {L}_{{\rm{G}}}|$, because neutrino loss is negligible) is two orders of magnitude smaller than the peak value of ${L}_{\mathrm{nuc}}^{\max }$. Shortly after the ignition, the photospheric luminosity approaches a constant value. This constant value is close to but slightly smaller than the Eddington luminosity at the photosphere,

$$\begin{eqnarray}{L}_{\mathrm{Edd},\mathrm{ph}} & = & \displaystyle \frac{4\pi {{cGM}}_{\mathrm{WD}}}{{\kappa }_{\mathrm{ph}}}=2.0\times {10}^{38}\,\mathrm{erg}\,{{\rm{s}}}^{-1}\\ & & \times \left(\displaystyle \frac{{M}_{\mathrm{WD}}}{1.38\,{M}_{\odot }}\right)\left(\displaystyle \frac{0.35}{{\kappa }_{\mathrm{ph}}}\right),\end{eqnarray} \tag{ 4 }$$

where ${\kappa }_{\mathrm{ph}}$ is the opacity at the photosphere. In other words, the photospheric luminosity stays below the Eddington luminosity in this early phase of a shell flash.

Figure 3 shows the H-R diagram of the rising phase of recurrent nova outbursts for various WD masses and recurrence periods. X-ray flashes correspond to the phase approximately from point B to C (the same marks denote the same stage in Figure 1). A more massive WD reaches a higher photospheric luminosity and maximum photospheric temperature; therefore, we expect larger X-ray luminosity during the X-ray flash on a more massive WD.

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The track in the H-R diagram depends not only on the WD mass but also more weakly on the recurrence period. For a longer recurrence period, the ignition mass is larger and the envelope begins to expand at a lower luminosity. Thus, the track locates slightly lower and toward the right (redder) side compared to that of a shorter recurrence period.

Figure 4(a) shows the photospheric temperature and luminosity during the X-ray flashes for the 1.38 and 1.385 ${M}_{\odot }$ WD models in Table 1. The photospheric luminosity quickly rises near the ${L}_{\mathrm{nuc}}$ peak (t = 0) and reaches a constant value. The photospheric temperature reaches its maximum immediately after the time of ignition and decreases with time. When the envelope expands and the photospheric temperature decreases to a critical temperature, the optically thick wind occurs (this epoch corresponds to point C in Figure 1). This critical temperature is indicated by small filled circles in Figure 4(a). Shortly before this epoch, the temperature drops quickly, corresponding to the opacity increase near the photosphere, which will be discussed in Section 2.6.

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Figure 4(b) shows the X-ray luminosity in the supersoft X-ray band (0.3–1.0 keV). The duration ($\mathrm{log}{L}_{X}/{L}_{\odot }\,\gt$ 4) of the X-ray flash is 14–19 hr (0.59–0.78 days) for ∼1 yr recurrence period novae and 22–34 hr (0.9–1.4 days) for ∼0.5 yr period novae. For a shorter recurrence period, the ignition is weaker, as explained before, so the expansion is slower than in longer recurrence period novae. The shortest duration among these four models is 14 hr (0.59 days) for 1.385 ${M}_{\odot }$ with ${P}_{\mathrm{rec}}=0.97\,\mathrm{yr}$. As 1.385 ${M}_{\odot }$ is almost the upper limit of a mass-accreting WD with no rotation (Nomoto et al. 1984), a duration of 14 hr (0.59 days) would be the minimum for novae with recurrence periods shorter than 1 yr.

The ultrashort recurrence period nova M31N 2008-12a shows a supersoft X-ray source phase (SSS) of 10 days (Henze et al. 2014a, 2015b; Tang et al. 2014). In general, the SSS phase (from E to F in Figure 1) is shorter for a more massive WD. The duration of the SSS phase of M31N 2008-12a is consistent with a $\sim 1.38\,{M}_{\odot }$ WD (Henze et al. 2015b). Such an SSS phase duration allows us to exclude WDs much more massive than 1.385 ${M}_{\odot }$. Similarly, we can also exclude a $1.35\,{M}_{\odot }$ WD because its SSS duration would be too long. The duration of the X-ray flash in a $1.38\mbox{--}1.385\,{M}_{\odot }$ WD ($\gt 14$ hr) is long enough to be detectable with the 6 hr cadence of our Swift observations (see Section 3).

We have calculated shell flash models on a $1.35\,{M}_{\odot }$ WD with ${P}_{\mathrm{rec}}=1$ and 12 yr for comparison. The corresponding mass accretion rates are listed in Table 1. Figure 5(a) shows the evolution of the nuclear luminosity and photospheric temperature. The outburst in the ${P}_{\mathrm{rec}}=1\,\mathrm{yr}$ case (red lines) is much weaker than in the ${P}_{\mathrm{rec}}=12\,\mathrm{yr}$ scenario (black lines), as indicated by the lower nuclear energy generation rate ${L}_{\mathrm{nuc}}$. As a result, in the ${P}_{\mathrm{rec}}=1\,\mathrm{yr}$ case, the photosphere slowly expands; therefore, the photospheric temperature decreases slowly, which results in a much longer X-ray flash, as demonstrated in Figure 5(b).

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Table 1 lists the maximum value of the nuclear energy generation rate ${L}_{\mathrm{nuc}}^{\max }$ and the maximum temperature in the hydrogen nuclear burning region ${T}_{\mathrm{nuc}}^{\max }$. There are three models of similar recurrence period, ${P}_{\mathrm{rec}}\sim 1$ yr, for 1.35, 1.38, and 1.385 $\,{M}_{\odot }$. Both ${T}_{\mathrm{nuc}}^{\max }$ and ${L}_{\mathrm{nuc}}^{\max }$ are larger in more massive WDs. This means that the shell flash is stronger and hence evolves faster in a more massive WD with the same recurrence period because of the stronger gravity of the WD. On the other hand, for a given WD mass, both ${T}_{\mathrm{nuc}}^{\max }$ and ${L}_{\mathrm{nuc}}^{\max }$ are smaller for a shorter recurrence period. This tendency is clearly shown in the two $1.35\,{M}_{\odot }$ models, in which ${L}_{\mathrm{nuc}}^{\max }$ is 19 times larger in ${P}_{\mathrm{rec}}=12$ yr than in ${P}_{\mathrm{rec}}=1\,\mathrm{yr}$. The duration of the X-ray flash is 6.8 times longer for the shorter recurrence period.

To summarize, more massive WDs undergo stronger shell flashes, but their flashes become weaker for shorter recurrence periods. Thus, the duration of X-ray flash is shorter in more massive WDs but longer for shorter recurrence periods. Even in WDs as massive as 1.38 $\,{M}_{\odot }$, the X-ray flash could last ∼0.5 days.

The X-ray flash ends when the envelope expands and the optically thick winds start blowing. In this subsection, we examine the possibility that the optically thick winds are accelerated much earlier (i.e., before point C in Figure 1), which shortens the duration of the X-ray flash.

Before going into the details of the envelope structure, it would be instructive to discuss the opacity in the envelope, which is closely related to the envelope expansion and occurrence of wind mass loss. Figure 6 shows the run of the OPAL opacity (Iglesias et al. 1987; Iglesias & Rogers 1996) with solar composition in an optically thick wind solution with $\mathrm{log}{T}_{\mathrm{ph}}$ (K) = 4.0 on the $1.38\,{M}_{\odot }$ WD. This model has a very large envelope mass and a uniform chemical composition that does not exactly correspond to the structure of a very short recurrence period nova, but it is sufficient to show the characteristic properties of the OPAL opacity. In our evolution calculation, the chemical composition varies from place to place, and the photospheric temperature is much higher than in this case.

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The opacity has several peaks above the constant value of the electron scattering opacity $\mathrm{log}{\kappa }_{\mathrm{el}}=$ $\mathrm{log}[0.2(1+X)]=\mathrm{log}0.34=-0.47$ for X = 0.7. The peak at $\mathrm{log}T$ (K) = 4.5 corresponds to the second helium ionization. The prominent peak at $\mathrm{log}T$ (K) ∼ 5.2 is due mainly to low/mid-degree ionized iron found in opacity projects (Iglesias et al. 1987; Seaton et al. 1994). Hereafter, we call it the "Fe peak." The peak at $\mathrm{log}T$ (K) = 6.2 relates to highly ionized Fe, C, O, and Ne. We call it the "C/O peak." A tiny peak around $\mathrm{log}T$ (K) = 7.0 is due to the highly ionized heavy elements Ar–Fe. The opacity is smaller than that of electron scattering at the highest temperature region because of the Compton effect.

A large peak in the opacity causes the envelope expansion and accelerates the optically thick winds. In the model in Figure 6, the critical point of the optically thick winds (Kato & Hachisu 1994), in which the velocity becomes equal to the isothermal sound velocity, appears just on the inside of the Fe peak. A critical point appears in the region of acceleration, which means that the envelope is accelerated outward where the opacity quickly increases outward.

Figure 7 shows the internal structures at the end of the X-ray flash in our $1.38\,{M}_{\odot }$ WD model with ${P}_{\mathrm{rec}}=0.95\,\mathrm{yr}$. The solid line represents the structure at point C in Figures 1, 3, and 4, and the dotted line corresponds to the stages shortly after point C. From top to bottom we show the escape velocity $\sqrt{2{{GM}}_{\mathrm{WD}}/r}$, wind velocity V, temperature T, density ρ, radiative luminosity ${L}_{{\rm{r}}}$, which is the summation of diffusive luminosity and convective luminosity, and local Eddington luminosity defined by

$$\begin{eqnarray}&&{L}_{\mathrm{Edd}}=\displaystyle \frac{4\pi {{cGM}}_{\mathrm{WD}}}{\kappa },\end{eqnarray} \tag{ 5 }$$

where κ is the opacity. As the opacity depends on the local temperature and density, the local Eddington luminosity also varies. Note that Equation (4) represents the photospheric value of Equation (5). The velocity is not plotted for the solution at point C.

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The local Eddington luminosity in Figure 7 shows a small dip at $\mathrm{log}r$ (cm) ∼ 9.2 corresponding to the C/O peak at $\mathrm{log}T\,({\rm{K}})=6.2$ in Figure 6. Here, the local Eddington luminosity is slightly lower than the diffusive luminosity, i.e., locally the luminosity is super-Eddington. However, this C/O peak does not result in the occurrence of optically thick winds. Instead, the temperature and density profiles become shallower in this region.

When the envelope expands enough and the photospheric temperature approaches the prominent Fe peak, optically thick winds occur. The Fe peak is so large that the local Eddington luminosity decreases to much below the radiative luminosity. The critical point (Kato & Hachisu 1994) appears near the photosphere, which corresponds to the inner edge of the Fe peak in Figure 6.

If the winds were accelerated by the C/O peak, the X-ray flash durations would be much shorter because the expansion and acceleration occur much earlier. We have confirmed in all of our calculated models that the wind is driven by the Fe peak and not by the C/O peak. Thus, we conclude that the X-ray flash should last at least half a day, as in Table 1, and could not be much shorter than that.

The multiwavelength coverage of the 2013 and 2014 eruptions of M31N 2008-12a (Darnley et al. 2014, 2015b; Henze et al. 2014a, 2015b) resulted in significantly improved predictions of future eruptions. Moreover, Henze et al. (2015a) combined new findings with archival data to arrive at a $1\sigma$ prediction accuracy of ±1 month (and suggest a recurrence period of 175 ± 11 days). Based on the updated forecast, we designed an observational campaign to monitor the emerging 2015 eruption and catch the elusive X-ray flash.

The project was crucially reliant on the unparalleled scheduling flexibility of the Swift satellite (Gehrels et al. 2004), whose X-ray telescope (XRT; Burrows et al. 2005) provided a high-cadence monitoring. Similarly, the unprecedented short recurrence time and predictability of M31N 2008-12a made it the only target for which such an endeavor was feasible.

Starting from 2015 August 20 UT, a 0.6 ks Swift XRT observation was obtained every 6 hr. After the first week of the monitoring campaign, the exposure time per observation was increased from 0.6 to 1 ks, because the actual exposure time often fell short of the goal. The nova eruption was discovered on August 28 (Darnley et al. 2015a), slightly earlier than predicted by Henze et al. (2015a), without any prior detection of an X-ray flash. Because of this early eruption date and the last-minute improvement in prediction accuracy, based on the recovery of the 2010 eruption (Henze et al. 2015a), only 8 days' worth of observations were obtained before the 2015 eruption. All individual observations until after the optical discovery are listed in Table 2. The campaign continued until the end of the SSS phase, and the analysis of the phase is presented by Darnley et al. (2016).

All Swift XRT data were obtained in photon counting (PC) mode and were reduced using the standard Swift and Heasarc tools (HEASOFT version 6.16). Our analysis started from the cleaned level 2 files that had been reprocessed locally with HEASOFT version 6.15.1 at the Swift UK data center.

We extracted source and background counts in xselect v2.4c based on the XRT point-spread function (PSF) of M31N 2008-12a observed during previous eruptions. We applied the standard grade selection 0–12 for PC mode observations. Based on the early SSS phase detections, we chose a circular region with a radius of 22'', which corresponds to a 78% PSF area (based on the merged detections of the 2013/4 eruptions), to optimize the ratio of source to background counts in the source region. The background region excluded the locations of nearby faint X-ray sources as derived from the merged data of the 2013 and 2014 eruption monitoring campaigns (see Henze et al. 2014a, 2015b). All counts were restricted to the 0.3–1.0 keV band (refer to the X-ray spectrum of the eruption discussed in Darnley et al. 2016).

We checked for a source detection using classical Poisson statistics and determined $3\sigma$ count rate upper limits using the method of Kraft et al. (1991). The number of background counts was scaled to the source region size and corrected for the differences in exposure, derived from the XRT exposure map, between the regions for each individual observation. To improve the signal-to-noise ratio of the detection procedure, the data set was smoothed by a two-observation-wide boxcar function to achieve a rolling ∼12 hr window. The added source and background counts were analyzed in the same way as the individual measurements. Note that, therefore, successive upper limits are not statistically independent.

The monitoring campaign was executed exceptionally well, with a median cadence of 6.3 hr between two consecutive observations. At no point was there more than a 10 hr gap between successive pointings. Therefore, the minimum flash duration of 14 hr (0.59 days) would have been covered by at least one observation, more likely two, during the entire 8 days prior to the eruption.

In Figure 8 the resulting $3\sigma$ and $5\sigma$ XRT count rate upper limits are shown for the individual and merged observations, respectively. The $5\sigma$ upper limits are in the range of (2–4) $\times {10}^{-2}$ counts s⁻¹ for the individual observations, which roughly corresponds to the variability range of the SSS phase around maximum (Henze et al. 2015b). The combined $5\sigma$ upper limits for each two successive merged observations (i.e., a rolling ∼12 hr period) were almost entirely well below the expected flash count rate of 2 $\times {10}^{-2}$ counts s⁻¹. This prediction assumes a similar luminosity and spectrum for the X-ray flash and the SSS phase (see Figure 1 and compare Henze et al. 2015b; Kato et al. 2015).

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The time of eruption (T_E) is defined as the midpoint between the last nondetection by the Liverpool Telescope (MJD 57262.16) and the first Swift UVOT detection (MJD 57262.40; see Darnley et al. 2016, for both). Therefore, ${T}_{E}={\rm{MJD}}\,57262.28\pm 0.12$ (August 28.28 UT), with the error corresponding to half the interval between both observations. The rightmost data points in Figure 8 feature the start of the SSS phase to compare the signatures of an actual detection. Additionally, the number of counts in the source region always remained below 2 for individual observations, except for the emergence of the SSS emission.

The strict $5\sigma$ limits indicate that we should have seen the X-ray flash if it had occurred with the predicted luminosity and spectrum during the time of the monitoring. The restrictive $3\sigma$ limits can be used to constrain the X-ray flux in a meaningful way. The corresponding data are given in Tables 2 and 3.

Table 2.  Swift Observations for the 2015 X-Ray Flash Monitoring of Nova M31N 2008-12a

ObsID	Expa	Dateb	MJDb	${\rm{\Delta }}t$ c	$3\sigma$ ulim	$5\sigma$ ulim
	(ks)	(UT)	(days)	(days)	(${10}^{-2}$ counts s−1)	(${10}^{-2}$ counts s−1)
00032613063	0.66	2015 Aug 20.027	57254.0273	−8.253	$\lt 1.4$	$\lt 3.3$
00032613064	0.47	2015 Aug 20.281	57254.2812	−7.999	$\lt 1.3$	$\lt 3.3$
00032613065	0.70	2015 Aug 20.547	57254.5469	−7.733	$\lt 0.9$	$\lt 2.1$
00032613066	0.50	2015 Aug 20.820	57254.8203	−7.460	$\lt 1.2$	$\lt 2.9$
00032613067	0.40	2015 Aug 21.023	57255.0234	−7.257	$\lt 1.5$	$\lt 3.7$
00032613068	0.48	2015 Aug 21.281	57255.2812	−6.999	$\lt 1.3$	$\lt 3.2$
00032613069	0.53	2015 Aug 21.555	57255.5547	−6.725	$\lt 1.6$	$\lt 3.4$
00032613070	0.41	2015 Aug 21.812	57255.8125	−6.467	$\lt 1.6$	$\lt 3.9$
00032613071	0.55	2015 Aug 22.023	57256.0234	−6.257	$\lt 1.1$	$\lt 2.7$
00032613072	0.72	2015 Aug 22.344	57256.3438	−5.936	$\lt 0.8$	$\lt 2.0$
00032613073	0.54	2015 Aug 22.543	57256.5430	−5.737	$\lt 1.4$	$\lt 3.4$
00032613074	0.42	2015 Aug 22.812	57256.8125	−5.467	$\lt 1.4$	$\lt 3.5$
00032613075	0.54	2015 Aug 23.020	57257.0195	−5.260	$\lt 1.1$	$\lt 2.7$
00032613076	0.78	2015 Aug 23.344	57257.3438	−4.936	$\lt 1.0$	$\lt 2.3$
00032613077	0.45	2015 Aug 23.543	57257.5430	−4.737	$\lt 1.4$	$\lt 3.4$
00032613078	0.51	2015 Aug 23.809	57257.8086	−4.471	$\lt 1.5$	$\lt 3.6$
00032613079	0.32	2015 Aug 24.020	57258.0195	−4.260	$\lt 1.9$	$\lt 4.6$
00032613080	0.64	2015 Aug 24.340	57258.3398	−3.940	$\lt 1.2$	$\lt 2.8$
00032613081	0.60	2015 Aug 24.539	57258.5391	−3.741	$\lt 1.3$	$\lt 3.2$
00032613082	0.49	2015 Aug 24.805	57258.8047	−3.475	$\lt 1.3$	$\lt 3.2$
00032613083	0.57	2015 Aug 25.016	57259.0156	−3.264	$\lt 1.3$	$\lt 3.2$
00032613084	0.59	2015 Aug 25.340	57259.3398	−2.940	$\lt 1.6$	$\lt 3.4$
00032613085	0.46	2015 Aug 25.559	57259.5586	−2.721	$\lt 1.4$	$\lt 3.3$
00032613086	0.47	2015 Aug 25.887	57259.8867	−2.393	$\lt 1.3$	$\lt 3.1$
00032613087	0.58	2015 Aug 26.012	57260.0117	−2.268	$\lt 1.3$	$\lt 3.2$
00032613088	0.49	2015 Aug 26.406	57260.4062	−1.874	$\lt 1.3$	$\lt 3.1$
00032613089	0.53	2015 Aug 26.613	57260.6133	−1.667	$\lt 1.2$	$\lt 2.9$
00032613090	0.51	2015 Aug 26.801	57260.8008	−1.479	$\lt 1.7$	$\lt 4.1$
00032613091	0.85	2015 Aug 27.012	57261.0117	−1.268	$\lt 1.0$	$\lt 2.5$
00032613092	0.79	2015 Aug 27.406	57261.4062	−0.874	$\lt 1.5$	$\lt 3.2$
00032613093	0.67	2015 Aug 27.602	57261.6016	−0.678	$\lt 1.3$	$\lt 3.1$
00032613094	0.87	2015 Aug 27.801	57261.8008	−0.479	$\lt 1.0$	$\lt 2.4$
00032613095	0.56	2015 Aug 27.012	57261.0117	−1.268	$\lt 1.2$	$\lt 3.0$
00032613096	0.74	2015 Aug 28.008	57262.0078	−0.272	$\lt 1.2$	$\lt 2.9$
00032613097	0.80	2015 Aug 28.406	57262.4062	0.126	$\lt 1.1$	$\lt 2.7$
00032613098	0.67	2015 Aug 28.602	57262.6016	0.322	$\lt 1.2$	$\lt 3.0$
00032613099	0.87	2015 Aug 28.801	57262.8008	0.521	$\lt 1.2$	$\lt 2.5$
00032613100	0.87	2015 Aug 29.004	57263.0039	0.724	$\lt 1.0$	$\lt 2.4$

Notes.

^aDead-time corrected exposure time. ^bStart date of the observation. ^cTime in days after the optical eruption of nova M31N 2008-12a on 2015 August 28.28 UT (MJD 57262.28).

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Table 3.  Swift Observations for the Merged Data

ObsID	Exp	Datea	MJDa	${\rm{\Delta }}t$ a	$3\sigma$ ulim	$5\sigma$ ulim
	(ks)	(UT)	(days)	(days)	(${10}^{-2}$ counts s−1)	(${10}^{-2}$ counts s−1)
00032613063/064	1.13	2015 Aug 20.15	57254.1542	−8.126	$\lt 0.7$	$\lt 1.6$
00032613064/065	1.17	2015 Aug 20.41	57254.4140	−7.866	$\lt 0.5$	$\lt 1.3$
00032613065/066	1.20	2015 Aug 20.68	57254.6836	−7.596	$\lt 0.5$	$\lt 1.2$
00032613066/067	0.90	2015 Aug 20.92	57254.9218	−7.358	$\lt 0.7$	$\lt 1.6$
00032613067/068	0.88	2015 Aug 21.15	57255.1523	−7.128	$\lt 0.7$	$\lt 1.7$
00032613068/069	1.01	2015 Aug 21.42	57255.4180	−6.862	$\lt 0.8$	$\lt 1.8$
00032613069/070	0.94	2015 Aug 21.68	57255.6836	−6.596	$\lt 0.9$	$\lt 1.9$
00032613070/071	0.96	2015 Aug 21.92	57255.9180	−6.362	$\lt 0.7$	$\lt 1.6$
00032613071/072	1.27	2015 Aug 22.18	57256.1836	−6.096	$\lt 0.5$	$\lt 1.2$
00032613072/073	1.26	2015 Aug 22.44	57256.4434	−5.837	$\lt 0.5$	$\lt 1.3$
00032613073/074	0.96	2015 Aug 22.68	57256.6778	−5.602	$\lt 0.7$	$\lt 1.7$
00032613074/075	0.96	2015 Aug 22.92	57256.9160	−5.364	$\lt 0.6$	$\lt 1.5$
00032613075/076	1.32	2015 Aug 23.18	57257.1816	−5.098	$\lt 0.5$	$\lt 1.3$
00032613076/077	1.23	2015 Aug 23.44	57257.4434	−4.837	$\lt 0.6$	$\lt 1.4$
00032613077/078	0.96	2015 Aug 23.68	57257.6758	−4.604	$\lt 0.7$	$\lt 1.7$
00032613078/079	0.83	2015 Aug 23.91	57257.9140	−4.366	$\lt 0.8$	$\lt 2.0$
00032613079/080	0.96	2015 Aug 24.18	57258.1797	−4.100	$\lt 0.7$	$\lt 1.7$
00032613080/081	1.24	2015 Aug 24.44	57258.4395	−3.841	$\lt 0.6$	$\lt 1.5$
00032613081/082	1.09	2015 Aug 24.67	57258.6719	−3.608	$\lt 0.7$	$\lt 1.6$
00032613082/083	1.06	2015 Aug 24.91	57258.9101	−3.370	$\lt 0.7$	$\lt 1.6$
00032613083/084	1.16	2015 Aug 25.18	57259.1777	−3.102	$\lt 0.8$	$\lt 1.8$
00032613084/085	1.05	2015 Aug 25.45	57259.4492	−2.831	$\lt 0.8$	$\lt 1.8$
00032613085/086	0.93	2015 Aug 25.72	57259.7226	−2.557	$\lt 0.7$	$\lt 1.6$
00032613086/087	1.05	2015 Aug 25.95	57259.9492	−2.331	$\lt 0.6$	$\lt 1.6$
00032613087/088	1.07	2015 Aug 26.21	57260.2090	−2.071	$\lt 0.6$	$\lt 1.6$
00032613088/089	1.02	2015 Aug 26.51	57260.5097	−1.770	$\lt 0.6$	$\lt 1.5$
00032613089/090	1.04	2015 Aug 26.71	57260.7070	−1.573	$\lt 0.7$	$\lt 1.7$
00032613090/091	1.36	2015 Aug 26.91	57260.9062	−1.374	$\lt 0.6$	$\lt 1.5$
00032613091/092	1.64	2015 Aug 27.21	57261.2090	−1.071	$\lt 0.7$	$\lt 1.5$
00032613092/093	1.46	2015 Aug 27.50	57261.5039	−0.776	$\lt 0.8$	$\lt 1.7$
00032613093/094	1.54	2015 Aug 27.70	57261.7012	−0.579	$\lt 0.6$	$\lt 1.4$
00032613094/096	1.61	2015 Aug 27.90	57261.9043	−0.376	$\lt 0.5$	$\lt 1.3$
00032613096/097	1.54	2015 Aug 28.21	57262.2070	−0.073	$\lt 0.6$	$\lt 1.4$
00032613097/098	1.47	2015 Aug 28.50	57262.5039	0.224	$\lt 0.6$	$\lt 1.4$
00032613098/099	1.54	2015 Aug 28.70	57262.7012	0.421	$\lt 0.7$	$\lt 1.5$
00032613099/100	1.74	2015 Aug 28.90	57262.9024	0.622	$\lt 0.6$	$\lt 1.3$

Note.

^aMidpoint between the two observations.

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A WD in a binary is possibly surrounded by ionized/neutral material originating from the companion star. If the WD is surrounded by a substantial amount of neutral hydrogen, X-ray photons emitted from the WD surface could be mostly absorbed, and thus one may not detect the X-ray flash. It is, however, poorly known whether the mass-accreting WDs in recurrent novae are surrounded by ionized or neutral matter in their early outburst phase.

The companion of M31N 2008-12a has not yet been identified. If the companion star is a Roche-lobe-filling subgiant, we can expect that the mass transfer is mainly through the accretion disk and a small proportion of the mass lost by the donor is spread over the circumbinary region. If the companion is a red giant, the binary could be embedded within the cool neutral wind, which absorbs supersoft X-ray photons from the WD.

Darnley et al. (2014) compared the spectral energy distribution (SED) of M31N 2008-12a in its quiescent phase with those of the Galactic recurrent novae, RS Oph, T CrB, and U Sco. Based on the similarity of the RS Oph SED, rather than U Sco, which is much fainter, the authors suggested that M31N 2008-12a likely contains a red giant companion with a significant accretion disk component that dominates the near-UV and optical flux. The authors note, however, that the possibility of a face-on subgiant companion remains because U Sco is an eclipsing binary and its edge-on disk may not be bright.

Hachisu & Kato (2016b) classified 40 classical novae into six classes according to their evolutionary path in the color–magnitude diagram and found that the different paths correspond to differences in the nova speed class and thus the envelope mass. These authors also displayed the color–magnitude evolution during the 2014 outburst of M31N 2008-12a and found that its characteristic properties are similar to those of U Sco and CI Aql, which are both recurrent novae with a subgiant companion, but different from RS Oph, which has a red giant companion (see their Figures 72(c), 72(d), and 76(b)). This suggests that M31N 2008-12a has a subgiant companion.

The Galactic object RS Oph is a well-observed recurrent nova. Its recorded outbursts were in 1898, 1933, 1958, 1967, 1985, and 2006 (Evans et al. 2008). In the 1985 outburst very soft X-ray emission was detected 251 days after the optical maximum (Mason et al. 1987). Hachisu & Kato (2001) regarded this X-ray emission to be due to the accretion luminosity and suggested that the accretion rate had dropped by a factor of six after the outburst. Dobrzycka & Kenyon (1994) also pointed out a decrease in the mass accretion rate from line fluxes in H i and He i that decreased by a factor of four after the 1985 outburst. Day 251 falls in the period of the postoutburst minimum of days ∼100–400, after which the visual luminosity increased by about a magnitude (Evans et al. 1988). X-rays were also observed in 1992 with ROSAT (Orio 1993), but the supersoft flux ($\lt 0.5$ keV) was very weak. One possible explanation is absorption by the massive cool wind (e.g., Shore et al. 1996) from the red giant companion, as suggested by Anupama & Mikolajewska (1999). After 21 yr of accumulation, the overlying RG wind reaches $(2\mbox{--}5)\times {10}^{22}$ cm⁻² (Bode et al. 2006; Sokoloski et al. 2006) in the 2006 outburst. However, the absorption effect of this overlying RG wind is quickly removed (Osborne et al. 2011). After the outburst, the mass-accretion rate had dropped in the postoutburst minimum phase and soft X-rays were observable because the ejecta swept away the red giant cool wind. After day 400, the mass transfer had recovered and the hot component could be surrounded by neutral hydrogen.

If the accretion disk is completely blown off by the ejecta, it may take a few orbital periods until a significant amount of the red giant wind falls onto the WD. Hachisu & Kato (2001) roughly estimated the resumption time of mass transfer in RS Oph to be ${\rm{\Delta }}t=a/v\sim 300{R}_{\odot }/10{\text{km s}}^{-1}=300$ days, where a is the binary separation and v is the velocity of infalling matter. This is roughly consistent with the recovery of the quiescent V luminosity 400 days after the 1985 outburst (see Figure 1 in Evans et al. 1988; Figure 2 in Hachisu & Kato 2006; Worters et al. 2007; also Darnley et al. 2008). M31N 2008-12a shows an ultrashort recurrence period of 1 or 0.5 yr. It is unlikely that systems like RS Oph produce successive outbursts with such a short recurrence period because of a long interruption of mass transfer unless the disk survives the eruption. Thus, we expect that M31N 2008-12a does not have a red giant companion.

U Sco is another well-observed Galactic recurrent nova with a subgiant companion. Ness et al. (2012) examined an X-ray eclipse during the 2010 outburst in detail and concluded that the mass accretion resumed as early as day 22.9, midway during the SSS phase. In a binary with a subgiant companion, thus, we can expect the mass accretion to resume just after an outburst.

For these reasons, we may conclude that M31N 2008-12a has a subgiant companion. In the case of close binaries, the transferred matter is mostly distributed in the orbital plane (see, e.g., Sytov et al. 2009, for a 3D calculation of mass flow in a close binary). Note that, in our binary models, the WD radiates ${L}_{\mathrm{ph}}=200$–$500\,{L}_{\odot }$ at ${T}_{\mathrm{ph}}=(4\mbox{--}5)$ $\,\times \,{10}^{5}$ K in its quiescent phase. Therefore, we expect that the matter surrounding the WD may be kept ionized during the quiescent phase. Thus, we consider that an X-ray flash should have been detected if it had occurred during our observing period.

The other explanation of the undetected X-ray flash is that the flash had already occurred and finished when we started our observations 8 days before the UV/optical discovery. This means that the evolution time from C to D in Figure 1 was longer than 8 days, and the optical/UV bright phase, from D to E, lasted about 5.5 days (Darnley et al. 2015b; Henze et al. 2015b). Darnley et al. (2015b) pointed out that M31N 2008-12a showed slow rise to the optical peak magnitude in the 2014 outburst. This suggests a slow evolution toward point D.

The timescale from C to E can be roughly estimated as follows. The decrease of the envelope mass from C to E is due to both nuclear burning and mass ejection. For example, in a $1.38\,{M}_{\odot }$ WD with ${P}_{\mathrm{rec}}=0.47\,\mathrm{yr}$, the envelope mass is $1.5\times {10}^{-7}\,{M}_{\odot }$ at C and decreases to $7.5\times {10}^{-8}\,{M}_{\odot }$ at E. In the 2014 outburst, the ejected hydrogen mass was estimated to be ${M}_{\mathrm{ej},{\rm{H}}}=(2.6\pm 0.4)\times {10}^{-8}\,{M}_{\odot }$ (Henze et al. 2015b), which corresponds to ${M}_{\mathrm{ej}}=4.7\times {10}^{-8}\,{M}_{\odot }$ for X = 0.55 (the hydrogen mass fraction is smaller than the initial X = 0.7 because of convective mixing with the nuclear burning region).

Darnley et al. (2015b) derived a total ejected mass of $\gtrsim 3\times {10}^{-8}{M}_{\odot }$. Here we assume the mass ejected by the wind to be ${M}_{\mathrm{ej}}=4.7\times {10}^{-8}\,{M}_{\odot }$. Thus, nuclear burning had consumed the rest of the mass, ${\rm{\Delta }}{M}_{\mathrm{env}}=1.5\times {10}^{-7}\,{M}_{\odot }$ $-7.5\times {10}^{-8}\,{M}_{\odot }-4.7\times$ ${10}^{-8}\,{M}_{\odot }=3.1\times {10}^{-8}\,{M}_{\odot }$ during the period from C to E. If we take the mean nuclear luminosity as $\mathrm{log}{L}_{\mathrm{nuc}}/{L}_{\odot }=$ 4.65, the evolution time from C to E is roughly estimated as $({\rm{\Delta }}{M}_{\mathrm{env}}\times X\times {\epsilon }_{{\rm{H}}})/{L}_{\mathrm{nuc}}=14.8$ days, where X = 0.55 and energy generation of hydrogen burning ${\epsilon }_{{\rm{H}}}=6.4\times {10}^{18}$ erg g⁻¹. So we obtain the duration between epochs C and D in Figure 1 to be $14.8-5.5=9.3$ days. For a longer recurrence period, ${P}_{\mathrm{rec}}=0.95\,\mathrm{yr}$, we obtain, in the same way, ($1.9\times {10}^{-7}\,{M}_{\odot }-7.3\times$ ${10}^{-8}\,{M}_{\odot }-4.7\times {10}^{-8}\,{M}_{\odot })$ $X{\epsilon }_{{\rm{H}}}/{L}_{\mathrm{nuc}}-5.5=21-5.5=15.5$ days. Here we assume X = 0.53 and the mean nuclear luminosity to be $\mathrm{log}{L}_{\mathrm{nuc}}/$ ${L}_{\odot }=4.85$ for a somewhat stronger shell flash than in the shorter recurrence period (see Figure 2).

In this way we may explain that the X-ray flash had occurred 15.5 days (${P}_{\mathrm{rec}}=0.95$ yr) or 9.3 days (${P}_{\mathrm{rec}}=0.47$ yr) before the optical/UV peak. These values should be considered as rough estimates because they are sensitive to our simplified value for the mean ${L}_{\mathrm{nuc}}$, besides other parameters such as the WD mass and recurrence period (i.e., mass accretion rate), even though these estimates suggest that the nova evolution is slow between C and D, and the X-ray flash could have occurred before our observing period (8 days before the optical/UV detection), rather than immediately before the optical maximum (Kato et al. 2015).

Observations of recurrent novae have shown that they evolve much faster than typical classical novae, which is demonstrated by their very short X-ray turn-on time (duration between the optical peak and the X-ray turn-on; see, e.g., Page et al. 2015, for the shortest 4-day case of V745 Sco). By analogy, and without observational support, we suspect that the rising phase of recurrent novae must also be fast. However, our 8 days of nondetection prior to the optical/UV peak suggest that it may not be as fast as predicted. It is partly suggested by our calculation that ${L}_{\mathrm{nuc}}^{\max }$ is rather small in very short recurrence period novae even though the WD is extremely massive. The small nuclear burning energy generation rate renders the recurrent nova eruption relatively weak. Because time-dependent calculations have many difficulties in the expanding phase of nova outbursts, no one has ever succeeded in reproducing reliable multiwavelength light curves that included the rising phase. We expect that the detection of X-ray flashes can confirm such a slow evolution in the very early phase of a nova outburst.

Many numerical calculations of shell flashes have been presented, but only a few of them provided sufficient information on the early stages corresponding to the X-ray flash. Nariai et al. (1980) calculated hydrogen shell flashes, in which the evolution time from ${L}_{\mathrm{nuc}}^{\max }$ (defined as t = 0) to a stage of $\mathrm{log}{T}_{\mathrm{ph}}$ (K) ∼ 5.45 is 1.5 hr for a 1.3 ${M}_{\odot }$ WD with ${\dot{M}}_{\mathrm{acc}}=1\times {10}^{-10}{M}_{\odot }$ yr⁻¹. Iben (1982) showed the timescale from t = 0 to $\mathrm{log}{T}_{\mathrm{ph}}$ (K) $=5.5$ to be about 100 days for a 0.964 ${M}_{\odot }$ WD with ${\dot{M}}_{\mathrm{acc}}=1.5\times {10}^{-8}{M}_{\odot }$ yr⁻¹ (in his Figure 8). For a 1.01 ${M}_{\odot }$ WD, it is about 20 days with ${\dot{M}}_{\mathrm{acc}}=1.5\times {10}^{-8}{M}_{\odot }$ yr⁻¹ and about 1 day for ${\dot{M}}_{\mathrm{acc}}=1.5\times {10}^{-9}{M}_{\odot }$ yr⁻¹ (in his Figures 15 and 21). These studies are based on the Los Alamos opacities that have no Fe peak, so the optically thick wind does not occur, resulting in a much longer total duration of the nova outburst. However, the timescales in the very early phase corresponding to the X-ray flash (defined by $\mathrm{log}{T}_{\mathrm{ph}}$ (K) $\gt \,5.6$) should not be much affected by the Fe peak because the photospheric temperature is higher than the Fe peak. We see a tendency of a longer X-ray flash for a less massive WD and for a larger mass accretion rate (i.e., a shorter recurrence period). This tendency agrees with our results.

Hillman et al. (2014) showed evolutionary change in the effective temperature of nova outbursts with the OPAL opacities. Their Figure 3 shows an X-ray flash duration (defined by $\mathrm{log}{T}_{\mathrm{eff}}$ (K) $\gt \,5.5$) of a few hours for a 1.4 ${M}_{\odot }$ WD with a mass accretion rate of ${10}^{-8}{M}_{\odot }$ yr⁻¹. This accretion rate corresponds to the recurrence period of 20 yr (Prialnik & Kovetz 1995). Considering the tendency that a longer-duration X-ray flash is obtained for a less massive WD and larger mass-accretion rate, their duration of a few hours is consistent with our results of 0.5–1 day (Table 1).

The masses of our WD models are very close to the Chandrasekhar mass limit, above which nonrotating WDs cannot exist. This limit is $1.457\,{({\mu }_{{\rm{e}}}/2)}^{-2}\,{M}_{\odot }$ for pure degenerate gas (e.g., Equation (6.10.26) in Shapiro & Teukolsky 1983), where ${\mu }_{{\rm{e}}}$ is the mean molecular weight of the electron. According to Shapiro & Teukolsky (1983), Kaplan (1949) first pointed out that general relativity probably induces a dynamical instability when the radius of a WD becomes smaller than $1.1\times {10}^{3}$ km. Chandrasekhar & Tooper (1964) independently showed that a WD of mass $\gt 1.4176\,{M}_{\odot }$ is dynamically unstable when its radius decreases below $1.0267\times {10}^{3}$ km. This means that the instability occurs at radii much larger than the Schwarzschild radius ${R}_{{\rm{S}}}=2{GM}/{c}^{2}$. In our model, the 1.38 ${M}_{\odot }$ WD has a radius of ∼2000 km, much larger than the Schwarzschild radius $2G(1.38{M}_{\odot })/{c}^{2}=4.1$ km, and the above stability limits of general relativity, ${R}_{\mathrm{GR}}\sim 1000$ km.

Assuming the polytropic relation $P\propto {\rho }^{{\rm{\Gamma }}}$, Shapiro & Teukolsky (1983) derived a different stability criterion (see their Equation (6.10.30)), i.e.,

$$\begin{eqnarray}&&{\rm{\Gamma }}-\displaystyle \frac{4}{3}=1.125\left(\displaystyle \frac{2{GM}}{{{Rc}}^{2}}\right).\end{eqnarray} \tag{ 6 }$$

In our 1.38 ${M}_{\odot }$ model with ${\dot{M}}_{\mathrm{acc}}=1.6\times {10}^{-7}\,{M}_{\odot }$ yr⁻¹ (${P}_{\mathrm{rec}}=0.95$ yr), the right-hand side of Equation (6) becomes maximum at point A in Figure 1, that is, $1.125\times 0.00215=0.00242$. Thus, the stability criterion becomes ${\rm{\Gamma }}\gt 1.3358$. For the 1.385 ${M}_{\odot }$ model with $1.4\times {10}^{-7}\,{M}_{\odot }$ yr⁻¹ (${P}_{\mathrm{rec}}=0.97$ yr), this criterion is ${\rm{\Gamma }}\gt 1.3359$, essentially the same as for the 1.38 ${M}_{\odot }$ model. We calculated the distribution of Γ in the accreting phase as shown in Figure 9. The black line depicts ${\rm{\Gamma }}=d\mathrm{log}P/d\mathrm{log}\rho$ of the 1.38 ${M}_{\odot }$ model, while the red line represents the 1.385 ${M}_{\odot }$ model. Both the red and black lines are located above the horizontal dashed line of ${\rm{\Gamma }}=1.336$. Therefore, both models satisfy the stability condition (${\rm{\Gamma }}\gt 1.336$). Note that the central part hardly changes during the flash. Thus, we conclude that our 1.38 and 1.385 ${M}_{\odot }$ WD models are stable against the general relativistic instability.

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MAXI J0158-744 is an X-ray transient, believed to be a Be star plus WD binary that appeared in the Small Magellanic Cloud (Li et al. 2012; Morii et al. 2013). MAXI detected a brief (<90 minutes) X-ray flux (<5 keV) of very high luminosity (several $\times {10}^{39}\mbox{--}{10}^{40}$ erg s⁻¹). Follow-up Swift observations detected soft X-ray emission (∼100 eV) that lasted 2 weeks (Li et al. 2012), resembling an SSS phase on a massive WD. Li et al. (2012) attributed the origin of the early brief X-ray flux to the interaction of the ejected nova shell with the Be star wind. Morii et al. (2013) concluded that the X-ray emission is unlikely to have a shock origin, but they associated it with the fireball stage of a nova outburst on an extremely massive WD.

In this paper we have considered the very early phase of shell flashes in the extreme limit of massive WDs and high mass-accretion rates. Our calculations have shown that, in this limit, the evolution is very slow (X-ray flash lasts ∼1 day) and the X-ray luminosity does not exceed the Eddington luminosity ($\sim 2\times {10}^{38}$ erg s⁻¹). The wind mass loss does not occur during the X-ray flash, and the energy range of the X-ray photons is up to 100–120 eV. These properties are incompatible with the bright (super-Eddington), high-energy ($\lt 5$ keV), very short duration (<90 minutes) X-ray emission seen early on in MAXI J0158-744. Therefore, we conclude that the brief early X-ray flux in MAXI J0158-744 is not associated with that expected in the extreme limit of massive nonrotating WDs with high mass-accretion rates.