Chandra observations of nova KT Eridani in outburst

Novae in outburst are natural laboratories of extreme physical phenomena. They increase in optical luminosity from 8 to 17 magnitudes within hours, reach Eddington luminosity for a 1 M_⊙ star ($\simeq$10³⁸ erg s^-1), and emit copious flux at all wavelengths, from radio to gamma rays. A recent observational review is the one by Poggiani (2018), while theoretical reviews can be found in Starrfield et al. (2012b); Starrfield et al. (2016) and Prialnik & Kovetz (2005). Nova eruptions are due to thermonuclear burning of hydrogen via the CNO cycle, at the bottom of a shell accreted by a white dwarf (WD) from a close binary companion. The outburst is repeated after periods ranging from a few years to hundreds of thousands years. Because the burning occurs in electron degenerate matter, it becomes explosive, inflating and possibly immediately ejecting part of the envelope. Since the initial suggestion of Bath & Shaviv (1976), it has been assumed that the bulk of the remaining envelope mass is then stripped by a radiation-pressure-driven wind, although a wind may also be triggered by Roche Lobe overflow (e.g., Wolf et al., 2013).

The evolutionary track of the post-nova is driven by a shift in the wavelength of the maximum energy toward shorter wavelengths, at a constant bolometric luminosity close to 10³⁸ erg s^-1 (e.g., Starrfield et al., 2012b; Wolf et al., 2013). Thus in X-rays, novae become some of the most luminous X-ray sources. The supersoft X-ray source (SSS) appears during post-maximum optical decline and lasts in different novae from one week to $\approx$ 10 years as the WD photosphere shrinks back to pre-outburst radius, while thermonuclear burning still occurs near the surface. The WD reaches effective temperature T${}_{\rm eff}>$250,000 K, so the energy peak is in the supersoft X-ray range. The SSS is indeed observed as predicted by the models (e.g., Orio, 2012). The SSS wavelength range is easily absorbed and if the column density exceeds 10²² cm^-2, the WD may never be detected. In most cases, however, the filling factor of the ejecta is sufficiently low that the WD becomes a luminous X-ray source, observable with X-ray gratings as far as the Magellanic Clouds. By fitting atmospheric models abundances, effective temperature, white dwarf composition and mass can be derived. Novae in the SSS phase also exhibit time variability, both periodic and aperiodic (e.g., Ness et al. 2015 for the first, Orio et al. 2018 for the latter).

Nova outflows also emit X-rays, usually with a thermal spectrum, but they rarely are luminous enough to obtain a grating spectrum with good S/N ratio. However, the emission lines of the ejecta may be superimposed on the spectrum of the central source, complicating the spectral fitting. In the nova we examine in this article, KT Eri, the central source appeared to be dominant and have a relatively “clean” spectrum without a very large contribution of the ejecta.

Classical nova KT Eridani was discovered by Itagaki (2009) at V=8.1 on November 25.536 UT (MJD 55160.536), 2009. In a pre-discovery study Hounsell et al. (2010) found that the maximum was on 2009 November 14.67 at unfiltered Solar Mass Ejection Imager (SMEI) magnitude 5.42$\pm$0.02 and V=5.4 (Ootsuki et al., 2009), after a pre-maximum halt for a few hours at 6th SMEI magnitude, with a pre-outburst rise of by 3 magnitudes in 1.6 days. The outburst amplitude was 9 mag and the estimated time for a decay by 2 magnitudes was t₂=6.6 days (Hounsell et al., 2010), indicating that KT Eri was a fast nova. KT Eri was spectroscopically classified as a “He/N nova”, implying characteristics that are not the most frequent in novae (Rudy et al., 2009), and are more often detected in recurrent novae. The ejecta velocity reached a maximum of 3400 km s^-1 in H$\alpha$ (Maehara & Fujii, 2009), and at later phases 2800$\pm$200 km s^-1 (Ribeiro et al., 2011). The distance is $3.69_{-0.42}^{+0.53}$ kpc, obtained thanks to the Gaia parallax¹¹1from the GAIA database using ARI’s Gaia Services at http://gaia.ari.uni-heidelberg.de/tap.html..

Ribeiro et al. (2013) modeled the evolution of the H$\alpha$ profile, finding that the nova ejecta had the shape of a dumbbell structure with a ratio between the major to minor axis of 4:1, and an inclination angle of 58${}^{\circ+6}_{-7}$. From infrared observations, Raj et al. (2013) estimated an upper limit for the mass of the ejecta in the range 2.4–7.4 $\times 10^{-5}$ M$\odot$, but this range should be decreased by a factor of $\simeq$3 to account for the fact that the authors assumed a larger distance than the GAIA limits imply. Drake et al. (2009) detected a variable progenitor and Jurdana-Šepić et al. (2012) found that at quiescence the variability had a 1 mag amplitude, with two distinct periods of 376 and 737 days. These authors also noted the similarity of the KT Eri outburst with those of known recurrent novae, but could not find any previous outburst in the Harvard plates and suggested that the outbursts may recur on timescales of few centuries. They also found evidence that the progenitor is very likely to be an evolved star, ascending towards the red giant branch.

KT Eri was first detected as an X-ray source in outburst with the Swift XRT on day 39.8 after optical maximum, as a relatively hard source (Bode et al., 2010). It was still hard on day 47.5, but by day 55.4 a luminous SSS emerged. On day 65.6 the SSS was softened dramatically. Bode et al. (2010) noted that the time-scale for the SSS turn-on was very similar in the recurrent nova LMC 2009a. The timing analysis of the Swift XRT data from day 66.60 to 79.25 revealed a 35 s modulation (Beardmore et al., 2010), that was later confirmed by Ness et al. (2014, 2015) with Chandra. Ness et al. (2015) showed that this modulation was detected only during the early SSS phase, and then again much later, on day 159. With the Chandra LETG, the nova X-ray spectrum had several similarities with that of N SMC 2016 (Orio et al., 2018), with the luminous continuum and deep absorption lines of many novae X-ray spectra (Ness et al., 2010).

KT Eri was observed by the HRC-S and the LETG of Chandra four times in 2010. The details of the observations are shown in Table 1. The principal investigator of the first observation was Jan-Uwe Ness (Ness et al., 2010), and Jeremy Drake was the principal investigator of the three following ones. The net exposure time for the first observation was about 15 ks, while the other three observations were shorter: the nominal exposures were to be of 5 ks, but some events could not be telemetered and the dead time corrected exposures were only of about 3 ks.

The Chandra X-ray data analysis software CIAO v4.11 and calibration package CALDB 4.8.5 were used for the data reduction. The background subtracted light curves measured with the Chandra HRC-S camera (0 order) were extracted from event files with “DMEXTRACT”. The script “chandra_-repro” was used to extracted the Chandra HRC-S+LETG high resolution spectra, and the script “combine_-grating_-spectra” was used to combine the first order grating redistribution matrix files (rmf), ancillary response files (arf) and the grating spectra.

The background subtracted zero order light curves measured with the HRC-S camera, binned every 20 s for visual purposes, are shown in Fig. 1. The nova was also monitored with Swift and in Fig. 2 we show the Swift X-Ray Telescope (XRT) light curve and the AAVSO optical light curve in the visual and V band. The Swift XRT exposures were typically about 1000 s long.

The count rates vary significantly during all the four Chandra observations on relatively short time scales, and the average count rate also varied in the different exposures.

On day 71.3, the count rate varied by a factor of 7.8 during the exposure. On day 79.3 the variation was by a factor of 1.6, on day 84.6 by a factor of 3.9, on day 158.8 by a factor of 1.4.

In Fig. 4 we show the summed +1 and -1 order LETG spectra of the four observations, and we indicate a number of clearly detected absorption and emission lines; these are the strongest ones.

Fig. 5 illustrates the spectral evolution during the two exposures with large flux variations, which also presented spectral variations with the flux, namely day 71.3 (top row) and day 84.6 (bottom row). The respective plots on the left are the observed spectra, and on the right we show the time maps normalized to a blackbody curve that approximately fits the continuum. We first found the best fit blackbody curve for each observation, shown in the top left panel of the original time map with the dashed blue line, and following the blackbody we adjusted the normalization for the respective spectra. In the central panel for day 71.3 the N vi line at 28.79 Å grows after $\sim 0.5$ hours, while the zero-order light curve indicates this happened during an episode of still rather low count rate, before a rise. In the blackbody-normalized time map, this emission line appears more constant, indicating that it has grown together with the underlying continuum. However, $\sim 2.8$ hours after the beginning of the exposure, this line has shrunk considerably more than the continuum. We also note that at the same time, the continuum shortward of $\sim 26$ Å (possibly related to the C vi ionization edge at 25.3 Å) has decreased notably while some emission lines at long wavelengths (e.g., 31.8 Å, 32.8 Å, 41 Å, possibly S xiii and C v) have increased in strength. Thus, the emission lines above the continuum have thus not evolved in correlation or anti-correlation with the strength of the continuum.

Similarly, on day 84.6, the evolution of emission lines is not aligned with that of the continuum. During the brightest part of the light curve, $\sim 1$ hour after the beginning of the exposure (grey-shaded area in the bottom right panel), the N vi line at 28.78 Å has become slightly weaker relative to the continuum (thus has not increased in flux as much as the continuum) while shortward of $\sim$ 23 Å (possibly related to O i ionization edge in the cool gas), a few emission features have grown substantially. Possibly, the higher count rate was caused by a temporary reduction of the neutral oxygen column density. The surrounding cool material may be inhomogeneous, or it may have been temporarily ionized which would make it more transparent to high-energy radiation.

We found absorption lines due to transitions of nitrogen, carbon, calcium and argon in all four spectra. The method described by Ness (2010); Ness et al. (2011) was used to determine the line shifts, widths, and optical depths at the line center of the absorption lines for the spectra for the four exposures. Following Ness et al. (2011), we did not include the absorption correction, because it is not important in determining velocity and optical depth. The narrow spectral region around each line is fitted with a function

.

Following Ness et al. (2011), the optical depth $\tau(\lambda)$ is defined as the Equation (2) in Ness (2010), and $\lambda_{\rm c}$ and $\sigma$ in this equation are the central wavelength and the Gaussian line width which is always larger than the instrumental broadening, respectively. We assumed $C(\lambda)$ is a linear function for each line in modelling the continuum. We did compare the result with a continuum modelled with an absorbed black-body model and an absorbed TMAP model, and found that the model chosen for the continuum in the small wavelength range subtended by each line does not change the results. The Gaussian width of each line in velocity space was computed as $v_{\rm width}=\sqrt{({\rm c}\sigma/\lambda_{0})^{2}-v_{\rm instr}^{2}}$, where c is the speed of light, $\lambda_{0}$ is the central wavelength, and $v_{\rm instr}$ is the instrumental line broadening. This varies with the wavelength, as the LETG resolution is $\sim$ 0.05 Å. The resulting parameters for the blue shift velocity, broadening and optical depth at which each line is formed are shown in Table 3. If our line identification is right, there is a large spread of blue-shift velocities, from 370 to 3100 km s^-1. While in some other novae, such as V2491 Cyg, RS Oph (Ness, 2010) and SMC 2016 (Orio et al., 2018), the blue-shift velocity of the absorption lines has a narrow variation range, there are at least three velocity systems in the spectra of V4743 Sgr (Ness et al., 2011).

The broadening of the lines also varies, and is larger than the instrumental width and broadening (expected to be less than $\simeq$ 300 km s^-1), so like in V2491 Cyg (Ness et al., 2011) the lines may have been produced in a region of plasma with a significant extension, allowing us to view a range of expansion velocities and thus a range of different plasma layers.

The absorption lines of N VII ($\lambda_{0}=24.779$ Å) and N VI ($\lambda_{0}=24.898$ Å) are blended, generating a flat bottom in the spectrum of day 84.6. Moreover, the N VI ($\lambda_{0}=24.898$ Å) has the largest optical depth it is saturated in all spectra. We derived wavelength, line shifts, widths, and optical depths by assuming an overlap of the lines, as shown in Fig. 6, and propose the possible fit for the spectra of days 79.3 and 158.8, but in the third observation the lines are detected, yet we were not able to obtain a fit. Even if the fit is acceptable, this blending introduces a large uncertainty.

We also identified emission lines of nitrogen, carbon and sulfur in all four spectra. As shown in Table 4, these emission lines are red-shifted with velocities in a large range, 1700-3200 km s^-1. We used a Gaussian model (AGAUSS in XSPEC) to fit the profiles of the emission lines to determine the measured wavelength, line width and line shifts, modeling the underlying continuum with TMAP as shown in the next Section (even in this case, however, the choice of continuum is not critical). The AGAUSS model in XSPEC computes the line profile as follows:

where $\lambda_{l}$ and $\sigma$ are the line central wavelength in Angstrom and the instrumental broadening corrected line width in Angstrom, respectively. The resulting parameters are shown in Table 4. Table 5 also shows the difference in flux for the “high” and “low” periods defined for Fig. 9 for day 71.3. The emission lines that are strong enough to be identified are in the wavelength band $\sim$ 24 $-$ 37 Å. The emission line N VII ($\lambda_{0}=24.779$ Å) merge in the continuum emission and is too weak to be identified in spectrum of day 71.3 which has the lowest count rate, but it can be identified in the spectra of the rest three observations. It is weak on day 84.6 when the count rate is low, and it is strong on days 79.3 and 158.8 when the count rates are high. The flux of emission line N VI r ($\lambda_{0}=28.787$ Å) on day 84.6 is higher than day 158.8 when the count rate is the highest. Therefore, the fluxes of the emission lines do not change monotonically with the count rate of the spectra.

Ness et al. (2013a) suggest that the emission lines in V2491 Cyg originated from the reprocessed emission far from the WD, in the clumpy ejecta of the nova wind. We also attribute them to the ejecta in KT Eri.

The X-ray luminosity of KT Eri and its variation is consistent with the possibility that we observed only a fraction of the WD surface, with visibility varying within hours. This seems to be a common phenomenon in many novae, and was observed, for instance, also in N LMC 2009 (Orio et al., 2021) and N SMC 2016 (Orio et al., 2018). Detailed calculations show that the thermonuclear runaway always expands all over the surface and is nearly spherically symmetric (Glasner et al., 1997), so the supersoft flux is also expected to be homogeneous in the WD surface, at least until the time magnetically driven accretion onto the WD is resumed on strongly magnetized WDs (see Aydi et al., 2018; Zemko et al., 2018). The likely explanation we propose for KT Eri is that there were dense clumps in the ejecta, which were optically thick to the X-rays. Although it may seem more likely to produce a clumpy outflow in the initial explosive emission, the SSS variation in KT Eri was observed so long after the outburst maximum that initial clumps must have been ejected far away from the WD, and be located where the WD would appear as a point source, so partial obscuration by these initial ejecta would be unlikely. We suggest that the optically thick radiation driven wind that is supposed to last for months (initially suggested by Bath & Shaviv, 1976, and always included in the nova models) is not a continuous and smooth phenomenon. Even if this variable wind has never been modeled, many data can be explained with distinct ejection episodes at different wind velocity, including observations of novae T Pyx (Chomiuk et al., 2014) and V906 Car (Sokolovsky et al., 2020). Distinct outflows may be a common occurrence also according to Aydi et al. (2020). Instabilities are likely to occur in such a “stunted” outflow, and may cause sufficiently small scale clumpiness to obscure only a portion of the WD, so that the filling factor of the ejecta along the line of sight varied within hours.

The X-ray grating spectra allow to draw some conclusions regarding the WD mass. van Rossum (2012) shows that the effect of an ongoing outflow is to lower the atmospheric temperature, and somewhat bloat the radius, reaching the same luminosity of a static configuration at lower T_eff. However, because the full fledged evolutionary models of the outburst (e.g., MESA used by Wolf et al. (2013), or the model calculated by Yaron et al. (2005) and references therein) also assume a static atmosphere, from which mass loss has ceased at the peak of the supersoft X-ray phase, the results of the outburst models can be compared with the parameters derived with TMAP, which is also static. For KT Eri, from the TMAP fit we obtain a peak T_eff of about 800,000 K, corresponding to a WD mass in the range 1.15 $-$ 1.25 M_⊙ according to all nova outburst models quoted above. It is interesting to notice that Jurdana-Šepić et al. (2012) estimated an approximate pre-outburst accretion rate $\dot{m}$ from the optical B luminosity at quiescence, and by assuming a recurrence time of more than 100 years (because no previous outburst was found in the Harvard plates), these authors reached the same conclusion concerning the WD mass of KT Eri.

The above result is in agreement with the parameters derived correlating also additional observational evidence with the models. The Swift XRT light curve shows that the SSS flux decreased by a factor close to 16 in exactly 7 months after optical maximum. 210 days is thus the duration of the “bolometric t₃” (time for a decrease by the equivalent of 3 mag in optical), which is the parameter adopted by Yaron et al. (2005) to evaluate the duration of the constant bolometric luminosity phase of a nova. This parameter turns out to be of the order of 200 days for a 1.25 M_⊙ WD for a large range of initial WD surface temperature and for a pre-outburst mass accretion rate $\dot{m}>10^{-11}$ M_⊙ yr^-1, while a 1 M_⊙ WD nova with the same “bolometric t₃” would have been initially cool, and would have undergone mass transfer in a narrow range $10^{-10}$ M_⊙ yr${}^{-1}<\dot{m}<10^{-9}$ M_⊙ yr^-1. We now know also the X-ray luminosity of KT Eri at quiescence: assuming that the X-rays originate in the boundary layer of a geometrically thin accretion disk, Sun et al. (2020) indeed derived a consistent value, $\dot{m}=2\times 10^{-10}$ M_⊙ yr^-1 9 years after the outburst, which can be regarded as a lower limit, because it may be higher if there is an accretion disk corona emitting only in the UV.

The spectra of novae in the X-ray supersoft phase are complex, but they contain a wealth of physical information. We found that the KT Eri spectrum has a range of blue shift velocity of the absorption lines and red shift velocity of the emission lines. By fitting models with a single velocity, the fit is driven by the strongest features. A future, comprehensive model should account also for absorption features produced in layers of different optical depth and velocity. We calculated the velocity of the strongest absorption features and optical depth at which they are produced, as useful data to study more complex physical models in the near future.

The analysis of the X-ray spectra of KT Eri is complicated by the large irregular variability in two of the exposures, and by the overlapping emission lines, which we attributed to the ejecta as suggested for most novae and SSS by Ness et al. (2013b). These emission lines are not predicted to originate from, or near, the WD by the static atmospheric models, neither by the wind-atmosphere models. In the static atmosphere, conspicuous emission lines are formed only for the lowest WD masses (Rauch et al., 2010), at much lower T_eff than that resulting from the KT Eri spectra. The wind-atmosphere model of van Rossum (2012) instead predicts more emission lines and actual P-Cyg profiles, but they are smoothed and even “washed out” by the wind velocity. We could not model the emission line spectrum by adding one or two CIE components, and concluded that it is produced in a complex emission region, and perhaps it is not only due to shock ionization. In at least two exposures, the variation of the flux in some emission lines is independent of the variations of the continuum SSS flux and may be related by variations in the neutral oxygen column density. We suggested that either the surrounding cool material is not homogeneous, or that it was temporarily ionized.

Our analysis of these spectra was phenomenological and included the comparison with atmospheric, wind and outburst models. We were able to conclude that the nova WD has mass in the 1.15-1.25 M_⊙ range and that the mass accretion rate $\dot{m}$ before the outburst was most likely close to a value of 10^-10 M_⊙ yr^-1.

Finally, we also confirmed that pulsations of the SSS with a $\simeq$35 s timescale appeared only late in the post-outburst X-ray light curve, more than 100 days after optical maximum. We note that this was quite different from the case of RS Oph, in which a $\simeq$35 s periodicity appeared only in the first $\simeq$55 days after optical maximum (see Nelson et al., 2008; Osborne et al., 2011; Ness et al., 2013b), We suggest that the search for the root cause of this phenomenon will have to make use of this fact and correlate it with other differences in the physical parameters of the two novae.

The data analyzed in this article are all available in the HEASARC archive of NASA at the following URL: https://heasarc.gsfc.nasa.gov/db-perl/W3Browse/w3browse.pl

We thank the anonymous referee for her or his constructive comments and suggestions, which helped us to improve the scientific content of this paper. S. Pei has been supported by the China Scholarship Council (No. 201704910918) and M. Orio by a Chandra-Smithsonian grant for archival research at the University of Wisconsin.