A helium-burning white dwarf binary as a supersoft X-ray source

Optical photometry

SkyMapper. The optical brightness, measured by SkyMapper36 (not simultaneously) is g′ = 15.82 ± 0.02 mag, r′ = 16.04 ± 0.02 mag, i′ = 16.41 ± 0.01 mag, z′ = 16.59 ± 0.04 mag and, after correcting for the Galactic and LMC reddening of EB−V = 0.105 mag (see below), results in an absolute V-band magnitude of MV = −2.8 mag (assuming a LMC distance16 of 50 kpc). This is about 5 mag (or a factor of 2.55 = 100) brighter than typical disks in high-accretion-rate nova-like cataclysmic variables 37 and still 15–40 times brighter for a face-on disk.

OGLE. The region of our X-ray source was monitored regularly in the V and I bands with the Optical Gravitational Lensing Experiment (OGLE)38,39 at a cadence of 1–3 days. Photometric calibration is done by means of zero-point measurements in photometric nights and colour terms have been used for both filters when transforming to the standard V–I system. The long-term light curve during the period 2010–2020 shows variations by a factor of 1.3 and little colour variation (see Extended Data Fig. 3). A Lomb–Scargle periodogram identifies a period of P = 1.1635 days with the largest power (Fig. 4a,b), in agreement with P = 1.163471 days listed in the EROS-2 catalogue of LMC periodic variables (EROS-ID lm0454n2690)40. Two other strong peaks at longer periods are aliases (see Extended Data Table 1). A much smaller peak is seen at 2.327 days (see the paragraphs on TESS below).

MACHO. The source was also covered by the MACHO project41, which monitored the brightnesses of 60 million stars in the Large and Small Magellanic Clouds and the Galactic bulge between 1992 and 1999. A visual (4,500–6,300 Å) and a red filter (6,300–7,600 Å) were used, the magnitudes of which were transformed to the standard Kron–Cousins V and R system, respectively, using previously determined colour terms42.

TESS. The Transiting Exoplanet Survey Satellite43 (TESS) is an all-sky transit survey to detect Earth-sized planets orbiting nearby M dwarfs. It continuously observes a given region of the sky for at least 27 days. For sources down to white-light magnitudes of about 16 mag, TESS achieves approximately 1% photometric precision in single 10-min exposures. However, its large plate scale (21 pixel−1) means that care must be taken with respect to blended sources.

[HP99] 159 was observed during all of TESS Sectors 27–39 (except Sector 33), that is, from July 2020 to June 2021. The analysis of [HP99] 159 is complicated by a 13-mag star at 12 distance. Yet, the 1.16-day period found in OGLE data (which resolves these two stars) is clearly visible in a Lomb–Scargle periodogram of the TESS data (Fig. 4) as the strongest peak by far. There is a signal at 2.3268 days, exactly twice that of the OGLE period, at a significance of 3σ. Although this is marginal, the folded (and rebinned) light curve shows a clear odd–even effect with smaller variance that leads us to believe that this is the true period, and the strong peak at 1.16 days is probably the first harmonic of this period. The small amplitude difference, at the 0.2% level, would explain that this is only marginally seen in the TESS periodogram. This period is also seen in the OGLE periodogram, demonstrating that it is a real feature. The phenomenon of asymmetrical maxima and minima, known in some detached binaries44, is unique in interacting binaries and is especially puzzling given our inferred near-face-on geometry.

With the TESS light curve45, we also carried out an independent, more sensitive search at even shorter periods that are inaccessible to OGLE. The TESS light curve was pre-whitened of the 1.16-day period and 25 of its harmonics, and the Fourier transform of the ‘cleaned’ data was calculated. There are no indications for a shorter period down to about 3 h (Fig. 4). There is also no signal at 0.538 days. This would be the fundamental period if the 1.16-day period were still an alias with the 1–3 days observing cadence of OGLE. On the other hand, two more periodicities are found, at P1 = 2.635 h and P2 = 1.32 h, with significances at the 4σ level (We assume that the noise is Gaussian and calculate the standard deviation in a 1,500-bin window (±0.1 cycles per day in frequency) around any identified peaks.). Given the non-Poissonian nature of the light curve after pre-whitening, we do not consider these two periods, which are not related harmonically, to be substantial enough for further investigation.

Swift/UVOT. A 1,061-s Swift observation was obtained on 9 August 2022, starting at 23:15 UT. Although not detected in X-rays (as expected, Extended Data Fig. 5), we detect [HP99] 159 in all filters of the Ultraviolet and Optical Telescope (UVOT), at AB magnitudes as follows: UVW2 = 15.29 ± 0.04 mag, UVW1 = 15.33 ± 0.04 mag, U = 15.44 ± 0.04 mag, B = 15.73 ± 0.04 mag and V = 15.93 ± 0.05 mag, for which the error is the quadratic sum of the statistical and systematic error. When added to the (non-simultaneous) measurements on the longer-wavelength bands (Extended Data Fig. 1), the spectral energy distribution is still well described by a straight power law, extending from 0.2 to 8.0 μm, without any sign of the He donor.

Spectral energy distribution modelling and extinction correction. The recent reddening map46 of the LMC returns a much smaller reddening than previous estimates. Furthermore, it provides a combined reddening value for the Galactic foreground and the median LMC-intrinsic value, together with a spread owing to variation within the LMC. Instead of trying an arbitrary extinction correction, we instead forward-fold a power-law model to all the photometry from Swift/UVOT, SkyMapper, 2MASS and Spitzer. We fit for the power-law slope extinguished by a combination of Milky Way and LMC dust. The power-law model fit is very good and does not require a more complicated spectral model (Extended Data Fig. 1). The best-fit values are a power-law slope of ν1.48±0.02 and EB−V values of 0.01 ± 0.01 mag for the Milky Way and 0.14 ± 0.01 mag for LMC dust. The latter is larger than the EB−V = 0.11 mag provided by the LMC reddening map46 (composed of EI−V = 0.08 mag to the centre of the LMC and a further EI−V = 0.06 mag towards the far end of the LMC). More importantly, the slope of the spectral energy distribution is different from that expected for a standard accretion disk Fνν1/3 (Extended Data Fig. 1). This is very similar to the spectral energy distributions of other supersoft X-ray sources, such as CAL 83 (ref. 47). The flatter slope has been interpreted as resulting from reprocessing of the high-luminosity soft X-rays, making the emission about 100–1,000 times larger than the accretion luminosity48.

Optical spectroscopy

Optical spectroscopy of our source was undertaken on the SALT. On 14 August 2020, a 1,200-s long-slit exposure was obtained using the RSS49 in the 4,070–7,100-Å range (Fig. 2). Three further exposures (16 September 2020, 6 October 2020 and 7 October 2020), using the HRS50, covered the 3,700–5,500-Å and 5,500–8,900-Å wavelength ranges. The primary reduction, which includes overscan correction, bias subtraction and gain correction, were carried out with the SALT science pipeline51.

X-ray analysis

XMM-Newton. 4XMM J052015.1–654426 was covered serendipitously in a 29-ks XMM-Newton observation (ObsId 0841320101, principal investigator Pierre Maggi) on 16/17 September 2019. The EPIC instruments were operating in full-frame mode, with thin and medium filters for the pn and MOS detectors, respectively. We used the XMM-Newton data analysis software SAS version 20.0.0 to process these data. Good time intervals were identified following the method described at A whole field-of-view light curve for single-pixel events with 10,000 < PI < 12,000 is created and visually inspected for periods of flaring. A quiescent rate of less than 0.46 counts s−1 is determined and a GTI file satisfying this condition is created and used to filter the observation. After this filtering and given the off-axis position (8.7 arcmin) of [HP99] 159, its resulting vignetted exposure was about 11.5 ks. The events used for the spectral analysis were filtered with the following expression using the SAS task evselect: ′(PATTERN == 0) && (PI in [150 : 15000]) && (FLAG == 0)′. The SAS task especget was used to extract (source and background) events from a circular region with radius 60 centred on the position RA (2000.0) = 05 h 20 min 15.4 s, dec. (2000.0) = −65° 44′ 32, as well as to calculate the response matrix file (RMF) and ancillary response file (ARF) for these events. The same was done with a circular region with radius 110 centred on the position RA (2000.0) = 05 h 20 m 15.5 s, dec. (2000.0) = −65° 41′ 11, to be used as the background only, after excising two point sources in that region. To estimate the spectral parameters of the source, a Bayesian approach was implemented using 3ML (refs. 52,53). The analysis was restricted to the 0.2–2.3-keV energy band. The background and source contribution to the detected photons were modelled and folded through the appropriate responses to calculate posterior distributions of the spectral parameters. The source was modelled as an absorbed blackbody, using the 3ML models TbAbs*Blackbody (no separate abundances are used for the foreground Galactic and the LMC-intrinsic absorption). The background was modelled as a combination of instrumental background (read noise and fluorescence lines) and astrophysical background (Fig. 4) as follows: (1) a Gaussian line with normalization, line energy and width left free to account for the low-energy noise introduced by the readout electronics, (2) a Gaussian line with line energy and width fixed representing the Al-K fluorescent line near 1.5 keV, which is excited by particles in the camera body, (3) an unabsorbed APEC model with temperature left free to vary around 0.11 keV, accounting for the hot gas of the local bubble, (4) an APEC model with temperature allowed to vary around 0.22 keV absorbed by the average Galactic hydrogen column in the direction of the source, describing the contribution from the Galactic halo, and (5) a power law with a fixed slope of −1.41, absorbed by the combined hydrogen column of the Galaxy and the LMC in the direction of the source, arising from unresolved active galactic nuclei. The contribution of the particle background is negligible in our spectral range. The photons in the source extraction region were modelled by adding the source spectrum and the background spectrum, scaled by the ratio of the extraction areas. During the fit of the data, the parameters describing the background models were linked. We obtain the following best-fit values (errors at the 1σ level): kT = 45 ± 3 eV, NH = (2.7 ± 0.4) × 1021 cm−2 and an unabsorbed bolometric luminosity of (6.{8}_{-3.5}^{+7.0}times 1{0}^{36},{rm{erg}},{{rm{s}}}^{-1}); see Fig. 1. This implies an emission radius of (3,70{0}_{-1,900}^{+3,900},{rm{km}}) km, consistent with a white dwarf radius.

Apart from the possibility of the flux oscillations owing to the accretion rate being slightly below the burning rate, two other factors may contribute to the discrepancy of the measured versus expected X-ray luminosity. First, owing to the accretion of pure helium, the burning proceeds by means of the triple-α process54, with logT(K) ≈ 8.4 and ρ ≈ 1,000 g cm−3 at the burning depth, leading to higher amounts of carbon and oxygen. Convective envelope mixing and subsequent wind ejection of CO-rich matter could lead to noticeable local X-ray absorption in the emission volume. Second, non-LTE model atmospheres (as frequently used for the supersoft phase in post-nova) usually give a higher peak intensity55 than blackbody models (at the same temperature). Both effects, if taken into account in future work with improved data, would probably result in a higher X-ray luminosity (and white dwarf radius) than that estimated above.

eROSITA. [HP99] 159 = eRASSU J052015.3-654429 was detected by eROSITA56 in each of the survey scans. Until the end of 2021, eROSITA scanned the source during five epochs as summarized in Extended Data Table 2. The X-ray position was determined from the combined four eRASS surveys to be RA (2000.0) = 05 h 20 min 15.52 s, dec. (2000.0) = −65° 44′ 28.9 with a 1σ statistical uncertainty of 0.6. The positional error is usually dominated by systematic uncertainties57, which amount to 5 in pointed and 1 in scanning observations at present.

Owing to the unprecedented energy resolution (about 56 eV at 0.28 keV), eROSITA data are particularly sensitive to temperature changes of the source. Thus, we decided to perform spectral fitting despite the low number of counts. The spectral analysis was carried out using the five detectors with the on-chip aluminium filter (telescope modules 1, 2, 3, 4 and 6), avoiding the light leak in the other two detectors56. The eSASS57 users version 211214 was used to process the data. Only single-pixel events without any rejection or information flag set were selected, using the eSASS task evtool. With the eSASS task srctool, a circular source region with radius 100, centred on the coordinates RA (2000.0) = 05 h 20 min 16.6 s, dec. (2000.0) = −65° 44′ 27 was defined to select source events. A background region of the same size and shape centred on RA (2000.0) = 05 h 21 min 9.4 s, dec. (2000.0) = −65° 46′ 0 was defined, so as to lie at the same ecliptic longitude as the source region and hence in the scanning direction of eROSITA. The corresponding ARF and RMF files were created by the same eSASS task. Spectra were constructed by combining all events within the respective regions for each of the five epochs of observation. An absorbed blackbody was fitted to each of the spectra using 3ML. The priors of the free parameters were chosen on the basis of the XMM-Newton fit results. For the absorbing column, a Gaussian centred at μ = 2.7 × 1021 cm−2 and with a width of σ = 0.4 × 1021 cm−2 was used. The prior on kT was a Gaussian with μ = 45 eV and σ = 4 eV, truncated at zero, and the prior on the normalization was a log-normal distribution with μ = log(400) and σ = 1. For the eROSITA data, the background was not modelled because of the low number of counts; rather, the data were binned to have at least one background photon in every bin and a profile Poisson likelihood was used. For the five epochs, we obtain best-fit temperatures of (k{T}_{1},=4{2}_{-2}^{+3},{rm{eV}}), (k{T}_{2},=4{4}_{-2}^{+3},{rm{eV}}), (k{T}_{3},=4{2}_{-2}^{+3},{rm{eV}}), kT4 = 42 ± 2 eV and kT5 = 43 ± 2 eV. The corresponding fluxes are listed in Extended Data Table 2 and shown in Extended Data Fig. 5, together with the fluxes (or limits) of the other X-ray missions.

ROSAT. [HP99] 159 was originally identified14 in a 8.3-ks ROSAT/PSPC pointed observation (ID 500053p) of April 1992. We have reanalysed this observation and find the source with a vignetting-corrected count rate of 0.005 ± 0.001 PSPC counts s−1 (40 ± 8 source counts). A blackbody fit with free parameters leads to kT = 38 ± 15 eV, ({N}_{{rm{H}}}=(0.{9}_{-0.3}^{+3.2})times 1{0}^{21},{{rm{cm}}}^{-2}) and an unabsorbed bolometric luminosity of (1.{3}_{-1.0}^{+41.7}times 1{0}^{36},{rm{erg}},{{rm{s}}}^{-1}). A fit with a fixed, XMM-derived temperature of 45 eV is statistically indistinguishable (owing to the very small number of counts and the low energy resolution) and results in an absorption-corrected bolometric luminosity of (1.{7}_{-1.0}^{+41}times 1{0}^{36},{rm{erg}},{{rm{s}}}^{-1}), consistent within the errors of the free fit. A fit with fixed, XMM-derived temperature and NH is substantially worse.

[HP99] 159 was not detected during the ROSAT all-sky survey, with a PSPC count rate upper limit of <0.012 counts s−1. Using the best-fit spectral model of the above ROSAT pointed observation leads to a luminosity limit <2.5 × 1036 erg s−1, whereas using the XMM-derived spectral parameters leads to <3.2 × 1037 erg s−1. For consistency with the Einstein and EXOSAT upper limits, we choose to plot the latter value in Extended Data Fig. 5.

Arguments against an AM CVn interpretation

The He-dominated accretion disk and the N II and Si II lines (Extended Data Fig. 2) allow the possibility of an AM CVn nature of [HP99] 159. However, a number of reasons argue against this interpretation. (1) AM CVn objects have luminosities58 in the range 1030–1032 erg s−1. For this to be applicable to [HP99] 159, it would need to be at a distance of order 100 pc. (2) This is incompatible with the Gaia data, which suggest a minimum distance of 8–12 kpc. (3) Similarly, all AM CVn stars have large proper motion58, on the order of 0.5 year−1, owing to their vicinity. This is a factor 100 larger than that of [HP99] 159. (4) Finally, and most convincing, the velocity shift of all the strong lines clearly indicates LMC membership. At that distance, an AM CVn system is incompatible with the parameters we observe.

Comparison with known similar systems

To our knowledge, the only other ‘known’ system of this kind was the progenitor of the He nova V445 Pup59. A pre-outburst luminosity of log(L/L) = 4.34 ± 0.36 would be compatible with a 1.2–1.3 M star burning helium in a shell60. No optical spectrum exists of the progenitor; the post-outburst spectra are H-deficient, with the strongest lines being C II and Fe II (ref. 61). On the basis of photographic plates taken before the outburst, an optical modulation by a factor of 1.25 and a period of 0.650654(10) days was found and interpreted as orbital variation of a common-envelope binary62. There are three possibilities for the X-ray non-detection: (1) the flux oscillations during burning with phases of low luminosity25, (2) the substantial Galactic foreground absorption in the case that the X-ray spectrum was as similarly soft as [HP99] 159 or (3) an only slightly lower temperature as compared with [HP99] 159, which would shift the emission below the X-ray detection window. Thus, the progenitor of the He nova V445 Pup could have been an object similar to [HP99] 159.

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