A Year-long Superoutburst from an Ultracompact White Dwarf Binary Reveals the Importance of Donor Star Irradiation

We used public optical observations of SDSS 0807 taken with the Zwicky Transient Facility (ZTF) in the g and r filters (Masci et al. 2019). Data were obtained from 2018 March 27 to 2019 December 29 with a gap from 2019 May 14 to 2019 August 28 due to the object's occultation. Public data obtained with the Gaia observatory (Gaia Collaboration et al. 2016, 2018) in the G filter were also used for the light -curve analysis. The first Gaia measurement corresponds to 2016 April 8, which together with data from 2017 and early 2018 helped to establish the full quiescent level. The last Gaia data point was obtained on 2020 June 1 during the post-outburst cooling phase. The ZTF data are calibrated to the AB magnitude system and only the observations flagged as good quality measurements were used for the analysis.

We looked for indications of outbursts or superoutbursts of SDSS 0807 in databases such as the Catalina Sky Survey and Pan-STARRS over the last 10 yr, and no indications of such an event were found. The monitoring cadence of these surveys was not short enough to provide a tight constraint on the existence of these events, but a long superoutburst as the one here presented likely did not occur. SDSS 0807 was not observed by ASAS-SN or DASCH.

The X-ray (0.3–10 keV) and UV data analyzed in this Letter were taken with the Neil Gehrels Swift Observatory (Swift) on 2020 April 15 and 2020 May 28. A total of 3300 s was obtained in both observations, which corresponds to 1700 s and 1600 s, respectively. Data were reprocessed and analyzed following the standard reduction threads,¹ which make use of XSPEC v12.11.0 (Arnaud 1996). To determine the X-ray flux we have assumed an absorbed power-law model (TBabs*pegpwrlw) to fit the X-ray spectrum obtained on 2020 April 20. We set the value of the neutral H column (N_H) to the Galactic value toward the binary's position (N_H = 3.89 × 10²⁰ cm⁻²). Given the small number of counts, we used C-statistics for the fit.

Observations in the optical and UV were obtained with UVOT, and the corresponding magnitudes and exposure times per observation are given in Table 1. For the UVOT measurements we used a circular region with a radius of 5'' centered on R.A. = 08:07:10.33, decl. = +48:52:59.6. A circular region with radius 30'' and located in a star-free region of the image close to the target was used for the background subtraction. Given the coordinates of SDSS 0807 it is difficult or not possible to observe it with ground- or space-based telescopes from mid-May to late August. But a few data points using Swift and Gaia were obtained during the post-outburst cooling period.

We analyze public Sloan Digital Sky Survey (SDSS) spectra of SDSS 0807 and, for comparison purposes, data from SDSS J141118.31+481257.6 (hereafter SDSS 1411). The latter is another long-period (P_orb = 46 minutes) AM CVn system that was also recently identified in superoutburst for the first time, with an amplitude of ∼7 mag in optical (Rivera Sandoval & Maccarone 2019). A total of four and three spectra were analyzed for SDSS 0807 and SDSS 1411, respectively. For SDSS 0807 the data consist of two pairs of spectra taken sequentially and divided in two observations. The first one observed on 2014 October 3 and the second one on 2014 October 5. A total exposure time of 3600 s was obtained for that binary. For SDSS 1411, the observations consist of one exposure of 1000 s and two observations of 800 s each taken sequentially on 2005 March 17. All spectra cover the range 3800–9200 Å  with a resolution of 1500 at 3800 Å (the blue channel) and 2500 at 9000 Å (the red channel). For each source, SDSS 0807 and SDSS 1411, the full width at half maximum (FWHM) values were obtained from Gaussian fits to individual 5875 Å He i profiles. Continuum-rectified spectra were fitted in a window of 200 Å, centered on that He i line (Appendix A).

In Figure 1 we show the combined light curve of SDSS 0807. Gaia data were used as reference for the superoutburst parameters given the smaller photometric errors. The superoutburst was considered to start on 2018 November 7 when Gaia measurements showed a brightness increase of ∼0.2 mag above the quiescent level. Previous Gaia measurements (not plotted in Figure 1) are scattered around the marked quiescent level. The peak value was given by the brightest Gaia measurements. The recording of several data points, which are consistent with each other, shows that the identified magnitude value was not due to systematics. The average magnitude of the several Gaia observations taken on 2019 November 28 was consistent with the one from observations on 2019 December 8 and thus defined the end of the superoutburst. Previous measurements were above that "stable level," suggesting that the object's flux was still decreasing. To account for this uncertainty we have included a 10% error in the duration of the superoutburst (Figure 1). The event lasted ∼390 days, which is the longest accretion outburst ever observed for either an AM CVn or their cousins, the H-rich accreting WDs also known as cataclysmic variables (CVs). In fact, the long duration of the event excludes the possibility of a normal outburst (which lasts no more than a few days).

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Superoutbursts in AM CVns are also characterized by amplitudes of several magnitudes. Indeed, for the period of SDSS 0807 an amplitude of ∼7 mag is expected (Levitan et al. 2015), which contrasts with the 2.7 mag observed (Figure 1). However, as in CVs with thick accretion disks and high inclinations where the luminosity can be reduced by 3.5 mag when observed at i = 85° (Warner 1986, 1987), a similar situation is likely to have occurred in SDSS 0807. We measured the FWHM of the 5875 Å He i line that is prominent in AM CVns to estimate the radial velocity of the donor (K₂; see Appendix A for details on this calculation) and compared it to that of SDSS 1411. We found that SDSS 0807 has a larger average FWHM (and hence K₂) than SDSS 1411. Given its longer P_orb, the broader He i line can only be explained if SDSS 0807 has a higher inclination angle, which, in turn, would explain the small observed amplitude of the superoutburst (Warner 1986, 1987). Note that the empirical relation between P_orb and the superoutburst amplitude found by Levitan et al. (2015) was determined for AM CVns with P_orb < 40 minutes, which means that validity of the extrapolation to larger periods is not well established. In fact, inaccurate predictions have already been observed for other AM CVns systems in superoutburst such as SDSS 1411, which predicted the amplitude is 5.8 mag, but it showed a ∼7 mag superoutburst (Rivera Sandoval & Maccarone 2019). This casts doubts whether the expected amplitude of SDSS 0807 is indeed ∼7 mag. Also, if the WD accretor in SDSS 0807 is not a very massive one (e.g., ∼0.6 M_⊙), this would also affect the outburst amplitude as the accretion luminosity is directly and inversely proportional to the WD mass and radius, respectively. Furthermore, Kotko et al. (2012) have also shown that a larger metallicity substantially reduces the outburst amplitudes in AM CVns.

We also determined the rise and decline timescales of SDSS 0807 which are 60 day mag⁻¹ and 115 day mag⁻¹, respectively. Both are remarkable because they are the slowest ever observed in any outbursting AM CVn or CV system. In fact, these rate values exceed by tens of times those expected for CVs (Bailey 1975), even if only long-duration outbursts or superoutbursts are considered (Otulakowska-Hypka et al. 2016), independently of their P_orb. The viscous time sets the slow decay of superoutbursts, and for SDSS 0807, that is expected to be ∼2 months (see Appendix B), which clearly contrasts with our observations (Figure 1).

From the Swift analysis we determined that on 2020 April 15 the object was clearly detected in X-rays with a count rate of 10.1 ± 2.7 × 10⁻³ counts s⁻¹ (or ${f}_{{\rm{X}}}={0.40}_{-0.14}^{+0.21}\times {10}^{-12}$ erg cm⁻² s⁻¹), with a photon index ${\rm{\Gamma }}={2.46}_{-0.73}^{+0.83}$. This indicates that the X-ray spectrum of SDSS 0807 is more dominated by lower-energy photons in that phase, perhaps due to a lower-mass WD or a more transparent boundary layer. On the other hand, the binary was not detected in X-rays on 2020 May 28, with an upper limit on the count rate of 4.5 × 10⁻³ counts s⁻¹ at the 97.5% confidence level (corresponding to 2σ for a one-sided tail for a Gaussian distribution). The source thus clearly faded between the 2020 April and May observations, probably by a factor more than 2. Meanwhile, measurements in the U band for both dates correspond to 20.48 ± 0.31 mag and 20.87 ± 0.32 mag, respectively. The optical decline corresponds to a reduction in flux by a factor of 1.6, but given that a substantial fraction of the optical flux in these faint states comes from the radiative cooling of the WD itself, the accretion rate likely dropped by a larger factor. These measurements are in agreement within errors with those taken by the SDSS on 2000 April 25, when the object had a magnitude in $u^{\prime}$ of 20.4 ± 0.06 mag and was fully in quiescence. On the other hand, in the UV band UVW1 (λ_c = 2600 Å) the binary showed a slightly decrease in magnitude (0.4 mag) between both dates, suggesting a correlation with the X-ray emission decrease. Interestingly, Gaia measurements indicate that ∼6 months after the event finished, the binary remained 0.4 mag brighter than its original quiescent level (Figure 1).

Enhanced emission in X-rays and UV at least 2 months after the end of an outburst has previously been observed in other AM CVns (Rivera Sandoval & Maccarone 2019), and the UV has been explained as heat released by the accreting WD, which was deposited on it during the intense accretion event (the superoutburst). The X-ray emission is explained as residual accretion, as the temperature of the accreting WD after the end of the superoutburst is not high enough to release X-rays (Godon et al. 2006). The Swift X-ray detection then shows that the binary was still accreting on 2020 April 15. On the other hand, the X-ray nondetection of SDSS 0807 on 2020 May 28 does not necessarily mean that the object reached its quiescent level, but it demonstrates that abrupt changes in the mass accretion rate occurred between 140 and 180 days after the end of the superoutburst. Note that the emission in the bluest UVOT band UVW2 (${\lambda }_{c}=1928$ Å) was consistent within errors during both UVOT observations and there was no flux increase in that band on 2020 May 28, when the binary was not detected in X-rays. This argues against the possibility of the boundary layer becoming optically thick (and thus reducing the X-ray emission) due to an episode of large accretion, as has been observed in CVs and AM CVns during (or near) the outburst peak (e.g., Wheatley et al. 2003; Ramsay et al. 2012b; Rivera Sandoval & Maccarone 2019).

A commonly invoked scenario to explain the outbursts and superoutbursts in AM CVns is the disk instability model (DIM; e.g., Smak 1983; Lasota et al. 2008; Kotko et al. 2012; Cannizzo & Nelemans 2015; Cannizzo & Ramsay 2019), given that it reproduces the relations between P_orb and several outburst observables such as their duration (τ_dur), the recurrence time, and the mass transfer rate relatively well (Cannizzo & Nelemans 2015; Cannizzo & Ramsay 2019). It also predicts the threshold period for stable versus unstable accretion disks (Kotko et al. 2012). That model is an extension of the model applied to CVs, with the difference that the disks in AM CVns are dominated by He instead than by H, and their sizes are much smaller. The model assumes that the mass-transfer rate from the donor is constant and the value of the accretion rate onto the accreting WD determines the stability of the disk and therefore the existence of outbursts/superoutbursts. In the DIM for AM CVns the duration of the superoutburst increases with P_orb and follows the relation τ_dur ∝ P_orb^0.4 (Cannizzo & Ramsay 2019), implying that SDSS 0807 should have had a superoutburst with a duration of 22 days, which contrasts with the ∼390 days observed. The observations presented here argue then against that model (Figure 2). Comparison between the superoutburst duration and the empirical relation derived by Levitan et al. (2015) is not well motivated as that relation was derived for systems with P_orb < 40 minutes and for more than one detected superoutburst. Thus, we limit our discussion regarding the superoutburst duration to the DIM (Figure 2).

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A poorly explored effect so far is the importance of irradiation of the donor by the accretor and its disk, which can enhance the mass transfer rates (Warner 1995; Hameury et al. 1997; Deloye et al. 2007; Kotko et al. 2012; Warner 2015). Given that the orbits in AM CVns have very short periods and the donors can be quite cold, this effect might be important in at least a fraction of the AM CVn systems. Irradiation could, in fact, explain the long superoutbursts such as in SDSS 0807, with longer rise and decline times due to changes in the mass transfer rate. Indeed, indications of changes in the mass transfer rates of other outbursting AM CVns have been observed (Patterson et al. 2000), as have anomalously long outbursts of a few months in duration (Ramsay et al. 2012a; Shears et al. 2012), suggesting that irradiation on the companion can be important and even relatively common. The extreme superoutburst characteristics of SDSS 0807 are the clearest and most extreme evidence of the action of this mechanism in AM CVns.

In fact, one can expect a significant effect on the structure of the donor star due to irradiation if the rate at which it absorbs heat from the accretor's radiative flux is comparable to the rate at which its internal energy is radiated. If we assume an initial mass of 0.2 M_⊙ and an initial temperature of 10⁸ K for the donor WD (both likely higher than the typical initial values for the donors in AM CVn systems), and then follow the cooling of the donor star (Mestel 1952), taking into account that mass is lost during the evolution, then at P_orb ∼ 53 minutes, we expect the luminosity of the donor to be about 3.8 × 10²⁹ erg s⁻¹ and the temperature to be 2600 K. Using the same approach, we find that we expect T = 1700 K for a 68 minute orbital period, in reasonable agreement with the recent discovery of a T  ≈  1850 K excess in SDSS J1505+0659 (Green et al. 2020). The donor will occupy about 0.0025 of the solid angle seen from the source. Thus, if the superoutburst luminosity is ≳10³² erg s⁻¹, the WD donor should heat substantially due to the outburst of the accretion disk, given that the albedo of a He star absorbing UV light should be low. Assuming a distance of at least 1 kpc (reasonable, given that the parallax to SDSS 0807 is not yet well constrained), the outburst does, indeed, reach this luminosity. The evolution of AM CVns indicates that they move from a short P_orb to a larger one as they evolve, with the donors significantly reducing their mass transfer rates and cooling as the orbit widens (Nelemans 2005). Thus, the long period of SDSS 0807 points toward an old, cold, and low-mass donor, which would be easy to heat during a superoutburst. These simple calculations show that the donor is susceptible to having irradiation affect it, but a more detailed quantification of the effects of donor irradiation is beyond the scope of this Letter given the complexity of the problem. However, Kotko et al. (2012) have shown that mass transfer enhancement does in fact substantially increase the duration of the outbursts in AM CVns besides affecting the shape of the light curves. Thus, the results of SDSS 0807 will certainly place constraints for a more detailed modeling of outbursts in these binaries.

The observations of SDSS 0807 then show that irradiation on the donor has to be considered in the evolution of AM CVns, as it can have important consequences for these binaries as gravitational-wave sources. If, for instance, enhanced mass transfer due to irradiation makes AM CVns evolve more quickly toward longer periods than currently predicted by models (which usually neglect this mechanism), then the number of ultracompact systems expected to be detected by LISA (Nelemans et al. 2004; Marsh 2011; Nissanke et al. 2012) will likely be smaller than currently thought; the LISA noise curve's shape will change as well, although this is likely to be dominated by detached double WDs. It is also possible that the abrupt changes in the mass transfer rates make the donor unstable, and therefore after the superoutburst (when the mass transfer rate will substantially drop), it will need to readjust its structure. This will likely make the recurrence times much longer than currently expected (either empirically or with the DIM; Levitan et al. 2015; Cannizzo & Ramsay 2019), therefore reducing the detection rate of these systems through their outbursts by all-sky variability surveys, directly influencing the density estimates. Detail modeling and further investigations on the accreting behavior of AM CVns is required in order to quantitatively assess how common this mechanism is on these binaries. Models will also help to investigate what are the causes that influence the donor's irradiation, among which could be the precession of a tilted/warped disk (e.g., Kotko et al. 2012, and references therein) and perhaps also the metallicity due to the type of donor (and hence the formation channel). Furthermore, to find these systems in deep quiescence new techniques should be developed.