Evolution of AM CVn Binaries with White Dwarf Donors

We present the final sample of 98 detached double white dwarf (WD) binaries found in the Extremely Low Mass (ELM) Survey, a spectroscopic survey targeting <0.3 M ⊙ He-core WDs completed in the Sloan Digital Sky Survey footprint. Over the course of the survey we observed ancillary low-mass WD candidates like GD 278, which we show is a P = 0.19 day double WD binary, as well as candidates that turn out to be field blue straggler/subdwarf A-type stars with luminosities too high to be WDs given their Gaia parallaxes. Here, we define a clean sample of ELM WDs that is complete within our target selection and magnitude range 15 < g 0 < 20 mag. The measurements are consistent with 100% of ELM WDs being 0.0089 < P < 1.5 day double WD binaries, 35% of which belong to the Galactic halo. We infer that these are mostly He+CO WD binaries given the measurement constraints. The merger rate of the observed He+CO WD binaries exceeds the formation rate of stable mass-transfer AM CVn binaries by a factor of 25, and so the majority of He+CO WD binaries must experience unstable mass transfer and merge. The systems with the shortest periods, such as J0651+2844, are signature LISA verification binaries that can be studied with gravitational waves and light.

The formation mechanism of AM CVn binary has not been well understood yet. Accurate measurements of the mass transfer rate can help us to determine the formation mechanism. But unfortunately such observation by electromagnetic means is quite challenging. One possible formation channel of AM CVn binary is a semidetached white dwarf binary. Such system emits strong gravitational wave radiation which could be measured by the future space-based detectors. We can simultaneously extract the mass transfer rate and the orbital period from the gravitational wave signal. We employ a post-Keplerian waveform model of gravitational wave and carry out a Fisher analysis to estimate the measurement accuracy of mass transfer rate through gravitational wave detection. Special attention is paid to the observed sources in Gaia Data Release 2. We found that we can accurately measure the mass transfer rate for those systems. Comparing to electromagnetic observations, gravitational wave detection improves the accuracy more than two orders of magnitude. Our results imply that the gravitational wave detection will help much in understanding the formation mechanism of AM CVn binaries.

Context. The binary system SDSS J1257+5428 consists of an extremely low-mass white dwarf (WD) with a mass ranging from ∼0.1 to ∼0.24 M⊙, along with a more massive WD companion of approximately 1 M⊙ that is significantly hotter. Recently, a tertiary WD orbiting this binary was discovered, setting a lower limit for the total age (∼4 Gyr) of the triple and providing further constraints on SDSS J1257+5428 that could be used to constrain its formation pathways. Up to now, the existence of this system has been described as paradoxical since tested models for its formation cannot account for its properties. Aims. Here we investigate under which conditions SDSS J1257+5428 could be understood as a descendant of a cataclysmic variable with an evolved donor star, which is a scenario that has never been explored in detail. Methods. We used the rapid BSE code for pre-common-envelope (CE) evolution and the detailed MESA code for post-CE evolution to carry out binary evolution simulations and searched for potential formation pathways for SDSS J1257+5428 that lead to its observed characteristics. For the post-CE evolution, we adopted a boosted version of the CARB model, which has been successfully used to explain the properties of close binary stars hosting evolved solar-type stars. Results. We find that SDSS J1257+5428 can be explained as a post-cataclysmic-variable system if (i) the progenitor of the extremely low-mass WD was initially a solar-type star that evolved into a subgiant before the onset of mass transfer and underwent hydrogen shell flashes after the mass transfer stopped, (ii) the massive WD was highly or entirely rejuvenated during the cataclysmic variable evolution, and (iii) magnetic braking was strong enough to make the evolution convergent. In this case, the torques due to magnetic braking need to be stronger than those provided by the CARB model by a factor of ∼100. Conclusions. We conclude that SDSS J1257+5428 can be reasonably well explained as having originated from a cataclysmic variable that hosted an evolved donor star and should no longer be regarded as paradoxical. If our formation channel is correct, our findings provide further support that stronger magnetic braking acts on progenitors of (i) close detached WD binaries, (ii) close detached millisecond pulsar with extremely low-mass WDs, (iii) AM CVn binaries, and (iv) ultra-compact X-ray binaries, in comparison to the magnetic braking strength required to explain binaries hosting main-sequence stars and single main-sequence stars.

Most close double helium white dwarfs will merge within a Hubble time due to orbital decay by gravitational wave radiation. However, a significant fraction with low mass ratios will survive for a long time as a consequence of stable mass transfer. Such stable mass transfer between two helium white dwarfs (HeWDs) provides one channel for the production of AM CVn binary stars. In previous calculations of double HeWD progenitors, the accreting HeWD was treated as a point mass. We have computed the evolution of 16 double HeWD models in order to investigate the consequences of treating the evolution of both components in detail. We find that the boundary between binaries having stable and unstable mass transfer is slightly modified by this approach. By comparing with observed periods and mass ratios, we redetermine masses of eight known AM CVn stars by our double HeWDs channel, i.e. HM Cnc, AM CVn, V406 Hya, J0926, J1240, GP Com, Gaia14aae and V396 Hya.We propose that central spikes in the triple-peaked emission spectra of J1240, GP Com and V396 Hya and the surface abundance ratios of N/C/O in GP Com can be explained by the stable double HeWD channel. The mass estimates derived from our calculations are used to discuss the predicted gravitational wave signal in the context of the Laser Interferometer Space Antenna (LISA) project.

AM CVn-type systems are ultracompact, helium-accreting binary systems that are evolutionarily linked to the progenitors of thermonuclear supernovae and are expected to be strong Galactic sources of gravitational waves detectable to upcoming space-based interferometers. AM CVn binaries with orbital periods ≲20–23 min exist in a constant high state with a permanently ionized accretion disc. We present the discovery of TIC 378898110, a bright (G = 14.3 mag), nearby (309.3 ± 1.8 pc), high-state AM CVn binary discovered in TESS two-minute-cadence photometry. At optical wavelengths, this is the third-brightest AM CVn binary known. The photometry of the system shows a 23.07172(6) min periodicity, which is likely to be the ‘superhump’ period and implies an orbital period in the range 22–23 min. There is no detectable spectroscopic variability. The system underwent an unusual, year-long brightening event during which the dominant photometric period changed to a shorter period (constrained to 20.5 ± 2.0 min), which we suggest may be evidence for the onset of disc-edge eclipses. The estimated mass transfer rate, $\log (\dot{M} / \mathrm{M_\odot } \, \mathrm{yr}^{-1}) = -6.8 \pm 1.0$, is unusually high and may suggest a high-mass or thermally inflated donor. The binary is detected as an X-ray source, with a flux of $9.2 ^{+4.2}_{-1.8} \times 10^{-13}$ erg cm−2 s−1 in the 0.3–10 keV range. TIC 378898110 is the shortest-period binary system discovered with TESS, and its large predicted gravitational-wave amplitude makes it a compelling verification binary for future space-based gravitational wave detectors.

We report on evolutionary calculations of the onset of mass transfer in AM CVn binaries, treating the donor's evolution in detail. We show that during the early contact phase, while the mass transfer rate, $\Mdot$, is increasing, gravity wave (GW) emission continues to drive the binary to shorter orbital period, $\Porb$. We argue that the phase where $\Mdot > 0$ and $\nudot > 0$ ($\nu = 1/\Porb$) can last between $10^3$ and $10^6$ yrs, significantly longer than previously estimated. These results are applied to RX J0806+1527 ($\Porb = 321$ s) and RX J914+2456 ($\Porb=569$ s), both of which have measured $\nudot > 0$. \emph{Thus, a $\nudot > 0$ does not select between the unipolar inductor and accretion driven models proposed as the source of X-rays in these systems}. For the accretion model, we predict for RX J0806 that $\ddot{\nu} \approx \ee{1.0-1.5}{-28}$ Hz s$^{-2}$ and argue that timing observations can probe $\ddot{\nu}$ at this level with a total $\approx 20$ yr baseline. We also place constraints on each system's initial parameters given current observational data.

We present Chandra and Swift X-ray observations of four extremely low-mass\n(ELM) white dwarfs with massive companions. We place stringent limits on X-ray\nemission from all four systems, indicating that neutron star companions are\nextremely unlikely and that the companions are almost certainly white dwarfs.\nGiven the observed orbital periods and radial velocity amplitudes, the total\nmasses of these binaries are greater than 1.02 to 1.39 Msun. The extreme mass\nratios between the two components make it unlikely that these binary white\ndwarfs will merge and explode as Type Ia or underluminous supernovae. Instead,\nthey will likely go through stable mass transfer through an accretion disk and\nturn into interacting AM CVn. Along with three previously known systems, we\nidentify two of our targets, J0811 and J2132, as systems that will definitely\nundergo stable mass transfer. In addition, we use the binary white dwarf sample\nfrom the ELM Survey to constrain the inspiral rate of systems with extreme mass\nratios. This rate, 0.00017/year, is consistent with the AM CVn space density\nestimated from the Sloan Digital Sky Survey. Hence, stable mass transfer double\nwhite dwarf progenitors can account for the entire AM CVn population in the\nGalaxy.\n

Three periodically variable stars have recently been discovered (V407 Vul, P=9.5 min; ES Cet, P=10.3 min; RX J0806.3+1527, P=5.3 min) with properties that suggest that their photometric periods are also their orbital periods, making them the most compact binary stars known. If true, this might indicate that close, detached, double white dwarfs are able to survive the onset of mass transfer caused by gravitational wave radiation and emerge as the semi-detached, hydrogen-deficient stars known as the AM CVn stars. The accreting white dwarfs in such systems are large compared to the orbital separations. This has two effects. First, it makes it likely that the mass-transfer stream can hit the accretor directly. Secondly, it causes a loss of angular momentum from the orbit which can destabilize the mass transfer unless the angular momentum lost to the accretor can be transferred back to the orbit. The effect of the destabilization is to reduce the number of systems which survive mass transfer by as much as one hundredfold. In this paper we analyse this destabilization and the stabilizing effect of a dissipative torque between the accretor and the binary orbit. We obtain analytical criteria for the stability of both disc-fed and direct impact accretion, and we carry out numerical integrations to assess the importance of secondary effects, the chief one being that otherwise stable systems can exceed the Eddington accretion rate. We show that to have any effect upon survival rates, the synchronizing torque must act on a time-scale of the order of 1000 yr or less. If synchronization torques are this strong, then they will play a significant role in the spin rates of white dwarfs in cataclysmic variable stars as well.

The evolution of binaries consisting of evolved main sequence stars (1 < M_d/Msun < 3.5) with white dwarf companions (0.7 < M_wd/Msun < 1.2) is investigated through the thermal mass transfer phase. Taking into account the stabilizing effect of a strong, optically thick wind from the accreting white dwarf surface, we have explored the formation of several evolutionary groups of systems for progenitors with initial orbital periods of 1 and 2 days. The numerical results show that CO white dwarfs can accrete sufficient mass to evolve to a Type Ia supernova and ONeMg white dwarfs can be built up to undergo accretion induced collapse for donors more massive than about 2 Msun. For donors less massive than ~2 Msun the system can evolve to form a He and CO or ONeMg white dwarf pair. In addition, sufficient helium can be accumulated (~0.1 Msun) in systems characterized by 1.6 < M_d/Msun < 1.9 and 0.8 < M_wd/Msun < 1 such that sub Chandrasekhar mass models for Type Ia supernovae, involving off center helium ignition, are possible for progenitor systems evolving via the Case A mass transfer phase. For systems characterized by mass ratios > 3 the system likely merges as a result of the occurrence of a delayed dynamical mass transfer instability. A semi-analytical model is developed to delineate these phases which can be easily incorporated in population synthesis studies of these systems.

We study the mass transfer rates and disk stability conditions of ultracompact X-ray binaries (UCXBs) using empirical time-averaged X-ray luminosities from Paper I (Cartwright et al. 2013) and compiled information from the literature. The majority of UCXBs are consistent with evolutionary tracks for white dwarf donors. Three UCXBs with orbital periods longer than 40 minutes have mass transfer rates above 10^{-10} Msun/year, inconsistent with white dwarf donor tracks. We show that if helium star donors can retain their initial high entropy, they can explain the observed mass transfer rates of these UCXBs. Several UCXBs show persistent luminosities apparently below the disk instability limit for irradiated He accretion disks. We point out that a predominantly C and/or O disk (as observed in the optical spectra of several) lowers the disk instability limit, explaining this disagreement. The orbital period and low time-averaged mass transfer rate of 2S 0918-549 provide evidence that the donor star is a low-entropy C/O white dwarf, consistent with optical spectra. We combine existing information to constrain the masses of the donors in 4U 1916-053 (0.064+-0.010 Msun) and 4U 1626-67 (<0.036 Msun for a 1.4 Msun neutron star). We show that 4U 1626-67 is indeed persistent, and not undergoing a transient outburst, leaving He star models as the best explanation for the donor.

The ultracompact binary systems V407 Vul (RX J1914.4+2456) and HM Cnc (RX J0806.3+1527) - a two-member subclass of the AM CVn stars - continue to pique interest because they defy unambiguous classification. Three proposed models remain viable at this time, but none of the three is significantly more compelling than the remaining two, and all three can satisfy the observational constraints if parameters in the models are tuned. One of the three proposed models is the direct impact model of Marsh & Steeghs (2002), in which the accretion stream impacts the surface of a rapidly-rotating primary white dwarf directly but at a near-glancing angle. One requirement of this model is that the accretion stream have a high enough density to advect its specific kinetic energy below the photosphere for progressively more-thermalized emission downstream, a constraint that requires an accretion spot size of roughly 1.2x10^5 km^2 or smaller. Having at hand a smoothed particle hydrodynamics code optimized for cataclysmic variable accretion disk simulations, it was relatively straightforward for us to adapt it to calculate the footprint of the accretion stream at the nominal radius of the primary white dwarf, and thus to test this constraint of the direct impact model. We find that the mass flux at the impact spot can be approximated by a bivariate Gaussian with standard deviation \sigma_{\phi} = 164 km in the orbital plane and \sigma_{\theta} = 23 km in the perpendicular direction. The area of the the 2\sigma ellipse into which 86% of the mass flux occurs is roughly 47,400 km^2, or roughly half the size estimated by Marsh & Steeghs (2002). We discuss the necessary parameters of a simple model of the luminosity distribution in the post-impact emission region.

We extend recent work that included the effect of pressure forces to derive the precession rate of eccentric accretion discs in cataclysmic variables to the case of double degenerate systems. We find that the logical scaling of the pressure force in such systems results in predictions of unrealistically high primary masses. Using the prototype AM CVn as a calibrator for the magnitude of the effect, we find that there is no scaling that applies consistently to all the systems in the class. We discuss the reasons for the lack of a superhump period to mass ratio relationship analogous to that known for SU UMa systems and suggest that this is because these secondaries do not have a single valued mass–radius relationship. We highlight the unreliability of mass ratios derived by applying the SU UMa expression to the AM CVn binaries.

Neutron star–white dwarf (NSWD) binaries are one of the most abundant sources of gravitational waves (GWs) in the Milky Way. These GW sources are the evolutionary products of primordial binaries that experienced many processes of binary interaction. We employ a binary population synthesis method to investigate the properties of Galactic NSWD binaries detectable by the Laser Interferometer Space Antenna (LISA). In this paper, only the NSWD systems with a COWD or ONeWD component are included. We consider various models related to mass-transfer efficiencies during primordial binary evolution, supernova explosion mechanisms at NS formation, common envelope ejection efficiencies, and critical WD masses that determine the stability of mass transfer between WDs and NSs. Based on our calculations, we estimate that tens to hundreds of LISA NSWD binaries exist in the Milky Way. We find that the detection of LISA NSWD binaries is able to provide profound insights into mass-transfer efficiencies during the evolution of primordial binaries and critical WD masses during mass transfer from a WD to an NS.

We present radial velocity observations of four extremely low-mass (0.2 Msol) white dwarfs. All four stars show peak-to-peak radial velocity variations of 540 - 710 km/s with 1.0 - 5.9 hr periods. The optical photometry rules out main-sequence companions. In addition, no milli-second pulsar companions are detected in radio observations. Thus the invisible companions are most likely white dwarfs. Two of the systems are the shortest period binary white dwarfs yet discovered. Due to the loss of angular momentum through gravitational radiation, three of the systems will merge within 500 Myr. The remaining system will merge within a Hubble time. The mass functions for three of the systems imply companions more massive than 0.46 Msol; thus those are carbon/oxygen core white dwarfs. The unknown inclination angles prohibit a definitive conclusion about the future of these systems. However, the chance of a supernova Ia event is only 1% to 5%. These systems are likely to form single R Coronae Borealis stars, providing evidence for a white dwarf + white dwarf merger mechanism for these unusual objects. One of the systems, SDSS J105353.89+520031.0 has a 70% chance of having a low-mass white dwarf companion. This system will probably form a single helium-enriched subdwarf O star. All four white dwarf systems have unusal mass ratios of < 0.2-0.8 that may also lead to the formation of AM CVn systems.

Double white dwarf (WD) merger process and their post-merger evolution are important in many fields of astronomy, such as supernovae, gamma-ray bursts, gravitational waves, and so on. The evolutionary outcomes of double ultra-massive WD merger remnants are still a subject of debate, though the general consensus is that the merger remnant will collapse to form a neutron star (NS). In this work, we investigate the evolution of a $2.20\, {\rm M}_{\odot }$ merger remnant stemmed from the coalescence of double $1.10\, {\rm M}_{\odot }$ ONe WDs. We find that the remnant ignites off-centre neon burning at the position near the surface of primary WD soon after the merger, resulting in the stable inwardly propagating oxygen/neon (O/Ne) flame. The final outcomes of the merger remnant are sensitive to the effect of convective boundary mixing. If the mixing cannot stall the O/Ne flame, the flame will reach the centre within 20 yr, leading to the formation of super Chandrasekhar mass silicon core, and its final fate probably be NS through iron-core-collapse supernova. In contrast, if the convective mixing is effective enough to prevent the O/Ne flame from reaching the centre, the merger remnant will undergo electron capture supernova to form an ONeFe WD. Meanwhile, we find that the wind mass loss process may hardly alter the final fate of the remnant due to its fast evolution. Our results imply that the coalescence of double ONe WDs can form short lived giant like object, but the final outcomes (NS or ONeFe WD) are influenced by the uncertain convective mixing in O/Ne flame.