We present a new model of the population of symbiotic X-ray binaries (SyXBs) that takes into account non-stationary character of quasi-spherical sub-sonic accretion of the red giant’s stellar wind onto slowly rotating neutron stars. Updates of the earlier models are given, which include more strict criteria of slow NS rotation for plasma entry into the NS magnetosphere via Rayleigh-Taylor instability, as well as more strict conditions for settling accretion for slow stellar winds, with an account of variations in the specific angular momentum of captured stellar wind in eccentric binaries. These modifications enabled a more adequate description of the distributions of observed systems over binary orbital periods, NS spin periods and their X-ray luminosity in the ∼10³² − 10³⁶ erg s⁻¹ range and brought their model Galactic number into reasonable agreement with the observed one. Reconciliation of the model and observed orbital periods of SyXBs requires a low efficiency of matter expulsion from common envelopes during the evolution that results in the formation of NS-components of symbiotic X-ray systems.

Using population synthesis, we study a double-degenerate (DD) scenario for Type Ia supernovae (SNe Ia), aiming to estimate the maximum possible contribution to the rate of SNe from this scenario and the dependence of the delay-time distribution (DTD) on it. We make an extreme assumption that all mergers of super-Chandrasekhar pairs of CO white dwarfs (WDs) and mergers of CO WDs more massive than 0.47 M_⊙ with hybrid or helium WDs more massive than 0.37 M_⊙ produce SNe Ia. The models are parametrized by the product of the common envelope efficiency and the parameter of binding energy of stellar envelopes, α_ce λ, which we vary between 0.25 and 2. The best agreement with observations is obtained for α_ce λ = 2. A substantial contribution to the rate of SNe Ia is provided by the pairs with a hybrid WD. The estimated Galactic rate of SNe Ia is 6.5 × 10⁻³ yr⁻¹ (for the mass of the bulge and thin disc equal to 7.2 × 10¹⁰ M_⊙), which is comparable to the observational estimate (5.4 ± 0.12) × 10⁻³ yr⁻¹. The model DTD for 1 ≤ t ≤ 8 Gyr satisfactorily fits the DTD for SNe Ia in the field galaxies (Maoz, Mannucci & Brandt). For this epoch, the model DTD is ∝t^−1.64. At earlier and later epochs, our DTD has a deficit of events, as in other studies. Marginal agreement with the observational DTD is achieved even if only CO+CO WDs with M₁ ≥ 0.8 M_⊙ and M₂ ≥ 0.6 M_⊙ produce SNe Ia. A better agreement of observed and modelled DTD may be obtained if tidal effects are weaker than assumed and/or the metallicity of the population is much lower than solar.

A comparative investigation of the population of Galactic binary stars is performed for two modes of star formation: star formation at a constant rate over 10¹⁰ yrs, and a burst of star formation that reprocesses the same mass of gas into stars over 10⁹ yrs. Estimates are presented for the star-formation rates and populations of about 100 types of binaries and the products of their evolution. For most close binary systems, the models depend only weakly on the common-envelope parameter α_ce.

AM Canum Venaticorum (AM CVn) systems are ultracompact binaries where a white dwarf accretes from a helium-rich degenerate or semidegenerate donor. Some AM CVn systems will be among the loudest sources of gravitational waves for the upcoming Laser Interferometer Space Antenna; yet the formation channel of AM CVns remains uncertain. We report the study and characterization of a new eclipsing AM CVn, SRGeJ045359.9+622444 (hereafter, SRGeJ0453), discovered from a joint Spektrum-Roentgen-Gamma (SRG) Extended Roentgen Survey with an Imaging Telescope Array (eROSITA) mission and Zwicky Transient Facility program to identify cataclysmic variables (CVs). We obtained optical photometry to confirm the eclipse of SRGeJ0453 and determine the orbital period to be P orb = 55.0802 ± 0.0003 min . We constrain the binary parameters by modeling the high-speed photometry and radial-velocity curves and find M _donor = 0.044 ± 0.024M _⊙ and R _donor = 0.078 ± 0.012R _⊙. The X-ray spectrum is approximated by a power-law model with an unusually flat photon index of Γ ∼ 1 previously seen in magnetic CVs with SRG/eROSITA, but verifying that the magnetic nature of SRGeJ0453 requires further investigation. Optical spectroscopy suggests that the donor star of SRGeJ0453 could have initially been a He star or a He white dwarf. SRGeJ0453 is the ninth eclipsing AM CVn system published to date, and its lack of optical outbursts have made it elusive in previous surveys. The discovery of SRGeJ0453 using joint X-ray and optical surveys highlights the potential for discovering similar systems in the near future.

We study the physical and evolutionary properties of the ‘white dwarf (WD) family’ of AM CVn stars by computing realistic models of interacting double-degenerate systems. We evaluate self-consistently both the mass-transfer rate from the donor, as determined by gravitational wave emission and interaction with the binary companion, and the thermal response of the accretor to mass deposition. We find that, after the onset of mass transfer, all the considered systems undergo a strong non-dynamical He-flash. However, due to the compactness of these systems, the expanding accretors fill their Roche lobe very soon, thus preventing the efficient heating of the external layers of the accreted CO WDs. Moreover, due to the loss of matter from the systems, the orbital separations enlarge and mass transfer comes to a halt. The further evolution depends on the value of $${\skew{3}\dot{M}}$$ after the donors fill again their lobe. On one hand, if the accretion rate, as determined by the actual value of (M_don, M_acc), is high enough, the accretors experience several He-flashes of decreasing strength and then quiescent He-burning sets in. Later on, since the mass-transfer rate in IDD is a permanently decreasing function of time, accretors experience several recurrent strong flashes. On the other hand, for intermediate and low values of $${\skew{3}\dot{M}}$$ the accretors enter directly the strong flashes accretion regime. As expected, in all the considered systems the last He-flash is the strongest one, even if the physical conditions suitable for a dynamical event are never attained. When the mass accretion rate decreases below (2–3) × 10⁻⁸ M_⊙ yr⁻¹, the compressional heating of the He-shell becomes less efficient than the neutrino cooling, so that all the accretors in the considered systems evolve into massive degenerate objects. Our results suggest that SNe .Ia or Type Ia Supernovae due to Edge-Lit Detonation in the WD family of AM CVn stars should be much more rare than previously expected.

HD 49798/RX J0648.0–4418 is a peculiar X-ray binary with a hot subdwarf (sdO) mass donor. The nature of the accreting compact object is not known, but its spin period P = 13.2 s and $$\dot{P} =-2.15 \times 10^{-15}$$s s⁻¹, prove that it can be only either a white dwarf or a neutron star. The spin-up has been very stable for more than 20 years. We demonstrate that the continuous stable spin-up of the compact companion of HD 49798 can be best explained by contraction of a young white dwarf with an age ∼2 Myrs. This allows us to interpret all the basic parameters of the system in the framework of an accreting white dwarf. We present examples of binary evolution which result in such systems. If correct, this is the first direct evidence for a white dwarf contraction on early evolutionary stages.