We model helium-rich stars with solar metallicity (X = 0.7, Z = 0.02) progenitors that evolve to form AM Canum Venaticorum systems through a helium-star formation channel, with the aim to explain the observed properties of Gaia14aae and ZTFJ1637+49. We show that semi-degenerate, H-exhausted (X ≤ 10−5), He-rich (Y ≈ 0.98) donors can be formed after a common envelope evolution (CEE) phase if either additional sources of energy are used to eject the common envelope, or a different formalism of CEE is implemented. We follow the evolution of such binary systems after the CEE phase using the Cambridge stellar evolution code, when they consist of a He-star and a white dwarf accretor, and report that the mass, radius, and mass-transfer rate of the donor, the orbital period of the system, and the lack of hydrogen in the spectrum of Gaia14aae and ZTFJ1637+49 match well with our modelled trajectories wherein, after the CEE phase Roche lobe overflow is governed not only by the angular momentum loss (AML) owing to gravitational wave radiation (AMLGR) but also an additional AML owing to α − Ω dynamos in the donor. This additional AML is modelled with our double-dynamo (DD) model of magnetic braking in the donor star. We explain that this additional AML is just a consequence of extending the DD model from canonical cataclysmic variable donors to evolved donors. We show that none of our modelled trajectories match with Gaia14aae or ZTFJ1637+49 if the systems are modelled only with AMLGR.

The stability criteria of rapid mass transfer and common-envelope evolution are fundamental in binary star evolution. They determine the mass, mass ratio, and orbital distribution of many important systems, such as X-ray binaries, type Ia supernovae, and merging gravitational-wave sources. We use our adiabatic mass-loss model to systematically survey intermediate-mass (IM) stars’ thresholds for dynamical timescale mass transfer. The impact of metallicity on the stellar responses and critical mass ratios is explored. Both tables (Z = 0.001) and fitting formulae (Z = 0.001 and Z = 0.02) of the critical mass ratios of IM stars are provided. An application of our results to intermediate-mass X-ray binaries (IMXBs) is discussed. We find that the predicted upper limit to mass ratios, as a function of orbital period, is consistent with the observed IMXBs that undergo thermal or nuclear timescale mass transfer. According to the observed peak X-ray luminosity, L X, we predict the range of L X for IMXBs as a function of the donor mass and the mass-transfer timescale.

We give an updated version of the analytical equation of state used in the Cambridge stellar evolution code (STARS) as a free to use open-source package that we have used to model cool white dwarfs down to temperatures log10(Teff/K) = 3. With this update in the STARS code we model the secular evolution of cataclysmic variable (CV) stars using a double dynamo model wherein there is an interplay between two α − Ω dynamos, one in the convective envelope and the other at the boundary of a slowly rotating shrinking radiative core and the growing convective envelope. We confirm that this model provides a physical formalism for the interrupted magnetic braking paradigm. In addition, our model also provides a mechanism for extra angular momentum loss below the period gap. We construct the relative probability distribution of orbital periods Porb using the mass distribution of white dwarfs in cataclysmic variables and find that our model excellently reproduces the period gap and the observed period minimum spike in CV distribution. We also compare the evolutionary trajectories from our model with those of other empirical models and find agreement between the two. We also report good agreement between our modelled systems and observational data.

Generally the virial theorem provides a relation between various components of energy integrated over a system. This helps us to understand the underlying equilibrium. Based on the virial theorem we can estimate, for example, the maximum allowed magnetic field in a star. Recent studies have proposed the existence of highly magnetized white dwarfs, with masses significantly higher than the Chandrasekhar limit. Surface magnetic fields of such white dwarfs could be more than 109G with the central magnitude several orders higher. These white dwarfs could be significantly smaller in size than their ordinary counterparts (with surface fields restricted to about 109G). In this paper we reformulate the virial theorem for non-rotating, highly magnetized white dwarfs (B-WDs) in which, unlike in previous formulations, the contribution of the magnetic pressure to the magnetohydrostatic balance cannot be neglected. Along with the new equation of magnetohydrostatic equilibrium, we approach the problem by invoking magnetic flux conservation and by varying the internal magnetic field with the matter density as a power law. Either of these choices are supported by previous independent work and neither violates any important physics. They are useful while there is no prior knowledge of field profile within a white dwarf. We then compute the modified gravitational, thermal and magnetic energies and examine how the magnetic pressure influences the properties of such white dwarfs. Based on our results we predict important properties of these B-WDs, which turn out to be independent of our chosen field profiles.

We model cataclysmic variables (CVs) with solar metallicity donors (X = 0.7, Z = 0.02) that evolve to form AM CVn stars through the Evolved CV formation channel using various angular momentum loss mechanisms by magnetic braking (AMLMB). We find that the time-scale for AMLMB in our double-dynamo (DD) model is shorter than that of previously used empirical formulae. Owing to the shorter time-scales, a larger parameter space of initial conditions evolves to form AM CVn stars with the DD model than with other models. We perform an analysis of the expected number of AM CVn stars formed through the Evolved CV channel and find about 3 times as many AM CVn stars as reported before. We evolve these systems in detail with the Cambridge stellar evolution code (stars) and show that evolved CVs populate a region with orbital period Porb ≥ 5.5 hr. We evolve our donors beyond their orbital period minimum and find that a significant number become extremely H-exhausted systems. This makes them indistinguishable from systems evolved from the He-star and the White Dwarf (WD) channels in terms of the absence of H in their spectra. We also compare the masses, mass-transfer rates of the donor, and the orbital period with observations. We find that the state of the donor and the absence of H in systems such as YZ LMi and V396 Hya match with our modelled trajectories, while systems such as CR Boo and HP Lib match with our modelled tracks if their actual donor mass lies on the lower-end of the observed mass range.