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We present the observational mass–radius (M–R) relation for a sample of 47 magnetized white dwarfs (WDs) with the magnetic field strength (B) ranging from 1 to 773 MG, identified from the SDSS data release 7 (DR7). We derive their effective temperature, surface gravity (log g), luminosity, radius, and mass. While atmospheric parameters are derived using a Virtual Observatory Spectral Energy Distribution Analyzer (VOSA), the mass is derived using their location in the HR diagram in comparison with the evolutionary tracks of different masses. We implement this mass measurement instead of a more traditional method of deriving masses from log g , which is unreliable as is based on SED and generates errors from other physical parameters involved. The main disadvantage of this method is that we need to assume a core composition of WDs. As it is complicated to identify the exact composition of these WDs from low-resolution spectra, we use tracks for the masses 0.2 to 0.4 M⊙ assuming a He-core, 0.5 to 1.0 M⊙ assuming CO core, and above M⊙ assuming O–Ne–Mg core. We compare the observed M–R relation with those predicted by the finite temperature model by considering different B , which are well in agreement considering their relatively low-surface fields, ≲109 G. Currently, there is no direct observational detection of magnetized WDs with B > 109 G. We propose that our model can be further extrapolated to higher B , which may indicate the existence of super-Chandrasekhar mass (M > 1.4 M⊙) WDs at higher B. [ABSTRACT FROM AUTHOR]

We model cataclysmic variables (CVs) with solar metallicity donors (X  = 0.7 and  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 |$P_\mathrm{orb}\ge 5.5\, \mathrm{hr}$|⁠. 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. [ABSTRACT FROM AUTHOR]

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 semidegenerate, 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. [ABSTRACT FROM AUTHOR]

We evolve stellar models to study the common envelope (CE) interaction of an early asymptotic giant branch star of initial mass |$5\, \rm M_{\odot }$| with a companion star of mass ranging from 0.1 to |$2\, \rm M_{\odot }$|⁠. We model the CE as a fast stripping phase in which the primary experiences rapid mass loss and loses about 80 per cent of its mass. The post-CE remnant is then allowed to thermally readjust during a Roche lobe overflow (RLOF) phase and the final binary system and its orbital period are investigated. We find that the post-CE RLOF phase is long enough to allow nuclear burning to proceed in the helium shell. By the end of this phase, the donor is stripped of both its hydrogen and helium and ends up as carbon–oxygen white dwarf of mass about |$0.8\, \rm M_{\odot }$|⁠. We study the sensitivity of our results to initial conditions of different companion masses and orbital separations at which the stripping phase begins. We find that the companion mass affects the final binary separation and that helium-shell burning causes the star to refill its Roche lobe leading to post-CE RLOF. Our results show that double mass transfer in such a binary interaction is able to strip the helium and hydrogen layers from the donor star without the need for any special conditions or fine tuning of the binary parameters. [ABSTRACT FROM AUTHOR]

A dynamo mechanism driven by differential rotation when stars merge has been proposed to explain the presence of strong fields in certain classes of magnetic stars. In the case of the high-field magnetic white dwarfs (HFMWDs), the site of the differential rotation has been variously thought to be the common envelope, the hot outer regions of a merged degenerate core or an accretion disc are formed by a tidally disrupted companion that is subsequently accreted by a degenerate core. We have shown previously that the observed incidence of magnetism and the mass distribution in HFMWDs are consistent with the hypothesis that they are the result of merging binaries during common envelope evolution. Here, we calculate the magnetic field strengths generated by common envelope interactions for synthetic populations using a simple prescription for the generation of fields and find that the observed magnetic field distribution is also consistent with the stellar merging hypothesis. We use the Kolmogorov–Smirnov test to study the correlation between the calculated and the observed field strengths and find that it is consistent for low envelope ejection efficiency. We also suggest that the field generation by the plunging of a giant gaseous planet on to a white dwarf may explain why magnetism among cool white dwarfs (including DZ white dwarfs) is higher than among hot white dwarfs. In this picture, a super-Jupiter residing in the outer regions of the white dwarf's planetary system is perturbed into a highly eccentric orbit by a close stellar encounter and is later accreted by the white dwarf. [ABSTRACT FROM AUTHOR]

Rotation and magnetism are increasingly recognized as important phenomena in stellar evolution. Surface magnetic fields from a few to 20 000 G have been observed and models have suggested that magnetohydrodynamic transport of angular momentum and chemical composition could explain the peculiar composition of some stars. Stellar remnants such as white dwarfs have been observed with fields from a few to more than 109 G. We investigate the origin of and the evolution, on thermal and nuclear rather than dynamical time-scales, of an averaged large-scale magnetic field throughout a star's life and its coupling to stellar rotation. Large-scale magnetic fields sustained until late stages of stellar evolution with conservation of magnetic flux could explain the very high fields observed in white dwarfs. We include these effects in the Cambridge stellar evolution code using three time-dependant advection-diffusion equations coupled to the structural and composition equations of stars to model the evolution of angular momentum and the two components of the magnetic field. We present the evolution in various cases for a $3\rm \,M_{{\odot }}$ star from the beginning to the late stages of its life. Our particular model assumes that turbulent motions, including convection, favour small-scale field at the expense of large-scale field. As a result, the large-scale field concentrates in radiative zones of the star and so is exchanged between the core and the envelope of the star as it evolves. The field is sustained until the end of the asymptotic giant branch, when it concentrates in the degenerate core. [ABSTRACT FROM AUTHOR]

The most frequently seen binary companions to millisecond pulsars (MSPs) are helium white dwarfs. The standard rejuvenation mechanism, in which a low- to intermediate-mass companion to a neutron star fills its Roche lobe between central hydrogen exhaustion and core helium ignition, is the most plausible formation mechanism. We have investigated whether the observed population can realistically be formed via this mechanism. We used the Cambridge STARS code to make models of Case B Roche-lobe overflow with Reimers' mass-loss from the donor. We find that the range of initial orbital periods required to produce the currently observed range of orbital periods of MSPs is extremely narrow. To reduce this fine tuning, we introduce a companion enhanced wind (CEW) that strips the donor of its envelope more quickly so that systems can detach at shorter periods. Our models indicate that the fine tuning can be significantly reduced if a CEW is active. Because significant mass is lost owing to a CEW, we expect some binary pulsars to accrete less than the 0.1Mʘ needed to spin them up to millisecond periods. This can account for mildly recycled pulsars present along the entire Mc-Porb relation. Systems with Pspin > 30 ms are consistent with this, but too few of these mildly recycled pulsars have yet been observed to make a significant comparison. [ABSTRACT FROM AUTHOR]

A magnetic dynamo driven by differential rotation generated when stars merge can explain strong fields in certain classes of magnetic stars, including the high field magnetic white dwarfs (HFMWDs). In their case the site of the differential rotation has been variously proposed to be within a common envelope, the massive hot outer regions of a merged degenerate core or an accretion disc formed by a tidally disrupted companion that is subsequently incorporated into a degenerate core. We synthesize a population of binary systems to investigate the stellar merging hypothesis for observed single HFMWDs. Our calculations provide mass distribution and the fractions of white dwarfs that merge during a common envelope phase or as double degenerate systems in a post-common-envelope phase. We vary the common envelope efficiency parameter a and compare with observations. We find that this hypothesis can explain both the observed incidence of magnetism and the mass distribution of HFMWDs for a wide range of α. In this model, the majority of the HFMWDs are of the carbon-oxygen type and merge within a common envelope. Less than about a quarter of a per cent of HFMWDs originate from double degenerate stars that merge after common envelope evolution and these populate the high-mass tail of the HFMWD mass distribution. [ABSTRACT FROM AUTHOR]

We examine the growing class of binary millisecond pulsars known as redbacks. In these systems, the pulsar's companion has a mass between 0.1 and about 0.5 M⊙ in an orbital period of less than 1.5 d. All show extended radio eclipses associated with circumbinary material. They do not lie on the period-companion mass relation expected from the canonical intermediate-mass X-ray binary evolution in which the companion filled its Roche lobe as a red giant and has now lost its envelope and cooled as a white dwarf. The redbacks lie closer to, but usually at higher period than, the period-companion mass relation followed by cataclysmic variables and low-mass X-ray binaries. In order to turn on as a pulsar mass accretion on to a neutron star must be sufficiently weak, considerably weaker than expected in systems with low-mass main-sequence companions driven together by magnetic braking or gravitational radiation. If a neutron star is formed by accretion-induced collapse of a white dwarf as it approaches the Chandrasekhar limit some baryonic mass is abruptly lost to its binding energy so that its effective gravitational mass falls. We propose that redbacks form when accretion-induced collapse of a white dwarf takes place during cataclysmic variable binary evolution because the loss of gravitational mass makes the orbit expand suddenly so that the companion no longer fills its Roche lobe. Once activated, the pulsar can ablate its companion and so further expand the orbit and also account for the extended eclipses in the radio emission of the pulsar that are characteristic of these systems. The whole period-companion mass space occupied by the redbacks can be populated in this way. [ABSTRACT FROM AUTHOR]

ABSTRACT Extrasolar planets and belts of debris orbiting post-main-sequence single stars may become unbound as the evolving star loses mass. In multiple-star systems, the presence or co-evolution of the additional stars can significantly complicate the prospects for orbital excitation and escape. Here, we investigate the dynamical consequences of multi-phasic, non-linear mass loss and establish a criterion for a system of any stellar multiplicity to retain a planet whose orbit surrounds all of the parent stars. For single stars which become white dwarfs, this criterion can be combined with the Chandrasekhar Limit to establish the maximum allowable mass-loss rate for planet retention. We then apply the criterion to circumbinary planets in evolving binary systems over the entire stellar mass phase space. Through about 105 stellar evolutionary track realizations, we characterize planetary ejection prospects as a function of binary separation, stellar mass and metallicity. This investigation reveals that planets residing at just a few tens of au from a central concentration of stars are susceptible to escape in a wide variety of multiple systems. Further, planets are significantly more susceptible to ejection from multiple-star systems than from single-star systems for a given system mass. For system masses greater than about 2 M⊙, multiple-star systems represent the greater source of free-floating planets. [ABSTRACT FROM AUTHOR]

White dwarfs have frozen in magnetic fields ranging from below the measurable limit of about 3×10 to 10 G. White dwarfs with surface magnetic fields in excess of 1 MG are found as isolated single stars and relatively more often in magnetic cataclysmic variables. Some 1253 white dwarfs with a detached low-mass main-sequence companion have been identified in the Sloan Digital Sky Survey (SDSS) but none of these shows sufficient evidence for Zeeman splitting of hydrogen lines for a magnetic field in excess of 1 MG. If such high magnetic fields in white dwarfs result from the isolated evolution of a single star then there should be the same fraction of high field white dwarfs among this SDSS binary sample as among single stars. Thus, we deduce that the origin of such high magnetic fields must be intimately tied to the formation of cataclysmic variables (CVs). The formation of a CV must involve orbital shrinkage from giant star to main-sequence star dimensions. It is believed that this shrinkage occurs as the low-mass companion and the white dwarf spiral together inside a common envelope. CVs emerge as very close but detached binary stars that are then brought together by magnetic braking or gravitational radiation. We propose that the smaller the orbital separation at the end of the common envelope phase, the stronger the magnetic field. The magnetic cataclysmic variables (MCVs) originate from those common envelope systems that almost merge. Those common envelope systems that do merge are the progenitors of the single high field white dwarfs. Thus all highly magnetic white dwarfs, be they single stars or the components of MCVs, have a binary origin. This accounts for the relative dearth of single white dwarfs with fields of 10-10 G. Such intermediate-field white dwarfs are found preferentially in cataclysmic variables. The bias towards higher masses for highly magnetic white dwarfs is expected if a fraction of these form when two degenerate cores merge in a common envelope. From the space density of single highly magnetic white dwarfs we estimate that about three times as many common envelope events lead to a merged core as to a cataclysmic variable. [ABSTRACT FROM AUTHOR]

The stellar origin of γ-ray bursts can be explained by the rapid release of energy in a highly collimated, extremely relativistic jet. This in turn appears to require a rapidly spinning highly magnetized stellar core that collapses into a magnetic neutron star or a black hole within a relatively massive envelope. They appear to be associated with Type Ib/c supernovae but, with a birth rate of around per galaxy, they are considerably rarer than such supernovae in general. To satisfy all these requirements we hypothesize a binary star model that ends with the merging of an oxygen/neon white dwarf with the carbon/oxygen core of a naked helium star during a common envelope phase of evolution. The rapid spin and high magnetic field are natural consequences of such a merging. The evolution that leads to these progenitors is convoluted and so naturally occurs only very rarely. To test the hypothesis we evolve a population of progenitors and find that the rate is as required. At low metallicity we calculate that a similar fraction of stars evolve to this point and so would expect the γ-ray burst rate to correlate with the star formation rate in any galaxy. This too is consistent with observations. These progenitors, being of intermediate mass, differ radically from the usually postulated high-mass stars. Thus we can reconcile observations that the bursts occur close to but not within massive star associations. [ABSTRACT FROM AUTHOR]

GD 356 is unique among magnetic white dwarfs because it shows Zeeman-split Balmer lines in pure emission. The lines originate from a region of nearly uniform field strength that covers 10 per cent of the stellar surface in which there is a temperature inversion. The energy source that heats the photosphere remains a mystery but it is likely to be associated with the presence of a companion. Based on current models, we use archival Spitzer Infrared Array Camera (IRAC) observations to place a new and stringent upper limit of for the mass of such a companion. In the light of this result and the recent discovery of a 115-min photometric period for GD 356, we exclude previous models that invoke accretion and revisit the unipolar inductor model that has been proposed for this system. In this model, a highly conducting planet with a metallic core orbits the magnetic white dwarf and, as it cuts through field lines, a current is set flowing between the two bodies. This current dissipates in the photosphere of the white dwarf and causes a temperature inversion. Such a planet is unlikely to have survived both the red and asymptotic giant branch phases of evolution so we argue that it may have formed from the circumstellar disc of a disrupted He or CO core during a rare merger of two white dwarfs. GD 356 would then be a white dwarf counterpart of the millisecond binary pulsar PSR 1257+12 which is known to host a planetary system. [ABSTRACT FROM AUTHOR]

It has generally been assumed that neutron stars (NSs) that become millisecond pulsars (MSPs) originated in a core–collapse supernova. The possibility of formation by accretion-induced collapse (AIC) of an oxygen/neon white dwarf (WD) has largely been ignored or considered negligible. Here, we demonstrate that population synthesis calculations with generic assumptions yield birthrates of binary MSPs via AIC that are comparable to and can exceed those for core collapse. Allowing both modes for NS formation, we estimate birthrates and orbital period distributions and compare these with observations of binary MSPs and low-mass X-ray binaries. Our calculations show that both the core–collapse and AIC routes lead to populations of binary systems that can be identified with X-ray binaries while transferring matter and binary MSPs at the end of an accretion phase. The estimated birthrates indicate that the often-neglected AIC route cannot be ignored. It also appears that this route can provide a better match to the period distributions of some types of binary MSPs. In particular, it appears to be the major route to the orbital period distribution of long-period (a few days or greater) systems with helium WD companions under certain model assumptions. The birthrate problem confronting the low- and intermediate-mass X-ray binaries remains but can still be resolved by invocation of irradiation-driven limit cycles. [ABSTRACT FROM AUTHOR]

The surface magnetic field strength of white dwarfs is observed to vary from very little to around . Here, we examine the proposal that the strongest fields are generated by dynamo action during the common envelope phase of strongly interacting stars that leads to binary systems containing at least one white dwarf. The resulting magnetic field depends strongly on the electrical conductivity of the white dwarf, the lifetime of the convective envelope and the variability of the magnetic dynamo. We assess the various energy sources available and estimate necessary lifetimes of the common envelope. In the case of a dynamo that leads a randomly oriented magnetic field, we find that the induced field is confined to a thin boundary layer at the surface of the white dwarf. This then decays away rapidly upon dispersal of the common envelope. The residual field is typically less than 10−8 times the strength of the external field. Only in the case where there is some preferential direction to the dynamo-generated field can an induced field, which avoids rapid decay, be produced. We show that a surface field of a magnitude a few per cent of the external field may be produced after a few Myr. In this case, the residual field strength is roughly proportional to the lifetime of the dynamo activity. [ABSTRACT FROM AUTHOR]

We study the formation of ultracompact binaries (AM CVn stars and ultracompact X-ray binaries) with emphasis on the surface chemical abundances of the donors in these systems. Hydrogen is not convincingly detected in the spectra of any these systems. Three different proposed formation scenarios involve different donor stars, white dwarfs, helium stars or evolved main-sequence stars. Using detailed evolutionary calculations we show that the abundances of helium white dwarf donors and evolved main-sequence stars are close to equilibrium CNO-processed material, and the detailed abundances correlate with the core temperature and thus mass of the main-sequence progenitors. Evolved main-sequence donors typically have traces of H left. For hybrid or carbon/oxygen white dwarf donors, the carbon and oxygen abundances depend on the temperature of the helium burning and thus on the helium core mass of the progenitors. For helium star donors, in addition to their mass, the abundances depend strongly on the amount of helium burnt before mass transfer starts and can range from unprocessed and thus almost equal to CNO-processed matter, to strongly processed and thus C/O rich and N-deficient. We briefly discuss the relative frequency of these cases for helium star donors, based on population synthesis results. Finally, we give diagnostics for applying our results to observed systems and find that the most important test is the N/C ratio, which can indicate the formation scenario as well as, in some cases, the mass of the progenitor of the donor. In addition, if observed, the N/O, O/He and O/C ratios can distinguish between helium star and white dwarf donors. Applied to the known systems, we find evidence for white dwarf donors in the AM CVn systems GP Com, CE 315 and SDSS J0804+16 and evidence for hybrid white dwarf or very evolved helium star donors in the ultracompact X-ray binaries 4U and 4U 0614+09. [ABSTRACT FROM AUTHOR]

Doubly-degenerate binary systems consisting of two white dwarfs (WDs) both composed of carbon and oxygen and close enough that mass is transferred from the less massive to the more massive are possible progenitors of Type Ia supernovae. If the mass-transfer rate is slow enough that the accreting WD can reach a mass of 1.38 M⊙, then it can ignite carbon degenerately at its centre. This can lead to a thermonuclear runaway and hence a supernova explosion. However, if the accretion rate is too high the outer layers of the WD heat up too much and carbon ignites there non-degenerately. A series of mild carbon flashes can then propagate inwards and convert the carbon to neon relatively gently. There is no thermonuclear runaway and no supernova. We examine the critical accretion rate at which ignition switches from the centre to the surface for a variety of WDs and find it to be about two-fifths of the Eddington rate. In a real binary star, the mass-transfer rate falls off as mass transfer proceeds and the system widens. Even if the initial transfer rate is high enough for carbon to ignite at the outer edge, if such rapid accretion were to persist, we find that it can extinguish if the rate drops sufficiently quickly. The interior of the WD remains carbon rich and, if sufficient mass can still be transferred from the companion, it can eventually ignite degenerately at the centre. The primary WD must be about 1.1 M⊙ or above and the companion about 0.3 M⊙. Though WDs of such low mass are expected to be pure helium, we note that a star of initial mass 2.5 M⊙ has a CO core of about 0.3 M⊙ when it begins to ascend the asymptotic giant branch. Alternatively, if the accretion rate can be limited to a maximum of 0.46 of the Eddington rate, then a 1.1-M⊙ WD accretes sufficiently slowly to explode from a companion WD of any large enough mass. [ABSTRACT FROM AUTHOR]

The old open cluster M67 is an ideal testbed for current cluster evolution models because of its dynamically evolved structure and rich stellar populations that show clear signs of interaction between stellar, binary and cluster evolution. Here, we present the first truly direct N-body model for M67, evolved from zero age to 4 Gyr taking full account of cluster dynamics as well as stellar and binary evolution. Our preferred model starts with 36 000 stars (12 000 single stars and 12 000 binaries) and a total mass of nearly , placed in a Galactic tidal field at 8.0 kpc from the Galactic Centre. Our choices for the initial conditions and for the primordial binary population are explained in detail. At 4 Gyr, the age of M67, the total mass has reduced to as a result of mass loss and stellar escapes. The mass and half-mass radius of luminous stars in the cluster are a good match to observations, although the model is more centrally concentrated than observations indicate. The stellar mass and luminosity functions (LFs) are significantly flattened by preferential escape of low-mass stars. We find that M67 is dynamically old enough that information about the initial mass function (IMF) is lost, both from the current LF and from the current mass fraction in white dwarfs (WDs). The model contains 20 blue stragglers (BSs) at 4 Gyr, which is slightly less than the 28 observed in M67. Nine are in binaries. The blue stragglers were formed by a variety of means and we find formation paths for the whole variety observed in M67. Both the primordial binary population and the dynamical cluster environment play an essential role in shaping the population. A substantial population of short-period primordial binaries (with periods less than a few days) is needed to explain the observed number of BSs in M67. The evolution and properties of two-thirds of the BSs, including all found in binaries, have been altered by cluster dynamics and nearly half would not have formed at all outside the cluster environment. On the other hand, the cluster environment is also instrumental in destroying potential BSs from the primordial binary population, so that the total number is in fact slightly smaller than what would be expected from evolving the same binary stars in isolation. [ABSTRACT FROM AUTHOR]

ABSTRACT The surface magnetic field strengths observed in the magnetic Ap, Bp stars (100-20 000 G) and in the high field magnetic white dwarfs (106-109 G) cover many decades but nevertheless the range of magnetic fluxes observed in each of these stellar groups is similar. An evolutionary link between them therefore appears plausible. For both groups of stars there is also information on field complexity. The magnetic white dwarfs in general show non-dipole field structures which can be best modelled if we assume contributions from higher order multipoles. The field structures of the Ap and Bp stars are similarly complex. We investigate the hypothesis that the magnetic fields of the white dwarfs could be fossil remnants from the main-sequence phase by focussing on the problem of how field complexity may arise and be maintained during evolution to the compact star state. We also address the question of to what extent magnetic fields seen in the early type stars could be fossil remnants from the pre-main-sequence phases of stellar evolution dating back perhaps to the time of star formation. [ABSTRACT FROM AUTHOR]