ABSTRACT
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 (WDs) down to temperatures $\log _{10}(T_\mathrm{eff}/\mathrm{K})\, =\, 3$. 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 WDs in CVs 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.
ABSTRACT
We extend a magnetic braking (MB) model, which has been used earlier to address the evolution of cataclysmic variables, to address the spin period Pspin evolution of fully convective M-dwarf ...(FCMD) stars. The MB mechanism is an α–Ω dynamo, which leads to stellar winds that carry away angular momentum. We model our MB torque such that the FCMDs experience an MB torque, approximately scaling as $P_\mathrm{spin}^{-1}$ at shorter periods, before transitioning into a Skumanich-type MB torque, scaling as $P_\mathrm{spin}^{-3}$. We also implement a parametrized reduction in the wind mass-loss owing to the entrapment of winds in dead zones. We choose a set of initial conditions and vary the two free parameters in our model to find a good match of our spin trajectories with open clusters containing FCMDs such as NGC2547, Pleiades, NGC2516, and Praesepe. We find that our model can explain the long spin periods of field stars and that a spread in spin distribution persists till over 3 Gyr. An advantage of our model is in relating physically motivated estimations of the magnetic field strength and stellar wind to properties of the stellar dynamo, which other models often remain agnostic about. We track the spin dependence of the wind mass-losses, Alfvén radii, and surface magnetic fields and find good agreement with observations. We discuss the implications of our results on the effect of the host FCMD on any orbiting exoplanets and our plans to extend this model to explain solar-like stars in the future.
When a core-collapse supernova occurs in a binary system, the surviving star as well as the compact remnant emerging from the supernova may reach a substantial space velocity. With binary population ...synthesis modelling at solar and one-fifth of solar metallicity, we predict the velocities of such runaway stars or binaries. We compile predictions for runaway OB stars, red supergiants and Wolf-Rayet stars, either isolated or with a compact companion. For those stars or binaries which undergo a second stellar explosion we compute their further evolution and the distance travelled until a Type II or Type Ibc supernova or a long or short gamma-ray burst (GRB) occurs. We find our predicted population of OB runaway stars broadly matches the observed population of stars but, to match the fastest observed Wolf-Rayet runaway stars, we require that black holes receive an asymmetric kick upon formation. We find that at solar metallicity Type Ic supernova progenitors travel shorter distances than the progenitors of other supernova types because they are typically more massive and thus have shorter lifetimes. Those of Type IIP supernovae can fly farthest about 48 pc on average at solar metallicity, with about 8 per cent of them reaching 100 pc. In considering the consequences of assuming that the progenitors of long GRBs are spun-up secondary stars that experience quasi-homogeneous evolution, we find that such evolution has a dramatic effect on the population of runaway Wolf-Rayet stars and that some 30 per cent of GRBs could occur a hundred parsec or more from their initial positions. We also consider mergers of double compact object binaries consisting of neutron stars and/or black holes. We find the most common type of visible mergers are neutron star-black hole mergers that are roughly 10 times more common than neutron star-neutron star mergers. All compact mergers have a wide range of merger times from years to Gyr and are predicted to occur 300 times less often than supernovae in the Milky Way. We also find that there may be a population of low-velocity neutron stars that are ejected from a binary rather than by their own natal kick. These neutron stars need to be included when the distribution of neutron star kicks is deduced from observations.
ABSTRACT
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
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
We explore the luminosity L of magnetized white dwarfs and its effect on the mass–radius relation. We self-consistently obtain the interface between the electron degenerate-gas dominated ...inner core and the outer ideal gas surface layer or envelope by incorporating both the components of gas throughout the model white dwarf. This is obtained by solving the set of magnetostatic equilibrium, photon diffusion, and mass conservation equations in the Newtonian framework, for different sets of luminosity and magnetic field. We appropriately use magnetic opacity, instead of Kramer’s opacity, wherever required. We show that the Chandrasekhar limit is retained, even at high luminosity up to about $10^{-2}\, L_\odot$ but without magnetic field, if the temperature is set constant inside the interface. However, there is an increased mass for large-radius white dwarfs, an effect of photon diffusion. Nevertheless, in the presence of strong magnetic fields, with central strength of about 1014 G, super-Chandrasekhar white dwarfs, with masses of about $1.9\, {\rm M}_{\odot }$, are obtained even when the temperature inside the interface is kept constant. Most interestingly, small-radius magnetic white dwarfs remain super-Chandrasekhar even if their luminosity decreases to as low as about $10^{-20}\, L_{\odot }$. However, their large-radius counterparts in the same mass–radius relation merge with Chandrasekhar’s result at low L. Hence, we argue for the possibility of highly magnetized, low luminous super-Chandrasekhar mass white dwarfs that, owing to their faintness, can be practically hidden.
We compare our latest single and binary stellar model results from the Cambridge stars code to several sets of observations. We examine four stellar population ratios: the number of blue to red ...supergiants, the number of Wolf–Rayet stars to O supergiants, the number of red supergiants to Wolf–Rayet stars and the relative number of Wolf–Rayet subtypes, WC to WN stars. These four ratios provide a quantitative measure of nuclear burning lifetimes and the importance of mass loss during various stages of the stars' lifetimes. In addition, we compare our models to the relative rate of Type Ib/c to Type II supernovae to measure the amount of mass lost over the entire lives of all stars. We find reasonable agreement between the observationally inferred values and our predicted values by mixing single and binary star populations. However, there is evidence that extra mass loss is required to improve the agreement further, to reduce the number of red supergiants and increase the number of Wolf–Rayet stars.
ABSTRACT
For stars with unresolved companions, motions of the centre of light and that of mass decouple, causing a single-source astrometric model to perform poorly. We show that such stars can be ...easily detected with the reduced χ2 statistic, or renormalized unit weight error (RUWE), provided as part of Gaia DR2. We convert RUWE into the amplitude of the image centroid wobble, which, if scaled by the source distance, is proportional to the physical separation between companions (for periods up to several years). We test this idea on a sample of known spectroscopic binaries and demonstrate that the amplitude of the centroid perturbation scales with the binary period and the mass ratio as expected. We apply this technique to the Gaia DR2 data and show how the binary fraction evolves across the Hertzsprung–Russell diagram. The observed incidence of unresolved companions is high for massive young stars and drops steadily with stellar mass, reaching its lowest levels for white dwarfs. We highlight the elevated binary fraction for the nearby blue stragglers and blue horizontal branch stars. We also illustrate how unresolved hierarchical triples inflate the relative velocity signal in wide binaries. Finally, we point out a hint of evidence for the existence of additional companions to the hosts of extrasolar hot Jupiters.
ABSTRACT
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 (B-WDs), with masses significantly higher than the Chandrasekhar limit. Surface magnetic fields of such white dwarfs could be more than $10^{9}$ G 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 $10^9$ G). In this paper, we reformulate the virial theorem for non-rotating 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 is 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.
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