The Theoretical Mass--Magnitude Relation of Low-Mass Stars and its Metallicity Dependence

We investigate the dependence of theoretically generated mass - (absolute magnitude) relations on stellar models. Using up to date physics we compute models in the mass range 0.1 < m < 1M_sun. We compare the solar-metallicity models with our older models, with recent models computed by others, and also with an empirical mass - (absolute magnitude) relation that best fits the observed data. At a given mass below 0.6M_sun the effective temperatures differ substantially from model to model. However taken individually each set of models is in good agreement with observations in the mass - luminosity plane. A minimum in the derivative dm/dM_V at M_V = 11.5, which is due to H_2 formation and establishment of a fully convective stellar interior, is present in all photometric bands, for all models. This minimum leads to a maximum in the stellar luminosity function for Galactic disk stars at M_V = 11.5, M_bol = 9.8. Stellar models should locate this maximum in the stellar luminosity function at the same magnitude as observations. Models which incorporate the most realistic theoretical atmospheres and the most recent equation of state and opacities can satisfy this constraint. These models are also in best agreement with the most recent luminosity - (effective temperature) and mass-luminosity data. Each set of our models of a given metallicity (with 0.2 > [Fe/H] > -2.3) shows a maximum in -dm/dM_bol, which moves to brighter bolometric magnitudes with decreasing metallicity. The change in location of the maximum, as a function of [Fe/H], follows the location of structure in luminosity functions for stellar populations with different metal abundances. This structure seen in all observed stellar populations can be accounted for by the mass--luminosity relation.Comment: MNRAS (in press), 15 pages, 1 appendix, plain TeX, 9 postscript figure

The Binary Second Sequence in Cluster Colour--Magnitude Diagrams

We show how the second sequence seen lying above the main sequence in cluster colour magnitude diagrams results from binaries with a large range of mass ratios and not just from those with equal masses. We conclude that the presence of a densely populated second sequence, with only sparse filling in between it and the single star main sequence, does not necessarily imply that binary mass ratios are close to unity.Comment: Accepted to MNRAS. 5 Pages including 3 figure

Hibernation Revived by Weak Magnetic Braking

Cataclysmic variables undergo periodic nova explosions during which a finite mass of material is expelled on a short timescale. The system widens and, as a result, the mass-transfer rate drops. This state of hibernation may account for the variety of cataclysmic variable types observed in systems of similar mass and period. In the light of recent changes to the theory of nova ignition and magnetic braking we investigate whether hibernation remains a viable mechanism for creating cataclysmic variable diversity. We model the ratio of time spent as dwarf novae (DNe) to nova-like systems (NLs). Above a critical mass-transfer rate the system is NL and below it a DN. The dominant loss of angular momentum is by magnetic braking but the rate is uncertain. It is also uncertain what fraction of the mass accreted is expelled during the novae. We compare the models of the ratios against the period of the system for different magnetic braking rates and different ejected masses with the ratio of the number of observed NLs to DNe. We deduce that a rate of angular momentum loss a factor of ten smaller than that traditionally assumed is necessary if hibernation is to account for the observed ratios

Spin Angular Momentum Evolution of the Long Period Algols

We consider the spin angular momentum evolution of the accreting components of Algol-type binary stars. In wider Algols the accretion is through a disc so that the accreted material can transfer enough angular momentum to the gainer that material at its equator should be spinning at break-up. We demonstrate that even a small amount of mass transfer, much less than required to produce today's mass ratios, transfers enough angular momentum to spin the gainer up to this critical rotation velocity. However the accretors in these systems have spins typically between 10 and $40\,$per cent of the critical rate. So some mechanism for angular momentum loss from the gainers is required. We consider generation of magnetic fields in the radiative atmospheres in a differentially rotating star and the possibility of angular momentum loss driven by strong stellar winds in the intermediate mass stars, such as the primaries of the Algols. Differential rotation, induced by the accretion itself, may produce such winds which carry away enough angular momentum to reduce their rotational velocities to the today's observed values. We apply this model to two systems with initial periods of 5\,d, one with initial masses 5 and $3\,\rm{M}_{\odot}$ and the other with 3.2 and $2\,\rm{M}_{\odot}$. Our calculations show that, if the mass outflow rate in the stellar wind is about $10\,$per cent of the accretion rate and the dipole magnetic field is stronger than about $1\,$kG, the spin rate of the gainer is reduced to below break-up velocity even in the fast phase of mass transfer. Larger mass loss is needed for smaller magnetic fields. The slow rotation of the gainers in the classical Algol systems is explained by a balance between the spin-up by mass accretion and spin-down by a stellar wind linked to a magnetic field.Comment: 12 figures, 26 pages, accepted in MNRA

The Most Magnetic Stars

Observations of magnetic A, B and O stars show that the poloidal magnetic flux per unit mass has an upper bound of 10^-6.5 G cm^2/g. A similar upper bound is found for magnetic white dwarfs even though the highest magnetic field strengths at their surfaces are much larger. For magnetic A and B stars there also appears to be a well defined lower bound below which the incidence of magnetism declines rapidly. According to recent hypotheses, both groups of stars may result from merging stars and owe their strong magnetism to fields generated by a dynamo mechanism as they merge. We postulate a simple dynamo that generates magnetic field from differential rotation. The growth of magnetic fields is limited by the requirement that the poloidal field stabilizes the toroidal and vice versa. While magnetic torques dissipate the differential rotation, toroidal field is generated from poloidal by an Omega dynamo. We further suppose that mechanisms that lead to the decay of toroidal field lead to the generation of poloidal. Both poloidal and toroidal fields reach a stable configuration which is independent of the size of small initial seed fields but proportional to the initial differential rotation. We pose the hypothesis that strongly magnetic stars form from the merging of two stellar objects. The highest fields are generated when the merge introduces differential rotation that amounts to critical break up velocity within the condensed object. Calibration of a simplistic dynamo model with the observed maximum flux per unit mass for main-sequence stars and white dwarfs indicates that about 1.5x10^-4 of the decaying toroidal flux must appear as poloidal. The highest fields in single white dwarfs are generated when two degenerate cores merge inside a common envelope or when two white dwarfs merge by gravitational-radiation angular momentum loss.Comment: accepted by MNRAS 8 pages, 3 figure

Evolution of binary stars and the effect of tides on binary populations

We present a rapid binary evolution algorithm that enables modelling of even the most complex binary systems. In addition to all aspects of single star evolution, features such as mass transfer, mass accretion, common-envelope evolution, collisions, supernova kicks and angular momentum loss mechanisms are included. In particular, circularization and synchronization of the orbit by tidal interactions are calculated for convective, radiative and degenerate damping mechanisms. We use this algorithm to study the formation and evolution of various binary systems. We also investigate the effect that tidal friction has on the outcome of binary evolution. Using the rapid binary code, we generate a series of large binary populations and evaluate the formation rate of interesting individual species and events. By comparing the results for populations with and without tidal friction we quantify the hitherto ignored systematic effect of tides and show that modelling of tidal evolution in binary systems is necessary in order to draw accurate conclusions from population synthesis work. Tidal synchronism is important but because orbits generally circularize before Roche-lobe overflow the outcome of the interactions of systems with the same semi-latus rectum is almost independent of eccentricity. It is not necessary to include a distribution of eccentricities in population synthesis of interacting binaries, however, the initial separations should be distributed according to the observed distribution of semi-latera recta rather than periods or semi-major axes.Comment: 36 pages, 12 figures, to be published in the Monthly Notices of the Royal Astronomical Societ