Zhanwen Han

The origin of subdwarf B stars – I. The formation channels

Subdwarf B (sdB) stars (and related sdO/sdOB stars) are believed to be helium-core-burning objects with very thin hydrogen-rich envelopes. In recent years it has become increasingly clear from observational surveys that a large fraction of these objects are members of binary systems. To understand their formation better, we present the results of a detailed investigation of the three main binary evolution channels that can lead to the formation of sdB stars: the common-envelope (CE) ejection channel, the stable Roche lobe overflow (RLOF) channel, and the double helium white dwarfs (WDs) merger channel. The CE ejection channel leads to the formation of sdB stars in short-period binaries with typical orbital periods between 0.1 and 10 d, very thin hydrogen-rich envelopes and a mass distribution sharply peaked around similar to0.46 M-.. On the other hand, under the assumption that all mass transferred is soon lost, the stable RLOF channel produces sdB stars with similar masses but long orbital periods (400-1500 d) and with rather thick hydrogen-rich envelopes. The merger channel gives rise to single sdB stars whose hydrogen-rich envelopes are extremely thin but which have a fairly wide distribution of masses (0.4-0.65 M-.). We obtained the conditions for the formation of sdB stars from each of these channels using detailed stellar and binary evolution calculations where we modelled the detailed evolution of sdB stars and carried out simplified binary population synthesis simulations. The observed period distribution of sdB stars in compact binaries strongly constrains the CE ejection parameters. The best fits to the observations are obtained for very efficient CE ejection where the envelope ionization energy is included, consistent with previous results. We also present the distribution of sdB stars in the T (eff) -log g diagram, the Hertzsprung-Russell diagram and the distribution of mass functions.

Approximate input physics for stellar modelling

We present a simple and efficient, yet reasonably accurate, equation of state, which at the moderately low temperatures and high densities found in the interiors of stars less massive than the Sun is substantially more accurate than its predecessor by Eggleton, Faulkner & Flannery. Along with the most recently available values in tabular form of opacities, neutrino loss rates, and nuclear reaction rates for a selection of the most important reactions, this provides a convenient package of input physics for stellar modelling. We briefly discuss a few results obtained with the updated stellar evolution code.

The origin of subdwarf B stars – II

We have carried out a detailed binary population synthesis (BPS) study of the formation of subdwarf B (sdB) stars and related objects (sdO, sdOB stars) using the latest version of the BPS code developed by Han and co-workers. We systematically investigate the importance of the five main evolutionary channels in which the sdB stars form after one or two common-envelope (CE) phases, one or two phases of stable Roche lobe overflow (RLOF) or as the result of the merger of two helium white dwarfs (WDs). Our best BPS model can satisfactorily explain the main observational characteristics of sdB stars, in particular their distributions in the orbital period-minimum companion mass (log P-M-comp) diagram and in the effective temperature-surface gravity (T-eff- log g) diagram, their distributions of orbital period, log (gtheta(4))(theta = 5040 K / T-eff) and mass function, their binary fraction and the fraction of sdB binaries with WD companions, their birth rates and their space density. We obtain a Galactic formation rate for sdB stars of 0.014- 0.063 yr(-1) with a best estimate of similar to0.05 yr(-1) and a total number in the Galaxy of 2.4-9.5 x 10(6) with a best estimate of similar to6 x 10(6); half of these may be missing in observational surveys owing to selection effects. The intrinsic binary fraction is 76-89 per cent, although the observed frequency may be substantially lower owing to the selection effects. The first CE ejection channel, the first stable RLOF channel and the merger channel are intrinsically the most important channels, although observational selection effects tend to increase the relative importance of the second CE ejection and merger channels. We also predict a distribution of masses for sdB stars that is wider than is commonly assumed and that some sdB stars have companions of spectral type as early as B. The percentage of A-type stars with sdB companions can in principle be used to constrain some of the important parameters in the binary evolution model. We conclude that (i) the first RLOF phase needs to be more stable than is commonly assumed, either because the critical mass ratio q(crit) for dynamical mass transfer is higher or because of tidally enhanced stellar wind mass loss; (ii) mass transfer in the first stable RLOF phase is non-conservative, and the mass lost from the system takes away a specific angular momentum similar to that of the system; and (iii) common-envelope ejection is very efficient.

The single-degenerate channel for the progenitors of Type Ia supernovae

We have carried out a detailed studyh of one of the most favoured evolutionary channels for the production of Type Ia supernova (SN Ia) progenitors, the single-degenerate channel (CO + MS), where a carbon/oxygen (CO) white dwarf (WD) accretes matter from an unevolved or slightly evolved non-degenerate star until it reaches the Chandrasekhar mass limit. Employing Eggletons stellar evolution code and adopting the prescription of Hachisu et al. for the accretion efficiency, we performed binary stellar evolution calculations for about 2300 close WD binary systems and mapped out the initial parameters in the orbital period-secondary mass (P-M(2)) plane (for a range of WD masses) which lead to a successful Type Ia supernova. We obtained accurate, analytical fitting formulae to describe this parameter range which can be used for binary population synthesis (BPS) studies. The contours in the P-M(2) plane differ from those obtained by Hachisu et al. for low-mass CO WDs, which are more common than massive CO WDs. We confirm that WDs with a mass as low as 0.67 M. can accrete efficiently and reach the Chandrasekhar limit. We have implemented these results in a BPS study to obtain the birth rates for SNe Ia and the evolution of birth rates with time of SNe Ia for both a constant star formation rate and a single starburst. The birth rates are lower than (but comparable to) those inferred observationally.

Common envelope evolution: where we stand and how we can move forward

This work aims to present our current best physical understanding of common-envelope evolution (CEE). We highlight areas of consensus and disagreement, and stress ideas which should point the way forward for progress in this important but long-standing and largely unconquered problem. Unusually for CEE-related work, we mostly try to avoid relying on results from population synthesis or observations, in order to avoid potentially being misled by previous misunderstandings. As far as possible we debate all the relevant issues starting from physics alone, all the way from the evolution of the binary system immediately before CEE begins to the processes which might occur just after the ejection of the envelope. In particular, we include extensive discussion about the energy sources and sinks operating in CEE, and hence examine the foundations of the standard energy formalism. Special attention is also given to comparing the results of hydrodynamic simulations from different groups and to discussing the potential effect of initial conditions on the differences in the outcomes. We compare current numerical techniques for the problem of CEE and also whether more appropriate tools could and should be produced (including new formulations of computational hydrodynamics, and attempts to include 3D processes within 1D codes). Finally we explore new ways to link CEE with observations. We compare previous simulations of CEE to the recent outburst from V1309 Sco, and discuss to what extent post-common-envelope binaries and nebulae can provide information, e.g. from binary eccentricities, which is not currently being fully exploited.

Progenitors of Type Ia Supernovae

Type Ia supernovae (SNe Ia) play an important role in astrophysics and are crucial for the studies of stellar evolution, galaxy evolution and cosmology. They are generally thought to be thermonuclear explosions of accreting carbon-oxygen white dwarfs (CO WDs) in close binaries, however, the nature of the mass donor star is still unclear. In this article, we review various progenitor models proposed in the past years and summarize many observational results that can be used to put constraints on the nature of their progenitors. We also discuss the origin of SN Ia diversity and the impacts of SN Ia progenitors on some fields. The currently favourable progenitor model is the single-degenerate (SD) model, in which the WD accretes material from a non-degenerate companion star. This model may explain the similarities of most SNe Ia. It has long been argued that the double-degenerate (DD) model, which involves the merger of two CO WDs, may lead to an accretion-induced collapse rather than a thermonuclear explosion. However, recent observations of a few SNe Ia seem to support the DD model, and this model can produce normal SN la explosion under certain conditions. Additionally, the sub-luminous SNe la may be explained by the sub-Chandrasekhar mass model. At present, it seems likely that more than one progenitor model, including some variants of the SD and DD models, may be required to explain the observed diversity of SNe Ia. Crown Copyright (C) 2012 Published by Elsevier B.V. All rights reserved.

On the formation and evolution of black hole binaries

We present the results of a systematic study of the formation and evolution of binaries containing black holes and normal-star companions with a wide range of masses. We first reexamine the standard formation scenario for close black hole binaries, where the progenitor system, a binary with at least one massive component, experienced a common-envelope phase and where the spiral-in of the companion in the envelope of the massive star caused the ejection of the envelope. We estimate the formation rates for different companion masses and different assumptions about the common-envelope structure and other model parameters. We find that black hole binaries with intermediate- and high-mass secondaries can form for a wide range of assumptions, while black hole binaries with low-mass secondaries can only form with apparently unrealistic assumptions (in agreement with previous studies). We then present detailed binary evolution sequences for black hole binaries with secondaries of 2 to 17 M(circle dot) and demonstrate that in these systems the black hole can accrete appreciably even if accretion is Eddington-limited (up to 7 M(circle dot) for an initial black hole mass of 10 M(circle dot) ) and that the black holes can be spun up significantly in the process. We discuss the implications of these calculations for well-studied black hole binaries (in particular GRS 1915+105) and ultraluminous X-ray sources of which GRS 1915+105 appears to represent a typical Galactic counterpart. We also present a detailed evolutionary model for Cygnus X-1, a massive black hole binary, which suggests that at present the system is most likely in a wind mass-transfer phase following an earlier Roche-lobe overflow phase. Finally, we discuss how some of the assumptions in the standard model could be relaxed to allow the formation of low-mass, short-period black hole binaries, which appear to be very abundant in nature.

Low and intermediate-mass close binary evolution and the initial - final mass relation

Using Eggletons stellar evolution code, we carry out 150 runs of Population I binary evolution calculations with the initial primary mass between 1 and 8 M-circle dot, the initial mass ratio q = M-1/M-2 between 1.1 and 4, and the onset of Roche lobe overflow (RLOF) at an early, middle or late Hertzsprung-gap stage. We assume that PLOP is conservative in the calculations, and find that the remnant mass of the primary may change by more than 40 per cent over the range of initial mass ratio or orbital period, for a given primary mass. This is contrary to the often-held belief that the remnant mass depends only on the progenitor mass if mass transfer begins in the Hertzsprung gap. We fit a formula, with an error less than 3.6 per cent, for the remnant (white dwarf) mass as a function of the initial mass M-li of the primary, the initial mass ratio q(i) and the radius of the primary at the onset of RLOF We also find that a carbon-oxygen white dwarf with mass as low as 0.33 M-circle dot may be formed if the initial mass of the primary is around 2.5 M-circle dot.

The helium star donor channel for the progenitors of Type Ia supernovae

Type Ia supernovae (SNe Ia) play an important role in astrophysics, especially in the study of cosmic evolution. Several progenitor models for SNe Ia have been proposed in the past. In this paper we carry out a detailed study of the He star donor channel, in which a carbon-oxygen white dwarf (CO WD) accretes material from a He main-sequence star or a He subgiant to increase its mass to the Chandrasekhar mass. Employing Eggletons stellar evolution code with an optically thick wind assumption, and adopting the prescription of Kato & Hachisu for the mass accumulation efficiency of the He-shell flashes on to the WDs, we performed binary evolution calculations for about 2600 close WD binary systems. According to these calculations, we mapped out the initial parameters for SNe Ia in the orbital period-secondary mass (log P(i)-M(2)(i)) plane for various WD masses from this channel. The study shows that the He star donor channel is noteworthy for producing SNe Ia (similar to 1.2 x 10(-3) yr(-1) in our Galaxy), and that the progenitors from this channel may appear as supersoft X-ray sources. Importantly, this channel can explain SNe Ia with short delay times (similar to 10(8) yr), which is consistent with the recent observational implications of young populations of SN Ia progenitors.

Observations of Doppler Boosting in Kepler Light Curves

Among the initial results from Kepler were two striking light curves, for KOI 74 and KOI 81, in which the relative depths of the primary and secondary eclipses showed that the more compact, less luminous object was hotter than its stellar host. That result became particularly intriguing because a substellar mass had been derived for the secondary in KOI 74, which would make the high temperature challenging to explain; in KOI 81, the mass range for the companion was also reported to be consistent with a substellar object. We re-analyze the Kepler data and demonstrate that both companions are likely to be white dwarfs. We also find that the photometric data for KOI 74 show a modulation in brightness as the more luminous star orbits, due to Doppler boosting. The magnitude of the effect is sufficiently large that we can use it to infer a radial velocity amplitude accurate to 1 km s(-1). As far as we are aware, this is the first time a radial-velocity curve has been measured photometrically. Combining our velocity amplitude with the inclination and primary mass derived from the eclipses and primary spectral type, we infer a secondary mass of 0.22 +/- 0.03 M(circle dot). We use our estimates to consider the likely evolutionary paths and mass-transfer episodes of these binary systems.