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Eclipsing binary millisecond pulsars (the so-called black widows and redbacks) can provide important information about accretion history, pulsar irradiation of their companion stars and the evolutionary link between accreting X-ray pulsars and isolated millisecond pulsars. However, the formation of such systems is not well understood, nor the difference in progenitor evolution between the two populations of black widows and redbacks. Whereas both populations have orbital periods between $0.1-1.0\;{\rm days}$ their companion masses differ by an order of magnitude. In this paper, we investigate the formation of these systems via evolution of converging low-mass X-ray binaries by employing the MESA stellar evolution code. Our results confirm that one can explain the formation of most of these eclipsing binary millisecond pulsars using this scenario. More notably, we find that the determining factor for producing either black widows or redbacks is the efficiency of the irradiation process, such that the redbacks absorb a larger fraction of the emitted spin-down energy of the radio pulsar (resulting in more efficient mass loss via evaporation) compared to that of the black widow systems. We argue that geometric effects (beaming) is responsible for the strong bimodality of these two populations. Finally, we conclude that redback systems do not evolve into black widow systems with time., Comment: 19 pages, 5 figures. Accepted for publication

The accretion of hydrogen-rich material onto carbon-oxygen white dwarfs (CO WDs) is crucial for understanding type Ia supernova (SN Ia) from the single-degenerate model, but this process has not been well understood due to the numerical difficulties in treating H and He flashes during the accretion. For the CO WD masses from 0.5 to $1.378\,{M}_\odot$ and accretion rates in the range from $10^{-8}$ to $10^{-5}\,{M}_\odot\,\mbox{yr}^{-1}$, we simulated the accretion of solar-composition material onto CO WDs using the state-of-the-art stellar evolution code of {\sc MESA}. For comparison with the steady-state models (e.g \citet{nskh07}), we firstly ignored the contribution from nuclear burning to the luminosity when determining the Eddington accretion rate and found that the properties of H burning in our accreting CO WD models are similar to those from the steady-state models, except that the critical accretion rates at which the WDs turn into red giants or H-shell flashes occur on their surfaces are slightly higher than those from the steady-state models. However, the super-Eddington wind is triggered at much lower accretion rates, than previously thought, when the contribution of nuclear burning to the total luminosity is included. This super-Eddington wind naturally prevents the CO WDs with high accretion rates from becoming red giants, thus presenting an alternative to the optically thick wind proposed by \cite{hkn96}. Furthermore, the super-Eddington wind works in low-metallicity environments, which may explain SNe Ia observed at high redshifts., Comment: 14 pages, 4 figures, 1 table. Accepted for publication in ApJL

Long-orbital-period subdwarf B (sdB) stars with main-sequence companions are believed to be the product of stable Roche Lobe overflow (RLOF), a scenario challenged by recent observations. Here we represent the results of a systematic study of the orbital-period distribution of sdB binaries in this channel using detailed binary evolution calculations. We show that the observed orbital-period distribution of long-period sdB binaries can be well explained by this scenario. Furthermore, we find that, if the progenitors of the sdB stars have initial masses below the helium flash mass, the sdB binaries produced from stable RLOF follow a unique mass -- orbital period relation for a given metallicity $Z$; increasing the orbital period from $\sim 400$ to $\sim 1100$\,d corresponds to increasing the mass of the sdB star from $\sim 0.40$ to $\sim 0.49\,M_\odot$ for $Z=0.02$. We suggest that the longest sdB binaries (with orbital period $> 1100$\,d) could be the result of atmospheric RLOF. The mass -- orbital period relation can be tested observationally if the mass of the sdB star can be determined precisely, e.g.\ from asteroseismology. Using this relation, we revise the orbital period distribution of sdB binaries produced by the first stable RLOF channel for the best fitting model of Han et al (2003), and show that the orbital period has a peak around 830\,d., Comment: 8 pages, 2 figures, accepted for publication in MNRAS

Recent theoretical and observational studies both argue that the merging of double carbon-oxygen white dwarfs (WDs) is responsible for at least some Type Ia supernovae (SNe Ia). Previous (standard) studies of the anticipated SN birthrate from this channel have assumed that the merger process is conservative and that the primary criterion for explosion is that the merged mass exceeds the Chandrasekhar mass. Han & Webbink (1999) demonstrated that mass transfer and merger in close double WDs will in many cases be non-conservative. Pakmor et al. (2011) further suggested that the merger process should be violent in order to initiate an explosion. We have therefore investigated how the SN Ia birthrate from the double-degenerate (DD) channel is affected by these constraints. Using the binary-star population-synthesis method, we have calculated the DD SN Ia birthrate under conservative and non-conservative approximations, and including lower mass and mass-ratio limits indicated by recent smoothed-particle-hydrodynamic calculations. The predicted DD SN Ia rate is significantly reduced by all of these constraints. With dynamical mass loss alone (violent merger) the birthrate is reduced to 56% of the conservative rate. Requiring that the mass ratio $q>2/3$ further reduces the birthrate to 18% that of the standard assumption. An upper limit of 0.0061 SNuM, or a Galactic rate of $4.6 \times 10^{-4}{\rm yr}^{-1}$, might be realistic., Comment: 13 pages, 2 figures; accepted by ApJ Letters

In the symbiotic (or WD+RG) channel of the single degenerate scenario for type Ia supernovae (SNe Ia) the explosions occur a relatively long time after star formation. The birthrate from this channel would be too low to account for all observed SNe Ia were it not for some mechanism to enhance the rate of accretion on to the white dwarf. A tidally enhanced stellar wind, of the type which has been postulated to explain many phenomena related to giant star evolution in binary systems, can do this. Compared to mass-stripping this model extends the space of SNe Ia progenitors to longer orbital periods and hence increases the birthrate to about $0.0069\,{\rm yr^{-1}}$ for the symbiotic channel. Two symbiotic stars, T CrB and RS Oph, considered to be the most likely progenitors of SNe Ia through the symbiotic channel, are well inside the period--companion mass space predicted by our models., Comment: 13 pages, 4 figures, accepted by ApJ Letters

Roche-lobe overflow and common envelope evolution are very important in binary evolution, which is believed to be the main evolutionary channel to hot subdwarf stars. The details of these processes are difficult to model, but adiabatic expansion provides an excellent approximation to the structure of a donor star undergoing dynamical time scale mass transfer. We can use this model to study the responses of stars of various masses and evolutionary stages as potential donor stars, with the urgent goal of obtaining more accurate stability criteria for dynamical mass transfer in binary population synthesis studies. As examples, we describe here several models with the initial masses equal to 1 Msun and 10 Msun, and identify potential limitations to the use of our results for giant-branch stars., Comment: 7 pages, 5 figures,Accepted for publication in AP&SS, Special issue Hot Sub-dwarf Stars, in Han Z., Jeffery S., Podsiadlowski Ph. eds

The asymptotic response of donor stars in interacting binary systems to very rapid mass loss is characterized by adiabatic expansion throughout their interiors. In this limit, energy generation and heat flow through the stellar interior can be neglected. We model this response by constructing model sequences, beginning with a donor star filling its Roche lobe at an arbitrary point in its evolution, holding its specific entropy and composition profiles fixed as mass is removed from the surface. The stellar interior remains in hydrostatic equilibrium. Luminosity profiles in these adiabatic models of mass-losing stars can be reconstructed from the specific entropy profiles and their gradients. These approximations are validated by comparison with time-dependent binary mass transfer calculations. We describe how adiabatic mass loss sequences can be used to quantify threshold conditions for dynamical time scale mass transfer, and to establish the range of post-common envelope binaries that are allowed energetically., Comment: 41 pages, 7 figures, Accepted for publication in ApJ, Abstract abridged

With more and more exoplanets being detected, it is paid closer attention to whether there are lives outside solar system. We try to obtain habitable zones and the probability distribution of terrestrial planets in habitable zones around host stars. Using Eggleton's code, we calculate the evolution of stars with masses less than 4.00 \mo. We also use the fitting formulae of stellar luminosity and radius, the boundary flux of habitable zones, the distribution of semimajor axis and mass of planets and the initial mass function of stars. We obtain the luminosity and radius of stars with masses from 0.08 to 4.00 \mo, and calculate the habitable zones of host stars, affected by stellar effective temperature. We achieve the probability distribution of terrestrial planets in habitable zones around host stars. We also calculate that the number of terrestrial planets in habitable zones of host stars is 45.5 billion, and the number of terrestrial planets in habitable zones around K type stars is the most, in the Milky Way., Comment: 6 pages, 5 figures

The single-degenerate model is currently a favourable progenitor model for Type Ia supernovae (SNe Ia). Recent investigations on the WD + He star channel of the single-degenerate model imply that this channel is noteworthy for producing SNe Ia. In this paper we studied SN Ia birthrates and delay times of this channel via a detailed binary population synthesis approach. We found that the Galactic SN Ia birthrate from the WD + He star channel is $\sim 0.3\times 10^{-3} {\rm yr}^{-1}$ according to our standard model, and that this channel can explain SNe Ia with short delay times ($\sim4.5\times10^7 - 1.4\times10^8$ yr). Meanwhile, these WD + He star systems may be related to the young supersoft X-ray sources prior to SN Ia explosions., Comment: 7 pages, 5 figures, 1 table, accepted for publication in ApJ

In this paper, we systematically studied blue stragglers produced from primordial binary evolution via a binary population synthesis approach, and examined their contribution to the integrated spectral energy distributions of the host clusters. The mass transfer efficiency, $\beta$, is an important parameter for the final products (then blue stragglers) after mass transfer, and it is set to be 0.5 except for case A binary evolution. The study shows that primordial binary evolution may produce blue stragglers at any given times and that different evolutionary channels are corresponding for blue stragglers in different visual magnitude regions (in V band) on the colour-magnitude diagram (CMD) of clusters. The specific frequency of blue stragglers obtained from primordial binary evolution decreases with time first, and then increases again when the age is larger than 10Gyr, while that from angular momentum loss induced by magnetic braking in low-mass binaries increases with time and exceeds that of primordial binary evolution in a population older than 3 Gyr. Meanwhile, blue stragglers resulting from primordial binary evolution are dominant contributors to the ISEDs in ultraviolet and blue bands in a population between 0.3 and 2.0 Gyr. The value of $\beta$ significantly affects on the final results. For old open clusters, the assumption of $\beta =1$ when the primary is in HG at the onset of mass transfer matches the observations better than that of $\beta =0.5$ from the locations of BSs on the CMDs. Our study also shows that, for most Galactic open clusters, the specific frequency of blue stragglers obtained from our simulations is lower than that of observations, which is puzzling., Comment: 17 pages, 13 figures. accepted by MNRAS(Feb.19, 2009)

We have carried out a detailed study of the single-degenerate channel for the progenitors of type Ia supernovae (SNe Ia). In the model, a carbon-oxygen white dwarf (CO WD) accretes hydrogen-rich material from an unevolved or a slightly evolved non-degenerate companion to increase its mass to Chandrasekhar mass limit. Incorporating the prescription of \cite{HAC99a} for the accretion efficiency into Eggleton's stellar evolution code and assuming that the prescription is valid for all metallicities, we performed binary stellar evolution calculations for more than 25,000 close WD binary systems with various metallicities. The initial parameter spaces for SNe Ia are presented in an orbital period-secondary mass ($\log P_{\rm i}, M_{\rm 2}^{\rm i}$) plane for each $Z$. Adopting the results above, we studied the birth rate of SNe Ia for various $Z$ via binary population synthesis. From the study, we see that for a high $Z$, SNe Ia occur systemically earlier and the peak value of the birth rate is larger if a single starburst is assumed. The Galactic birth rate from the channel is lower than (but comparable to) that inferred from observations. We also showed the distributions of the parameters of the binary systems at the moment of supernova explosion and the distributions of the properties of companions after supernova explosion. The former provides physics input to simulate the interaction between supernova ejecta and its companion, and the latter is helpful to search for the companions in supernova remnants., Comment: 4 pages, 4 figures, oral talk, to appear in the Proceedings of IAU Symp. 252 "The Art of Modelling Stars in the 21st Century", Sanya, China, 6th-11th April 2008, (L. Deng, K.L. Chan & C. Chiosi, eds.)

Binary population synthesis shows that mass transfer from a giant star to a main-sequence (MS) companion may account for some observed long-orbital period blue stragglers. However, little attention {\bf is paid to this blue straggler formation scenario} as dynamical instability often happens when the mass donor is a giant star. In this paper, we have studied the critical mass ratio, $q_{\rm c}$, for dynamically stable mass transfer from a giant star to a MS companion using detailed evolution calculations. The results show that a more evolved star is generally less stable for Roche lobe overflow. Meanwhile, $q_{\rm c}$ almost linearly increases with the amount of the mass and angular momentum {\bf lost} during mass transfer, but has little dependance on stellar wind. To conveniently use the result, we give a fit of $q_{\rm c}$ as a function of the stellar radius at the onset of Roche lobe overflow and of the mass transfer efficiency during the Roche lobe overflow. To examine the formation of blue stragglers from mass transfer between giants and MS stars, we have performed Monte Carlo simulations with various $q_{\rm c}$. {\bf The simulations show that some binaries with the mass donor on the first giant branch may contribute to blue stragglers with $q_{\rm c}$ obtained in this paper but will not from previous $q_{\rm c}$. Meanwhile, from our $q_{\rm c}$, blue stragglers from the mass transfer between an AGB star and a MS companion may be more numerous and have a wider range of orbital periods than those from the other $q_{\rm c}$., Comment: 16 pages, 17 figures. accepted by MNRAS

We constructed some main-sequence mergers from case A binary evolution and studied their characteristics via Eggleton's stellar evolution code. Both total mass and orbital angular momentum are conservative in our binary evolutions. Some mergers might be on the left of the ZAMS as defined by normal surface composition on a CMD because of enhanced surface helium content. The study also shows that central hydrogen content of the mergers is independent of mass. As a consequence, we fit the formula of magnitude and B-V of the mergers when they return back to thermal equilibrium with maximum error 0.29 and 0.037, respectively. Employing the consequences above, we performed Monte Carlo simulations to examine our models in NGC 2682 and NGC 2660. In NGC 2682, binary mergers from our models cover the region with high luminosity, but its importance is much less than that of AML. Our results are well-matched to the observations of NGC2660 if there is about 0.5Mo of mass loss in the merger process., Comment: 14 pages, 12 figures. accepted by MNRAS

Based on the work of OPAL (Iglesias & Rogers 1996) and Alexander & Ferguson (1994), we construct a series of opacity tables for various metallicities Z=0, 0.00001, 0.00003, 0.0001, 0.0003, 0.001, 0.004, 0.01, 0.02, 0.03, 0.04, 0.05, 0.06, 0.08 and 0.1. These tables can be easily used in Eggleton's stellar evolution code in place of the old tables without changing the code. The OPAL tables are used for ${\log}_{10}(T/{\rm K})> 3.95$ and Alexander's for ${\log}_{10}(T/{\rm K})< 3.95$. At ${\rm log}_{10}(T/{\rm K})=3.95$, the two groups' data fit well for all hydrogen mass fractions. Conductive opacities are included by reciprocal addition according to the formulae of Yakovlev & Urpin (1980). For different metallicities $1M_\odot$ models are constructed with the new opacity tables. Comparison of 1 and $5M\odot$ models constructed with the older OPAL tables (Iglesias & Rogers 1992) shows that the new opacities have most effect in the late stages of evolution, the extension of the blue loop during helium burning for intermediate-mass and massive stars., Comment: 8 pages, 5 figures