We calculated a grid of evolutionary tracks of rotating models with masses between 1.0 and 3.0 M⊙ and resolution δM 〈 0.02 M⊙, which can be used to study the effects of rotation on stellar evolution and on the characteristics of star clusters. The value of ～ 2.05 Me is a critical mass for the effects of rotation on stellar struc- ture and evolution. For stars with M 〉 2.05 Me, rotation leads to an increase in the convective core and prolongs their lifetime on the main sequence （MS）; rotating mod- els evolve more slowly than non-rotating ones; the effects of rotation on the evolution of these stars are similar to those of convective core overshooting. However for stars with 1.1 〈 M/M⊙ 〈 2.05, rotation results in a decrease in the convective core and shortens the duration of the MS stage; rotating models evolve faster than non-rotating ones. When the mass has values in the range ～ 1.7 - 2.0 M⊙, the mixing caused by rotationally induced instabilities is not efficient; the hydrostatic effects dominate pro- cesses associated with the evolution of these stars. For models with masses between about 1.6 and 2.0 M⊙, rotating models always exhibit lower effective temperatures than non-rotating ones at the same age during the MS stage. For a given age, the lower the mass, the smaller the change in the effective temperature. Thus rotations could lead to a color spread near the MS turnoff in the color-magnitude diagram for intermediate-age star clusters.
The light curve is one of the most important photometric characteristics of variable stars,which can supply physical information about many stars.So,light curves are the best candidate to inspect a theoretical model of binaries.One important feature of the light curve is the difference of two light minima of the light curve,namely the difference between the primary eclipse depth and the secondary eclipse depth(DED).In this paper,the secondary eclipse depths of theoretical and observational light curves are studied.Firstly,a method to calculate the theoretical light curves of an eclipsing binary with non-spherical components is proposed,which can be put into the HSB contact binary model [Huang R Q,et al.Chin J Astron Astrophys,2007,7:235-244;Song H F,et al.Chin J Astron Astrophys,2007,7:539-550].Theoretical light curves and the DED of the binary can be obtained at every evolutionary phase.The relationships of DED with mass and luminosity are presented and show special features for the contact binaries.Secondly,a large amount of observational data is collected,from which 11 massive,intermediate-mass contact binaries and 9 low-mass contact binaries are chosen and the two relationships are obtained using theoretical light curves.Finally,in order to check whether the HSB contact binary model can be used in contact binary systems with massive,intermediate-mass and low-mass components,a comparison is performed for the above mentioned relationships obtained from theoretical light curves with those from the astronomical observations.The results show a good agreement for contact binary systems with all different masses.
The W UMa-type contact binaries have been observed for several decades.To construct the evolutionary model for W UMa-type contact binaries,many difficulties were encountered due to the existence of complicated physical processes in such systems.The model introduced by Huang,Song and Bi includes some special and unique understandings of the physical processes of contact binaries.It is necessary to test whether this model can be used for W UMa-type contact binaries.The best way to test a theoretical model is to know whether this model can explain the observational phenomena of such systems.For this aim,a comparison is performed for the relations of mass-luminosity,mass-radius,and the distribution in the HR diagram obtained from the model introduced by Huang et al.and those from the astronomical observations.The result of the comparison indicates that this model can be applied to W UMa-type contact binaries and can explain the observational phenomena of such binaries.
During the evolution of the binary system, many physical processes occur, which can influence the orbital angular velocity and the spin angular velocities of the two components, and influence the non-synchronous or synchronous rotation of the system. These processes include the transfer of masses and angular momentums between the component stars, the loss of mass and angular momentum via stellar winds, and the deformation of the structure of component stars. A study of these processes indicates that they are closely related to the combined effects of tide and rotation. This means, to study the synchronous or non-synchronous rotation of binary systems, one has to consider the contributions of different physical processes simultaneously, instead of the tidal effect alone. A way to know whether the rotation of a binary system is synchronous or non-synchronous is to calculate the orbital angular velocity and the spin angular velocities of the component stars. If all of these angular velocities are equal, the rotation of the system is synchronous. If not, the rotation of the system is non-synchronous. For this aim, a series of equations are developed to calculate the orbital and spin angular velocities. The evolutionary calculation of a binary system with masses of 10M~ ＋ 6Me shows that the transfer of masses and angular momentums between the two components, and the deformation of the components structure in the semidetached or in the contact phase can change the rotation of the system from synchronous into non-synchronous rotation.
Contact binary systems,including massive,middle-mass and low-mass systems,have been observed.It is necessary to construct the evolutionary model for contact binary systems with all different masses.The model introduced by Huang,Song and Bi indicates some special and unique understandings of the physical processes occurring in the contact binaries.It is necessary to test whether this model can be applied to the early-type contact binaries.The best way to test a theoretical model is to know whether this model can explain the observational phenomena of such binaries.For this aim,a comparison is performed for the relations of mass-luminosity,mass-radius,and the distribution in the HR diagram obtained from the model introduced by Huang et al.and those from the astronomical observations.A good result is obtained by the comparison.This means the model can be used in calculating the evolution of early-type contact binaries,and can explain the observational phenomena of such binaries.
We test the possible evolutionary tracks of stars with various masses （1.8 M,1.9 M,2.0 M,2.1 M,2.2 M）and metallicities Z（0.008,0.010, 0.012）,including both models with and without convective core overshooting.At a given mass and metallicity,the models with a larger overshoot predict a larger radius and age of the star.Based on the observed frequency of oscillations and the position of Oph on the H-R diagram,we obtain two distinct better-fitting models：the solutions with mass M=1.9 M favor a radius in the range 10.55±0.03 R with an age of 1.01±0.08 Gyr;the solutions with mass M=2.0 M favor a radius in the range 10.74±0.03 R with an age of 0.95±0.11 Gyr.Furthermore,we investigate the influence of overshooting on the internal structure and the pulsation properties,and find that increasing the convective core overshoot significantly decreases non-radial mode inertia,while also increasing the mode amplitude.Therefore,the estimation of stellar mass and age might be modified by convective core penetration.
The theoretical light curves of contact binaries are calculated with and without putting in the contact binary evolution model.Firstly,we do not use the contact binary evolution model.A comparison of the light curve is performed with and without the deformation caused by rotation and tides.It shows that the light curve presents many differences,especially on the bottom and top.Secondly,we adopt the contact binary model [Huang R Q,et al.Chin J Astron Astrophys,2007,7:235-244;Song H F,et al.Chin J Astron Astrophys,2007,7:539-550] and compute the theoretical light curve with and without rotational and tidal effects by studying three binary systems(with low-,intermediate-and high-mass components).The bottom and top of the theoretical light curves are discussed and compared to observations.The results show that taking into account the rotational effect has a better agreement with observations than without it.Therefore,the deformation of the light curve of contact binaries caused by rotation and tides is very important.Meanwhile,the rotational and tidal effect can advance the start of the semi-detached,contact phase and the time of mass-reversal.
Most close double helium white dwarfs will merge within a Hubble time due to orbital decay by gravitational wave radiation.However,a significant fraction with low mass ratios will survive for a long time as a consequence of stable mass transfer.Such stable mass transfer between two helium white dwarfs（He WDs） provides one channel for the production of AM CVn binary stars.In previous calculations of double He WD progenitors,the accreting He WD was treated as a point mass.We have computed the evolution of 16 double He WD models in order to investigate the consequences of treating the evolution of both components in detail.We find that the boundary between binaries having stable and unstable mass transfer is slightly modified by this approach.By comparing with observed periods and mass ratios,we redetermine masses of eight known AM CVn stars by our double He WDs channel,i.e.HM Cnc,AM CVn,V406 Hya,J0926,J1240,GP Com,Gaia14 aae and V396 Hya.We propose that central spikes in the triple-peaked emission spectra of J1240,GP Com and V396 Hya and the surface abundance ratios of N/C/O in GP Com can be explained by the stable double He WD channel.The mass estimates derived from our calculations are used to discuss the predicted gravitational wave signal in the context of the Laser Interferometer Space Antenna（LISA） project.
Xian-Fei ZhangJin-Zhong LiuC.Simon JefferyPhilip D.HallShao-Lan Bi
High precision and long-lasting Kepler data enabled us to estimate stellar properties with asteroseismology as an accurate tool. We performed asteroseismic analysis on six solar-like stars observed by the Kepler mission： KIC 6064910, KIC 6766513, KIC 7107778, KIC 10079226, KIC 10147635 and KIC 12069127. The extraction of seismic information includes two parts. First, we obtained two global asteroseismic parameters, mean large separation ？_ν and frequency of maximum power ν_（max）,with autocorrelation function and collapsed autocorrelation function. Second, we extracted individual oscillation modes ν_（nl） with low-l degree using a least-squares fit. Stellar grid models were built with Yale Rotating Stellar Evolution Code（YREC） to analyze stellar properties. They covered the range of M = 0.8 ~ 1.8 M_⊙with a step of 0.02 M_⊙ and [Fe/H] =-0.3 ~ 0.4 dex with a step of 0.1 dex.We used a Bayesian approach to estimate stellar fundamental parameters of the six stars, under the constraints of asteroseismic parameters（？_ν, ν_（max）） and non-asteroseismic parameters（Teff, [Fe/H]）. We discover that the six targets include five sub-giant stars with 1.2 ~1.5 M_⊙ and one main-sequence star with 1.08 M_⊙, and with ages in the range of 3 ~5 Gyr.
Ya-Guang LiMing-Hao DuBo-Han XieZhi-Jia TianShao-Lan BiTan-Da LiYa-Qian WuKang Liu
