Element diffusion has small but significant effects on the structure of the stellar interior.It is interesting to investigate the effects of element diffusion using asteroseismology.We have constructed two grids of st...Element diffusion has small but significant effects on the structure of the stellar interior.It is interesting to investigate the effects of element diffusion using asteroseismology.We have constructed two grids of stellar models,one with diffusion and one without,for solar-like stars with masses between 0.9 and 1.4 solar masses,and varied initial helium abundance and metallicity.The oscillation frequencies of all stellar models have also been calculated.Piecewise Hermite cubic polynomials are adopted to interpolate stellar p-mode frequencies at an arbitrary age on a stellar evolutionary track.We have investigated 16 Kepler solar-like stars by comparing the model frequencies with observations.The suggested ranges of stellar parameters and some global variables are obtained.For all stars,the best model reproduces the observational frequencies with aχ^(2)of the order of unity.It has been found that element diffusion is important in modeling solar-like stars.Without diffusion,the best value of the initial helium abundance is below the primordial helium abundance from Big Bang nucleosynthesis.When diffusion is taken into account,the required initial helium abundance increases to be higher than the primordial abundance.Diffusion also generally improves the frequency fitting results by reducing the minimum ofχ^(2).Investigation of the second difference of the oscillation frequencies on KIC 8694723 and KIC 10454113 indicates that the current model of element diffusion may underestimate the strength of settling.展开更多
In this work, we present a cogent and physically well-behaved solution for neutron stars envisaged with a core layer having quark matter satisfying the MIT-bag equation of state(Eo S), meso layer with Bose-Einstein co...In this work, we present a cogent and physically well-behaved solution for neutron stars envisaged with a core layer having quark matter satisfying the MIT-bag equation of state(Eo S), meso layer with Bose-Einstein condensate(BEC) matter satisfying modified BEC Eo S and an envelope having neutron fluid and Coulomb liquids satisfying quadratic Eo S. All the required physical and geometrical parameters like gravitational potentials, pressures, radial velocity, anisotropy, adiabatic index, mass function, compactification factor, and gravitational and surface redshift functions show a feasible trend and are continuous with smooth variation throughout the interior and across the regions of the star.Further, causality condition, energy conditions, static stability criterion(using Tolman-OppenheimerVolkoff equation) and Herrera cracking stability criterion are met throughout the star. The approach seems to be resulting in more realistic and accurate modeling of stellar objects, particularly realized by us for X-ray binary stars 4 U 1608–52(M = 1.7 M_⊙, R = 9.5 km) and SAX J1808.4–3658(M = 1.2 M_⊙,R = 7.2 km). Furthermore, we have ascertained that the continuity of the stability factor in all three regions of the stars demand a smaller core. As the core region of the star increases, the stability factor becomes discontinuous at all the interfaces inside the star.展开更多
Asteroseismic observations are crucial to constrain stellar models with precision.Bayesian Estimation of STellar Parameters(BESTP)is a tool that utilizes Bayesian statistics and nested sampling Monte Carlo algorithm t...Asteroseismic observations are crucial to constrain stellar models with precision.Bayesian Estimation of STellar Parameters(BESTP)is a tool that utilizes Bayesian statistics and nested sampling Monte Carlo algorithm to search for the stellar models that best match a given set of classical and asteroseismic constraints from observations.The computation and evaluation of models are efficiently performed in an automated and multi-threaded way.To illustrate the capabilities of BESTP,we estimate fundamental stellar properties for the Sun and the red-giant star HD 222076.In both cases,we find models that are consistent with observations.We also evaluate the improvement in the precision of stellar parameters when the oscillation frequencies of individual modes are included as constraints,compared to the case when only the large frequency separation is included.For the solar case,the uncertainties of estimated masses,radii and ages are reduced by 0.7%,0.3%and 8%respectively.For HD 222076,they are reduced even more noticeably by 2%,0.5%and 4.7%respectively.We also note an improvement of 10%for the age of HD 222076 when the Gaia parallax is included as a constraint compared to the case when only the large separation is included as a constraint.展开更多
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 cha...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.展开更多
Within the framework of a non-local time-dependent stellar convection theory, we study in detail the effect of turbulent anisotropy on stellar pulsation stability. The results show that anisotropy has no substantial i...Within the framework of a non-local time-dependent stellar convection theory, we study in detail the effect of turbulent anisotropy on stellar pulsation stability. The results show that anisotropy has no substantial influence on pulsation stability of g modes and low-order （radial order nr 〈 5） p modes. The effect of turbulent anisotropy increases as the radial order increases. When turbulent anisotropy is neglected, most high-order （nr 〉 5） p modes of all low-temperature stars become unstable. Fortunately, within a wide range of the anisotropic parameter c3, stellar pulsation stability is not sensitive to the specific value of ca. Therefore it is safe to say that calibration errors of the convective parameter ca do not cause any uncertainty in the calculation of stellar pulsation stability.展开更多
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...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.展开更多
Grids of stellar evolution omy/astrophysics, such as planet hosting are required in many fields of astron- stars, binaries, clusters, chemically peculiar stars, etc. In this study, a grid of stellar evolution models w...Grids of stellar evolution omy/astrophysics, such as planet hosting are required in many fields of astron- stars, binaries, clusters, chemically peculiar stars, etc. In this study, a grid of stellar evolution models with updated ingredients and recently determined solar abundances is presented. The solar values for the initial abundances of hydrogen, heavy elements and mixing-length parameter are 0.0172, 0.7024 and 1.98, respectively. The mass step is small enough （0.01 M） that interpolation for a given star mass is not required. The range of stellar mass is 0.74 to 10.00M. We present results in different forms of tables for easy and general appli- cation. The second stellar harmonic, required for analysis of apsidal motion of eclips- ing binaries, is also listed. We also construct rotating models to determine the effect of rotation on stellar structure and derive fitting formulae for luminosity, radius and the second harmonic as a function of rotational parameter. We also compute and list colors and bolometric corrections of models required for transformation between theo- retical and observational results. The results are tested for the Sun, the Hyades cluster, the slowly rotating chemically peculiar Am stars and eclipsing binaries with apsidal motion. The theoretical and observational results along isochrones are in good agree- ment. The grids are also applicable to rotating stars provided that equatorial velocity is given.展开更多
Taking into account the helium and metal diffusion, we explore the possible evolutionary status with a seismic analysis, of the MOST （Microvariability and Oscillations of STars） target： the star e Eri. We adopt dif...Taking into account the helium and metal diffusion, we explore the possible evolutionary status with a seismic analysis, of the MOST （Microvariability and Oscillations of STars） target： the star e Eri. We adopt different input parameters to construct models to fit the available observational constraints in, e.g., Teff, L, R and [Fe/H]. From the computation we obtain the average large spacings of e Eri to be about 194 ± 1μHz. The age of the diffused models was found to be about 1 Gyr, which is younger than the age determined previously by models without diffusion. We found that the effect of pure helium diffusion on the internal structure of the young low-mass star is slight, but that of metal diffusion is obvious. The metal diffusion leads the models to have much higher temperature in the radiative interior, and, correspondingly a higher sound speed there, hence a larger frequency and spacings.展开更多
We present an exact analytical solution of the gravitational field equations describing a static spherically symmetric anisotropic quark matter distribution. The radial pressure inside the star is assumed to obey a li...We present an exact analytical solution of the gravitational field equations describing a static spherically symmetric anisotropic quark matter distribution. The radial pressure inside the star is assumed to obey a linear equation of state, while the tangential pressure is a complicated function of the radial coordinate. In order to obtain the general solution of the field equations a particular density profile inside the star is also assumed. The anisotropic pressure distribution leads to an increase in the maximum radius and mass of the quark star, which in the present model is around three solar masses.展开更多
In our time, experimental physicists have obtained data on a very large number of phenomena and objects of the physical world. Very rarely there is a situation when theoretical physicists do not have enough experiment...In our time, experimental physicists have obtained data on a very large number of phenomena and objects of the physical world. Very rarely there is a situation when theoretical physicists do not have enough experimental data to understand some known fundamental law of Nature. This situation arose almost a hundred years ago and sparked a discussion between A. Einstein and N. Bohr on the probabilistic nature of microcosm phenomena. From the time, it seemed that most physicists are inclined to believe that the proponents of a quantum explanation of the randomness of the phenomena of radioactive decay are right. Now this problem has been solved experimentally. The results of these measurements [1] show that A. Einstein and other proponents of determinism were right. In most cases, theoretical models are based on some already existing experimental data and are intended to explain them. At the same time, in the twentieth century, among microscopic, well-mathematically based models, there were several that raise doubts about their correctness, since they cannot explain a number of other experimental data that can be attributed to the fundamentally important properties of the studied objects [2] [3]. Therefore, the usual criterion for the correctness of the theory, which consists of its agreement with the measurement data, is ambiguous in this case. An additional criterion for the correctness of a microscopic theory can be formulated if it is assumed that the microscopic theory must be quantum one. The coefficients of quantum equations are world constants. Therefore, the solutions of these equations must be equalities made up of world constants only. For this reason, a correct microscopic model must rely on equalities consisting of world constants only. This criterion is shown to work successfully for models of superfluidity and superconductivity, for models of a number of particles, and models of the star interior.展开更多
基金Funding for Yunnan Observatories is co-sponsored by the National Key R&D Program of China(Grant No.2021YFA1600400/2021YFA1600402)the Strategic Priority Research Program of the Chinese Academy of Sciences(Grant No.XDB 41000000)+3 种基金the National Natural Science Foundation of China(Grant Nos.1177064 and 12133011)the Foundation of the Chinese Academy of Sciences(Light of West China Program and Youth Innovation Promotion Association)the Yunnan Ten Thousand Talents Plan Young and Elite Talents ProjectInternational Centre of Supernovae,Yunnan Key Laboratory(No.202302AN360001)。
文摘Element diffusion has small but significant effects on the structure of the stellar interior.It is interesting to investigate the effects of element diffusion using asteroseismology.We have constructed two grids of stellar models,one with diffusion and one without,for solar-like stars with masses between 0.9 and 1.4 solar masses,and varied initial helium abundance and metallicity.The oscillation frequencies of all stellar models have also been calculated.Piecewise Hermite cubic polynomials are adopted to interpolate stellar p-mode frequencies at an arbitrary age on a stellar evolutionary track.We have investigated 16 Kepler solar-like stars by comparing the model frequencies with observations.The suggested ranges of stellar parameters and some global variables are obtained.For all stars,the best model reproduces the observational frequencies with aχ^(2)of the order of unity.It has been found that element diffusion is important in modeling solar-like stars.Without diffusion,the best value of the initial helium abundance is below the primordial helium abundance from Big Bang nucleosynthesis.When diffusion is taken into account,the required initial helium abundance increases to be higher than the primordial abundance.Diffusion also generally improves the frequency fitting results by reducing the minimum ofχ^(2).Investigation of the second difference of the oscillation frequencies on KIC 8694723 and KIC 10454113 indicates that the current model of element diffusion may underestimate the strength of settling.
文摘In this work, we present a cogent and physically well-behaved solution for neutron stars envisaged with a core layer having quark matter satisfying the MIT-bag equation of state(Eo S), meso layer with Bose-Einstein condensate(BEC) matter satisfying modified BEC Eo S and an envelope having neutron fluid and Coulomb liquids satisfying quadratic Eo S. All the required physical and geometrical parameters like gravitational potentials, pressures, radial velocity, anisotropy, adiabatic index, mass function, compactification factor, and gravitational and surface redshift functions show a feasible trend and are continuous with smooth variation throughout the interior and across the regions of the star.Further, causality condition, energy conditions, static stability criterion(using Tolman-OppenheimerVolkoff equation) and Herrera cracking stability criterion are met throughout the star. The approach seems to be resulting in more realistic and accurate modeling of stellar objects, particularly realized by us for X-ray binary stars 4 U 1608–52(M = 1.7 M_⊙, R = 9.5 km) and SAX J1808.4–3658(M = 1.2 M_⊙,R = 7.2 km). Furthermore, we have ascertained that the continuity of the stability factor in all three regions of the stars demand a smaller core. As the core region of the star increases, the stability factor becomes discontinuous at all the interfaces inside the star.
基金funded by the Fundamental Research Funds for the Central Universities(Grant 19lgpy278)supported by a grant from the Max Planck Society to prepare for the scientific exploitation of the PLATO mission。
文摘Asteroseismic observations are crucial to constrain stellar models with precision.Bayesian Estimation of STellar Parameters(BESTP)is a tool that utilizes Bayesian statistics and nested sampling Monte Carlo algorithm to search for the stellar models that best match a given set of classical and asteroseismic constraints from observations.The computation and evaluation of models are efficiently performed in an automated and multi-threaded way.To illustrate the capabilities of BESTP,we estimate fundamental stellar properties for the Sun and the red-giant star HD 222076.In both cases,we find models that are consistent with observations.We also evaluate the improvement in the precision of stellar parameters when the oscillation frequencies of individual modes are included as constraints,compared to the case when only the large frequency separation is included.For the solar case,the uncertainties of estimated masses,radii and ages are reduced by 0.7%,0.3%and 8%respectively.For HD 222076,they are reduced even more noticeably by 2%,0.5%and 4.7%respectively.We also note an improvement of 10%for the age of HD 222076 when the Gaia parallax is included as a constraint compared to the case when only the large separation is included as a constraint.
基金supported by the China Postdoctoral Science Foundation(Grant No.20100480222)the National Natural Science Foundation of China(Grant Nos.11273012,11273007,10933002and11003003)the Project of Science and Technology from the Ministryof Education(211102)
文摘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.
基金supported by the National Natural Science Foundation of China (NSFC, Grant Nos. 11403039, 11473037 and 11373069)
文摘Within the framework of a non-local time-dependent stellar convection theory, we study in detail the effect of turbulent anisotropy on stellar pulsation stability. The results show that anisotropy has no substantial influence on pulsation stability of g modes and low-order （radial order nr 〈 5） p modes. The effect of turbulent anisotropy increases as the radial order increases. When turbulent anisotropy is neglected, most high-order （nr 〉 5） p modes of all low-temperature stars become unstable. Fortunately, within a wide range of the anisotropic parameter c3, stellar pulsation stability is not sensitive to the specific value of ca. Therefore it is safe to say that calibration errors of the convective parameter ca do not cause any uncertainty in the calculation of stellar pulsation stability.
基金Supported by the National Natural Science Foundation of Chinasupported by the Ministry of Science and Technology of the People's Republic of China(Grant No.2007CB815406)the National Natural Science Foundation of China(Grant Nos.10773003,10933002 and 10778601)
文摘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.
基金supported by the Scientific and Technological Research Council of Turkey(TBTAK 112T989)
文摘Grids of stellar evolution omy/astrophysics, such as planet hosting are required in many fields of astron- stars, binaries, clusters, chemically peculiar stars, etc. In this study, a grid of stellar evolution models with updated ingredients and recently determined solar abundances is presented. The solar values for the initial abundances of hydrogen, heavy elements and mixing-length parameter are 0.0172, 0.7024 and 1.98, respectively. The mass step is small enough （0.01 M） that interpolation for a given star mass is not required. The range of stellar mass is 0.74 to 10.00M. We present results in different forms of tables for easy and general appli- cation. The second stellar harmonic, required for analysis of apsidal motion of eclips- ing binaries, is also listed. We also construct rotating models to determine the effect of rotation on stellar structure and derive fitting formulae for luminosity, radius and the second harmonic as a function of rotational parameter. We also compute and list colors and bolometric corrections of models required for transformation between theo- retical and observational results. The results are tested for the Sun, the Hyades cluster, the slowly rotating chemically peculiar Am stars and eclipsing binaries with apsidal motion. The theoretical and observational results along isochrones are in good agree- ment. The grids are also applicable to rotating stars provided that equatorial velocity is given.
基金the National Natural Science Foundation of China
文摘Taking into account the helium and metal diffusion, we explore the possible evolutionary status with a seismic analysis, of the MOST （Microvariability and Oscillations of STars） target： the star e Eri. We adopt different input parameters to construct models to fit the available observational constraints in, e.g., Teff, L, R and [Fe/H]. From the computation we obtain the average large spacings of e Eri to be about 194 ± 1μHz. The age of the diffused models was found to be about 1 Gyr, which is younger than the age determined previously by models without diffusion. We found that the effect of pure helium diffusion on the internal structure of the young low-mass star is slight, but that of metal diffusion is obvious. The metal diffusion leads the models to have much higher temperature in the radiative interior, and, correspondingly a higher sound speed there, hence a larger frequency and spacings.
文摘We present an exact analytical solution of the gravitational field equations describing a static spherically symmetric anisotropic quark matter distribution. The radial pressure inside the star is assumed to obey a linear equation of state, while the tangential pressure is a complicated function of the radial coordinate. In order to obtain the general solution of the field equations a particular density profile inside the star is also assumed. The anisotropic pressure distribution leads to an increase in the maximum radius and mass of the quark star, which in the present model is around three solar masses.
文摘In our time, experimental physicists have obtained data on a very large number of phenomena and objects of the physical world. Very rarely there is a situation when theoretical physicists do not have enough experimental data to understand some known fundamental law of Nature. This situation arose almost a hundred years ago and sparked a discussion between A. Einstein and N. Bohr on the probabilistic nature of microcosm phenomena. From the time, it seemed that most physicists are inclined to believe that the proponents of a quantum explanation of the randomness of the phenomena of radioactive decay are right. Now this problem has been solved experimentally. The results of these measurements [1] show that A. Einstein and other proponents of determinism were right. In most cases, theoretical models are based on some already existing experimental data and are intended to explain them. At the same time, in the twentieth century, among microscopic, well-mathematically based models, there were several that raise doubts about their correctness, since they cannot explain a number of other experimental data that can be attributed to the fundamentally important properties of the studied objects [2] [3]. Therefore, the usual criterion for the correctness of the theory, which consists of its agreement with the measurement data, is ambiguous in this case. An additional criterion for the correctness of a microscopic theory can be formulated if it is assumed that the microscopic theory must be quantum one. The coefficients of quantum equations are world constants. Therefore, the solutions of these equations must be equalities made up of world constants only. For this reason, a correct microscopic model must rely on equalities consisting of world constants only. This criterion is shown to work successfully for models of superfluidity and superconductivity, for models of a number of particles, and models of the star interior.
