A Note on the Supersonic Convection in Stellar Atmospheres

By using a non-local convection theory, both the local and nonlocal convective envelope models of evolutionary series of stars with masses from 1 to 30 solar masses are calculated. The problem of supersonic convection is reviewed. The results show that the convective velocities in the stellar atmosphere are seriously overestimated by the local mixing-length theory. Convection is strongly supersonic in the atmospheres of yellow giant and super-giants, while the local mixing-length theory is used. However, it becomes subsonic for most stars when convection returns to the normal nonlocal treatment. Convection velocities increase with increase of luminosities of stars. There is still weak supersonic convection in few red and yellow giant and super-giants. It is suspected whether this supersonic convection in stellar atmospheres is true.     

A Theoretical Probe for Excitation Mechanisms of Sun-like and Mira-like Oscillations of Stars

The linear nonadiabatic oscillations for evolutionary models of 0.6- 3M8 stars are calculated by using a nonlocal and time-dependent convection theory. The results show that in the HR diagram the pulsation-unstable low- temperature stars on the right side of instability strip can be divided into two groups. One group indicates the Sun-like oscillation stars composed of the main- sequence dwarfs, sub-giants and red giants (RGs) of low and intermediate lu- minosities, which are unstable in the intermediate- and high-order (n ≥ 12) p- modes, and stable in the low-order (n ≤ 5) p-modes. Another group indicates the Mira-like stars composed of the bright RGs and asymptotic giant branch (AGB) stars, which are just contrary to Sun-like stars, unstable in low-order (n ≤ 5) p-modes and stable in the intermediate- and high-order (n ≥ 12) p-modes. The oscillations for the red edge of Cepheid (δ Scuti) instability strip, Sun-like and Mira-like stars can be explained uniformly by the coupling between convection and oscillation (CCO). For the low-temperature stars on the right side of in- stability strip, CCO is the dominant excitation and damping mechanism of the oscillations of low- and intermediate-order p-modes, and the turbulent stochas- tic excitation becomes important only for the high-order p-modes of Sun-like oscillations.     

Supersonic convection in stellar interiors

According to the result of the numerical simulation on stellar convective envelopes by the traditional mixing length theory, supersonic convection would occur on the top of the convective regions of the yellow-and-red giants and supergiants. This, however, is not self-consistent with the local convection theory itself. This paper is devoted to analyze in details the origin of supersonic convection, and at the same time to present a plot of the supersonic convection region on the H-R diagram based on the evolutionary track of population I stars. The main results of this paper are as follows: in the process of evolution, (1) no supersonic convection occurs in low-mass stars; (2) for intermediate-mass stars, because of the ionization of hydrogen, the supersonic convection occurs chiefly in the region of 3.6< lgT_e <4.0, tilting from the lower left to the upper right on the H-R diagram and extending to the region of red giants for relatively massive stars; (3) for massive stars, the supersonic convection occurs after they deviate from ZAMS, the greater the stellar mass is, the earlier the supersonic convection emerges. For blue supergiants, the supersonic convection occurs at the absorbtion peak (lg T ∼5.3) of Fe and in the secondary ionization region of helium, but for the red- and yellow-giants and supergiants, it occurs in the ionization region of hydrogen.     

Numerical simulations of downward convective overshooting in giants

An attempt at understanding downward overshooting in the convective envelopes of post-main-sequence stars has been made on the basis of three-dimensional large-eddy simulations, using artificially modified OPAL opacity and taking into account radiation and ionization in the equation of state. Two types of star, an intermediate-mass star and a massive star, were considered. To avoid a long thermal relaxation time of the intermediate-mass star, we increased the stellar energy flux artificially while trying to maintain a structure close to the one given by a 1D stellar model. A parametric study of the flux factor was performed. For the massive star, no such process was necessary. Numerical results were analysed when the system reached the statistical steady state. It was shown that the penetration distance in pressure scaleheights is of the order of unity. The scaling relations between penetration distance, input flux and vertical velocity fluctuations studied by Singh et al. were checked. The anisotropy of the turbulent convection and the diffusion models of the third-order moments representing the non-local transport were also investigated. These models are dramatically affected by the velocity fields and no universal constant parameters seem to exist. The limitations of the numerical results were also discussed.     

X-ray emission as a tracer of circumstellar matter around herbig ae/be stars

We have detected X-ray emission (1 keV) from young intermediate-mass stars (Herbig Ae/Be stars). Since these stars are not supposed to produce intrinsic X-ray emission (no convection, no coronae), we believe that our results suggest that the X-ray emission actually traces the shock interaction of the Ae/Be star stellar winds with remnant circumstellar matter left over from the star formation process, the presence of which is also indicated by far-infrared (IRAS) and submm/mm continuum data.     

On the effect of turbulent anisotropy on pulsation stability of stars

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 n_r 5) p modes.The effect of turbulent anisotropy increases as the radial order increases. When turbulent anisotropy is neglected, most high-order(n r 5) p modes of all low-temperature stars become unstable. Fortunately,within a wide range of the anisotropic parameter c_3, stellar pulsation stability is not sensitive to the specific value of c_3. Therefore it is safe to say that calibration errors of the convective parameter c_3 do not cause any uncertainty in the calculation of stellar pulsation stability.     

中等质量恒星在赫罗图中由E-AGB星进入TP-AGB星的分界点

通过对3～10 M_☉恒星在赫罗图上演化轨迹的研究,分析恒星内部氦壳层燃烧峰值处能量、密度、温度、氦壳层表面光度与恒星表面光度比及恒星半径的变化,给出了中等质量恒星由早期AGB星演化至热脉冲AGB星阶段在赫罗图上的分界点,与119颗碳星的观测结果吻合得相当好.同时提出:在恒星演化至该分界点之后,其星风物质损失公式可能需要引入一个与表面光度无关的量以主导超星风的形成.在此基础上,通过对考虑湍流压效应下5 M_☉恒星的结构和演化及星风物质损失率的分析,发现湍流压在热脉冲AGB星阶段对星风物质损失影响较大,从而使得热脉冲AGB星的湍流压不可忽略,进而提出了影响热脉冲AGB星星风物质损失的可能的物理因素.     

Sounding stellar cycles with Kepler – I. Strategy for selecting targets

The long-term monitoring and high photometric precision of the Kepler satellite will provide a unique opportunity to sound the stellar cycles of many solar-type stars using asteroseismology. This can be achieved by studying periodic changes in the amplitudes and frequencies of the oscillation modes observed in these stars. By comparing these measurements with conventional ground-based chromospheric activity indices, we can improve our understanding of the relationship between chromospheric changes and those taking place deep in the interior throughout the stellar activity cycle. In addition, asteroseismic measurements of the convection zone depth and differential rotation may help us determine whether stellar cycles are driven at the top or at the base of the convection zone. In this paper, we analyse the precision that will be possible using Kepler to measure stellar cycles, convection zone depths and differential rotation. Based on this analysis, we describe a strategy for selecting specific targets to be observed by the Kepler Asteroseismic Investigation for the full length of the mission, to optimize their suitability for probing stellar cycles in a wide variety of solar-type stars.     

一种改进的恒星辐射流体动力学方程

本文将本文作者发展的辐流体动力学方程精细化了，在新的理论公式中，描述物质与辐射场的热力学变量被彻底分开了，这不仅使得理论自身内部更为一致，也给变星脉动理论计算带来方便，本文亦证明了新老理论是相容的。     

Multisite campaign on the open cluster M67 – II. Evidence for solar-like oscillations in red giant stars

Measuring solar-like oscillations in an ensemble of stars in a cluster, holds promise for testing stellar structure and evolution more stringently than just fitting parameters to single field stars. The most-ambitious attempt to pursue these prospects was by Gilliland et al. who targeted 11 turn-off stars in the open cluster M67 (NGC 2682), but the oscillation amplitudes were too small (<20 μmag) to obtain unambiguous detections. Like Gilliland et al. we also aim at detecting solar-like oscillations in M67, but we target red giant stars with expected amplitudes in the range 50–  500 μmag  and periods of 1 to 8 h. We analyse our recently published photometry measurements, obtained during a six-week multisite campaign using nine telescopes around the world. The observations are compared with simulations and with estimated properties of the stellar oscillations. Noise levels in the Fourier spectra as low as  27 μmag  are obtained for single sites, while the combined data reach  19 μmag  , making this the best photometric time series of an ensemble of red giant stars. These data enable us to make the first test of the scaling relations (used to estimate frequency and amplitude) with an homogeneous ensemble of stars. The detected excess power is consistent with the expected signal from stellar oscillations, both in terms of its frequency range and amplitude. However, our results are limited by apparent high levels of non-white noise, which cannot be clearly separated from the stellar signal.     

An essay on stellar oscillations and evolution

It is cautioned that solar models adjusted in such a way as to achieve a match between theoretical solar oscillation characteristics and observed ones may produce neutrino fluxes inconsistent with the observations and that this is likely to be explicable as a deficiency in modeling that portion of the envelope which is most strongly affected by uncertainties in the treatment of convection. Then follows a summary of how the results of pulsation theory and of stellar evolution theory have been used together to learn about the structure and evolution of RR Lyrae stars, classical Cepheids, and high luminosity AGB stars.     

Stellar turbulence and mode physics

An overview of selected topical problems on modelling oscillation properties in solar-like stars is presented. High-quality oscillation data from both space-borne intensity observations and ground-based spectroscopic measurements provide first tests of the still-ill-understood superficial layers in distant stars. Emphasis will be given to modelling the pulsation dynamics of the stellar surface layers, the stochastic excitation processes and the associated dynamics of the turbulent fluxes of heat and momentum.     

Radiative accelerations, accumulation of iron and thermohaline convection inside stars

The radiative acceleration on iron inside stars may lead to an accumulation of this element in stellar internal layers. As discussed by several authors, this iron accumulation has many important consequences. It may lead to an extra convective zone, and in some cases it may help triggering stellar pulsations. However, the computations which have been done up to now ignore an important effect: the double-diffusive, or “thermohaline” convection induced by the inverse μ gradient. Detailed computations of all these processes have been introduced in the TGEC stellar evolution code. We show how thermohaline convection modifies the profiles of iron inside stars, with important consequences     

A Theoretical Probe for Excitation Mechanisms of Solar-like and Mira-like Oscillations of Stars

The linear stability analysis of the radial and non-radial oscillations for the evolutionary model of a star with the mass of 0.6∼3 M8 has been per- formed by using the nonlocal and time-dependent convection theory. The results show that the unstable low-temperature stars on the right side of the instabil- ity strip in the HR diagram can be divided into two groups. One is of the stars of solar-like oscillations, composed of the main-sequence dwarfs, subgiants, and the red giants with low- and intermediate-luminosity, which are unstable in the intermediate- and high-order (nr ≥ 12) p-modes, but stable in the low- order (nr ≤ 5) p-modes. Another is of the Mira-like stars, composed of the luminous red giants and AGB stars, which are just contrary to the solar-like stars, unstable in the low-order (nr ≤ 5) p-modes, but stable in the intermediate- and high-order (nr ≥ 12) p-modes. On the red edge of Cepheid (δ Scuti) insta- bility strip, the oscillations of solar-like and Mira-like stars can be explained uniformly by the coupling between convection and oscillations (CCO). For the low-temperature stars on the right side of the instability strip, the CCO is the dominant excitation and damping mechanism for the low- and intermediate-order p-modes, and the stochastic excitation of turbulence becomes important only for the high-order p-modes of solar-like oscillations.     

Non-adiabatic oscillations of red giants

Using our non-local time-dependent theory of convection, the linear non-adiabatic oscillations of 10 evolutionary model series with masses of  1–3 M_⊙  are calculated. The results show that there is a red giant instability strip in the lower temperature side of the Hertzsprung–Russell diagram which goes along the sequences of the red giant branch and the asymptotic giant branch. For red giants of lower luminosities, pulsation instability is found at high order overtones; the lower order modes from the fundamental to the second overtone are stable. Towards higher luminosity and lower effective temperature, instability moves to lower order modes, and the amplitude growth rate of oscillations also grows. At the high luminosity end of the strip, the fundamental and the first overtone become unstable, while all the modes above the fourth order become stable. The excitation mechanisms have been studied in detail. It is found that turbulent pressure plays a key role for excitation of red variables. The frozen convection approximation is unavailable for the low temperature stars with extended convective envelopes. In any case, this approximation can explain neither the red edge of the Cepheid instability strip, nor the blue edge of the pulsating red giant instability strip. An analytic expression of a pulsation constant as a function of stellar mass, luminosity and effective temperature is presented from this work.     

Turbulence properties in the solar convection envelope： properties of the overshooting regions

We apply the turbulent convection model (TCM) to investigate properties of tur-bulence in the solar convective envelope, especially in overshooting regions. The results show TCM gives negative turbulent heat flux uγ′T′in overshooting regions, which is sim-ilar to other nonlocal turbulent convection theories. The turbulent temperature fluctuation T′T′shows peaks in overshooting regions. Most important, we find that the downward overshooting region below the base of the solar convection zone is a thin cellular layer filled with roll-shaped convective cells. The overshooting length for the temperature gradi-ent is much shorter than that for element mixing because turbulent heat flux of downward and upward moving convective cells counteract each other in this cellular overshooting region. Comparing the models' sound speed with observations, we find that raking the convective overshooting into account helps to improve the sound speed profile of our nonlocal solar models. Comparing the p-mode oscillation frequencies with observations,we validated that increasing the diffusion parameters and decreasing the dissipation pa-rameters of TCM make the p-mode oscillation frequencies of the solar model be in betteragreement with observations.     

Parametrization of single and binary stars

Stellar masses and ages are not directly observable parameters, and the methods used to determine them are based on the calibrating relations. In particular, the mass–luminosity relation, based on the masses of less than 200 well-studied binaries, is virtually the only way to estimate the mass of single stars. Thus, the development of methods for estimating stellar masses with accuracy comparable to direct methods is a problem of vital importance.
Here, we describe a method for estimating stellar masses and ages, which is based on the geometric similarity of evolutionary tracks for the stars at the same evolutionary stage in the Hertzsprung–Russell (HR) diagram. To examine the proposed approach, it has been applied to various test data sets. Application of the method, using synthetic stellar spectra Basel Stellar Library (of theoretical spectra; BaSeL), demonstrates that it allows determination of masses and ages of stars with a predictable distribution of uncertainties.
This statistical approach allows us to demonstrate the viability of the method using it on the set of double-lined eclipsing binaries with intermediate-mass and low-mass components which allows us to compare calculated characteristics with observational ones. As a result, the uncertainties of the stellar masses estimated with the proposed method are comparable with the accuracy of ones obtained from direct observations. This allows us to recommend the method for mass estimates of masses of single stars by the localization in the HR diagram.
As for the ages, the estimates for intermediate-mass stars are more reliable, while those obtained for low-mass stars are very uncertain, due both to slower movement of these stars in the HR diagram with age at stages close to the main sequence and to certain disagreements between theoretical models for this mass range.     

On the effect of overshooting as predicted by the modelling of the pre-main-sequence evolution of a 2 M⊙ star

We discuss the effects of convective overshooting in the pre-main-sequence (PMS) evolution of intermediate-mass stars, by analysing in detail the early evolution towards the main sequence of a  2 M_⊙  stellar model. These effects can be extremely important in the end of the PMS, when the abundances in CNO elements approach the equilibrium in the centre. We provide a possible physical explanation on why a moderate amount of overshooting produces, as the star approaches the zero-age main-sequence, an extra loop in the evolutionary tracks on the Hertzsprung–Russell diagram.
An interesting feature is that there is a very well defined amount of overshooting (for a given stellar mass and chemical composition) beyond which a loop is produced. For smaller amounts of overshooting such a loop does not take place and the evolutionary tracks are similar to those found in the literature. The amount of overshooting needed to produce the loop decreases with stellar mass.
We discuss the underlining physical reasons for the behaviour predicted by the evolution models and argue that it provides a crucial observational test for convective overshooting in the core of intermediate-mass stars.     

Sensitivity of the C and O production on the 3α rate

We investigate the dependence of the carbon and oxygen production in stars on the 3α rate by varying the energy of the 0⁺ ₂-state of ¹²C and determine the resulting yields for a selection of low-mass, intermediate-mass and massive stars. The yields are obtained using modern stellar evolution codes that follow the entire evolution of massive stars, including the supernova explosion, and consider in detail the 3^rd dredge-up process during the thermally pulsating asymptotic giant branch of low-mass and intermediate-mass stars. Our results show that the C and O production in massive stars depends strongly on the initial mass, and that it is crucial to follow the entire evolution. A rather strong C production during the He-shell flashes compared to quiescent He burning leads to a lower sensitivity of the C and O production in low-mass and intermediate-mass stars on the 3α-rate than predicted in our previous work. In particular, the C production of intermediate-mass stars seems to have a maximum close to the actual value of the 0⁺ ₂ energy level of ¹²C. This revised version was published online in August 2006 with corrections to the Cover Date.     

Gaussian process modelling of asteroseismic data

The measured properties of stellar oscillations can provide powerful constraints on the internal structure and composition of stars. To begin this process, oscillation frequencies must be extracted from the observational data, typically time series of the star's brightness or radial velocity. In this paper, a probabilistic model is introduced for inferring the frequencies and amplitudes of stellar oscillation modes from data, assuming that there is some periodic character to the oscillations, but that they may not be exactly sinusoidal. Effectively, we fit damped oscillations to the time series, and hence the mode lifetime is also recovered. While this approach is computationally demanding for large time series (>1500 points), it should at least allow improved analysis of observations of solar-like oscillations in subgiant and red giant stars, as well as sparse observations of semiregular stars, where the number of points in the time series is often low. The method is demonstrated on simulated data and then applied to radial velocity measurements of the red giant star  ξ Hydrae  , yielding a mode lifetime between 0.41 and 2.65 d with 95 per cent posterior probability. The large frequency separation between modes is ambiguous, however we argue that the most plausible value is 6.3 μHz, based on the radial velocity data and the star's position in the Hertzsprung–Russell diagram.