On the properties of strange modes

Properties of the so-called strange modes occurring in linear stability calculations of stellar models are discussed. The behaviour of these modes is compared for two different sets of stellar models, for very massive zero-age main-sequence stars and for luminous hydrogen-deficient stars, both with high luminosity-to-mass ratios. We have found that the peculiar behaviour of the frequencies of the strange modes with the change of a control parameter is caused by the pulsation amplitude of a particular eigenmode being strongly confined to the outer part of the envelope, around the density inversion zone. The frequency of a strange mode changes because the depth of the confinement zone changes with the control parameter. Weakly non-adiabatic strange modes tend to be overstable because the amplitude confinement quenches the effect of radiative damping. On the other hand, extremely non-adiabatic strange modes become overstable because the perturbation of radiation force (gradient of radiation pressure) provides a restoring force that can be out of phase with the density perturbation. We discuss this mechanism by using a plane-parallel two-zone model.     

Colliding stellar wind models with non-equilibrium ionization: X-rays from WR 147

The effects of non-equilibrium ionization are explicitly taken into account in a numerical model which describes colliding stellar winds (CSW) in massive binary systems. This new model is used to analyse the most recent X-ray spectra of the WR+OB binary system WR 147. The basic result is that it can adequately reproduce the observed X-ray emission (spectral shape, observed flux) but some adjustment in the stellar wind parameters is required. Namely (i) the stellar wind velocities must be higher by a factor of 1.4–1.6 and (ii) the mass loss must be reduced by a factor of ∼2. The reduction factor for the mass loss is well within the uncertainties for this parameter in massive stars, but given the fact that the orbital parameters (e.g. inclination angle and eccentricity) are not well constrained for WR 147, even smaller corrections to the mass loss might be sufficient. Only CSW models with non-equilibrium ionization and equal (or nearly equal) electron and ion post-shock temperature are successful. Therefore, the analysis of the X-ray spectra of WR 147 provides evidence that the CSW shocks in this object must be collisionless .     

Tomography of stellar non‐radial pulsations

The stellar surface imaging technique is used for studying stellar non‐radial pulsations on the basis of inversions of time series of variable line profiles without making assumptions on the specific shape of the pulsations. The inversion results in an image of the stellar surface in which sectoral and tesseral modes can be distinguished in many cases and the pulsational degree and the azimuthal order can be determined. The capability of the technique is studied with simulated data. Then, the surface imaging technique is applied to high‐resolution spectra of the rapidly rotating Beta Cep‐type star ω¹ Sco, which shows strong line‐profile variations. Stellar surface imaging is concluded to be a useful technique for pulsation‐mode identification. (© 2004 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Non-adiabatic linear pulsation models for low-mass helium stars

Non-adiabatic linear pulsation models have been calculated for low-mass stars with effective temperatures between 16 000 and 35 000 K, and with surface gravities in the range 3⊙, X =0.00, Z =0.02. It is shown that the Z -bump instability persists to low masses ( M ∼0.4 M_⊙) but is suppressed either by a reduction in metallicity Z or by a selective enhancement of the carbon abundance. An unexpected result is the discovery that Z -bump instability persists at hydrogen abundances X >0.3, although the position of the red edge is sensitive to X . We have found that non-radial pulsations are also excited in the same instability region as radial pulsations.
The implications of these results for individual low-mass helium stars are discussed. It is concluded that Z -bump driven pulsations (radial and/or non-radial) may be excited in some helium-rich subdwarf B stars, representing a possible major extension to the class of variable stars represented by the prototype V652 Her.     

On the nature of the radial velocity variability of Aldebaran: a search for spectral line bisector variations

The shape of the Ti  i 6303.8-Å spectral line of Aldebaran as measured by the line bisector was investigated using high signal-to-noise ratio, high-resolution data. The goal of this study was to understand the nature of the 643-d period in the radial velocity for this star reported by Hatzes & Cochran. Variations in the line bisector with the radial velocity period would provide strong evidence in support of rotational modulation or stellar pulsations as the cause of the 643-d period. A lack of any bisector variability at this period would support the planet hypothesis.
Variations in the line asymmetries are found with a period of 49.93 d. These variations are uncorrelated with the 643-d period found previously in the radial velocity measurements. It is demonstrated that this 50-d period is consistent with an m =4 non-radial sectoral g-mode oscillation. The lack of spectral variability with the radial velocity period of 643 d may provide strong evidence in support of the hypothesis that this variability stems from the reflex motion of the central star due to a planetary companion having a mass of 11 Jupiter masses. However, this long-period variability may still be the result of a low-order ( m =2) pulsation mode as these would cause bisector variations of less than the error measurement.     

Eccentric instability of a two-dimensional fluid disc with a central massive object

In this paper we investigate, by linear modal analysis, the one-armed dynamical instability of a two-dimensional fluid disc that has a massive object at its centre. The model of the disc is chosen to avoid the artificial instabilities that originate from the unrealistic disc configurations that have been adopted in previous studies. We find a one-armed instability for which the central massive object is displaced from the centre, which is generally called the 'eccentric instability'. However, to excite the eccentric instability, the mass of the central object should be appreciably smaller than that of the disc, and this mass ratio is far smaller than what was originally proposed. The instability shown in this paper is likely to be excited in a stellar system with a central massive object, e.g. a galactic nucleus harbouring a massive black hole, and further studies are desirable via techniques such as numerical simulations.     

Pulsations and planets: The asteroseismology‐extrasolar‐planet connection

The disciplines of asteroseismology and extrasolar planet science overlap methodically in the branch of high‐precision photometric time series observations. Light curves are, amongst others, useful to measure intrinsic stellar variability due to oscillations, as well as to discover and characterize those extrasolar planets that transit in front of their host stars, periodically causing shallow dips in the observed brightness. Both fields ultimately derive fundamental parameters of stellar and planetary objects, allowing to study for example the physics of various classes of pulsating stars, or the variety of planetary systems, in the overall context of stellar and planetary system formation and evolution. Both methods typically also require extensive spectroscopic follow‐up to fully explore the dynamic characteristics of the processes under investigation. In particularly interesting cases, a combination of observed pulsations and signatures of a planet allows to characterize a system's components to a very high degree of completeness by combining complementary information. The planning of the relevant space missions has consequently converged with respect to science cases, where at the outset there was primarily a coincidence in instrumentation and techniques. Whether space‐ or ground‐based, a specific type of stellar pulsations can themselves be used in an innovative way to search for extrasolar planets. Results from this additional method at the interface of stellar pulsation studies and exoplanet hunts in a beyond‐mainstream area are presented (© 2010 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

The magnetosphere of oscillating neutron stars in general relativity

Just as a rotating magnetized neutron star has material pulled away from its surface to populate a magnetosphere, a similar process can occur as a result of neutron-star pulsations rather than rotation. This is of interest in connection with the overall study of neutron star oscillation modes but with a particular focus on the situation for magnetars. Following a previous Newtonian analysis of the production of a force-free magnetosphere in this way Timokhin et al., we present here a corresponding general-relativistic analysis. We give a derivation of the general relativistic Maxwell equations for small-amplitude arbitrary oscillations of a non-rotating neutron star with a generic magnetic field and show that these can be solved analytically under the assumption of low current density in the magnetosphere. We apply our formalism to toroidal oscillations of a neutron star with a dipole magnetic field and find that the low current density approximation is valid for at least half of the oscillation modes, similarly to the Newtonian case. Using an improved formula for the determination of the last closed field line, we calculate the energy losses resulting from toroidal stellar oscillations for all of the modes for which the size of the polar cap is small. We find that general relativistic effects lead to shrinking of the size of the polar cap and an increase in the energy density of the outflowing plasma. These effects act in opposite directions but the net result is that the energy loss from the neutron star is significantly smaller than suggested by the Newtonian treatment.     

恒星物质的不透明度

简介介绍了恒星物质的透明性质在恒星结构、演化、振动等许多恒星物理基本问题研究中的重要性和决定恒星物质不透明度的物理过程,回顾了第一代不透明度数据ＬＡＯＬ的发展历程与存在的问题,介绍了新一代不透明度数据ＯＰＡＬ的发展和目前观测与理论之间依然不一致的地方。     

Discovery and asteroseismological analysis of a new pulsating DB white dwarf star, PG 2246+121

We report 36.6 h of time-resolved CCD photometry of the DB white dwarf star PG 2246+121 and the discovery that it is a new pulsating variable. Analysis of our compact single-site data set allowed the detection of three mode multiplets, two triplets at 256 and 329 s, respectively, and one doublet at 286 s. The frequency splitting within those structures is exactly the same within the length and accuracy of our data set.
We argue that these multiplets are the result of non-radial g-mode pulsations, most probably of spherical degree ℓ=1, which then yields a formal stellar rotation period of 2.00±0.12 d. We suggest that the excited modes are three consecutive radial overtones of order 3–7, most likely k =4,5,6. This discovery's impact on the understanding of pulsating DB white dwarfs is discussed.     

Accretion to magnetized stars through the Rayleigh–Taylor instability: global 3D simulations

We present results of 3D simulations of magnetohydrodynamics (MHD) instabilities at the accretion disc–magnetosphere boundary. The instability is Rayleigh–Taylor, and develops for a fairly broad range of accretion rates and stellar rotation rates and magnetic fields. It manifests itself in the form of tall, thin tongues of plasma that penetrate the magnetosphere in the equatorial plane. The shape and number of the tongues changes with time on the inner disc dynamical time-scale. In contrast with funnel flows, which deposit matter mainly in the polar region, the tongues deposit matter much closer to the stellar equator. The instability appears for relatively small misalignment angles, Θ≲ 30°, between the star's rotation and magnetic axes, and is associated with higher accretion rates. The hotspots and light curves during accretion through instability are generally much more chaotic than during stable accretion. The unstable state of accretion has possible implications for quasi-periodic oscillations and intermittent pulsations from accreting systems, as well as planet migration.     

The evolutionary status of W Ursae Majoris-type systems

Well-determined physical parameters of 130 W Ursae Majoris (W UMa) systems were collected from the literature. Based on these data, the evolutionary status and dynamical evolution of W UMa systems are investigated. It is found that there is no evolutionary difference between W- and A-type systems in the   M – J   diagram, which is consistent with the results derived from the analysis of observed spectral type and of   M – R   and   M – L   diagrams of W UMa systems.   M – R   and   M – L   diagrams of W- and A-type systems indicate that a large amount of energy should be transferred from the more massive to the less massive component, so that they are not in thermal equilibrium and undergo thermal relaxation oscillation. Moreover, the distribution of angular momentum, together with the distribution of the mass ratio, suggests that the mass ratio of the observed W UMa systems decreases with decreasing total mass. This could be the result of the dynamical evolution of W UMa systems, which suffer angular momentum loss and mass loss as a result of the magnetic stellar wind. Consequently, the tidal instability forces these systems towards lower q values and finally to rapidly rotating single stars.     

Seismic signatures of strange stars with crust

We study acoustic oscillations (eigenfrequencies, velocity distributions, damping times) of normal crusts of strange stars. These oscillations are very specific because of huge density jump at the interface between the normal crust and the strange matter core. The oscillation problem is shown to be self-similar. For a low (but non-zero) multipolarity l , the fundamental mode (without radial nodes) has a frequency of ∼300 Hz and mostly horizontal oscillation velocity; other pressure modes have frequencies ≳20 kHz and almost radial oscillation velocities. The latter modes are similar to radial oscillations (having approximately the same frequencies and radial velocity profiles). The oscillation spectrum of strange stars with crust differs from the spectrum of neutron stars. If detected, acoustic oscillations would allow one to discriminate between strange stars with crust and neutron stars and constrain the mass and radius of the star.     

The influence of multiple stars on the high-mass stellar initial mass function and age dating of young massive star clusters

The study of young stellar populations has revealed that most stars are in binary or higher order multiple systems. In this study, the influence on the stellar initial mass function (IMF) of large quantities of unresolved multiple massive stars is investigated by taking into account the stellar evolution and photometrically determined system masses. The models, where initial masses are derived from the luminosity and colour of unresolved multiple systems, show that even under extreme circumstances (100 per cent binaries or higher order multiples), the difference between the power-law index of the mass function (MF) of all stars and the observed MF is small (≲0.1). Thus, if the observed IMF has the Salpeter index  α= 2.35  , then the true stellar IMF has an index not flatter than  α= 2.25  . Additionally, unresolved multiple systems may hide between 15 and 60 per cent of the underlying true mass of a star cluster. While already a known result, it is important to point out that the presence of a large number of unresolved binaries amongst pre-main-sequence stars induces a significant spread in the measured ages of these stars even if there is none. Also, lower mass stars in a single-age binary-rich cluster appear older than the massive stars by about 0.6 Myr.     

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.     

Spot signatures of a solar‐type dynamo in close binary stars

Magnetic activity signatures in the atmosphere of active stars can be used to place constrains on the underlying processes of flux transport and dynamo operation in its convective envelope. The ‘solar paradigm’ for magnetic activity suggests that the magnetic field is amplified and stored at the base of the convection zone. Once a critical field strength is exceeded, perturbations initiate the onset of instabilities and the growth of magnetic flux loops, which rise through the convection zone, emerge at the stellar surface, and eventually lead to the formation of starspots and active regions. In close binaries, the proximity of the companion star breaks the rotational symmetry. Although the magnitude of tidal distortions is rather small, non‐linear MHD simulations have nevertheless shown in the case of main‐sequence binary components that they can cause non‐uniform surface distributions of flux tube eruptions. The present work extends the investigation to post‐mainsequence components to explore the specific influence of the stellar structure on the surface pattern of erupting flux tubes. In contrast to the case of main‐sequence components, where the consistency between simulation results and observations supports the presumption of a solar‐like dynamo mechanism, the numerical results here do not recover the starspot properties frequently observed on evolved binary components. This aspect points out an insufficiency of the applied flux tube model and leads to the conclusion that additional flux transport and possibly amplification mechanisms have to be taken into account. (© 2004 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Non-linear hydrodynamical evolution of rotating relativistic stars: numerical methods and code tests

We present numerical hydrodynamical evolutions of rapidly rotating relativistic stars, using an axisymmetric, non-linear relativistic hydrodynamics code. We use four different high-resolution shock-capturing (HRSC) finite-difference schemes (based on approximate Riemann solvers) and compare their accuracy in preserving uniformly rotating stationary initial configurations in long-term evolutions. Among these four schemes, we find that the third-order piecewise parabolic method scheme is superior in maintaining the initial rotation law in long-term evolutions, especially near the surface of the star. It is further shown that HRSC schemes are suitable for the evolution of perturbed neutron stars and for the accurate identification (via Fourier transforms) of normal modes of oscillation. This is demonstrated for radial and quadrupolar pulsations in the non-rotating limit, where we find good agreement with frequencies obtained with a linear perturbation code. The code can be used for studying small-amplitude or non-linear pulsations of differentially rotating neutron stars, while our present results serve as testbed computations for three-dimensional general-relativistic evolution codes.     

The formation of brown dwarfs

We review four mechanisms for forming brown dwarfs: (i) turbulent fragmentation (producing very low‐mass prestellar cores); (ii) gravitational instabilities in discs; (iii) dynamical ejection of stellar embryos from their placental cores; and (iv) photo‐erosion of pre‐existing cores in HII regions. We argue (a) that these are simply the mechanisms of low‐mass star formation , and (b) that they are not mutually exclusive. If, as seems possible, all four mechanisms operate in nature, their relative importance may eventually be constrained by their ability to reproduce the binary statistics of brown dwarfs, but this will require fully 3‐D radiative magneto‐hydrodynamic simulations. (© 2005 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

kHz QPOs in LMXBs, relations between different frequencies and compactness of stars

We suggest that the mass of four compact stars SAX J1808.4-3658, KS 1731-260, SAX J1750.8-2900 and IGR J17191-2821 can be determined from the difference in the observed kiloHertz quasi periodic oscillations (kHz QPO-s) of these stars. The stellar radius is very close to the marginally stable orbit R_ms as predicted by Einstein’s general relativity. It may be noted that the first of these stars was suggested to be a strange star more than a decade back by Li et al. (1999a) from the unique millisecond X-ray pulsations with an accurate determination of its rotation period. It showed kHz QPO-s eight years back and so far it is the only set that has been observed. This is the first time we give an estimate of the mass of the star and of three other compact stars in low-mass X-ray binaries using their observed kHz QPO-s.     

大质量双星系统的非守恒演化

由于大质量双星系统有强大的星风物质损失,因而在研究其结构和演化时必须考虑星风物质损失,动量损失,物质交换以及由以上原因引起的轨道参量的变化,此外,天文观测又证实,一些大质量双星系统中存在星风冲击波,有Ｘ射线辐射以及有致密天体（白矮星,中子星）的存在,因此在研究大质量双星的演化时,又会遇到在星风冲击波理论及其对演化的影响,双星系统何时会演化成为公共外壳的系统,以及双星系统中如果发生超新星爆发,是否会