A method for empirical determination of stellar atmospheric structure

A technique for obtaining information on the temperature structure of a stellar atmosphere from spectral line data where only flux observations are available is discussed. The direct inversion of the flux integral to obtain the line source function can be circumvented by making the physically plausible assumptions of (1) source function equality in a multiplet and (2) the dominance of line absorption over continuum absorption at line center. Consistency of the technique is demonstrated by treating a synthetic spectrum as input data and attempting to recover the temperature structure of the input atmosphere. Using high quality solar spectrum scans obtained from K.P.N.O. we demonstrate the accuracy of source function equality for several Fe i multiplets and use one of these multiplets to obtain an empirical outer atmosphere for the Sun. Our empirical atmosphere agrees well with current solar models.     

A PCA approach to stellar abundances I. testing of the method validity

The derivation of element abundances of stars is a key step in detailed spectroscopic analysis. A spectroscopic method may suffer from errors associated with model simplifications. We have developed a new method of deriving the various element abundances of stars based on the calibration established from a group of standard stars. We perform principal component analysis(PCA) on a homogeneous library of stellar spectra, and then use machine learning to calibrate the relationship between principal components and element abundances. By testing with spectral libraries S4 N and MILES, we find that our procedure provides good consistency when spectra from a homogeneous set of observations are used, and it could be expanded to stars with quite a wide range of stellar parameters, with both dwarfs and giants. Moreover, we discuss the four key factors that have a significant impact on the results of derived element abundances,including the resolution of the spectra, wavelength range, the signal-to-noise ratio(S/N) of spectra and the number of principal components adopted.     

A relaxation method for the computation of model stellar atmospheres

A general Monte Carlo relaxation method has been formulated for the computation of physically self-consistent model stellar atmospheres. The local physical state is obtained by solving simultaneously the equations of statistical equilibrium for the atomic and ionic level populations, the kinetic energy balance equation for the electron gas to obtain the electron temperature, and the equation of radiative transfer. Anisotropic Thomson scattering is included in the equation of transfer and radiation pressure effects are included in the hydrostatic equation. The constraints of hydrostatic and radiative equilibrium are enforced. Local thermodynamic equilibrium (L.T.E.) is assumed as a boundary condition deep in the atmosphere. Elsewhere in the atmosphere L.T.E. is not assumed.The statistical equilibrium equations are solved with no assumptions made concerning detailed balance for the bound-bound radiative processes. The source function is formulated in microscopic detail. All atomic processes contributing to the absorption and emission of radiation are included. The kinetic energy balance equation for the electron gas is formulated in detail. All atomic processes by which kinetic energy is gained and lost by the electron gas are included.The method has been applied to the computation of a model atmosphere for a pure hydrogen early-type star. An idealized model of the hydrogen atom with five bound levels and the continuum was adopted. The results of the trial calculation are discussed with reference to stability, accuracy, and convergence of the solution.Contribution No. 385 from the Kitt Peak National Observatory.Operated by the Association of Universities for Research in Astronomy, Inc., under contract with the National Science Foundation.     

A graphical method for estimating overshoot in convective stellar atmospheres

A graphical method for estimating convective overshoot in stellar atmospheres is proposed. Applying the method to the solar atmosphere, we find that a convective element which starts at a depth of about 1000 km below the top of convection zone can penetrate to a height about 300 km above it.The National Center for Atmospheric Research is sponsored by the National Science Foundation.     

Application of the stroboscopic method to the stellar three-body problem

The stellar three-body problem has been approached by directly integrating the equations of motion in the orbital elements. The problem is set up in a barycentric chain with the orbits as perturbed ellipses.The integration was performed using the semi-analytical stroboscopic method, which is particularly useful for solving differential systems that depend on several slow variables and one fast, angular variable. Perturbation theory is applied and the solution for a particular order is obtained by way of successive approximations on the fundamental period of the fast variable.     

A non-parametric method of estimating the physical parameters of stellar atmosphere

The physical parameters of stellar atmosphere, e.g. the effective temperature, surface gravity and chemical abundance, are the main factors for the differences in stellar spectra, and the automatic measurement of these parameters is an important content in the automatic processing of the immense amount of spectral data provided by LAMOST and other patrol telescopes. Aiming at the estimation of the physical parameters for every star in large samples of stellar spectral data, a variable window-width algorithm is proposed in this article. It consists of the following three steps: (1) A PCA (principal component analysis) treatment of historical stellar spectral data is carried out to obtain a low-dimensional characteristic data of the spectra. (2) Establish the correlation between the characteristic data and the physical parameters using a non-parametric estimator with variable window-width. (3) By means of this estimator, the three physical parameters of the star are directly calculated. As shown by results of experiments, in comparison with the fixed window-width estimator and other algorithms reported in literature, our algorithm is more accurate and robust.     

A direct imaging search for close stellar and sub‐stellar companions to young nearby stars

A total of 28 young nearby stars (ages ≤60 Myr) have been observed in the K_s‐band with the adaptive optics imager Naos‐Conica of the Very Large Telescope at the Paranal Observatory in Chile. Among the targets are ten visual binaries and one triple system at distances between 10 and 130 pc, all previously known. During a first observing epoch a total of 20 faint stellar or sub‐stellar companion‐candidates were detected around seven of the targets. These fields, as well as most of the stellar binaries, were re‐observed with the same instrument during a second epoch, about one year later. We present the astrometric observations of all binaries. Their analysis revealed that all stellar binaries are co‐moving. In two cases (HD 119022 AB and FG Aqr B/C) indications for significant orbital motions were found. However, all sub‐stellar companion candidates turned out to be non‐moving background objects except PZ Tel which is part of this project but whose results were published elsewhere. Detection limits were determined for all targets, and limiting masses were derived adopting three different age values; they turn out to be less than 10 Jupiter masses in most cases, well below the brown dwarf mass range. The fraction of stellar multiplicity and of the sub‐stellar companion occurrence in the star forming regions in Chamaeleon are compared to the statistics of our search, and possible reasons for the observed differences are discussed. (© 2015 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Euler potential method in three-dimensional stellar wind problems

A theoretical scheme is developed to deal with the problems of stellar winds in three-dimensional situations, and relativistic fluid equations are integrated formally under isentropic and quasi-stationary conditions, in a flat space-time.The relativistic Euler equation for a one-component plasma is expressed in the same form as the ideal-MHD condition for the effective electromagnetic field which combines the inertial and pressure terms with the true electromagnetic field. This equation and that of mass continuity are integrated formally by introducing Euler-type potentials for the effective magnetic field and for the mass flux in the rotating frame, respectively. Functional form of one of these Euler potentials, which represents the total energy per unit charge in the rotating frame, is specified as an integral of motion. For an electron-proton plasma, the integrals for both components are combined to yield the energy integral of the plasma as a whole and the integrated Ohm's law, in the limit of vanishing mass ratio of an electron to a proton.Maxwell's equations are divided in two parts: i.e., the co-rotational and non-corotational parts. It is shown that the electromagnetic potentials for these parts are derived from a scalar super-potential and a vector super-potential, respectively.     

Sensitivity of solar eigenfrequencies to the age of the sun

The increasing central concentration of the Sun with age modifies the acoustic eigenfrequencies. In particular, the frequency separation d _l =3(2l+3)^–1v _n,l –v _n–1,l+2 for modes with l + 1/2 n decreases as nuclear reactions augment the molecular-weight gradient in the energy-generating core. If, for example, the Sun were older than is generally believed, one might therefore expect d _l to be smaller than current theoretical predictions. On the other hand, to ensure that the luminosity is consistent with observations, the presumed initial hydrogen abundance would need to be enhanced, thereby reducing the resultant molecular-weight gradient. Thus there is some degree of cancellation of the two major factors that determine d _l .Various authors have either reported directly on the sensitivity of d _l , or have provided the information from which it can be calculated. We have added our own computations. There is broad agreement amongst the results: d _l diminishes with the presumed age of the Sun at the rate of about 1 Hz per Gy for l = 0; the magnitude of the rate appears to decline with increasing l.     

Statistical method for distance determination of a stellar group

In this paper, we developed statistical method for distance determination of a stellar group. The method depends on the assumption that, the stars scatter around a mean magnitude in a Gaussian distribution. The mean apparent magnitude of the stars is then expressed in terms of the frequency function of the apparent magnitudes, so as to correct for observational incompleteness at the faint end. The problem reduces to the solution of a highly transcendental equation for a given apparent magnitude parameter α. Computational algorithm of the method is illustrated and the numerical solutions of the basic equation are given for some values of α .     

Applications to stellar and galactic dynamics

Computation and a wealth of new observational techniques have reinvigorated dynamical studies of galaxies and star clusters. These objects are examples of the gravitationaln-body problem withn in the range from a few hundred to 10¹¹. Relaxation effects dominate at the low end and are completely negligible at the high end. The gravitationaln-body problem is chaotic, and the principal challenge in doing physics where that problem is involved (whether computationally or with analytic theory) is to ensure that chaos has not vitiated the results. Enforcing a Liouville theorem accomplishes this with collision-free large-n problems, but equivalent recipes are not in common use for smallern. We describe some important insights and discoveries that have come from computation in stellar dynamics, discuss chaos briefly, and indicate the way the physics that comes up in different astronomical contexts is addressed in numerical methods currently in use. Graphics is a vital part of any computational approach. The long range prospects are very promising for continued high scientific productivity in stellar dynamics.     

A phenomenological interpretation of stellar chromospheres

An attempt is made to develop a phenomenological interpretation of stellar chromospheres. The following problems are examined: observed emission powers of magnesium chromospheres on stars based on the ultraviolet doublet, 2800 Mgii, observations; dependence of chromosphere emission on spectral and luminosity classes; stellar chromospheres as an accidental event; chromospheres of stars-components of binary systems; stars with the chromospheres of solar type (S) and nonsolar (NS) type; distribution of stars by means of the type of their chromosphere on luminosity class; stars with superpower magnesium emission; emission measures for both the magnesium and calcium chromospheres; interrelation between chromosphere, transition zone and corona; chromospheric activity and rotation of stars; possibility of the existence of chromospheres on hot stars; phenomenological picture of stellar chromospheres; stars without the line 2800 Mgii, in emission or in absorption; syndrome of red giant HD 4174. At the end, the problem of heating of stellar chromospheres is discussed.     

A prediction method for ground-based stellar occultations by ellipsoidal solar system bodies and its application

A new programmable prediction method is developed to refine the occultation band by taking into consideration the triaxiality of an occulting body, as well as two more factors, namely, the barycenter offset of an occulting planet from the relevant planetary satellite system and the gravitational deflection of light rays due to an occulting planet. Although these factors can be neglected in most cases, it is shown that there are cases when these factors can cause a variation ranging from several tens to thousands of kilometers in the boundaries of occultation bands. Knowledge of analytic geometry simplifies the process of derivation and computation. This method is applied to long-term predictions of Jovian and Saturnian events.     

A new class of relativistic stellar models

Einstein field equations for a static and spherically symmetric perfect fluid are considered. A formulation given by Patiño and Rago is used to obtain a class of nine solutions, two of them are Tolman solutions I, IV and the remaining seven are new. The solutions are the correct ones corresponding to expressions derived by Patiño and Rago which have been shown by Knutsen to be incorrect. Similar to Tolman solution IV each of the new solutions satisfies energy conditions inside a sphere in some range of two independent parameters. Besides, each solution could be matched to the exterior Schwarzschild solution at a boundary where the pressure vanishes and thus the solutions constitute a class of new physically reasonable stellar models.