An iterative method for constructing equilibrium phase models of stellar systems

We present a new method for constructing equilibrium phase models for stellar systems, which we call the iterative method. It relies on constrained, or guided evolution, so that the equilibrium solution has a number of desired parameters and/or constraints. This method is very powerful, to a large extent due to its simplicity. It can be used for mass distributions with an arbitrary geometry and a large variety of kinematical constraints. We present several examples illustrating it. Applications of this method include the creation of initial conditions for N -body simulations and the modelling of galaxies from their photometric and kinematic observations.     

Fluctuations in finite-N equilibrium stellar systems

Gravitational amplification of Poisson noise in stellar systems is important on large scales. For example, it increases the dipole noise power by roughly a factor of 6 and the quadrupole noise by 50 per cent for a King model profile. The dipole noise is amplified by a factor of 15 for the core-free Hernquist model. The predictions are computed by summing over the wakes caused by each star in the system — the dressed-particle formalism of Rostoker & Rosenbluth — and are demonstrated by N -body simulation.   This result implies that a collisionless N -body simulation is impossible; the fluctuation noise which causes relaxation is an intrinic part of self-gravity. In other words, eliminating two-body scattering at interparticle scales does not eliminate relaxation altogether.   Applied to dark matter haloes of disc galaxies, particle numbers of at least 10⁶ will be necessary to suppress this noise at a level that does not dominate or significantly affect the disc response. Conversely, haloes are most likely far from phase-mixed equilibrium and the resulting noise spectrum may seed or excite observed structure such as warps, spiral arms and bars. For example, discreteness noise in the halo, similar to that caused by a population of 10⁶-M⊙ black holes, can produce observable warping and possibly excite or seed other disc structure.     

Asteroseismology of solar and stellar models

I discuss several asteroseismology diagnostic techniques that can be applied to the high quality data on stellar oscillations obtained, and to be obtained in the future, from ground based and space based experiments. In particular I discuss techniques using the representation of oscillation frequencies in terms of inner and outer phase shifts which can be used both for model fitting and inversion procedures to probe the inner structure of stars, and hence to test and improve our modelling.     

Relativistic isentropic stellar models

Relativistic, isentropic, homogeneous models are constructed by a method that automatically detects instabilities, and evolutionary tracks of central conditions are shown on a (T, ) diagram. Models heavier than 20M become unstable because of pair creation. Iron photodisintegration causes instability in the mass range between 1.5M and 20M . General relativistic effects bring about the onset of instability in models of 1.2–1.5M when the central density is about 10¹⁰ g/cm³. Lighter models become white dwarfs. It is pointed out that general relativistic instability will prevent the formation of neutron stars through hydrostatic evolution and may be relevant in setting off low-mass supernovae.     

Degenerate equilibrium states of collisionless stellar systems

We study spherically symmetrical equilibrium states of collisionless stellar systems confined to a spherical box. These equilibrium states correspond to the statistics introduced by Lynden-Bell in his theory of 'violent relaxation', and are described by a Fermi–Dirac distribution function. We compute the corresponding equilibrium diagram and show that a global entropy maximum exists for any accessible control parameter. This equilibrium state shows a pronounced separation between a degenerate core and a halo. We therefore check that degeneracy is able to stop the gravitational collapse (of a collisionless system), and we propose a simple model for the 'core–halo' structure. We also discuss the relevance of our study for real galaxies or other astrophysical systems such as massive neutrinos.     

Uniform density equilibrium model of self-gravitating stellar systems

A class of equilibrium solutions of the Vlasov equation for self-gravitating systems is discussed. The density and the potential are derived in form of Jacobi polynomials, which in a special case give rise to a model with uniform density.     

Hydrodynamic models of solar and stellar flares

This paper discusses the hydrodynamic modeling of flaring plasma confined in magnetic loops and its objectives within the broader scope of flare physics. In particular, the Palermo-Harvard model is discussed along with its applications to the detailed fitting of X-ray light curves of solar flares and to the simulation of high-resolution Ca xix spectra in the impulsive phase. These two approaches provide complementary constraints on the relevant features of solar flares. The extension to the stellar case, with the fitting of the light curve of an X-ray flare which occurred on Proxima Centauri, demonstrates the feasibility of using this kind of model for stars too. Although the stellar observations do not provide the wealth of details available for the Sun, and, therefore, constrain the model more loosely, there are strong motivations to pursue this line of research: the wider range of physical parameters in stellar flares and the possibility of studying further the solar-stellar connection.     

The photon-neutrino coupling theory and stellar models

The effect of the photon-neutrino coupling theory, developed by Bandyopadhyay (1968), on stellar structure is studied by constructing a chemically homogeneous model of one solar mass in thermal equilibrium, and taking into account the neutrinos according to the theory. As anticipated, the effect is large and leads to great difficulties in the understanding of stellar constitution.     

Linear and nonlinear oscillations of simple stellar models

A general property for the stability of the one zone model is derived in the case of linear nonadiabatic radial oscillations. The problem of the nonlinear adiabatic radial oscillations of the homogeneous model with a slow rotational velocity is discussed.     

Roche harmonics for tidally-distorted stellar models

Kopal's analysis for Roche harmonics associated with the Roche model of a star, distorted by the tidal forces of a companion star, has been extended further to obtain the explicit expressions for Roche harmonics when terms up to second order of smallness in tidal effects are considered.On leave from University of Roorkee, Institute of Paper Technology, Saharampur (U.P.), India.     

Reference grids of stellar models and oscillation frequencies

We present grids of stellar models and their associated oscillation frequencies that have been used by the CoRoT Seismology Working Group during the scientific preparation of the CoRoT mission. The stellar models have been calculated with the CESAM stellar internal structure and evolution code while the oscillation frequencies have been obtained from the CESAM models by means of the ADIPLS adiabatic oscillation programme. The grids cover a range of masses, chemical compositions and evolutionary stages corresponding to those of the CoRoT primary targets. The stellar models and oscillation frequencies are available on line through the Evolution and Seismic Tools Activity (ESTA) web site.     

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.     

The oscillation frequencies of magnetic stellar models

A first-order perturbation theory method developed by Goossens to determine the perturbation to the eigenfrequencies of stellar models caused by the presence of a magnetic field is modified slightly, and applied to models with toroidal and poloidal fields. Some limitations of the analysis are pointed out.     

Nonlinear hydrodynamical models of stellar convective zones

Large-eddy simulation (LES) of turbulent convection is discussed in various versions (mixing-length theory, modal theory and spectral theory) in respect to the application to stellar convective zones. For the model construction, the non-local mixing-length formalism is suitable. However, for the determination of basic flow patterns and of mixing-length, the quasi-linear and nonlinear modal theories are useful. The eddy diffusivities are essential in these theories, and the nonlinear treatment of convection consistent with turbulent diffusivities (of effective Reynolds number of about 20 and Prandtl number of 0.4) offers a simple method of constructing stellar models without the use of the mixing-length.Paper presented at the IAU Third Asian-Pacific Regional Meeting, held in Kyoto, Japan, between 30 September–6 October, 1984.