Astronomy and Astrophysics – Astronomy
Scientific paper
Aug 1992
adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1992phdt.........5n&link_type=abstract
Ph.D. Thesis Stanford Univ., CA.
Astronomy and Astrophysics
Astronomy
5
Accretion Disks, Black Holes (Astronomy), Neutron Stars, Stellar Oscillations, Stellar Structure, Eigenvectors, Helioseismology, Partial Differential Equations, Stellar Models, Turbulence
Scientific paper
Helioseismology has provided a wealth of information about the structure of the solar atmosphere. Little is known, however, about the structure of accretion disks that are thought to exist around black holes and neutron stars. In this thesis we present calculations of modes that are trapped in thin Keplerian accretion disks. We hope to use observations of thes modes to elucidate the structure of the inner relativistic regions of accretion disks. Our calculations assume that the thin disk is terminated by an innermost stable orbit, as would occur around a slowly rotating black hole or weakly magnetized compact neutron star. The dominant relativistic effects, which allow modes to be trapped within the inner region of the disk, are approximated via a modified Newtonian potential. Using the Lagrangian formulation of Friedman and Schutz, we develop a general formalism for investigating the adiabatic oscillations of arbitrary unperturbed disk models. First we consider the special case of acoustic waves in disks with isothermal atmospheres. Next we describe the Lagrangian perturbation vectors in terms of the derivatives of a scalar potential, as has been done by Ipser and Lindblom. Using this potential, we derive a single partial differential equation governing the oscillations of a disk. The eigenfunctions and eigenfrequencies of a variety of disk models are found to fall into two main classes which are analogous to the p-modes and g-modes in the sun. Specifically we use the potential formalism to compute the g-modes for disks with isothermal atmospheres. Physical arguments show that both the p-modes and g-modes belong to the same family of modes as the p-modes and g-modes in the sun, just viewed in a different parameter regime. With the aid of the Lagrangian formalism we consider possible growth or damping mechanisms and compute the (assumed) relatively small rates of growth or damping of the modes. Specifically, we consider gravitational radiation reaction and parameterized models of viscosity. Both isotropic and anisotropic viscosity models are considered. We find that isotropic viscosity models tend to lead toward mode growth, while anisotropic viscosity models tend to lead toward damping. We consider possible physical explanations for this effect.
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