Relativistic Diskoseismology. I. Analytical Results for “Gravity Modes”

Abstract

We generalize previous calculations to a fully relativistic treatment of adiabatic oscillations that are trapped in the inner regions of accretion disks by non-Newtonian gravitational e †ects of a black hole. We employ the Kerr geometry within the scalar potential formalism of Ipser and Lindblom, neglecting the gravitational Ðeld of the disk. This approach treats perturbations of arbitrary stationary, axisymmetric, perfect Ñuid models. It is applied here to thin accretion disks. Approximate analytic eigenfunctions and eigenfrequencies are obtained for the most robust and observable class of modes, which corresponds roughly to the gravity (internal) oscillations of stars. The dependence of the oscillation frequencies on the mass and angular momentum of the black hole is exhibited. These trapped modes do not exist in Newtonian gravity, and thus provide a signature and probe of the strong-Ðeld structure of black holes. Our predictions are relevant to observations that could detect modulation of the X-ray luminosity from stellar mass black holes in our Galaxy and the UV and optical luminosity from supermassive black holes in active galactic nuclei.

Relativistic Diskoseismology. II. Analytical Results for c‐modes

“…We want to know how the frequency changes as the luminosity (proportional to the mass accretion rate) varies with time. That dependence is known to be very weak for the g-modes (Perez et al 1997 Nowak & Wagoner 1991 ;Perez 1993).…”

Testing the space-time geometry around black hole candidates with the available radio and X-ray data

“…If that is correct, they may be used to probe the geometry around stellar-mass BH candidates. For the time being, however, the exact physical mechanism responsible for the production of the high-frequency QPOs is not known and several different scenarios have been proposed, including hot-spot models (Stella & Vietri 1998, diskoseismology models (Perez et al 1997;Silbergleit et al 2001;Wagoner et al 2001;Kato 2001), resonance models (Abramowicz & Kluzniak 2001;Abramowicz et al 2003;Kluzniak & Abramowicz 2005;Török et al 2005), and p-mode oscillations of a small accretion torus (Rezzolla et al 2003a,b;Schnittman & Rezzolla 2006). In these models, the frequencies of the QPOs are directly related to the three characteristic orbital frequencies of a test-particle: the Keplerian frequency ν K (which is the inverse of the orbital period), the radial epicyclic frequency ν r (the frequency of radial oscillations around the mean orbit), and the vertical epicyclic frequency ν θ (the frequency of vertical oscillations around the mean orbit).…”

Relativistic Diskoseismology. III. Low‐Frequency Fundamentalp‐Modes

“…Together with the appropriate homogeneous boundary conditions (discussed by Perez et al 1997 ;Silbergleit et al No. 2, 2002 RELATIVISTIC DISKOSEISMOLOGY.…”

“…Along with the angular mode number m, we employ j and n for the vertical and radial mode numbers (number of nodes in the corresponding eigenfunction), respectively, as in Perez et al (1997) and Silbergleit et al (2001).…”