Superhump periods in SU Ursae Majoris stars: Eigenfrequency of the eccentric mode of an accretion disk

Details Superhump periods in SU Ursae Majoris stars: Eigenfrequency of the eccentric mode of an accretion disk Superhump periods in SU Ursae Majoris stars: Eigenfrequency of the eccentric mode of an accretion disk

Aug 1993

adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1993pasj...45..595h&link_type=abstract

PASJ: Publications of the Astronomical Society of Japan (ISSN 0004-6264), vol. 45, no. 4, p. 595-604

Computer Science

Numerical Analysis

18

Accretion Disks, Cataclysmic Variables, Dwarf Novae, Eigenvalues, Eigenvectors, Hydrodynamics, Precession, Hydrodynamic Equations, Numerical Analysis, Sturm-Liouville Theory

Scientific paper

Superhump periods of SU UMa-type dwarf novae are thought to be given by the synodic (beat) periods between a slowly-precessing eccentric disk and the orbiting secondary star. The precession rate of the eccentric disk in SU UMa stars is formulated as an eigenvalue of the oscillation of the eccentric (one-armed) mode in the accretion disk. It is shown that the eigenvalue problem is reduced to that of the Sturm-Liouville type and that the precession rate of the eccentric disk is given by the eigenfrequency of the fundamental mode. The eigenfrequency of this mode is examined both analytically and numerically. The eigenfunction of the fundamental eccentric mode is found to be confined to the outer-most part of the disk. Its eigenfrequency is given by a kind of (eigenfunction weighted) average of the local precession rate over the outermost part of the disk if the temperature of the disk is low (or the geometrical thickness of the disk is small) and its frequency decreases with increasing disk temperature.

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