Journal Article

Unstable <i>m</i>= 1 modes of counter-rotating Keplerian discs

Mamta Gulati, Tarun Deep Saini and S. Sridhar

in Monthly Notices of the Royal Astronomical Society

Published on behalf of The Royal Astronomical Society

Volume 424, issue 1, pages 348-360
Published in print July 2012 | ISSN: 0035-8711
Published online July 2012 | e-ISSN: 1365-2966 | DOI:
Unstable m= 1 modes of counter-rotating Keplerian discs

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We study the linear m= 1 counter-rotating instability in a two-component, nearly Keplerian disc. Our goal is to understand these slow modes in discs orbiting massive black holes in galactic nuclei. They are of interest not only because they are of large spatial scale – and can hence dominate observations – but also because they can be growing modes that are readily excited by accretion events. Self-gravity being non-local, the eigenvalue problem results in a pair of coupled integral equations, which we derive for a two-component softened gravity disc. We solve this integral eigenvalue problem numerically for various values of mass fraction in the counter-rotating component. The eigenvalues are in general complex, being real only in the absence of the counter-rotating component, or imaginary when both components have identical surface density profiles. Our main results are as follows: (i) the pattern speed appears to be non-negative, with the growth (or damping) rate being larger for larger values of the pattern speed; (ii) for a given value of the pattern speed, the growth (or damping) rate increases as the mass in the counter-rotating component increases; (iii) the number of nodes of the eigenfunctions decreases with increasing pattern speed and growth rate. Observations of lopsided brightness distributions would then be dominated by modes with the least number of nodes, which also possess the largest pattern speeds and growth rates.

Keywords: instabilities; celestial mechanics; galaxies: nuclei

Journal Article.  6466 words.  Illustrated.

Subjects: Astronomy and Astrophysics

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