Title:	Unstable m= 1 modes of counter-rotating Keplerian discs
Authors:	Gulati, Mamta Saini, T.D. Sridhar, S.
Keywords:	instabilities - celestial mechanics galaxies - nuclei
Issue Date:	Jul-2012
Publisher:	Wiley Interscience for the RAS
Citation:	Monthly Notices of the Royal Astronomical Society, 2012, Vol.424, p348
Abstract:	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.
Description:	Restricted Access. An open-access version is available at arXiv.org (one of the alternative locations)
URI:	http://hdl.handle.net/2289/5020
ISSN:	0035-8711 1365-2966 (Online)
Alternative Location:	http://adsabs.harvard.edu/abs/2012MNRAS.424..348G http://arxiv.org/abs/1203.2239 http://dx.doi.org/10.1111/j.1365-2966.2012.21199.x
Copyright:	2012 The authors & Royal Astronomical Society.
Appears in Collections:	Research Papers (A&A)

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