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Please use this identifier to cite or link to this item: http://hdl.handle.net/2289/6596
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dc.contributor.authorGulati, Mamta-
dc.contributor.authorSaini, T.D.-
dc.date.accessioned2017-01-17T09:29:47Z-
dc.date.available2017-01-17T09:29:47Z-
dc.date.issued2016-07-21-
dc.identifier.citationMonthly Notices of the Royal Astronomical Society, 2016, Vol.460, p1019-1032en_US
dc.identifier.issn1365-2966 - (online)-
dc.identifier.issn0035-8711-
dc.identifier.urihttp://hdl.handle.net/2289/6596-
dc.descriptionOpen accessen_US
dc.description.abstractThe short-wave asymptotics (WKB) of spiral density waves in self-gravitating stellar discs is well suited for the study of the dynamics of tightly-wound wavepackets. But the textbook WKB theory is not well adapted to the study of the linear eigenmodes in a collisionless self-gravitating disc because of the transcendental nature of the dispersion relation. We present a modified WKB theory of spiral density waves, for collisionless discs in the epicyclic limit, in which the perturbed gravitational potential is related to the perturbed surface density by the Poisson integral in Kalnaj's logarithmic spiral form. An integral equation is obtained for the surface density perturbation, which is seen to also reduce to the standard WKB dispersion relation. Although our formulation is general and applies to all discs, we present our analysis only for nearly Keplerian, low-mass, self-gravitating discs revolving around massive central objects, and derive an integral equation governing the slow precessional modes of such discs. For a prograde disc, the integral kernel turns out be real and symmetric, implying that all slow modes are stable. We apply the slow mode integral equation to two unperturbed disc profiles, the Jalali–Tremaine annular discs, and the Kuzmin disc. We determine eigenvalues and eigenfunctions for both m = 1 and m = 2 slow modes for these profiles and discuss their properties. Our results compare well with those of Jalali–Tremaine.en_US
dc.language.isoenen_US
dc.publisherOxford University Press for the RASen_US
dc.relation.urihttp://adsabs.harvard.edu/abs/2016MNRAS.460.1019Gen_US
dc.relation.urihttp://arxiv.org/abs/1601.04148en_US
dc.relation.urihttp://dx.doi.org/10.1093/mnras/stw970en_US
dc.rights2016 The authors & the Royal Astronomical Society.en_US
dc.subjectanalytical galaxiesen_US
dc.subjectkinematics and dynamicsen_US
dc.subjectgalaxies nucleien_US
dc.titleA modified WKB formulation for linear eigenmodes of a collisionless self-gravitating disc in the epicyclic approximationen_US
dc.typeArticleen_US
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