NONAXISYMMETRIC SECULAR INSTABILITIES DRIVEN BY STAR DISK COUPLING

Citation
Jn. Imamura et al., NONAXISYMMETRIC SECULAR INSTABILITIES DRIVEN BY STAR DISK COUPLING, The Astrophysical journal, 444(1), 1995, pp. 363-375
Citations number
45
Categorie Soggetti
Astronomy & Astrophysics
Journal title
ISSN journal
0004637X
Volume
444
Issue
1
Year of publication
1995
Part
1
Pages
363 - 375
Database
ISI
SICI code
0004-637X(1995)444:1<363:NSIDBS>2.0.ZU;2-1
Abstract
We determine conditions for the onset of nonaxisymmetric secular insta bilities in polytropes with a wide range of angular momentum distribut ions using Lagrangian techniques, and then calculate the growth rate o f such instabilities when driven by the coupling of the perturbed star to a circumstellar disk. We use Lagrangian displacement vectors with azimuthal dependence proportional to exp (im phi), where m is an integ er and phi is the azimuthal coordinate. The onset of secular instabili ty in terms of the quantity T/\W\, the ratio of rotational kinetic ene rgy to gravitational potential energy, is affected by both the compres sibility and the angular momentum distribution of the polytrope. The l argest effects occur when the angular momentum distribution is varied. For polytropic index n = 3/2, the onset of secular instability for th e m = 2 mode (the bar mode), as determined by its neutral point, shift s from T/\W\ = 0.141 to 0.093, while the m = 5 mode neutral point shif ts from T/\W\ = 0.088 to 0.031 over the range of angular momentum dist ributions we consider. The smallest critical T/\W\-values occur for th e angular momentum distributions which are the most peaked toward the equator. For the angular momentum distribution of a Maclaurin spheroid , as the polytropic index n is increased from 3/2 to 5/2, the neutral point for m = 2 shifts from T/\W\ = 0.141 to 0.144 and the neutral poi nt for m = 5 shifts from T/\W\ = 0.069 to 0.078. The neutral points fo r m = 2 and 5 for the Maclaurin sequence (n = 0) are 0.137 and 0.0629, respectively. As the angular momentum distribution becomes more peake d toward the equatorial radius of the polytropes, the critical T/\W\-v alues generally become less sensitive to the compressibility of the po lytrope. Star/disk coupling can drive the secular instability in syste ms where the star is surrounded by a massive disk and, if the instabil ity can grow to moderate amplitude, then the coupling can transport si gnificant amounts of angular momentum from the star into the circumste llar disk. We find, for the particular case of rotating protostars dur ing the accretion phase, that the instability growth time can be short er than the accretion time. Further, if the instability can grow to am plitudes on the order of several percent, the star/disk coupling can r emove angular momentum from the forming star faster than it is added b y accretion.