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.