As an extension of our previous work , we investigate the dynamical instability against nonaxisymmetric bar-mode deformations of differentially rotating stars in Newtonian gravity varying the equations of state and velocity profiles .
We performed the numerical simulation and the followup linear stability analysis adopting polytropic equations of state with the polytropic indices n = 1 , 3/2 , and 5/2 and with two types of angular velocity profiles ( the so-called j -constant-like and Kepler-like laws ) .
It is confirmed that rotating stars of a high degree of differential rotation are dynamically unstable against the bar-mode deformation , even for the ratio of the kinetic energy to the gravitational potential energy \beta of order 0.01 .
The criterion for onset of the bar-mode dynamical instability depends weakly on the polytropic index n and the angular velocity profile as long as the degree of differential rotation is high .
Gravitational waves from the final nonaxisymmetric quasi-stationary states are calculated in the quadrupole formula .
For proto-neutron stars of mass 1.4 M _ { \odot } , radius \sim 30 km and \beta \mathrel { \raise 1.29 pt \hbox { $ < $ } \mkern - 14.0 mu \lower 2.58 pt \hbox { $ \sim$ } } 0.1 , such gravitational waves have the frequency of \sim 600–1,400 Hz , and the effective amplitude is larger than 10 ^ { -22 } at a distance of about 100 Mpc irrespective of n and the angular velocity profile .