R-mode oscillations of differentially and rapidly rotating Newtonian polytropic stars

Abstract

For the analysis of the r-mode oscillation of hot young neutron stars, it is necessary to consider the effect of differential rotation, because viscosity is not strong enough for differentially rotating young neutron stars to be lead to uniformly rotating configurations on a very short time scale after their birth. In this paper, we have developed a numerical scheme to solve r-mode oscillations of differentially rotating polytropic inviscid stars. This is the extended version of the method which was applied to compute r-mode oscillations of uniformly rotating Newtonian polytropic stars. By using this new method, we have succeeded in obtaining eigenvalues and eigenfunctions of r-mode oscillations of differentially rotating polytropic stars.Our numerical results show that as the degree of differential rotation is increased, it becomes more difficult to solve r-mode oscillations for slightly deformed configurations from sphere compared to solving r-mode oscillations of considerably deformed stars. One reason for it seems that for slightly deformed stars corotation points appear near the surface region if the degree of differential rotation is strong enough. This is similar to the situation that the perturbational approach of r-mode oscillations for slowly rotating stars in general relativity results in a singular eigenvalue problem.

Linear Stability Analysis of Differentially Rotating Polytropes: New Results for them = 2f‐Mode Dynamical Instability

“…Therefore, such young neutron stars could be important targets of ground-based laser interferometric detectors of gravitational waves (Brown 2000;Shibata et al 2002). 1 Concerning the rotation-law dependence of the critical values for the m ¼ 2 f-mode dynamical instability, we have performed linear stability analysis for equilibrium models with the v-constant rotation law (Karino et al 2001). However, the effect of differential rotation seems very weak, and the dynamical instability occurs only for models with very stiff equations of state and/or extremely small values of the parameter A. Additionally, the change of the critical values of is very little.…”

“…As mentioned before, the linearized equations are solved by the scheme developed by Karino et al (2000Karino et al ( , 2001. The perturbed quantities are expanded as follows:…”

Differential rotation and r-modes in magnetized neutron stars

“…Recently, Chirenti, Skákala & Yoshida (2013) ;Chirenti, Skákala & Yoshida (2014) confirm that rmodes are rather insensitive to small differential rotation within general relativity Cowling approximation. Note, however, that in case of very strong differential rotation, r-modes can be suppressed (see Karino et al (2001), for more details).…”

The Nature of Low T /| W | Dynamical Instabilities in Differentially Rotating Stars

“…In these scenarios the corotating f-mode would enter the corotation band as either a zero-step or decaying mode (although no decay is observed), merging inside the band with another zero-step or decaying mode to go unstable. What it could be merging with, however, is unclear: the counterrotating f-mode is outside the band at low b, and the r-modes never enter (Karino et al 2001). In addition, it is not clear whether or not the unstable mode could retain a barlike character if it arose through merger with another mode type; the corotation mechanism, by contrast, permits barlike instability as the f-mode would not merge with any other mode.…”