Gravitational waves from isolated neutron stars: Mass dependence of $r$-mode instability

In this work, we study the $r$-mode instability windows and the gravitational wave signatures of neutron stars in the slow rotation approximation using the equation of state obtained from the density-dependent M3Y effective interaction. We consider the neutron star matter to be $\beta$-equilibrated neutron-proton-electron matter at the core with a rigid crust. The fiducial gravitational and viscous timescales, the critical frequencies, the time evolutions of the frequencies, and the rates of frequency change are calculated for a range of neutron star masses. We show that the young and hot rotating neutron stars lie in the $r$-mode instability region. We also emphasize that if the dominant dissipative mechanism of the $r$ mode is the shear viscosity along the boundary layer of the crust-core interface, then the neutron stars with low $L$ value lie in the $r$-mode instability region and hence emit gravitational radiation.

Figure 1

Plots of the nuclear symmetry energy NSE as a function of $\rho /{\rho }_0$ for the present calculation using DDM3Y interaction and its comparison, with those for Akmal-Pandharipande-Ravenhall (APR) [42] and the MDI interactions for the variable $\mathrm{x}=0.0$, 0.5 defined in Ref. [43].

Figure 2

The plots of $K_{\tau }$ vs $K_{\infty }$ ($K_{\inf }$). Present calculation (DDM3Y) is compared with other predictions as tabulated in Refs. [56, 57] and the dotted rectangular region encompasses the values of $K_{\infty }=250–270$ MeV [40] and $K_{\tau }=-370\pm 120$ MeV [54].

Figure 3

Mass-equatorial radius plot of slowly rotating neutron stars for the DDM3Y EoS.

Figure 4

Plots of fiducial timescales with gravitational mass of neutron stars with DDM3Y EoS.

Figure 5

Plots of reduced critical angular frequency with temperature for different masses of neutron stars.

Figure 6

Plots of critical temperature versus mass.

Figure 7

Plots of critical frequency with temperature for different masses of neutron stars. The square dots represent observational data [82] of Table 4.

Figure 8

Plots of time evolution of frequencies.

Figure 9

Plots of time evolution of spin-down rates.

Figure 10

Plots of spin-down rates vs frequencies.