Non-analytic behavior of the relativistic r-modes in slowly rotating neutron stars

Abstract

An inconsistency between the theoretical analysis and numerical calculations of the relativistic r-modes puzzles the neutron star community since the Kojima's finding of the continuous part in the r-mode oscillation spectrum in 1997. In this paper, after a brief review of the Newtonian rmode theory and of the literature devoted to the continuous spectrum of r-modes, we apply our original approach to the study of relativistic oscillation equations. Working within the Cowling approximation, we derive the general equations, governing the dynamics of discrete relativistic rmodes for both barotropic (isentropic) and nonbarotropic stars. A detailed analysis of the obtained equations in the limit of extremely slow stellar rotation rate reveals that, because of the effect of inertial reference frame-dragging, the relativistic r-mode eigenfunctions and eigenfrequencies become non-analytic functions of the stellar angular velocity, Ω. We also derive the explicit expressions for the r-mode eigenfunctions and eigenfrequencies for very small values of Ω. These expressions explain the asymptotic behavior of the numerically calculated eigenfrequencies and eigenfunctions in the limit Ω → 0. All the obtained r-mode eigenfrequencies take discrete values in the frequency range, usually associated with the continuous part of the spectrum. No indications of the continuous spectrum, at least in the vicinity of the Newtonian l = m = 2 r-mode frequency σ = −4/3 Ω, are found.

Observability of HOFNARs at SRG/eROSITA

“…The main uncertainty is related to unknown properties of instability windows-the regions in the temperature-spin frequency diagram, where an NS is unstable with respect to the r-modes. The instability windows strongly depend on the NS microphysics, including composition and superfluid properties (see, e.g., [34] for a review and [35][36][37] for some recent results). Thus, detection of HOFNARs by eROSITA will provide crucial constraints on internal properties of NSs.…”

“…The instability windows strongly depend on the NS microphysics, including composition and superfluid properties (see, e.g. [34] for a review and [35][36][37] for some recent results). Thus, detection of HOFNARs by eROSITA will provide crucial constraints on internal properties of NSs.…”