R-mode constraints from neutron star equation of state

Abstract

The gravitational radiation has been proposed a long time before, as an explanation for the observed relatively low spin frequencies of young neutron stars and of accreting neutron stars in low-mass X-ray binaries as well. In the present work we studied the effects of the neutron star equation of state on the r-mode instability window of rotating neutron stars. Firstly, we employed a set of analytical solution of the Tolman-Oppemheimer-Volkoff equations with special emphasis on the Tolman VII solution. In particular, we tried to clarify the effects of the bulk neutron star properties (mass, radius, density distribution, crust size and elasticity) on the r-mode instability window. We found that the critical angular velocity Ω c depends mainly on the neutron star radius. The effects of the gravitational mass and the mass distribution are almost negligible. Secondly, we studied the effect of the elasticity of the crust, via to the slippage factor S and also the effect of the nuclear equation of state, via the slope parameter L, on the instability window. We found that the crust effects are more pronounced, compared to those originated from the equation of state. Moreover, we proposed simple analytical expressions which relate the macroscopic quantity Ω c to the radius, the parameter L and the factor S. We also investigated the possibility to measure the radius of a neutron star and the factor S with the help of accurate measures of Ω c and the neutron star temperature. Finally, we studied the effects of the mutual friction on the instability window and discussed the results in comparison with previous similar studies.

Influence of the nuclear matter equation of state on ther-mode instability using the finite-range simple effective interaction

“…The bulk viscosity in equation ( 6) should be computed for the modified URCA process, but here we have used the approximate expression used in Refs. [35,25,65], given by…”

The stability of relativistic stars and the role of the adiabatic index

“…The Nariai IV solution [17,18,19] is the most complicated and less known, compared to the previous ones. This solution has been employed in neutron stars studies [22,25]. However, the stability of this solution, according to our knowledge, is examined for a first time in the literature.…”

$R$-mode Stability of GW190814's Secondary Component as a Supermassive and Superfast Pulsar

“…The r-mode instability (Andersson 1998;Friedman & Morsink 1998;Andersson & Kokkotas 1998;Ho & Lai 2000) can trigger the exponential growth of gravitational wave (GW) emission in rapidly rotating neutron stars through the Chandrasekhar-Friedman-Schutz mechanism (Chandrasekhar 1970;Friedman & Schutz 1978) if the GW growth rate is faster than its damping rate. Over the past two decades, significant efforts have been devoted to better understanding the r-mode instability and its damping mechanisms with many interesting findings (see, e.g., Madsen 2000;Yang et al 2011;Wen et al 2012;Vidaña 2012;Haskell et al 2012;Alford & Schwenzer 2014a,b;Idrisy et al 2015;Moustakidis 2015;Dai et al 2016;Papazoglou & Moustakidis 2016;Ofengeim et al 2019;Wang et al 2019;Krüger & Kokkotas 2020). In particular, it was found that the r-mode instability window (a region in the spin frequency versus temperature plane) in which the r-mode is unstable depends sensitively on the EOS of neutron-rich matter, especially its symmetry energy term which encodes the information about the energy cost to make nuclear matter more neutron-rich.…”