R -mode frequencies of rapidly and differentially rotating relativistic neutron stars

Abstract

R-modes of neutron stars could be a source of gravitational waves for ground based detectors. If the precise frequency σ is known, guided gravitational wave searches with enhanced detectability are possible. Because of its physical importance many authors have calculated the r-mode frequency. For the dominant mode, the associated gravitational wave frequency is 4/3 times the angular velocity of the star Ω, subject to various corrections of which relativistic and rotational corrections are the most important. This has led several authors to investigate the dependence of the r-mode frequency on factors such as the relativistic compactness parameter (M/R) and the angular velocity of stars with different equations of state. The results found so far, however, are almost independent of the equation of state. Here we investigate the effect of rapid rotation and differential rotation on σ. We evolve the perturbation equations using the Cowling approximation by applying finite differencing methods to compute the r-mode frequency for a series of rotating neutron stars with polytropic equations of state. We find that rotational effects in the r-mode frequency can be larger than relativistic effects for rapidly spinning stars with low compactness, reducing the observed frequency. Differential rotation also acts to decrease σ, but its effect inscreases with the compactness. The results presented here are relevant to the design of gravitational wave and electromagnetic r-mode searches.

Continuous Gravitational Waves from Neutron Stars: Current Status and Prospects

“…This relation is independent on EOS and it is a good approximation for the slowly rotating NSs. However, according to numerical results, inclusion of relativistic corrections may increase f GW by a few tens of percent (Lockitch et al, 2003;Pons et al, 2005;Idrisy et al, 2015;Jasiulek & Chirenti, 2017). Exact value depends mostly on the object compactness C (dimensionless massradius ratio: C ≈ 0.207 M 1.4 M 10 km R , for NSs typically 0.11 C 0.31), but also on rotational frequency of the object (Lindblom et al, 1999;Idrisy et al, 2015;Jasiulek & Chirenti, 2017), including rigid versus differential rotation (Stavridis et al, 2007;Idrisy 12 Unlike in the case of the elastic deformations, what was shown in Section 2, r-modes affect equation of motion δv = α(r/R) l RωY B lm exp(iω r t), where α is dimensionless amplitude and ω r = − 2m l(l+1) ω is the angular frequency in co-rotating frame.…”

“…2019)). For the more detailed review of the topic see Kokkotas & Schwenzer (2016Jasiulek & Chirenti, 2017), stiffness of the crust Levin & Ushomirsky, 2001) and EOS (Lockitch et al, 2003;Pons et al, 2005;Lattimer & Prakash, 2007;Idrisy et al, 2015). Additionally, as it was shown in Arras et al (2003), consideration of the non-linear coupling forces among internal modes leads to the result that r-mode signal from both newly born NSs and LMXB in the spin-down phase of Levin's limit cycle 13 (Levin , 1999) will be detectable by enhanced LIGO detectors out to ∼100-200 kpc.…”

M/R estimates for two neutron stars in LMXBs with possible r-mode frequencies detected

“…The most obvious and important improvement that is needed is to go beyond the Cowling approximation. In Jasiulek & Chirenti (2017) we presented a first direct computation of the error in the r-mode frequencies due to the Cowling approximation. This was done by extrapolating our numerical results, obtained for fast rotating relativistic polytropic stars in the Cowling approximation, to f → 0 (which gives the κ 0 term in eq.…”

“…A small amount of differential rotation could be present in neutron stars in LMXBs, and it might be relevant for the determination of the r-mode frequencies in stars with high compactness (Jasiulek & Chirenti 2017). More specifically, r-modes (as well as accretion) could be responsible for generating differential rotation in a neutron star, but viscosity in general and magnetic braking in particular could quickly bring the star back to uniform rotation (Rezzolla et al 2001a,b).…”

“…In a previous work (Jasiulek & Chirenti 2017) we have carefully calculated the corrections to the r-mode frequencies taking into account relativist and rotational effects in fast rotating neutron stars, also including a possibly strong differential rotation. These results were obtained in the relativistic Cowling approximation (that neglects all metric perturbations), by numerically solving the linear perturbation equations in the fixed stellar background and extending to fast rotation our previous results calculated in the slow rotation approximation ).…”