Low-$T/|W|$ instabilities in differentially rotating neutron stars resembling merger remnants

Abstract

We construct constant rest-mass sequences of equilibrium models of differentially rotating neutron stars which resemble binary neutron star post-merger remnants. For a more realistic description of the post-merger remnant, we impose that each model carries approximately $95\%$ of the angular momentum that a binary system with the same total rest-mass has at the moment of merging, based on an empirical relation informed from neutron star merger simulations. We account for equation of state effects by employing two distinct microphysical descriptions for high density matter. We dynamically evolve the equilibrium models with a three-dimensional general relativistic hydrodynamics code that employs the conformal flatness approximation. We investigate the connection between the occurrence of the instability and the existence of corotation radii within the stellar configurations and determine the instability window for both equation of state sequences. The occurrence of low-$T/|W|$ instabilities leads to pronounced gravitational wave emission in the range $0.13 \lessapproxβ\lessapprox 0.2$, while models outside this range exhibit less pronounced features in the gravitational wave spectrum. The prominence of gravitational wave emission is primarily determined by $β$, while the equation of state seems to have a more minor effect. We present correlations between the strength of the gravitational wave emission associated with the instability and properties of the equilibrium models. Stellar configurations modelled by different equations of state display differences in the timescales over which the various dynamical features develop, as well as whether they exhibit a pronounced $m=1$ deformation. Potential relations between the instability growth timescales and properties of the stellar models are studied.

Figures (35)

• Figure 1: Rotational profiles for our reference models versus the coordinate radius $r$, calculated via the rns code. The angular velocity $\Omega$ follows rotation law \ref{['eq:Uryuetal_rotlaw8']}.
• Figure 2: Gravitational mass $M$ versus maximum energy density $\epsilon_\text{max}$ for the SFHo EOS. The solid line denotes the nonrotating sequence, the dashed line the Kepler sequence, and the dotted line the axisymmetric instability limit for uniform rotation. The filled circle line denotes a constant rest mass sequence with $M_0$ equal to our model's rest mass (see Table \ref{['tab:SFHO_DD2_M0_const_sequence']}). The reference model is shown with an orange triangle.
• Figure 3: Same as Figure \ref{['Mass_density_SFHO']}, but for the DD2 EOS.
• Figure 4: Corotation band for SFHo: The filled circles represent $\Omega/2\pi$ values of a constant rest-mass sequence with $M_0$ equal to our reference model's rest mass (see Table \ref{['tab:SFHO_DD2_M0_const_sequence']}). The solid and dashed lines represent the edges $\Omega_\textrm{max}/2\pi$ and $\Omega_c/2\pi$ of the corotation region (grey shaded area) respectively. The pattern frequencies of the selected evolved models are shown as blue up triangles, whereas the orange down triangles represent secondary frequencies identified for some of the models (see Table \ref{['tab:frequencies']} and Secs. \ref{['sec:IV']}, \ref{['sec:VI']}). The reference model's frequencies are shown as empty up and down triangles. The grey dotted line represents the center of the corotation band, while the green crosses depict estimated frequencies based on the assumption that the local vortensity minimum is a corotation radius (see discussion in Sec. \ref{['sec:VII']}). The green dash-dotted line connects the aforementioned frequencies.
• Figure 5: Same as Figure \ref{['fig:corot_sfho']} for the DD2 EOS. For two models, we identify additional tertiary frequencies shown as red diamonds.