$f$-mode oscillations of compact stars in dynamical spacetimes: Equation of state dependencies and universal relations studies. (arXiv:2108.04643v2 [gr-qc] UPDATED)

$f$-mode oscillations of compact stars in dynamical spacetimes: Equation of state dependencies and universal relations studies. (arXiv:2108.04643v2 [gr-qc] UPDATED)
<a href="http://arxiv.org/find/gr-qc/1/au:+Shashank_S/0/1/0/all/0/1">Swarnim Shashank</a>, <a href="http://arxiv.org/find/gr-qc/1/au:+Nouri_F/0/1/0/all/0/1">Fatemeh Hossein Nouri</a>, <a href="http://arxiv.org/find/gr-qc/1/au:+Gupta_A/0/1/0/all/0/1">Anshu Gupta</a>

In this article, we study the fundamental ($f$-)modes of non-rotating compact
stars with realistic equations of state (EoS), extracted in the dynamical
spacetime using numerical relativity simulations. We use a set of EoS with
varying degree of stiffness and numerically evolve perturbed stellar models for
several mass configurations (in the range of $1.2 – 2.0$ $M_{odot}$) for each
of these EoS. We observe the $f$-mode frequency is lower for the stiffer EoS,
and it increases linearly with the square root of mean density for each set of
EoS. We notice that the frequencies are distinguishable for soft, intermediate
and stiffer EoS, thus it might be possible to constrain the EoS based on the
detected signal frequency from the binary neutron star merger. More
specifically for the softer EoS, the $f$-mode frequency is in the range of
$1.8-2.2$ kHz for the masses between $1.2-1.8 M_{odot}$. On the other hand, in
the case of stiffer EoS, such as ‘BHB’ and ‘DD2’ frequency is shifted to lower
values $1.55-1.8$ kHz for the same mass range. We also compare our single
perturbed star simulation with recently studied binary simulations and find a
good agreement.

In this article, we study the fundamental ($f$-)modes of non-rotating compact
stars with realistic equations of state (EoS), extracted in the dynamical
spacetime using numerical relativity simulations. We use a set of EoS with
varying degree of stiffness and numerically evolve perturbed stellar models for
several mass configurations (in the range of $1.2 – 2.0$ $M_{odot}$) for each
of these EoS. We observe the $f$-mode frequency is lower for the stiffer EoS,
and it increases linearly with the square root of mean density for each set of
EoS. We notice that the frequencies are distinguishable for soft, intermediate
and stiffer EoS, thus it might be possible to constrain the EoS based on the
detected signal frequency from the binary neutron star merger. More
specifically for the softer EoS, the $f$-mode frequency is in the range of
$1.8-2.2$ kHz for the masses between $1.2-1.8 M_{odot}$. On the other hand, in
the case of stiffer EoS, such as ‘BHB’ and ‘DD2’ frequency is shifted to lower
values $1.55-1.8$ kHz for the same mass range. We also compare our single
perturbed star simulation with recently studied binary simulations and find a
good agreement.

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