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General Relativity and Quantum Cosmology, gr-qc, Astrophysics, High Energy Astrophysical Phenomena, astro-ph.HE
Abstract:
Observations of gravitational waves from inspiralling neutron star
binaries---such as GW170817---can be used to constrain the nuclear equation of
state by placing bounds on stellar tidal deformability. For slowly rotating
neutron stars, the response to a weak quadrupolar tidal field is characterized
by four internal-structure-dependent constants called Love numbers. The tidal
Love numbers $K_2^\text{el}$ and $K_2^\text{mag}$ measure the tides raised by
the gravitoelectric and gravitomagnetic components of the applied field, and
the rotational-tidal Love numbers $\mathfrak{F}^\text{o}$ and
$\mathfrak{K}^\text{o}$ measure those raised by couplings between the applied
field and the neutron star spin. In this work we compute these four Love
numbers for perfect fluid neutron stars with realistic equations of state. We
discover (nearly) equation-of-state independent relations between the
rotational-tidal Love numbers and the moment of inertia, thereby extending the
scope of I-Love-Q universality. We find that similar relations hold among the
tidal and rotational-tidal Love numbers, and we explicitly compute those
involving $K_2^{\text{el}}$. These relations extend the applications of I-Love
universality in gravitational-wave astronomy. As our findings differ from those
reported in the literature, we derive general formulas for the rotational-tidal
Love numbers in post-Newtonian theory and confirm numerically that they agree
with our general-relativistic computations in the weak-field limit.
