Impact of the neutron star crust on the tidal polarizability

Background: The first direct detection of a binary neutron star merger by the LIGO Scientific Collaboration and the Virgo Collaboration (LIGO-Virgo) [Phys. Rev. Lett. 119, 161101 (2017)] has opened the brand new era of multimessenger astronomy. This historic detection has been instrumental in providing initial constraints on the tidal polarizability (or deformability) of neutron stars. In turn, the tidal polarizability-an observable highly sensitive to stellar compactness-has been used to impose limits on stellar radii and ultimately on the underlying equation of state (EOS). Purpose: Besides its strong dependence on the stellar compactness, the tidal polarizability is also sensitive to the second tidal Love number k(2). It is the main purpose of this paper to perform a detailed study of k(2) which, for a given compactness parameter, encodes the entire sensitivity of the tidal polarizability to the underlying equation of state. In particular, we examine the important role that the crustal component of the EOS plays in the determination of k(2). Methods: A set of realistic models of the equation of state that yield an accurate description of the properties of finite nuclei support neutron stars of two solar masses and provide a Lorentz covariant extrapolation to dense matter are used to solve both the Tolman-Oppenheimer-Volkoff and the differential equations for the induced quadrupole gravitational field from which k(2) is extracted. Results: Given that the tidal polarizability scales as the fifth power of the compactness parameter, a universal relation exists among the tidal polarizability and the compactness parameter that is highly insensitive to the underlying equation of state. Thus, besides an extraction of the tidal polarizabilities, a measurement of the individual stellar masses is also required to impact the mass-radius relation. However, we observe a strong sensitivity of the second Love number to the underlying equation of state-particularly to the contribution from the inner crust. Conclusions: Although by itself the tidal polarizability cannot contribute to the determination of the mass-radius relation, future detections of binary neutron star mergers by the LIGO-Virgo Collaborations during the third observing run and beyond are poised to provide significant constraints on both the tidal polarizabilities and the masses of the individual stars, and thus ultimately on the mass-radius relation. Yet, subleading corrections to the tidal polarizability are encoded in the second Love number k(2), which displays a large sensitivity to the entire-crust-plus-core-equation of state.