Low-mass neutron stars: universal relations, the nuclear symmetry energy and gravitational radiation

The lowest neutron star masses currently measured are in the range 1.0-1.1 M-aS (TM), but these measurement have either large uncertainties or refer to isolated neutron stars. The recent claim of a precisely measured mass M/M-aS (TM) = 1.174 +/- 0.004 (Martinez et al. 2015) in a double neutron star system suggests that low-mass neutron stars may be an interesting target for gravitational-wave detectors. Furthermore, Sotani et al. recently found empirical formulas relating the mass and surface redshift of non-rotating neutron stars to the star's central density and to the parameter eta a parts per thousand (K0L2)(1/3), where K-0 is the incompressibility of symmetric nuclear matter and L is the slope of the symmetry energy at saturation density. Motivated by these considerations, we extend the work by Sotani et al. to slowly rotating and tidally deformed neutron stars. We compute the moment of inertia, quadrupole moment, quadrupole ellipticity, tidal and rotational Love number and apsidal constant of slowly rotating neutron stars by integrating the Hartle-Thorne equations at second order in rotation, and we fit all of these quantities as functions of eta and of the central density. These fits may be used to constrain eta, either via observations of binary pulsars in the electromagnetic spectrum, or via near-future observations of inspiralling compact binaries in the gravitational-wave spectrum.