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

Abstract

The lowest neutron star masses currently measured are in the range 1.0 − 1.1 M ⊙ , but these measurement have either large uncertainties or refer to isolated neutron stars. The recent claim of a precisely measured mass M/M ⊙ = 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. (2014) recently found empirical formulas relating the mass and surface redshift of nonrotating neutron stars to the star's central density and to the parameter η ≡ (K 0 L 2 ) 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. (2014) 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 η and of the central density. These fits may be used to constrain η, either via observations of binary pulsars in the electromagnetic spectrum, or via near-future observations of inspiralling compact binaries in the gravitationalwave spectrum.

Future prospects for constraining nuclear matter parameters with gravitational waves

“…Here we consider the following multiplicative combinations for comparison purposes: K 0 L η 0 , M 0 L µ 0 , and K sym,0 L ν 0 , where coefficients η, µ, and ν are similarly chosen to achieve maximal correlation. Such multiplicative combinations are similar to those considered in [30,31]. Figure 14 presents the correlations betweenΛ and all 6 multiplicative and linear combinations of nuclear parameters considered in this analysis.…”

Constraining nuclear matter parameters with GW170817

“…Additionally shown in dotted blue are the corresponding bounds on M0 and Ksym,0 computed by Ref. [11], using priors ofΛ ∈ [70,720] and L0 ∈ [30,86] MeV. Observe how the results for the 90% confidence intervals obtained in this section are slightly smaller than those found in Sec.…”

“…Interestingly, approximate universal relations exist among nuclear physics parameters mentioned above and NS radius at a given mass [28] (see e.g. [29,30] for other universal relations involving nuclear parameters). The authors found that while individual nuclear parameters are only weakly correlated with the stellar radius, linear combinations of the form K 0 + αL 0 and M 0 + βL 0 become highly correlated, where α and β are chosen such that the correlation becomes maximum.…”

Effect of nuclear saturation parameters on a possible maximum mass of neutron stars

“…(4) and (5)], while the dashed lines are plotted with using Eqs. (6) - (9). Now, I can get the fitting formulae expressing the maximum mass and radius of neutron star with maximum mass as a function of η and α.…”

“…In particular, the nuclear saturation parameters are important for expressing lower density region. It is practically known that the neutron star constructed with the central density lower than 2ρ 0 can be described nicely with parameters constructed as the combination of the incompressibility of the symmetric nuclear matter, K 0 , and the so-called slope parameter of nuclear symmetry energy, L, via η = (K 0 L 2 ) 1/3 [8,9]. Therefore, it is expected that the maximum mass of neutron stars should also depend on η, where η has been already constrained in some range via the constraints on K 0 and L [10][11][12] and will be further constrained in the future.…”