Constraints on the nuclear equation of state and the neutron star structure from crustal torsional oscillations

Abstract

We systematically examine torsional shear oscillations of neutron star crusts by newly taking into account the possible presence of the phase of cylindrical nuclei. In this study, we neglect an effect of magnetic fields, under which the shear oscillations can be damped by the magnetic interaction. First, by identifying the low frequency quasiperiodic oscillations (QPOs) observed in the soft-gamma repeaters (SGRs) as the fundamental torsional oscillations, we constrain the slope parameter of the nuclear symmetry energy, L, for reasonable values of the star's mass M and radius R. Meanwhile, we find that the 1st overtone of torsional oscillations obtained for given M and R can be expressed well as a function of a new parameter ς ≡ (K 4 0 L 5 ) 1/9 , where K 0 is the incompressibility of symmetric nuclear matter. Assuming that the lowest of the QPO frequencies above 500 Hz observed in SGR 1806-20 comes from the 1st overtone, we can constrain the value of ς. Then, for each neutron star model, such a value of L as can be obtained from the observed low frequency QPOs translates to the optimal value of K 0 via the above constraint on ς. Finally, its consistency with allowed values of K 0 from empirical giant monopole resonances leads to neutron star models with relatively low mass and large radius, which are qualitatively similar to the prediction in earlier investigations. This result suggests that L ≃ 58-73 MeV, even when uncertainties in the neutron superfluid density inside the phase of cylindrical nuclei are allowed for.

Astrophysical implications of double-layer torsional oscillations in a neutron star crust as a lasagna sandwich

“…We can thus conclude that light neutron star models are favored over heavy ones in our identification. Incidentally, the (M, R) = (1.3M⊙, 13km) case is consistent with the neutron star models considered to be relevant as a result of the comparison of the constraint on K0, which is obtained by assuming that the lowest overtone frequency in the sphere-cylinder layer is equal to the QPO frequency of 626.5 Hz observed from SGR 1806-20, with the terrestrial constraint on K0 (Sotani, Iida & Oyamatsu 2018). Furthermore, the (M, R) = (1.3M⊙, 13km) case is consistent with the mass and radius formulas for low-mass neutron stars , given the optimal value of L ∼ 70 MeV, and also with the constraint on the mass and radius of each of the merging binary neutron stars (Abbott et al 2018).…”

“…1, we illustrate the profile of the shear modulus inside the tube and bubble phases for neutron star models constructed from the first three sets of the OI-EOSs listed in Table 1. From this figure, one can observe that the shear modulus becomes discontinuous at the transition between the tube and bubble phases, which is similar to the case of the transition between the phases of spherical and cylindrical nuclei (Sotani, Iida & Oyamatsu 2018). In addition, it is to be noted that the shear modulus in the tube phase can decrease as the density increases and that this tendency becomes stronger for larger L. This tendency may well come from the decrease of the volume fraction of a gas of dripped neutrons with density (e.g., Watanabe & Iida (2003)).…”

“…(2) ℓ . Hereafter we will thus attempt to identify the observed QPO frequencies by using the fitting formula (10) for the tube-bubble layer, in addition to the formula given in Sotani, Iida & Oyamatsu (2018) for the sphere-cylinder layer.…”

Crustal torsional oscillations inside the deeper pasta structures

“…On the crust equilibrium, the frequency of torsional oscillations can be determined by solving the eigenvalue problem. The concrete perturbation equation and boundary conditions for torsional oscillations can be seen in Sotani et al () and Sotani et al (, ). In Figure , we show the ℓ = 2 fundamental frequency of the torsional oscillations excited in the phase of tube and bubble as a function of L , where the marks denote the results obtained with various sets of EOS parameters.…”

“…On the other hand, we have already shown that the fundamental frequency excited in the phase of spherical and cylindrical nuclei can be fitted with the different functional form of L (Sotani et al , , , ; Sotani et al ). In addition, we could constrain L as L ≃ 58 − 73 MeV by identifying the 626.5 Hz QPO in SGR 1806‐20 as the first overtone of torsional oscillation with the help of the terrestrial constraint on K 0 , where we also showed that relatively low mass neutron star models are favored more from the experimental constraints and QPO observations (Sotani et al ).…”