Neutron star mass–radius constraints using the high-frequency quasi-periodic oscillations of GRB 200415A

Abstract

Context. Quasi-periodic oscillations (QPOs) observed in a giant flare of a strongly magnetized neutron star (magnetar) carry crucial information for extracting the properties od neutron stars. Aims. The aim of this study is to constrain the mass and radius of the neutron star model for GRB 200415A by identifying the observed QPOs with crustal torsional oscillations and comparing these with experimental constraints on the nuclear matter properties. The frequencies of the crustal torsional oscillations are determined by solving the eigenvalue problem with the Cowling approximation, assuming a magnetic field of about 1015 G. Methods. We find that the observed QPOs can be identified with several overtones of crustal oscillations for carefully selected combinations of the nuclear saturation parameters. Thus, we can inversely constrain the neutron star mass and radius for GRB 200415A by comparing them to the values of nuclear saturation parameters obtained from terrestrial experiments. Results. We impose further constraints on the neutron star mass and radius while the candidate neutron star models examined here are consistent with the constraints obtained from other available astronomical and experimental observations.

Magnetar QPOs and Neutron Star Crust Elasticity

“…This is because the shear velocity is higher than the Alfvén velocity, v A ≡ B/ 4πρ, with the magnetic field strength, B, and density, ρ, at the basis of the crust, which leads to the oscillations being controlled by shear properties. In general, the critical field strength, above which magnetic oscillations become dominant, depends on the EOS (or crust properties), which is considered around a few times 10 14 G [79,81,103]. Therefore, to avoid uncertainty in the magnetic geometry and profile, assuming that the field strength is not so strong, we focus on only crustal oscillations without magnetic effects in this review.…”

“…In Figure 12, we show the first overtones of ℓ = 2 torsional oscillations for a neutron star model with 1.4M ⊙ and 12 km constructed with various EOS parameters, where the thick, solid line denotes the fitting formula for the first overtones of torsional oscillations provided by [103,142]…”

“…Using the fitting of the overtone frequencies provided by Equation ( 13), we plot the ς dependence of n t 2 in the left panel of Figure 17 for a neutron star model with 1.6M ⊙ and 12 km with N s /N d = 0 in the phase of cylindrical nuclei, where the horizontal shaded regions denote the QPOs observed in GRB 200415A. We note that the overtone frequencies weakly depend on the ratio of N s /N d in the phase of cylindrical nuclei [103]. In this subsection, we only consider the case with N s /N d = 0 in the phase of cylindrical nuclei.…”

“…In the right panel, we show the constraint on the neutron star mass and radius obtained from the QPOs in GRB 200415A (the same as the left panel) together with those estimated with the mass formula for a low-mass neutron star as a function of η = (K 0 L 2 ) 1/3 derived in [44] (the right-bottom region), assuming that the central density of neutron stars should be less than twice the nuclear saturation density. Taken from [103].…”

“…Additionally, the mass and radius relations for neutron stars constructed with several EOSs, as in Figure 1, are also plotted. Taken from [103].…”