Constraint on nuclear symmetry energy imposed by f-mode oscillation of neutron stars

Abstract

Due to improvements in the sensitivity of gravitational wave (GW) detectors, the detection of GWs originating from the fundamental quasi-normal mode (f-mode) of neutron stars has become possible. The future detection of GWs originating from the f-mode of neutron stars will provide a potential way to improve our understanding of the nature of nuclear matter inside neutron stars. In this work, we investigate the constraint imposed by the f-mode oscillation of neutron stars on the symmetry energy of nuclear matter using Bayesian analysis and parametric EOS. It is shown that if the frequency of the f-mode of a neutron star of known mass is observed precisely, the symmetry energy at twice the saturation density (E sym(2ρ 0)) of nuclear matter can be constrained within a relatively narrow range. For example, when all the following parameters are within the given intervals: 220 ≤ K 0 ≤ 260 MeV, 28 ≤ E sym(ρ 0) ≤ 36 MeV, 30 ≤ L ≤ 90 MeV, −800 ≤ J 0 ≤ 400 MeV, − 400 ≤ K sym ≤ 100 MeV, −200 ≤ J sym ≤ 800 MeV, E sym(2ρ 0) will be constrained to within MeV if the f-mode frequency of a canonical neutron star (1.4 M⊙) is observed to be 1.720 kHz with a 1% relative error. Furthermore, if only f-mode frequency detection is available, i.e. there is no stellar mass measurement, a precisely detected f-mode frequency can also impose an accurate constraint on the symmetry energy. For example, given the same parameter space and the same assumed observed f-mode frequency mentioned above, and assuming that the stellar mass is in the range of 1.2–2.0 M⊙, E sym(2ρ 0) will be constrained to within . In addition, it is shown that a higher slope of 69 ≤ L ≤ 143 MeV will give a higher posterior distribution of E sym(2ρ 0), .