FRB 181112 as a Rapidly-Rotating Massive Neutron Star just after a Binary Neutron Star Merger?: Implications for Future Constraints on Neutron Star Equations of State

Abstract

The light curve of the fast radio burst (FRB) 181112 is resolved into four successive pulses, and the time interval ($\sim0.8$ ms) between the first and third pulses coincides with that between the second and fourth pulses, which can be interpreted as a neutron star (NS) spinning at a period of about $0.8$ ms. Although this period is shorter than the most rapidly rotating pulsar currently known ($1.4$ ms), it is typical for a simulated massive NS formed immediately after the coalescence of binary neutron stars (BNS). Therefore, a BNS merger is a good candidate for the origin of this FRB if the periodicity is real. We discuss the future implications that can be obtained if such a periodicity is detected from FRBs simultaneously with gravitational waves (GW). The remnant spin period $P_{\rm rem}$ inferred from the FRB observation is unique information which is not readily obtained by current GW observations at the post-merger phase. If combined with the mass of the merger remnant $M_{\rm rem}$ inferred from GW data, it would set a new constraint on the equation of state of nuclear matter. Furthermore, the post-merger quantity $P_{\rm rem}/M_{\rm rem}$, or the tidal deformability of the merger remnant, is closely related to the binary tidal deformability parameter $\Lambda$ of NSs before they merge, and a joint FRB-GW observation will establish a new limit on $\Lambda$. Thus, if $\Lambda$ is also well measured by GW data, a comparison between these two will provide further insights into the nature of nuclear matter and BNS mergers.