Mass and radius of the most massive neutron star: The probe of the equation of state and perturbative QCD

Recently, an association of GW190425 and FRB 20190425A had been claimed and a highly magnetized neutron star (NS) remnant was speculated. Given the $\sim 2.5$-h delay of the occurrence of FRB 20190425A, a uniformly rotating supramassive magnetar is favored since the differential rotation would have been promptly terminated by the magnetic braking. The required maximum gravitational mass ($M_{\rm TOV}$) of the nonrotating NS is $\approx 2.77M_\odot$, which is strongly in tension with the relatively low $M_{\rm TOV}\approx 2.25M_\odot$ obtained in current equation of state (EOS) constraints incorporating perturbative quantum chromodynamics (pQCD) information. However, the current mass-radius and mass-tidal deformability measurements of NSs alone do not convincingly exclude the high $M_{\rm TOV}$ possibility. By performing EOS constraints with mock measurements, we find that with a $2\%$ determination for the radius of PSR J0740+6620-like NS it is possible to distinguish between the low and high $M_{\rm TOV}$ scenarios. We further explore the prospect to resolve the issue of the appropriate density to impose the pQCD constraints with future massive NS observations or determinations of $M_{\rm TOV}$ and/or $R_{\rm TOV}$. It turns out that measuring the radius of a PSR J0740+6620-like NS is insufficient to probe the EOSs around 5 nuclear saturation density, where the information from pQCD becomes relevant. The additional precise $M_{\rm TOV}$ measurements anyhow could provide insights into the EOS at such a density. Indeed, supposing the central engine of GRB 170817A is a black hole formed via the collapse of a supramassive NS, the resulting $M_{\rm TOV}\approx 2.2M_\odot$ considerably softens the EOS at the center of the most massive NS, which is in favor of imposing the pQCD constraint at density beyond the one achievable in the NSs.