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 ($M_{\mathrm{TOV}}$) of the nonrotating NS is $\approx 2.77M_{\odot }$, which is strongly in tension with the relatively low $M_{\mathrm{TOV}}\approx 2.25M_{\odot }$ 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 $M_{\mathrm{TOV}}$ possibility. By performing EOS constraints with mock measurements, we find that with a 2% determination for the radius of PSR $\mathrm{J}0740+6620$-like NS it is possible to distinguish between the low and high $M_{\mathrm{TOV}}$ 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 $M_{\mathrm{TOV}}$ and/or $R_{\mathrm{TOV}}$. It turns out that measuring the radius of a PSR $\mathrm{J}0740+6620$-like NS is insufficient to probe the EOSs around 5 nuclear saturation density, where the information from pQCD becomes relevant. The additional precise $M_{\mathrm{TOV}}$ 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 $M_{\mathrm{TOV}}\approx 2.2M_{\odot }$ 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.

Figure 1

Posterior distributions of $M_{\mathrm{TOV}}$ and $R_{\mathrm{TOV}}$. The gray dashed-dotted, black solid, and orange dashed lines represent the results derived with the fiducial “Data,” “$\mathrm{Data}+\mathrm{p}(M_{\max })+\mathrm{pQCD}(10n_s)$” (adopted from Ref. [5]), and “$\mathrm{Data}+\mathrm{FRB}+\mathrm{SMNS}$” datasets, respectively. The primary distinction between the left and right panels lies in the source of the measurements: for both PSR $\mathrm{J}0030+0451$ and PSR $\mathrm{J}0740+6620$; the left panel utilizes data from Riley et al. [40, 72], whereas the right panel incorporates measurements from Miller et al. [41, 73].

Figure 2

Reconstructed 90% intervals of mass-radius curves for the $\mathrm{Data}+\mathrm{p}(M_{\max })+\mathrm{pQCD}(10n_s)$ (black line; adopted from Ref. [5]), and $\mathrm{Data}+\mathrm{FRB}+\mathrm{SMNS}$ (filled in orange) datasets. The green, cyan, purple, and gray dashed-dotted contours represent the 68.3% mass-radius measurements for the isolated NS PSR $\mathrm{J}0030+0451$, the massive NS PSR $\mathrm{J}0740+6620$, the primary NS of GW170817, and the secondary component of GW170817 [75], respectively. The sole distinction between the left and right panels is the source of mass-radius measurements for PSR $\mathrm{J}0030+0451$ and PSR $\mathrm{J}0740+6620$. In the left panel, we incorporate data from Riley et al. [40, 72], whereas in the right panel, measurements are taken from Miller et al. [41, 73].

Figure 3

The 90% pressure vs rest-mass density intervals (top panel) and the speed of sound squared vs rest-mass density intervals (bottom panel). The orange areas and black dashed lines represent the results of $\mathrm{Data}+\mathrm{FRB}+\mathrm{SMNS}$ and $\mathrm{Data}+\mathrm{p}(M_{\max })+\mathrm{pQCD}(10n_s)$ (adopted from Ref. [5]) datasets, respectively. The vertical dashed-dotted lines mark the intervals of the central densities of the maximum-mass nonrotating NS. The horizontal black dashed line denotes the conformal limit.

Figure 4

The 90% pressure vs rest-mass density intervals. The areas filled in red and blue represent the results of $\mathrm{Data}+\mathrm{Mock}$ ($M_{\mathrm{TOV}}$, $R_{\mathrm{TOV}}$) and $\mathrm{Data}+\mathrm{Mock}$ ($M_{\mathrm{J}0740}$, $R_{\mathrm{J}0740}$), respectively. The orange dashed lines in the top panel represent the results of the $\mathrm{Data}+\mathrm{FRB}+\mathrm{SMNS}$ dataset, which are identical to that presented in Fig. 3. The black dashed lines in the bottom panel represent the results obtained with the $\mathrm{Data}+\mathrm{p}(M_{\max })+\mathrm{pQCD}(10n_s)$ dataset as found in Fan et al. [5]. The vertical lines indicate the intervals of the central density of the maximum-mass nonrotating NS.

Figure 5

The 90% pressure vs rest-mass density intervals. The area filled in blue in the top panel represent the result of the “$\mathrm{Data}+\mathrm{Fan}$ et al. (2020)” dataset. The gray, black, red dashed lines, and blue dashed-dotted lines represent the results of the $\mathrm{Data}+\mathrm{p}(M_{\max })+\mathrm{pQCD}(n_{\mathrm{c},\mathrm{TOV}})$, $\mathrm{Data}+\mathrm{p}(M_{\max })+\mathrm{pQCD}(10n_s)$, $\mathrm{Data}+\mathrm{Mock}$ ($M_{\mathrm{TOV}}$, $R_{\mathrm{TOV}}$), and $\mathrm{Data}+\mathrm{Mock}$ ($M_{\mathrm{TOV}}$, $R_{\mathrm{J}0740}$) datasets, respectively. The results of $\mathrm{Data}+\mathrm{p}(M_{\max })+\mathrm{pQCD}(n_{\mathrm{c},\mathrm{TOV}})$ and $\mathrm{Data}+\mathrm{p}(M_{\max })+\mathrm{pQCD}(10n_s)$ datasets are taken from Fan et al. [5]. The vertical lines indicate the intervals of the central density of the maximum-mass nonrotating NS.