Maximum mass cutoff in the neutron star mass distribution and the prospect of forming supramassive objects in the double neutron star mergers

The sample of neutron stars with a measured mass is growing quickly. With the latest sample, we adopt both a flexible Gaussian mixture model and a Gaussian plus Cauchy-Lorentz component model to infer the mass distribution of neutron stars and use the Bayesian model selection to explore evidence for multimodality and a sharp cutoff in the mass distribution. The two models yield rather similar results. Consistent with previous studies, we find evidence for a bimodal distribution together with a cutoff at a mass of $M_{\max }=2.26_{-0.05}^{+0.12}{M}_{\odot }$ (68% credible interval, for the Gaussian mixture model). If such a cutoff is interpreted as the maximum gravitational mass of nonrotating cold neutron stars, the prospect of forming supramassive remnants is found to be quite promising for the double neutron star mergers with a total gravitational mass less than or equal to $2.7M_{\odot }$ unless the thermal pions could substantially soften the equation of state for the very hot neutron star matter. These supramassive remnants have a typical kinetic rotational energy of approximately $1-2\times {10}^{53}\mathrm{ergs}$. Together with a high neutron star merger rate approximately ${10}^3{\mathrm{Gpc}}^{-3}{\mathrm{yr}}^{-3}$, the neutron star mergers are expected to be significant sources of EeV ($10^{18}$ eV) cosmic-ray protons.

Figure 1

Distributions of parameters ($\overrightarrow{\theta }$) of the NS mass distribution obtained with some different priors and models.

Figure 2

Maximum a posteriori NS mass distribution (blue) with 1000 independent posterior samples to give a visual guide for the uncertainties, under the considered model that is most preferred by the data. Left panel: the two-component Gaussian mixture with a sharp cutoff of approximately $2.26M_{\odot }$ (median value). Right panel: the mixture of Gaussian and Cauchy-Lorentz components with a sharp cutoff of approximately $2.28M_{\odot }$ (median value).

Figure 3

Statistical characteristics of pulsar mass vs spin period, magnetic field strength on surface, age, and distance. The most massive neutron stars (which may be heavier than $2.0M_{\odot }$) are displayed in colored circles, triangles, and squares with $1\sigma$ error bar.

Figure 4

Pulsar mass vs radio luminosity. The massive neutron stars (which may be heavier than $1.6M_{\odot }$) are displayed in magenta crosses with $1\sigma$ error bar. The radio luminosities were measured at 1.4 (most events) or 0.35 GHz (a few objects) [32] except $\mathrm{J}0348+0432$ at 0.82 GHz [36] and J1807-2500B at 2 GHz [37]. All the luminosities have been normalized to 1.4 GHz (if the spectral index is unavailable, we take the mean value of $-1.4$ [38]).

Figure 5

$M_{\mathrm{TOV}}-{\zeta }_{\mathrm{TOV}}$ correlation inferred from the joint constraints set by the data of PSR $\mathrm{J}0030+0451$, GW170817, and some nuclear data (see Ref. [45] for the technical details). The red solid line shows the best-fit model. The blue dashed line, the green dashed line, and the magenta dashed line represent the $1\sigma$, $2\sigma$, and $3\sigma$ contours, respectively.

Figure 6

Critical total gravitational mass of DNSs vs $M_{\mathrm{TOV}}$, supposing $M_{\mathrm{loss}}=0.05M_{\odot }$. The vertical cyan region represents our evaluated mass cutoff in the NS mass distribution (see Fig. 1). The horizontal gray regions, from the top to the bottom, represent the total gravitational mass of GW190425, GW170817, and PSR J0514-4002A (so far, the lightest double NS system identified in the Galaxy), respectively. Note that the regions shown in this plot are for the 68% confidence intervals.

Figure 7

The “hypothesized” $\mathcal{R}$ to collapse for the given $M_{\mathrm{tot}}$ (in particular, for the lightest NSs or double NS binaries) and the zero temperature $M_{\mathrm{TOV}}$. The dashed and dotted lines are for $j/j_{\mathrm{kep}}=1$ and 0.8, respectively. A minimum $M_{\mathrm{tot}}=2.34M_{\odot }$ is adopted because the lightest neutron star detected so far has an accurately measured mass of $1.17M_{\odot }$ [50]. For simplicity, the best-fit ${\zeta }_{\mathrm{TOV}}-M_{\mathrm{TOV}}$ relation presented in Fig. 5 is adopted.

Figure 8

Left panel: kinetic rotational energy of NS with mass shedding configuration. Right panel: kinetic rotational energy of NS at the critical point of certain angular momentum.

Figure 9

Capability of the shocks driven by the kilonova ejecta and the possible energy injection from the central SMNS. The solid, dotted, dashed, and dot-dashed lines are for $B_s={10}^{11},{10}^{12},{10}^{13},{10}^{14}\mathrm{G}$, respectively, while the colors of the lines (black, blue, red) correspond to the cases of $n_m=({10}^{-1},{10}^{-3},{10}^{-5}){\mathrm{cm}}^{-3}$, respectively. For $n_m={10}^{-5}{\mathrm{cm}}^{-3}$, the red solid line terminates at $t/\tau \sim 0.03$ because at later times we have $R>1.7\times {10}^{19}\mathrm{cm}$, for which the plasma frequency is lower than the frequency of pulsar wind and the pulsar wind will escape freely rather than be absorbed by the outmoving ejecta.