Gravitational waves or deconfined quarks: What causes the premature collapse of neutron stars born in short gamma-ray bursts?

We infer the collapse times of long-lived neutron stars into black holes using the x-ray afterglows of 18 short gamma-ray bursts. We then apply hierarchical inference to infer properties of the neutron star equation of state and dominant spin-down mechanism. We measure the maximum non-rotating neutron star mass $M_{\mathrm{TOV}}=2.31_{-0.21}^{+0.36}{M}_{\odot }$ and constrain the fraction of remnants spinning down predominantly through gravitational-wave emission to $\eta =0.69_{-0.39}^{+0.21}$ with 68% uncertainties. In principle, this method can determine the difference between hadronic and quark equation of states. In practice, however, the data is not yet informative with indications that these neutron stars do not have hadronic equation of states at the $1\sigma$ level. These inferences all depend on the underlying progenitor mass distribution for short gamma-ray bursts produced by binary neutron star mergers. The recently announced gravitational-wave detection of GW190425 suggests this underlying distribution is different from the locally measured population of double neutron stars. We show that $M_{\mathrm{TOV}}$ and $\eta$ constraints depend on the fraction of binary mergers that form through a distribution consistent with the locally measured population and a distribution that can explain GW190425. The more binaries that form from the latter distribution, the larger $M_{\mathrm{TOV}}$ needs to be to satisfy the x-ray observations. Our measurements above are marginalized over this unknown fraction. If instead, we assume GW190425 is not a binary neutron star merger, i.e., the underlying mass distribution of double neutron stars is the same as observed locally, we measure $M_{\mathrm{TOV}}=2.26_{-0.17}^{+0.31}{M}_{\odot }$.

Figure 1

One-dimensional posterior distributions for the collapse times of all short gamma-ray bursts that have observations supporting a collapsing neutron star model. The top panel shows posteriors for short gamma-ray bursts with known redshifts, while the bottom panel shows posteriors for gamma-ray bursts with unknown redshifts.

Figure 2

X-ray lightcurves for all gamma-ray bursts indicative of a collapsing neutron star. Black points indicate flux data from Swift binned using the Swift automated binning strategy. The blue curve shows the maximum likelihood model for the collapsing magnetar model (Eq. (1)). The dark red band is the superposition of 100 predicted lightcurves randomly drawn from the posterior distribution.

Figure 3

Neutron star mass distributions. Left panel: In blue are the measured neutron star masses for those in double neutron star systems, and in red are the masses of neutron stars in binaries with white dwarfs, main sequence stars, etc [47]. The black curve is the best-fit mass distribution to these from Alsing et al. [47]. Right panel: in blue are the same double neutron star systems, this time converted to chirp mass. In green and magenta are the chirp masses of the two gravitational-wave events GW170817 and GW190425, respectively. The solid black curve is the chirp-mass distribution associated with the solid black curve in the left panel. The dashed and dot-dashed black curves assume similar distributions to the solid-black curve, except the mixing fraction between the two binary populations is $\epsilon =0.5$ and 0.8, respectively (cf. $\epsilon =0.35$ for the solid black curve).

Figure 4

One (top panel) and two-dimensional (bottom panel) posterior distributions on $M_{\mathrm{TOV}}$ and $M_{\mathrm{TOV}}-\epsilon$. We also show a slice through the two-dimensional posterior for $\epsilon =0$. i.e., a mass distribution similar to the galactic double neutron star systems but inconsistent with the progenitors of GW190425. We measure $M_{\mathrm{TOV}}=2.26_{-0.17}^{+0.31}{M}_{\odot }$ assuming a mixing fraction $\epsilon =0$. which implies a mass distribution inconsistent with the progenitors of GW190425. We plot few other constraints for $M_{\mathrm{TOV}}$ based on pulsar observations [52, 53] and inferred fate of GW170817 [e.g., 54]. For clarity, we only plot the median of these measurements but we stress that several of these measurements have large uncertainties and the later constraint, based on the inferred fate of the postmerger remnant of GW170817 could realistically be anywhere between the two hypermassive (green) or stable (red) scenarios.

Figure 5

Average braking index distribution. The blue curve indicates the median value of the posterior while the red curves are two-sigma confidence intervals.

Figure 6

Two-dimensional posterior distribution of $\alpha$ and $\beta$ with hadronic equation of states marked by circles and quark star equation of states marked by crosses. The shades of blue correspond to one-two-three sigma confidence intervals.

Figure 7

Corner plot showing the one and two-dimensional posterior distributions on ${\mu }_{⟨n⟩}$, $⟨n{⟩}_{\sigma ,1}$, $⟨n{⟩}_{\sigma ,2}$ and $\eta$. The shades of blue correspond to one-two-three sigma confidence intervals.