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 ^ { +0.36 } _ { -0.21 } M _ { \odot } and constrain the fraction of remnants spinning down predominantly through gravitational-wave emission to \eta = 0.69 ^ { +0.21 } _ { -0.39 } 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 marginalised 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 ^ { +0.31 } _ { -0.17 } M _ { \odot } .