Testing the Formation Scenarios of Binary Neutron Star Systems with Measurements of the Neutron Star Moment of Inertia

Two low-mass (M <. 1.4 M-circle dot) neutron stars, J0737-3039B and the companion to J1756-2251, show strong evidence of being formed in an ultra-stripped supernova explosion (US-SN) with a ONeMg or Fe progenitor. Using systematically generated sets of equations of state we map out the relationship between the moment of inertia of J0737-3039A, a candidate for a moment of inertia measurement within a decade, and the binding energy of the two low-mass neutron stars. This relationship, similar to the I-Love-Q relations, is more robust than a previously explored correlation between the binding energy and the slope of the nuclear symmetry energy L. We find that, if either J0737-3039B or the J1756-2251 companion were formed in a US-SN, no more than 0.06 M-circle dot could have been lost from the progenitor core. Furthermore, a measurement of the moment of inertia of J0737-3039A to within 10% accuracy can discriminate between formation scenarios and, given current constraints on the predicted core mass loss, potentially rule them out. Advanced LIGO can potentially measure the neutron star tidal polarizability to equivalent accuracy which, using the I-Love-Q relations, would obtain similar constraints on the formation scenarios. Such information would help constrain important aspects of binary evolution used for population synthesis predictions of the rate of binary neutron star mergers and resulting electromagnetic and gravitational wave signals. Further progress needs to be made in modeling the core-collapse process that leads to low-mass neutron stars, particularly in making robust predictions for the mass loss from the progenitor core.