GRMHD simulations of prompt-collapse neutron star mergers: the absence of jets

Abstract: Inspiraling and merging binary neutron stars are not only important source of gravitational waves, but also promising candidates for coincident electromagnetic counterparts. These systems are thought to be progenitors of short gamma-ray bursts (sGRBs). We have shown previously that binary neutron star mergers that undergo {\it delayed} collapse to a black hole surrounded by a {\it weighty} magnetized accretion disk can drive magnetically-powered jets. We now perform magnetohydrodynamic simulations in full general relativity of binary neutron stars mergers that undergo {\it prompt} collapse to explore the possibility of jet formation from black hole-{\it light} accretion disk remnants. We find that after $t-t_{\rm BH}\sim 26(M_{\rm NS}/1.8M_\odot)$ms [$M_{\rm NS}$ is the ADM mass] following prompt black hole formation, there is no evidence of mass outflow or magnetic field collimation. The rapid formation of the black hole following merger prevents magnetic energy from approaching force-free values above the magnetic poles, which is required for the launching of a jet by the usual Blandford--Znajek mechanism. Detection of gravitational waves in coincidence with sGRBs may provide constraints on the nuclear equation of state (EOS): the fate of an NSNS merger--delayed or prompt collapse, and hence the appearance or nonappearance of an sGRB--depends on a critical value of the total mass of the binary, and this value is sensitive to the EOS.