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Mergers of compact binaries containing two neutron stars (NS-NS), or aneutron star and a stellar-mass black hole (NS-BH), are likely progenitors ofshort-duration gamma ray bursts (SGRBs). A fraction >20% of SGRBs are followedby temporally-extended (>~ minute-long), variable X-ray emission, attributed toongoing activity of the central engine. One source of late-time engine activityis fall-back accretion of bound tidal ejecta; however, observed extendedemission light curves do not track the naively-anticipated, uninterrupted~t^{-5/3} power-law decay, instead showing a lull or gap in emission typicallylasting tens of seconds after the burst. Here, we re-examine the impact ofheating due to rapid neutron capture (r-process) nucleosynthesis on rate of thefall-back accretion, using ejecta properties obtained from numerical relativitysimulations of NS-BH mergers in a toy model for the dynamical influence ofnuclear heating. Depending on the mass of the remnant black hole, r-processheating can imprint a variety of fall-back curve shapes, ranging from temporallulls of up to tens of seconds to complete late-time cut-off in the fall-backrate. This behavior is robust to realistic variations in the nuclear heatingexperienced by different parts of the ejecta. Central black holes with masses<~ 3 Msun typically experience absolute cut-offs in the fall-back rate, whilemore massive >6-8 Msun black holes instead show temporal gaps. We thus proposethat SGRBs with extended emission arise from NS-BH, rather than NS-NS, mergers.Our model implies a NS-BH merger detection rate by LIGO which, in steady-state,is comparable to or greater than that of NS-NS mergers.

Imprints of r-process heating on fall-back accretion: distinguishing black hole-neutron star from double neutron star mergers