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

Mergers of compact binaries containing two neutron stars (NS-NS), or a neutron star and a stellar mass black hole (NS-BH), are likely progenitors of short-duration gamma-ray bursts (SGRBs). A fraction greater than or similar to 20 per cent of SGRBs is followed by temporally extended (greater than or similar to minute-long), variable X-ray emission, attributed to ongoing activity of the central engine. One source of late-time engine activity is fall-back accretion of bound tidal ejecta; however, observed extended emission light curves do not track the naively anticipated, uninterrupted t(-5/3) power-law decay, instead showing a lull or gap in emission typically lasting tens of seconds after the burst. Here, we re-examine the impact of heating due to rapid neutron capture (r-process) nucleosynthesis on the rate of the fall-back accretion, using ejecta properties extracted from numerical relativity simulations of NS-BH mergers. Heating by the r-process has its greatest impact on marginally bound matter, hence its relevance to late-time fall-back. Depending on the electron fraction of the ejecta and the mass of the remnant black hole, r-process heating can imprint a range of fall-back behaviour, ranging from temporal gaps of up to tens of seconds to complete late-time cut-off in the accretion rate. This behaviour is robust to realistic variations in the nuclear heating experienced by different parts of the ejecta. Central black holes with masses less than or similar to 3 M-circle dot typically experience absolute cut-offs in the fall-back rate, while more massive greater than or similar to 6-8 M-circle dot black holes instead show temporal gaps. We thus propose that SGRBs showing extended X-ray emission arise from NS-BH, rather than NS-NS, mergers. Our model implies an NS-BH merger detection rate by LIGO that, in steady state, is comparable to or greater than that of NS-NS mergers.