Transient Survey Rates for Orphan Afterglows from Compact Merger Jets

Orphan afterglows from short $\gamma$-ray bursts (GRB) are potential candidates for electromagnetic (EM) counterpart searches to gravitational wave (GW) detected neutron star or neutron star black hole mergers. Various jet dynamical and structure models have been proposed that can be tested by the detection of a large sample of GW-EM counterparts. We make predictions for the expected rate of optical transients from these jet models for future survey telescopes, without a GW or GRB trigger. A sample of merger jets is generated in the redshift limits $0\leq z\leq 3.0$, and the expected peak $r$-band flux and timescale above the LSST or ZTF detection threshold, $m_r=24.5$ and $20.4$ respectively, is calculated. General all-sky rates are shown for $m_r\leq26.0$ and $m_r\leq21.0$. The detected orphan and GRB afterglow rate depends on jet model, typically $16\lesssim R\lesssim 76$ yr$^{-1}$ for the LSST, and $2\lesssim R \lesssim 8$ yr$^{-1}$ for ZTF. An excess in the rate of orphan afterglows for a survey to a depth of $m_r\leq26$ would indicate that merger jets have a dominant low-Lorentz factor population, or the jets exhibit intrinsic jet structure. Careful filtering of transients is required to successfully identify orphan afterglows from either short or long GRB progenitors.