Follow-up of the Neutron Star Bearing Gravitational Wave Candidate Events S190425z and S190426c with MMT and SOAR

On 2019 April 25.346 and 26.640 UT the LIGO and Virgo gravitational wave (GW) observatories announced the detection of the first candidate events in Observing Run 3 that contain at least one neutron star. S190425z is a likely binary neutron star (BNS) merger at $d_L = 156 \pm 41$ Mpc, while S190426c is possibly the first NS-BH merger ever detected, at $d_L = 377 \pm 100$ Mpc, although with marginal statistical significance. Here we report our optical follow-up observations for both events using the MMT 6.5-m telescope, as well as our spectroscopic follow-up of candidate counterparts (which turned out to be unrelated) with the 4.1-m SOAR telescope. We compare to publicly reported searches, explore the overall areal coverage and depth, and evaluate those in relation to the optical/NIR kilonova emission from the BNS merger GW170817, to theoretical kilonova models, and to short GRB afterglows. We find that for a GW170817-like kilonova, the partial volume covered spans up to about 40% for S190425z and 60% for S190426c. For an on-axis jet typical of short GRBs, the search effective volume is larger, but such a configuration is expected in at most a few percent of mergers. We further find that wide-field $\gamma$-ray and X-ray limits rule out luminous on-axis SGRBs, for a large fraction of the localization regions, although these searches are not sufficiently deep in the context of the $\gamma$-ray emission from GW170817 or off-axis SGRB afterglows. The results indicate that some optical follow-up searches are sufficiently deep for counterpart identification to about 300 Mpc, but that localizations better than 1000 deg$^2$ are likely essential.