LOFAR observations of gravitational wave merger events: O3 results and O4 strategy

The electromagnetic counterparts to gravitational wave (GW) merger events hold immense scientific value, but are difficult to detect due to the typically large localization errors associated with GW events. The Low-Frequency Array (LOFAR) is an attractive GW follow-up instrument owing to its high sensitivity, large instantaneous field of view, and ability to automatically trigger on events to probe potential prompt emission within minutes. Here, we report on 144-MHz LOFAR radio observations of three GW merger events containing at least one neutron star that were detected during the third GW observing run. Specifically, we probe 9 and 16 per cent of the location probability density maps of S190426c and S200213t, respectively, and place limits at the location of an interesting optical transient (PS19hgw/AT2019wxt) found within the localization map of S191213g. While these GW events are not particularly significant, we use multi-epoch LOFAR data to devise a sensitive wide-field GW follow-up strategy to be used in future GW observing runs. In particular, we improve on our previously published strategy by implementing direction-dependent calibration and mosaicing, resulting in nearly an order of magnitude increase in sensitivity and more uniform coverage. We achieve a uniform 5 & sigma; sensitivity of 870 & mu;Jy beam(-1) across a single instantaneous LOFAR pointing's 21 deg(2) core, and a median sensitivity of 1.1 mJy beam(-1) when including the full 89 deg(2) hexagonal beam pattern. We also place the deepest transient surface density limits yet on time-scales of the order of month for surveys between 60 and 340 MHz (0.017 deg(-2) above 2.0 mJy beam(-1) and 0.073 deg(-2) above 1.5 mJy beam(-1)).