Panning for gold with the Neil Gehrels Swift Observatory: an optimal strategy for finding the counterparts to gravitational wave events

The LIGO, Virgo and KAGRA gravitational wave observatories are currently undertaking their O4 observing run offering the opportunity to discover new electromagnetic counterparts to gravitational wave events. We examine the capability of the Neil Gehrels Swift Observatory (Swift) to respond to these triggers, primarily binary neutron star mergers, with both the UV/Optical Telescope (UVOT) and the X-ray Telescope (XRT). We simulate Swift's response to a trigger under different strategies using model skymaps, convolving these with the 2MPZ catalogue to produce an ordered list of observing fields, deriving the time taken for Swift to reach the correct field and simulating the instrumental responses to modelled kilonovae and short gamma-ray burst afterglows. We find that UVOT using the $u$ filter with an exposure time of order 120 s is optimal for most follow-up observations and that we are likely to detect counterparts in $\sim6$% of all binary neutron star triggers. We find that the gravitational wave 90% error area and measured distance to the trigger allow us to select optimal triggers to follow-up. Focussing on sources less than 300 Mpc away or 500 Mpc if the error area is less than a few hundred square degrees, distances greater than previously assumed, offer the best opportunity for discovery by Swift with $\sim5 - 30$% of triggers having detection probabilities $\geq 0.5$. At even greater distances, we can further optimise our follow-up by adopting a longer 250 s or 500 s exposure time.