The H.E.S.S. gravitational wave rapid follow-up program

Gravitational Wave (GW) events are physical processes that significantly perturbate space-time, e.g. compact binary coalescenses, causing the production of GWs. The detection of GWs by a worldwide network of advanced interferometers offers unique opportunities for multi-messenger searches and electromagnetic counterpart associations. While carrying extremely useful information, searches for associated electromagnetic emission are challenging due to large sky localisation uncertainties provided by the current GW observatories LIGO and Virgo. Here we present the methods and procedures used within the High Energy Stereoscopic System (H.E.S.S.) in searches for very-high-energy (VHE) gamma-ray emission associated to the emission of GWs from extreme events. To do so we create several algorithms dedicated to schedule GW follow-up observations by creating optimized pointing paterns. We describe algorithms using 2-dimensional GW localisation information and algorithms correlating the galaxy distribution in the local universe, by using galaxy catalogs, with the 3-dimensional GW localisation information and evaluate their performances. The H.E.S.S. automatic GW follow-up chain, described in this paper, is optimized to initiate GW follow-up observations within less than 1 minute after the alert reception. These developements allowed H.E.S.S. observations of 6 GW events out of the 67 non-retracted GW events detected during the first three observation runs of LIGO and Virgo reaching VHE γ-ray coverages of up to 70% of the GW localisation. (paper)