Search for neutrino counterparts to the gravitational wave sources from O3 catalogues with the ANTARES detector

International audience; Since 2015 the LIGO and Virgo interferometers have detected gravitational waves from almost one hundred coalescences of compact objects (black holes and neutron stars). This article presents the results of a search performed with data from the ANTARES telescope to identify neutrino counterparts to the gravitational wave sources detected during the third LIGO/Virgo observing run and reported in the catalogues GWTC-2, GWTC-2.1, and GWTC-3. This search is sensitive to all-sky neutrinos of all flavours and of energies $>100\,$GeV, thanks to the inclusion of both track-like events (mainly induced by $\nu_\mu$ charged-current interactions) and shower-like events (induced by other interaction types). Neutrinos are selected if they are detected within $\pm 500\,$s from the GW merger and with a reconstructed direction compatible with its sky localisation. No significant excess is found for any of the 80 analysed GW events, and upper limits on the neutrino emission are derived. Using the information from the GW catalogues and assuming isotropic emission, upper limits on the total energy $E_{\rm tot, \nu}$ and on the fraction of the total energy budget $f_\nu = E_{\rm tot, \nu}/E_{\rm rad}$ emitted as neutrinos of all flavours are also computed. Finally, a stacked analysis of all the 72 binary black hole mergers (respectively the 7 neutron star - black hole merger candidates) has been performed to constrain the typical neutrino emission within this population, leading to the limits: $E_{\rm tot, \nu} < 4.0 \times 10^{53}\,$erg and $f_\nu < 0.15$ (respectively, $E_{\rm tot, \nu} < 3.2 \times 10^{53}\,$erg and $f_\nu < 0.88$) for $E^{-2}$ spectrum and isotropic emission. Other assumptions including softer spectra and non-isotropic scenarios have also been tested.