Constraining the cosmic-ray pressure in the inner Virgo Cluster using HESS observations of M 87

The origin of the gamma-ray emission from M 87 is currently a matter of debate. This work aims to localize the very high-energy (VHE; 100 ?GeV - 100 ?TeV) gamma-ray emission from M 87 and probe a potential extended hadronic emission component in the inner Virgo Cluster. The search for a steady and extended gamma-ray signal around M 87 can constrain the cosmic-ray energy density and the pressure exerted by the cosmic rays onto the intracluster medium and allow us to investigate the role of cosmic rays in the active galactic nucleus feedback as a heating mechanism in the Virgo Cluster. The High Energy Stereoscopic System (H.E.S.S.) telescopes are sensitive to VHE gamma rays and have been used to observe M 87 since 2004. We utilized a Bayesian block analysis to identify M 87 emission states with H.E.S.S. observations from 2004 to 2021, dividing them into low, intermediate, and high states. Because of the causality argument, an extended (& GSIM;1 ?kpc) signal is allowed only in steady emission states. Hence, we fitted the morphology of the 120 ?h low-state data and find no significant gamma-ray extension. Therefore, we derive for the low state an upper limit of 58 & DPRIME;(corresponding to & AP;4.6 ?kpc) in the extension of a single-component morphological model described by a rotationally symmetric 2D Gaussian model at the 99.7% confidence level. Our results exclude the radio lobes (& AP;30 ?kpc) as the principal component of the VHE gamma-ray emission from the low state of M 87. The gamma-ray emission is compatible with a single emission region at the radio core of M 87. These results, with the help of two multiple-component models, constrain the maximum cosmic-ray to thermal pressure ratio to X-CR,X-?max.?& LSIM;?0.32 and the total energy in cosmic-ray protons to U-CR ??& LSIM;??5 ? x ?10(58)?erg in the inner 20 ?kpc of the Virgo Cluster for an assumed cosmic-ray proton power-law distribution in momentum with spectral index & alpha;(p)?=?2.1.