HESS J1813$-$178 is a very-high-energy $\gamma$-ray source spatially coincident with the young and energetic pulsar PSR J1813$-$1749 and thought to be associated with its pulsar wind nebula (PWN). Recently, evidence for extended high-energy emission in the vicinity of the pulsar has been revealed in the Fermi Large Area Telescope (LAT) data. This motivates revisiting the HESS J1813$-$178 region, taking advantage of improved analysis methods and an extended data set. Using data taken by the High Energy Stereoscopic System (H.E.S.S.) experiment and the Fermi-LAT, we aim to describe the $\gamma$-ray emission in the region with a consistent model, to provide insights into its origin. We performed a likelihood-based analysis on 32 hours of H.E.S.S. data and 12 years of Fermi-LAT data and fit a spectro-morphological model to the combined datasets. These results allowed us to develop a physical model for the origin of the observed $\gamma$-ray emission in the region. In addition to the compact very-high-energy $\gamma$-ray emission centered on the pulsar, we find a significant yet previously undetected component along the Galactic plane. With Fermi-LAT data, we confirm extended high-energy emission consistent with the position and elongation of the extended emission observed with H.E.S.S. These results establish a consistent description of the emission in the region from GeV energies to several tens of TeV. This study suggests that HESS J1813$-$178 is associated with a $\gamma$-ray PWN powered by PSR J1813$-$1749. A possible origin of the extended emission component is inverse Compton emission from electrons and positrons that have escaped the confines of the pulsar and form a halo around the PWN.
Comment: 13+5 pages, 13+11 figures. Accepted for publication in A&A. Corresponding authors: T.Wach, A.Mitchell, V.Joshi, P.Chamb\'ery