Investigating the emission signatures of pulsar halo candidate HESS J1813-126

Context. Extended gamma-ray sources surrounding middle-aged pulsars, primarily observed at teraelectronvolt energies, have been interpreted as pulsar halos, where relativistic e± diffuse into the interstellar medium and produce inverse-Compton (IC) emission. HESS J1813-126, associated with the energetic, radio-quiet gamma-ray pulsar PSR J1813-1246, has been suggested as a candidate pulsar halo, though its nature remains uncertain. Aims. We interpreted the high-energy emission of PSR J1813-1246 using the synchro-curvature (SC) radiation model and tested whether the gamma-ray spectral energy distribution (SED) of HESS J1813-126 can be explained as a pulsar halo powered by PSR J1813-1246. Methods. We explain the X-ray and gamma-ray SEDs of the pulsar using the SC framework. We further computed the transport and losses of e± injected by the pulsar through time-dependent diffusion-loss equations, exploring various common pulsar halo transport models. The resulting IC emission was compared with Fermi-LAT, H.E.S.S., HAWC, and LHAASO data. We present predictions for the surface brightness profiles (SBPs) and the aperture-dependent emission for the different transport models, providing key diagnostics for assessing the observability of HESS J1813-126 with current and future instruments. Resuls. The SC framework successfully reproduces the emission of PSR J1813-1246. The SED of HESS J1813-126 can be consistently reproduced within different pulsar halo frameworks, albeit with distinct predictions across different transport models. The corresponding SBP predictions and aperture-dependent emission offer testable signatures for future imaging atmospheric Cherenkov telescopes, which will be crucial for discriminating between the transport models. We further examined the link between the pulsar central engine and its extended halo by comparing the pair multiplicities in the magnetospheric and halo regions.