Features of the gamma-ray pulsar halo HESS <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mrow><mml:mi mathvariant="normal">J</mml:mi><mml:mn>1831</mml:mn><mml:mo>−</mml:mo><mml:mn>098</mml:mn></mml:mrow></mml:math>

Gamma-ray pulsar halos are ideal indicators of cosmic-ray propagation in localized regions the Galaxy and electron injection from wind nebulae. HESS~J1831$-$098 is a candidate halo observed by both H.E.S.S. HAWC experiments. We adopt flux map Galactic plane survey spectrum measurements \textit{Fermi}-LAT to study HESS~J1831$-$098. find that meets all criteria for halo. The diffusion coefficient inside conversion efficiency spin-down energy similar Geminga halo, canonical can be well described an exponentially-cutoff power law. However, needed power-law term very hard with $p\lesssim1$ if spatially temporally independent. Considering possible origins slow-diffusion environment, we two-zone model time-delayed model. Both models interpret results milder $p$. A modified time profile may have effect.