Implications of a Magnetar Origin for 1LHAASO J0500$+$4454

We investigate the origin of unidentified, extended TeV source 1LHAASO J0500$+$4454. We consider three possible origins: cosmic rays interacting with a molecular cloud (MC), particles accelerated in a supernova remnant (SNR), and an energetic outflow powered by magnetar SGR 0501$+$4516. The MC and SNR scenarios are disfavored by upper limits on the coincident CO and X-ray emission, respectively. If SGR 0501$+$4516 powered 1LHAASO J0500$+$4454, then the TeV γ-rays are produced by inverse Compton (IC) emission from ~50 TeV e^± located within the resultant pulsar wind nebula (PWN). SED modeling indicates a total PWN particle energy ~10⁴⁸ erg. If the magnetar’s rotational energy powered 1LHAASO J0500$+$4454, a conservative energy budget indicates an initial pulsar spin period P₀ ≲ 20 ms, and a spin-down timescale τ_sd ≲ 10 yr which has implications for the origins of magnetars.