Modeling the X-ray emission of the Boomerang nebula and implication for its potential ultrahigh-energy gamma-ray emission

Abstract: The Boomerang nebula is a bright radio and X-ray pulsar wind nebula (PWN) powered by an energetic pulsar, PSR~J2229+6114. It is spatially coincident with one of the brightest ultrahigh-energy (UHE, $\ge 100$\,TeV) gamma-ray sources, LHAASO~J2226+6057. While X-ray observations have provided radial profiles for both the intensity and photon index of the nebula, previous theoretical studies have not reached an agreement on their physical interpretation, which also lead to different anticipation of the UHE emission from the nebula. In this work, we model its X-ray emission with a dynamical evolution model of PWN, considering both convective and diffusive transport of electrons. On the premise of fitting the X-ray intensity and photon index profiles, we find that the magnetic field within the Boomerang nebula is weak ($\sim 10\mu$G in the core region and diminishing to $1\mu\,G$ at the periphery), which therefore implies a significant contribution to the UHE gamma-ray emission by the inverse Compton (IC) radiation of injected electron/positron pairs. Depending on the particle transport mechanism, the UHE gamma-ray flux contributed by the Boomerang nebula via the IC radiation may constitute about $10-50\%$ of the flux of LHAASO~J2226+6057 at 100\,TeV, and up to 30\% at 500\,TeV. Finally, we compare our results with previous studies and discuss potential hadronic UHE emission from the PWN. In our modeling, most of the spindown luminosity of the pulsar may be transformed into thermal particles or relativistic protons.