Ruo-Yu Liu, Yong Shao, Yu-Dong Nie

Recent observations by LHAASO and HAWC have revealed extended ultrahigh-energy (UHE; $E>100$ TeV) gamma-ray emission assoicated to the black-hole X-ray binary (BHXRB) V4641 Sgr, with a spectrum extending up to $\sim0.8$ PeV. Interpreting this emission requires a very {high time-averaged non-thermal particle power}, significantly exceeding the long-term observed X-ray luminosity which is commonly used as a proxy for the accretion power, leading to an apparent ``energy crisis''. To address this, we perform detailed binary-evolution simulations with \textit{MESA}, constrained by the known system parameters. The simulations suggest that V4641 Sgr is likely in a long-lasting, slow mass-transfer phase, with a time-averaged intrinsic X-ray luminosity of over evolutionary timescales of order $L_X\sim10^{38}$ erg/s, far above the observed luminosity over the last few decades. This is consistent with earlier suggestions of an extended obscuring/reprocessing envelope or outflow in V4641 Sgr. The inferred intrinsic accretion power can then readily supply the energy required to explain the UHE emission under the leptonic model, and is also marginally consistent with the requirement from the hadronic model, resolving the energy crisis. This supports V4641 Sgr as a Galactic PeV particle accelerator.