Off-Pulse GeV Emission from PSR J0437–4715 and Statistical Properties of Bow-Shock Pulsar Wind Nebulae

Abstract PSR J0437−4715 is a γ-ray millisecond pulsar, which has been detected by Fermi Large Area Telescope (LAT). To understand the nature, we analyze the GeV γ-ray data obtained with Fermi-LAT around the pulsar region. Based on the pulsar timing ephemeris, we derived the γ-ray pulse profile and defined on-pulse and off-pulse phase intervals. A binned likelihood analysis was performed to investigate the spectral properties of the pulsar across different phase ranges. No spatial extension was detected for off-pulse, with an upper limit radius of 0.12○. The relationship between Lγ and LX is found as $L_{\gamma } \sim L_{X}^{0.6}$. The conversion efficiency from spin-down power to GeV emission of the outer gap model is consistent with a termination shock located close to the pulsar. We discuss the potential nature of off-pulse GeV emission and the connection to bow shock pulsar wind nebulae (PWNe). As a benchmark, the detailed phase-resolved properties of PSR J0437−4715 are first examined; we then place this pulsar within a larger sample of 17 bow-shock PWNe to test whether its emission characteristics conform to the global scaling relations between γ-ray luminosity, X-ray luminosity, and bow-shock radius. These two approaches allow us to assess the origin of the off-pulse emission and the universality of particle acceleration physics in MSP nebulae.