Searches for diffuse X-ray emission around millisecond pulsars: an X-ray nebula associated with PSR J2124-3358

We report on diffuse X-ray emission associated with the nearby solitary millisecond pulsar PSR J2124-3358 detected with XMM-Newton and Chandra. The emission extends from the pulsar to the northwest by ~$ 0.5$ arcmin. The spectrum of the nebular emission can be modeled with a power-law of photon index $2.2\pm0.4$, in line with the emission originating from accelerated particles in the post shock flow. For PSR J0437-4715, PSR J0030+0451 and PSR J1024-0719, which all have spin parameters comparable to that of PSR J2124-3358, no diffuse emission is detected down to a $3{-}\sigma$ limiting flux of ~$ 4{-}7\times10^{-15}$ erg s-1 cm-2.