  We present results from Chandra and XMM-Newton observations of the radio
pulsar B1046-58. A high-resolution spatial analysis reveals an asymmetric
pulsar wind nebula (PWN) ~6"x11" in size. The combined emission from the pulsar
and its PWN is faint, with a best-fit power-law photon index of $\Gamma$=1.7
and unabsorbed luminosity of ~10^32 ergs/s in the 0.5-10.0 keV range (assuming
a distance of 2.7 kpc). A spatially resolved imaging analysis suggests the
presence of softer emission from the pulsar. No pulsations are detected from
PSR B1046-58; assuming a worst-case sinusoidal pulse profile, we derive a
3$\sigma$ upper limit for the pulsed fraction in the 0.5-10.0 keV range of 53%.
Extended PWN emission is seen within 2" of the pulsar; the additional
structures are highly asymmetric and extend predominantly to the south-east. We
discuss the emission from the PWN as resulting from material downstream of the
wind termination shock, as outflow from the pulsar or as structures confined by
a high space velocity. The first two interpretations imply equipartition fields
in the observed structures of ~40-100 uG, while the latter case implies a
velocity for the pulsar of ~ 190 n^-1/2 km/s (where n is the ambient number
density in units of cm^-3). No emission from an associated supernova remnant is
detected.
