We discuss the properties and implications of the recently discovered 35 × 09 (3.7 × 0.9 kpc) region of spatially coincident X-ray and Hα emission about 11' (11.6 kpc) to the north of the prototypical starburst/superwind galaxy M82. The total Hα flux from this ridge of emission is 1.5 × 10-13 ergs s-1 cm -2, or about 0.3% of the total M82 Hα flux. The implied Hα luminosity of this region is 2.4 × 1038 ergs s-1. Diffuse soft X-ray emission is seen over the same region by the ROSAT PSPC and HRI. The PSPC X-ray spectrum is fitted by thermal plasma absorbed by only the Galactic foreground column density (NH = 3.7 × 1020 cm-2) and having a temperature of kT = 0.80 ± 0.17 keV. The total unabsorbed flux from the ridge is 1.4 × 10-13 ergs cm-2 s-1 (~2.2 × 1038 ergs s-1), comprising about 0.7% of the total X-ray emission from M82. We evaluate the relationship of the X-ray/Hα ridge to the M82 superwind. The Hα emission could be excited by ionizing radiation from the starburst that propagates into the galactic halo along the cavity carved by the superwind. However, the main properties of the X-ray emission can all be explained as being due to shock heating driven as the superwind encounters a massive ionized cloud in the halo of M82 (possibly related to the tidal debris seen in H I in the interacting M81/M82/NGC 3077 system). This encounter drives a slow shock into the cloud, which contributes to the excitation of the observed Hα emission. At the same time, a fast bow shock develops in the superwind just upstream of the cloud, and this produces the observed X-ray emission. This interpretation would imply that the superwind has an outflow speed of roughly 800 km s-1, consistent with indirect estimates based on its general X-ray properties and the kinematics of the inner kiloparsec-scale region of Hα filaments. The alternative, in which a much faster and more tenuous wind drives a fast radiative shock into a cloud that then produces both the X-ray and Hα emission, is ruled out by the long radiative cooling times and the relatively quiescent Hα kinematics in this region. We suggest that wind-cloud interactions may be an important mechanism for generating X-ray and optical line emission in the halos of starbursts. Such interactions can establish that the wind has propagated out to substantially greater radii than could otherwise be surmised. This has potentially interesting implications for the fate of the outflowing metal-enriched material, and bears on the role of superwinds in the metal enrichment and heating of galactic halos and the intergalactic medium. In particular, the gas in the M82 ridge is roughly 2 orders of magnitude hotter than the minimum "escape temperature" at this radius, so this gas will not be retained by M82.
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