  Hot gas trapped in a dark matter halo will produce a decrement in the surface
brightness of the microwave background, the Sunyaev-Zel'dovich (SZ) effect.
While massive clusters produce the strongest central SZ decrements, we point
out that a local galaxy halo, specifically the halo of M31, may be one of the
brightest integrated SZ sources in the sky. For various realistic gas
distributions consistent with current X-ray limits, we show that the integrated
SZ decrement from M31 will be comparable to decrements already detected in more
distant sources, provided its halo contains an appreciable quantity of hot gas.
A measurement of this decrement would provide direct information on the mass,
spatial distribution and thermodynamic state of hot gas in a low-mass halo, and
could place important constraints on current models of galaxy formation.
Detecting such an extended (~ 10 degree), low-amplitude signal will be
challenging, but should be possible with all-sky SZ maps from satellite
missions such as the Wilkinson Microwave Anisotropy Probe or the Planck
Surveyor.
