  The origin of the closest compact elliptical galaxy (cE) M32 is a
longstanding problem of galaxy formation in the Local Group. Our N-body/SPH
simulations suggest a new scenario in which the strong tidal field of M31 can
transform a spiral galaxy into a compact elliptical. As a low luminosity spiral
galaxy plunges into the central region of M31, most of the outer stellar and
gaseous components of its disk are dramatically stripped due to M31's tidal
field The central bulge component, on the other hand, is just weakly influenced
by the tidal field owing to its compact configuration, and retains its
morphology. M31's strong tidal field also induces rapid gas transfer to the
central region, triggers a nuclear starburst, and consequently forms the
central high density and more metal-rich stellar populations with relatively
young ages. Thus, in this scenario, M32 was previously the bulge of a spiral
tidally interacting with M31 several Gyr ago. Furthermore, we suggest cEs like
M32 are rare, the result of both the rather narrow parameter space for tidal
interactions which morphologically transform spirals into cEs and the very
short time scale ($<$ a few $10^9$ yr) for cEs to be swallowed.
