  We evaluate the prompt observational signatures of the merger between a
massive close-in planet (a `hot Jupiter') and its host star, events with an
estimated Galactic rate of ~0.1-1/yr. Depending on the ratio of the mean
density of the planet rho_p to that of the star rho_star, a merger results in
three possible outcomes. If rho_p/rho_star > 5, then the planet directly
plunges below the stellar atmosphere before being disrupted by tidal forces.
Dissipation of orbital energy creates a hot wake behind the planet, producing a
EUV/soft X-ray transient as the planet sinks below the stellar surface. The
peak luminosity L_X ~ 1e36 erg/s is achieved weeks-months prior to merger,
after which the stellar surface is enshrouded by an outflow. The final inspiral
is accompanied by an optical transient powered by the recombination of hydrogen
in the outflow, which peaks at L~1e37-38 erg/s on a timescale ~days. If instead
rho_planet/rho_star < 5, then Roche Lobe overflow occurs above the stellar
surface. For rho_p/rho_star < 1, mass transfer is stable, resulting the planet
being accreted on a relatively slow timescale. However, for 1 < rho_p/rho_star
< 5, mass transfer may instead be unstable, resulting in the planet being
dynamically disrupted into an accretion disk around the star. Super-Eddington
outflows from the disk power an optical transient with L~1e37-38 erg/s and
characteristic duration ~week-months. The disk itself becomes visible once the
accretion rate become sub-Eddington, resulting in a bolometric brightening and
spectral shift to the UV. Optical transients from planet merger events may
resemble classical novae, but are distinguished by lower ejecta mass and
velocity ~100s km/s, and by hard pre- and post-cursor emission, respectively.
Promising search strategies include combined optical, UV, and X-ray surveys of
nearby massive galaxies with cadences from days to months.
