  We have obtained deep optical images with the Very Large Telescope at ESO of
the first well-localized short-duration gamma-ray burst, GRB 050509B. From V
and R imaging, initiated ~2 days after the GRB trigger and lasting up to three
weeks, we detect no variable object inside the small Swift/XRT X-ray error
circle down to 2sigma limits of V = 26.5 and R = 25.1. The X-ray error circle
includes a giant elliptical galaxy at z = 0.225, which has been proposed as the
likely host of this GRB. Our limits indicate that if the GRB originated at z =
0.225, any supernova-like event accompanying the GRB would have to be over 100
times fainter than normal Type Ia SNe or Type Ic hypernovae, 5 times fainter
than the faintest known Ia or Ic SNe, and fainter than the faintest known Type
II SNe. Moreover, we use the optical limits to constrain the energetics of the
GRB outflow. Simple models indicate that, unless the intrinsic energy in the
outflow from GRB 050509B was << 10^51 erg, there was very little radioactive
material with efficient decay timescales for generating a large luminosity.
These limits strongly constrain progenitor models for this short GRB.
