  The recent detection of a 3-hr X-ray flare by the Chandra Observatory has
raised the possibility of enhanced emission over a broad range of wavelengths
from Sgr A*, the suspected 2.6 x 10^6 solar mass black hole at the Galactic
Center, during a flaring event. We have, therefore, reconstructed 3-hr data
sets from 2 micron speckle and adaptive optics images (theta_core = 50 - 100
mas) obtained with the W. M. Keck 10-m telescopes between 1995 and 2001. In 25
separate observations, no evidence of any significant excess emission
associated with Sgr A* was detected. The lowest of our detection limits gives
an observed limit for the quiescent state of Sgr A* of 0.09+/-0.005 mJy, or,
equivalently, a dereddened value of 2.0+/-0.1 mJy, which is a factor of 2 lower
than the best previously published quiescent value. Under the assumption that
there are random 3-hr flares producing both enhanced X-ray and near-infrared
emission, our highest limit constrains the variable state of Sgr A* to <0.8 mJy
(observed) or 19 mJy (dereddened). These results suggest that the model favored
by Markoff et al. (2001), in which the flare is produced through local heating
of relativistic particles surrounding Sgr A* (e.g., a sudden magnetic
reconnection event), is unlikely, because it predicts peak 2 micron emission of
300 mJy, well above our detection limit.
