Tiny scale opacity fluctuations from VLBA, MERLIN and VLA observations
  of HI absorption toward 3C 138
  The structure function of opacity fluctuations is a useful statistical tool
to study tiny scale structures of neutral hydrogen. Here we present high
resolution observation of HI absorption towards 3C 138, and estimate the
structure function of opacity fluctuations from the combined VLA, MERLIN and
VLBA data. The angular scales probed in this work are ~ 10-200 milliarcsec
(about 5-100 AU). The structure function in this range is found to be well
represented by a power law S_tau(x) ~ x^{beta} with index beta ~ 0.33 +/- 0.07
corresponding to a power spectrum P_tau(U) ~ U^{-2.33}. This is slightly
shallower than the earlier reported power law index of ~ 2.5-3.0 at ~ 1000 AU
to few pc scales. The amplitude of the derived structure function is a factor
of ~ 20-60 times higher than the extrapolated amplitude from observation of Cas
A at larger scales. On the other hand, extrapolating the AU scale structure
function for 3C 138 predicts the observed structure function for Cas A at the
pc scale correctly. These results clearly establish that the atomic gas has
significantly more structures in AU scales than expected from earlier pc scale
observations. Some plausible reasons are identified and discussed here to
explain these results. The observational evidence of a shallower slope and the
presence of rich small scale structures may have implications for the current
understanding of the interstellar turbulence.
