Power spectrum to probe turbulence in Interstellar medium using 21cm
  line
  Turbulent dynamics generate random fluctuations in density and velocity in
the Interstellar Medium (ISM) of spiral and dwarf galaxies. Observationally,
H~{\sc i} 21-cm radiation provides a good probe of these stochastic processes
and helps us to know more about their nature and generating mechanism.
Structure function, auto-correlation function, power spectrum are some of
statistical estimators of these fluctuations which have been used in
literature, whose studies helps in understanding the generating mechanisms of
these structures. In this thesis we are interested in estimating the column
density and velocity power spectrum at scales as large as 10 Kpc, to understand
the energy associated with these structures and the type of forcing of the
turbulence. Estimating power spectrum from observations can be done either by
using the directly measured quantity visibility or by reconstructing the sky
brightness distribution (or image) from the visibilities. By using simulated
observations of a model galaxy with known power spectrum we find that the
visibility based estimator reproduce the true power spectrum. The image based
estimator has a scale dependent bias that is highly correlated to the
incompleteness in the baseline coverage of the interferometer. Interestingly,
we found that the noise in the reconstructed image has zero mean and hence the
locally averaged quantities estimated from the reconstructed image are
unbiased. We implement the visibility moment estimator as discussed in Dutta et
al. (2015) and estimate the line of sight velocity fluctuation of the spiral
galaxy NGC6946. Our result strongly indicate presence of large scale turbulence
in the spiral galaxies. We conclude that we would need to have higher signal to
noise H~{\sc i}observations to definitively comment on the generating
mechanisms of the large scale turbulence.
