A self-consistent hydrostatic mass modelling of pressure supported dwarf
  galaxy Leo T
  Assuming a hydrostatic equilibrium in an HI cloud, the joint Poisson's
equation is set up and numerically solved to calculate the expected HI
distribution. Unlike previous studies, the cloud is considered to be
non-isothermal, and an {\it iterative} method is employed to iteratively
estimate the intrinsic velocity dispersion profile using the observed
second-moment of the HI data. We apply our {\it iterative} method to a recently
discovered dwarf galaxy Leo T and find that its observed HI distribution does
not comply with the expected one if one assumes no dark matter in it. To model
the mass distribution in Leo T, we solve the Poisson's equation using a large
number of trial dark matter halos and compare the model HI surface density
($\Sigma_{HI}$) profiles to the observed one to identify the best dark matter
halo parameters. For Leo T, we find a pseudo-isothermal halo with core density,
$\rho_0 \sim 0.67$ $\rm M_{\odot} \thinspace pc^{-3}$ and core radius, $r_s
\sim 37$ parsec explains the observation best. The resulting dark matter halo
mass within the central 300 pc, $M_{300}$, found to be $\sim 2.7 \times 10^6$
$\rm M_{\odot}$. We also find that a set of dark matter halos with similar
$M_{300} \sim 3.7 \times 10^6$ $\rm M_{\odot}$ but very different $\rho_0$ and
$r_s$ values, can produce equally good $\Sigma_{HI}$ profile within the
observational uncertainties. This, in turn, indicates a strong degeneracy
between the halo parameters and the best fit values are not unique.
Interestingly, it also implies that the mass of a dark matter halo, rather than
its structure primarily directs the expected HI distribution under hydrostatic
equilibrium.
