Assuming a hydrostatic equilibrium in an H i cloud , the joint Poisson ’ s equation is set up and numerically solved to calculate the expected H i distribution .
Unlike previous studies , the cloud is considered to be non-isothermal , and an iterative method is employed to iteratively estimate the intrinsic velocity dispersion profile using the observed second-moment of the H i data .
We apply our iterative method to a recently discovered dwarf galaxy Leo T and find that its observed H i 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 H i 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 M _ { \odot } 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 } M _ { \odot } .
We also find that a set of dark matter halos with similar M _ { 300 } \sim 3.7 \times 10 ^ { 6 } 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 H i distribution under hydrostatic equilibrium .