DARK MATTER PROPERTIES IN GALAXY U5750

We investigate the properties of dark matter (DM) distribution in spiral galaxy U5750, employing thewell known and widely used phenomenological density profiles such as pseudo-isothermal, Burkert, Navarro-Frenk-White, Einasto, Moore and exponential sphere. For simplicity we assume that DM distribution is sphericallysymmetric without accounting for the complex internal structure of the galaxy. We fit the rotation curveobservational data of galaxy U5750 for each profile. We infer the model free parameters and estimate the total DMmass, and compare them with those reported in the literature. To discriminate the best fit profile among theconsidered ones, we make use of the Bayesian Information Criterion (BIC). On the basis of the performed statisticalanalysis, we provide physical interpretations for choosing certain profiles. In addition, by assuming that DMpossesses non-zero pressure, we solve the Newtonian hydrostatic equilibrium equation and construct the pressureprofiles as a functionof the radial coordinate for each above mentioned profile. Combining the density profiles withthe pressure profiles we obtain equations of state for the DM in the considered galaxy. Further, we calculate thespeed of soundin the DM medium and show that it behaves not unequivocally for the adopted profiles, though itdecreaseswith an increasing DM density. Finally, we calculate the refracting index and discuss about astrophysicalimplications of the obtained results.