We investigate the luminosity of the accretion disk of a static black hole surrounded by dark matter with anisotropic pressure. We calculate all basic orbital parameters of test particles in the accretion disk, such as angular velocity, angular momentum, energy, and radius of the innermost circular stable orbit as functions of the dark matter density, radial pressure, and anisotropic parameter, which establishes the relationship between the radial and tangential pressures. We show that the presence of dark matter with anisotropic pressure makes a noticeable difference in the geometry around a Schwarzschild black hole, affecting the radiative flux, differential luminosity, and spectral luminosity of the accretion disk.

We consider the possibility that the Milky Way’s dark matter halo possesses a non vanishing equation of state. Consequently, we evaluate the contribution due to the speed of sound, assuming that the dark matter content of the galaxy behaves like a fluid with pressure. In particular, we model the dark matter distribution via an exponential sphere profile in the galactic core, and inner parts of the galaxy whereas we compare the exponential sphere with three widely-used profiles for the halo, i.e. the Einasto, Burkert and Isothermal profile. For the galactic core we also compare the effects due to a dark matter distribution without black hole with the case of a supermassive black hole in vacuum and show that present observations are unable to distinguish them. Finally we investigate the expected experimental signature provided by gravitational lensing due to the presence of dark matter in the core.

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We investigate the dark matter distribution in the spiral galaxy ESO0140040, employing the most widely used density profiles: the pseudo-isothermal, exponential sphere, Burkert, Navarro-Frenk-White, Moore and Einasto profiles. We infer the model parameters and estimate the total dark matter content from the rotation curve data. For simplicity, we assume that dark matter distribution is spherically symmetric without accounting for the complex structure of the galaxy. Our predictions are compared with previous results and the fitted parameters are statistically confronted for each profile. We thus show that although one does not include the galaxy structure it is possible to account for the same dynamics assuming that dark matter provides a non-zero pressure in the Newtonian approximation. In this respect, we solve the hydrostatic equilibrium equation and construct the dark matter pressure as a function for each profile. Consequently, we discuss the dark matter equation of state and calculate the speed of sound in dark matter. Furthermore, we interpret our results in view of our approach and we discuss the role of the refractive index as an observational signature to discriminate between our approach and the standard one.