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We investigate the properties of dark matter (DM) distribution in spiral galaxy U5750, employing the well 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 spherically symmetric without accounting for the complex internal structure of the galaxy. We fit the rotation curve observational data of galaxy U5750 for each profile. We infer the model free parameters and estimate the total DM mass, and compare them with those reported in the literature. To discriminate the best fit profile among the considered ones, we make use of the Bayesian Information Criterion (BIC). On the basis of the performed statistical analysis, we provide physical interpretations for choosing certain profiles. In addition, by assuming that DM possesses non-zero pressure, we solve the Newtonian hydrostatic equilibrium equation and construct the pressure profiles as a functionof the radial coordinate for each above mentioned profile. Combining the density profiles with the pressure profiles we obtain equations of state for the DM in the considered galaxy. Further, we calculate the speed of soundin the DM medium and show that it behaves not unequivocally for the adopted profiles, though it decreaseswith an increasing DM density. Finally, we calculate the refracting index and discuss about astrophysical implications of the obtained results.

We consider the circular motion of test particles in the gravitational field of a static and axially-symmetric compact object described by the $q$-metric. To this end, we calculate orbital parameters of test particles on accretion disks such as angular velocity ($\Omega$), total energy ($E$), angular momentum ($L$), and radius of the innermost stable circular orbit ($r_{ISCO}$) as functions of the mass ($m$) and quadrupole ($q$) parameters of the source. The radiative flux, differential, and spectral luminosity of the accretion disk, which are quantities that can be experimentally measured, are then explored in detail. The obtained results are compared with the corresponding ones for the Schwarzschild and Kerr black holes in order to establish whether black holes may be distinguished from the $q$-metric via observations of the accretion disk's spectrum., Comment: 10 pages, 8 figures

We check the dynamical and observational features of four typologies of logotropic dark energy models, leading to a \emph{thermodynamic cosmic speed up} fueled by a single fluid that unifies dark energy and dark matter. We first present two principal Anton-Schmidt fluids where the Gr\"uneisen parameter $\gamma_{\rm G}$ is free to vary and then fixed to the special value $\gamma_{\rm G}=\tfrac{5}{6}$. We also investigate the pure logotropic model, corresponding to $\gamma_{\rm G}=-\frac{1}{6}$. Finally, we propose a new logotropic paradigm that works as a generalized logotropic fluid, in which we split the role of dark matter and baryons. We demonstrate that the logotropic paradigms may present drawbacks in perturbations, showing a negative adiabatic sound speed which make perturbations unstable. The Anton-Schmidt model with $\gamma_{\rm G}=\frac{5}{6}$ is ruled out while the generalized logotropic fluid seems to be the most suitable one, albeit weakly disfavored than the $\Lambda$CDM model. We combine low- and higher-redshift domains through experimental fits based on Monte Carlo Markov Chain procedures, taking into account supernovae Ia catalogue, Hubble measurements and $\sigma_8$ data points. We consider two model selection criteria to infer the statistical significance of the four models. We conclude there is statistical advantage to handle the Anton-Schmidt fluid with the Gr\"uneisen parameter free to vary and/or fixed to $\gamma_{\rm G}=-\frac{1}{6}$. The generalized logotropic fluid indicates suitable results, statistically favored than the other models, until the sound speed is positive, becoming unstable in perturbations elsewhere. We emphasize that the $\Lambda$CDM paradigm works statistically better than any kinds of logotropic and generalized logotropic models, while the Chevallier-Polarski-Linder parametrization is statistically comparable with logotropic scenarios., Comment: 15 pages, 3 tables, 4 figures. It matches the published version