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Register a new userDark matter equation of state from rotational curves of galaxies
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In this work we model galactic halos describing the dark matter as a non zero pressure fluid and derive, not impose, a dark matter equation of state by using observational data of the rotation curves of galaxies. In order to reach hydrostatic equilibrium, as expected for the halo, it is mandatory that dark fluids pressure should not be zero. The equation of state is obtained by solving the matter-geometry system of equations assuming different dark matter density or rotational velocity profiles. The resulting equations of state are, in general, different to a barotropic equation of state. The free parameters of the equation of state are fixed by fitting the observed rotational velocities of a set of galaxies.
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In this work we have used the recent cosmic chronometers data along with the latest estimation of the local Hubble parameter value, $H_0$ at 2.4% precision as well as the standard dark energy probes, such as the Supernovae Type Ia, baryon acoustic oscillation distance measurements, and cosmic microwave background measurements (PlanckTT $+$ lowP) to constrain a dark energy model where the dark energy is allowed to interact with the dark matter. A general equation of state of dark energy parametrized by a dimensionless parameter `$beta$ is utilized. From our analysis, we find that the interaction is compatible with zero within the 1$sigma$ confidence limit. We also show that the same evolution history can be reproduced by a small pressure of the dark matter.
We find the distribution function f(E) for dark matter (DM) halos in galaxies and the corresponding equation of state from the (empirical) DM density profiles derived from observations. We solve for DM in galaxies the analogous of the Eddington equation originally used for the gas of stars in globular clusters. The observed density profiles are a good realistic starting point and the distribution functions derived from them are realistic. We do not make any assumption about the DM nature, the methods developed here apply to any DM kind, though all results are consistent with Warm DM. With these methods we find: (i) Cored density profiles behaving quadratically for small distances rho(r) r -> 0 = rho(0) - K r^2 produce distribution functions which are finite and positive at the halo center while cusped density profiles always produce divergent distribution functions at the center. (ii) Cored density profiles produce approximate thermal Boltzmann distribution functions for r < 3 r_h where r_h is the halo radius. (iii) Analytic expressions for the dispersion velocity and the pressure are derived yielding an ideal DM gas equation of state with local temperature T(r) = m v^2(r)/3. T(r) turns to be constant in the same region where the distribution function is thermal and exhibits the same temperature within the percent. The self-gravitating DM gas can thermalize despite being collisionless because it is an ergodic system. (iv) The DM halo can be consistently considered at local thermal equilibrium with: (a) a constant temperature T(r) = T_0 for r < 3 ; r_h, (b) a space dependent temperature T(r) for 3 r_h < r < R_{virial}, which slowly decreases with r. That is, the DM halo is realistically a collisionless self-gravitating thermal gas for r < R_{virial}. (v) T(r) outside the halo radius nicely follows the decrease of the circular velocity squared.
The immediate observational consequence of a non-trivial spatial topology of the Universe is that an observer could potentially detect multiple images of radiating sources. In particular, a non-trivial topology will generate pairs of correlated circles of temperature fluctuations in the anisotropies maps of the cosmic microwave background (CMB), the so-called circles-in-the-sky. In this way, a detectable non-trivial spatial topology may be seen as an observable attribute, which can be probed through the circles-in-the-sky for all locally homogeneous and isotropic universes with no assumptions on the cosmological dark energy (DE) equation of state (EOS) parameters. We show that the knowledge of the spatial topology through the circles-in-the-sky offers an effective way of reducing the degeneracies in the DE EOS parameters. We concretely illustrate the topological role by assuming, as an exanple, a Poincar{e} dodecahedral space topology and reanalyzing the constraints on the parameters of a specific EOS which arise from the supernovae type Ia, baryon acoustic oscillations and the CMB plus the statistical topological contribution.
The model-independent piecewise parametrizations (0-spline, linear-spline and cubic-spline) are used to estimate constraints of equation of state of dark energy ($w_{de}$) from current observational data (including SNIa, BAO and Hubble parameter) and the simulated future data. A combination of fitting results of $w_{de}$ from these three spline methods reveal essential properties of real equation of state $w_{de}$. It is shown that $w_{de}$ beyond redshift $zsim0.5$ is poorly constrained from current data, and the mock future $sim2300$ supernovae data give poor constraints of $w_{de}$ beyond $zsim1$. The fitting results also indicate that there might exist a rapid transition of $w_{de}$ around $zsim0.5$. The difference between three spline methods in reconstructing and constraining $w_{de}$ has also been discussed.
We argue that combined observations of galaxy rotation curves and gravitational lensing not only allow the deduction of a galaxys mass profile, but also yield information about the pressure in the galactic fluid. We quantify this statement by enhancing the standard formalism for rotation curve and lensing measurements to a first post-Newtonian approximation. This enhanced formalism is compatible with currently employed and established data analysis techniques, and can in principle be used to reinterpret existing data in a more general context. The resulting density and pressure profiles from this new approach can be used to constrain the equation of state of the galactic fluid, and therefore might shed new light on the persistent question of the nature of dark matter.
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