Energy density profile inspired by noncommutativity

Abstract

An important consequence which comes from noncommutativity (NC) is undoubtedly the energy density characterized by a microscopic free parameter; indeed a Trans-Planckian parameter. However, its functional form is an interesting and useful equation which can be analyzed in astrophysical scenarios giving now astrophysical constraints. In this sense, this paper is devoted to explore the astrophysical consequences of an energy density with the same functional form of NC; mainly in stellar dynamics and rotation curves of galaxies. We start exploring toy models of stars with incompressible and polytropic fluids respectively, with the addition and coexistence with this new fluid. In both cases, we propose an appropriate constriction based on the difference between a correct and an anomalous behavior. As a complement, we explore the rotation curves of galaxies assuming that the halo is a fluid with the same characteristic of a NC equation, obtaining the range of values for the free parameter through the analysis of eighteen LSB galaxies. Our results are compared with traditional models studied in literature like Pseudoisothermal (PISO), Navarro-Frenk-White (NFW), Burkert and WaveDM dark matter models. Finally, we have computed the surface density, $\rho_i r_i$ for each dark matter model, where $i$ is for PISO, NFW, Burkert, WaveDM and NC macroscopic version. In the later case, following the results found using SPARC galaxy catalog, we have found a theoretical value of 116.97 M$_\odot$ pc$^{-2}$ while the data analysis gives us a value of 144.21 M$_\odot$ pc$^{-2}$. The values of the surface density $\rho_i r_i$ are roughly constant and their mean values depend on the dark matter model. Also we have computed the mass of each dark matter model within $300$ pc and found that there is a common mass for spiral galaxies of the order of 10$^7$ M$_\odot$, that is in agreement with the results for dSph Milky Way satellites. This would give a central density for the halo of $\sim 0.1$ M$_\odot$ pc$^{-2}$ independent of the dark matter model.