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تسجيل مستخدم جديدUpper Limit on the Central Density of Dark Matter in the Eddington inspired Born-Infield (EiBI) Gravity
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We investigate the stability of circular material orbits in the analytic galactic metric recently derived by Harko textit{et al.} (2014). It turnsout that stability depends more strongly on the dark matter central density $%rho_{0}$ than on other parameters of the solution. This property then yields an upper limit on $rho _{0}$ for each individual galaxy, which we call here $rho _{0}^{text{upper}}$, such that stable circular orbits are possible textit{only} when the constraint $rho _{0}leq rho _{0}^{text{upper}}$ is satisfied. This is our new result. To approximately quantify the upper limit, we consider as a familiar example our Milky Way galaxy that has a projected dark matter radius $R_{text{DM}}sim 180$ kpc and find that $rho _{0}^{text{upper}}sim 2.37times 10^{11}$ $M_{odot }$kpc$^{-3}$. This limit turns out to be about four orders of magnitude larger than the latest data on central density $rho _{0}$ arising from the fit to the Navarro-Frenk-White (NFW) and Burkert density profiles. Such consistency indicates that the EiBI solution could qualify as yet another viable alternative model for dark matter.
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Recently, Harko et al. (2014) derived an approximate metric of the galactic halo in the Eddington inspired Born-Infeld (EiBI) gravity. In this metric, we show that there is an upper limit $rho _{0}^{text{upper}}$ on the central density $rho _{0}$ of
dark matter such that stable circular orbits are possible only when the constraint $rho _{0}leq rho_{0}^{text{upper}}$ is satisfied in each galactic sample. To quantify different $rho _{0}^{text{upper}}$ for different samples, we follow the novel approach of Edery & Paranjape (1998), where we use as input the geometric halo radius $R_{text{WR}}$ from Weyl gravity and equate it with the dark matter radius $R_{text{DM}}$ from EiBI gravity for the same halo boundary. This input then shows that the known fitted values of $rho _{0}$ obey the constraint $rho_{0}leqrho_{0}^{text{upper}}propto $ ($R_{text{WR}}$)$^{-2}$. Using the mass-to-light ratios giving $alpha $, we shall also evaluate $rho _{0}^{text{lower}}$ $propto $ $(alpha -1)M_{text{lum}}R_{text{WR}}^{-3}$ and the average dark matter density $leftlangle rhorightrangle ^{text{lower}}$. Quantitatively, it turns out that the interval $rho _{0}^{text{lower}}$ $leq rho _{0}leq $ $rho _{0}^{text{upper}}$ verifies reasonably well against many dark matter dominated low surface brightness (LSB) galaxies for which values of $rho _{0}$ are independently known. The interval holds also in the case of Milky Way galaxy. Qualitatively, the existence of a stability induced upper limit $rho _{0}^{text{upper}}$ is a remarkable prediction of the EiBI theory.
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