Upper Limit on the Central Density of Dark Matter in the Eddington inspired Born-Infield (EiBI) Gravity

TL;DR

This paper derives an upper limit on the central dark matter density in galaxies within EiBI gravity, showing that stability of orbits constrains dark matter density and that the model aligns with observed data.

Contribution

It introduces a novel upper limit on dark matter density in galaxies based on orbit stability in EiBI gravity, supporting its viability as a dark matter model.

Findings

Upper limit on dark matter density depends strongly on orbit stability.

The derived upper limit is consistent with observed galaxy data.

EiBI gravity can serve as a viable alternative dark matter model.

Abstract

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 $\rho _{0}^{\text{upper}}\sim 2.37\times 10^{11}$ $M_{\odot }$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.