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.
Categories: gr-qc