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arXiv 1506.04023gr-qc
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Eddington启发的Born-Infield（EiBI）引力中暗物质中心密度的上限

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

Ramil Izmailov, Alexander A. Potapov, Alexander I. Filippov, Mithun Ghosh, Kamal K. Nandi

备注：
12 pages, 3 figures. arXiv admin note: substantial text overlap with arXiv:1412.7897
发表信息：
Modern Physics Letters A, Vol. 30, No. 11 1550056 (2015)
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摘要：

我们研究了Harko \textit{et al.}（2014）最近导出的解析银河度规中圆形物质轨道的稳定性。结果表明，稳定性对暗物质中心密度$%ρ_{0}$的依赖性比对溶液的其他参数的依赖性更强。这个属性然后产生一个上限$ρ_{0}$为每个单独的星系，我们称之为$ρ_{0}^{\text{upper}}$，这样稳定的圆形轨道是可能的\textit{only}时，约束$ρ_{0}\leq ρ_{0}^{\text{upper}}$是满足的。这是我们的新成果。为了近似地量化上限，我们认为作为一个熟悉的例子，我们的银河系有一个投影的暗物质半径$R_{\text{DM}}\sim 180$ kpc，并发现$ρ_{0}^{\text{upper}}\sim 2.37\times 10^{11}$ $M_{\odot }$ kpc $^{-3}$。这个极限比最新的中心密度$ρ_{0}$数据大约大四个数量级，这些数据是由Navarro-Frenk-White（NFW）和Burkert密度分布拟合而得的。这种一致性表明EiBI解决方案可以作为暗物质的另一种可行的替代模型。

英文摘要：

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 $%ρ_{0}$ than on other parameters of the solution. This property then yields an upper limit on $ρ_{0}$ for each individual galaxy, which we call here $ρ_{0}^{\text{upper}}$, such that stable circular orbits are possible \textit{only} when the constraint $ρ_{0}\leq ρ_{0}^{\text{upper}}$ 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 $ρ_{0}^{\text{upper}}\sim 2.37\times 10^{11}$ $M_{\odot }$kpc$^{-3}$. This limit turns out to be about four orders of magnitude larger than the latest data on central density $ρ_{0}$ 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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