arXiv 1412.78972014-12gr-qc

由外尔引力输入的Eddington启发的Born-Infeld（EiBI）引力对暗物质中心密度的约束

Constraint on dark matter central density in the Eddington inspired Born-Infeld (EiBI) gravity with input from Weyl gravity

Alexander A. Potapov, Ramil Izmailov, Olga Mikolaychuk, Nikolay Mikolaychuk, Mithun Ghosh, Kamal K. Nandi

备注：: 37 pages, 6 figures
发表信息：: JCAP 07(2015) 018
DOI：: 10.1088/1475-7516/2015/07/018

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摘要：

最近，Harko等人（2014）推导了爱丁顿启发的玻恩-因菲尔德（EiBI）引力中星系晕的近似度量。在这个度量中，我们表明，有一个上限$ρ_{0}^{\text{upper}}$上的中心密度$ρ_{0}$的暗物质，使稳定的圆形轨道是可能的，只有当约束$ρ_{0}\leq ρ_{0}^{\text{upper}}$是满足每个星系样本。为了量化不同样本的不同$ρ_{0}^{\text{upper}}$，我们遵循Edery & Paranjape（1998）的新方法，其中我们使用来自Weyl引力的几何晕半径$R_{\text{WR}}$作为输入，并将其与来自EiBI引力的暗物质半径$R_{\text{DM}}$等同。然后，该输入示出$ρ_{0}$的已知拟合值服从约束$ρ_{0}\leqρ_{0}^{\text{upper}}\propto $（$R_{\text{WR}}$）$^{-2}$。利用给出$α$的质光比，我们还将计算$ρ_{0}^{\text{lower}}$ $\propto $ $(α-1)M_{\text{lum}}R_{\text{WR}}^{-3}$和平均暗物质密度$\left\langle ρ\right\rangle ^{\text{lower}}$。定量地，事实证明，间隔$ρ_{0}^{\text{lower}}$ $\leq ρ_{0}\leq $ $ρ_{0}^{\text{upper}}$验证相当不错，对许多暗物质为主的低表面亮度（LSB）的$ρ_{0}$值是独立已知的星系。这个间隔也适用于银河系。定性地说，稳定性诱导上限$ρ_{0}^{\text{upper}}$的存在是EiBI理论的显著预测。

英文摘要：

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 $ρ_{0}^{\text{upper}}$ on the central density $ρ_{0}$ of dark matter such that stable circular orbits are possible only when the constraint $ρ_{0}\leq ρ_{0}^{\text{upper}}$ is satisfied in each galactic sample. To quantify different $ρ_{0}^{\text{upper}}$ 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 $ρ_{0}$ obey the constraint $ρ_{0}\leqρ_{0}^{\text{upper}}\propto $ ($R_{\text{WR}}$)$^{-2}$. Using the mass-to-light ratios giving $α$, we shall also evaluate $ρ_{0}^{\text{lower}}$ $\propto $ $(α-1)M_{\text{lum}}R_{\text{WR}}^{-3}$ and the average dark matter density $\left\langle ρ\right\rangle ^{\text{lower}}$. Quantitatively, it turns out that the interval $ρ_{0}^{\text{lower}}$ $\leq ρ_{0}\leq $ $ρ_{0}^{\text{upper}}$ verifies reasonably well against many dark matter dominated low surface brightness (LSB) galaxies for which values of $ρ_{0}$ are independently known. The interval holds also in the case of Milky Way galaxy. Qualitatively, the existence of a stability induced upper limit $ρ_{0}^{\text{upper}}$ is a remarkable prediction of the EiBI theory.

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