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arXiv 2210.02306astro-ph.GAastro-ph.COgr-qc
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矮星系在$f(R)$引力下的动力学

Dynamics of dwarf galaxies in $f(R)$ gravity

Ivan de Martino, Antonaldo Diaferio, Luisa Ostorero

备注：
11 pages, 4 figures, 2 Tables. Accepted for publication on MNRAS
发表信息：
Monthly Notices of the Royal Astronomical Society, 519, 4424-4433 (2023)
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摘要：

我们使用的恒星在8个矮球状星系的运动学数据，以评估是否$f(R)$重力可以适合这些系统的视线速度色散的观测配置文件，而不诉诸暗物质。我们的模型假设每个星系是球对称的，并有一个恒定的速度各向异性参数$β$和恒定的质光比与恒星人口合成模型一致。我们解决了球形Jeans方程，其中包括Yukawa的引力势出现在弱场极限的$f(R)$重力，和一个Plummer密度分布的恒星。的$f(R)$速度色散分布取决于两个参数：尺度长度$ξ^{-1}$，以下的汤川项是可以忽略的，和提升的引力场$δ>-1$。$δ$和$ξ$不是通用参数，但它们在同一类对象中的变化预计是有限的。的$f(R)$速度色散配置文件适合的数据与整个星系样本的值$ξ^{-1}= 1.2^{+18.6}_{-0.9}$ Mpc。相反，$δ$的值显示在$\barδ=-0.986\pm0.002$和$\barδ=-0.92\pm0.01$处拾取的双峰分布。这两个值在$6σ$处不一致，表明$f(R)$重力存在严重的张力。是否矮星系的改进模型或未来天体测量太空任务测量的恒星自行提供的额外约束可以为整个样本返回一致的$δ$，并消除这种张力，还有待观察。

英文摘要：

We use the kinematic data of the stars in eight dwarf spheroidal galaxies to assess whether $f(R)$ gravity can fit the observed profiles of the line-of-sight velocity dispersion of these systems without resorting to dark matter. Our model assumes that each galaxy is spherically symmetric and has a constant velocity anisotropy parameter $β$ and constant mass-to-light ratio consistent with stellar population synthesis models. We solve the spherical Jeans equation that includes the Yukawa-like gravitational potential appearing in the weak field limit of $f(R)$ gravity, and a Plummer density profile for the stellar distribution. The $f(R)$ velocity dispersion profiles depend on two parameters: the scale length $ξ^{-1}$, below which the Yukawa term is negligible, and the boost of the gravitational field $δ>-1$. $δ$ and $ξ$ are not universal parameters, but their variation within the same class of objects is expected to be limited. The $f(R)$ velocity dispersion profiles fit the data with a value $ξ^{-1}= 1.2^{+18.6}_{-0.9}$ Mpc for the entire galaxy sample. On the contrary, the values of $δ$ show a bimodal distribution that picks at $\barδ=-0.986\pm0.002$ and $\barδ=-0.92\pm0.01$. These two values disagree at $6σ$ and suggest a severe tension for $f(R)$ gravity. It remains to be seen whether an improved model of the dwarf galaxies or additional constraints provided by the proper motions of stars measured by future astrometric space missions can return consistent $δ$'s for the entire sample and remove this tension.

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