arXiv 1306.63832013-06astro-ph.GAgr-qc

MOG弱场近似与星系自转曲线的观测检验

The MOG weak field approximation and observational test of galaxy rotation curves

J. W. Moffat, S. Rahvar

备注：: 14 pages, 5 figures, v2: Minor corrections, accepted in MNRAS
发表信息：: Monthly Notices of the Royal Astronomical Society 436, 1439-1451 (2013)
DOI：: 10.1093/mnras/stt1670

摘要：

作为暗物质模型的替代，修正引力（MOG）理论可以通过爱因斯坦引力的协变修正来补偿暗物质。该理论引入了两个额外的标量场和一个矢量场。其目的是解释仅基于重子物质的天文系统的动力学。理论中的矢量场效应类似于洛伦兹力，其中每个质量都有与惯性质量成比例的电荷。本文通过微扰Minkowski时空周围的场和度规，得到了MOG的弱场近似。我们推导出一个有效的引力势，它产生的牛顿吸引力加上排斥汤川力。除了牛顿引力常量$G_N$之外，这个势还有两个额外的常数参数$α$和$μ$。我们使用星系的THINGS星表，将理论中的两个参数$α$和$μ$固定为$α=8.89 \pm 0.34$和$μ=0.04 \pm 0.004 {\rm kpc}^{-1}$。然后，我们适用于固定的通用参数的有效潜力的大熊座星系目录，并获得良好的拟合星系旋转曲线数据的平均值为$\bar{χ^2} = 1.07 $。在拟合过程中，只有星系的恒星质光比$(M/L)$是自由参数。作为MOG的预测，我们推导的$M/L$与星系的颜色相关，并且我们拟合了星系的塔利-费舍尔关系。作为暗物质的替代，引入有效弱场势为MOG理论的天体物理应用打开了一扇新的窗口。

英文摘要：

As an alternative to dark matter models, MOdified Gravity (MOG) theory can compensate for dark matter by a covariant modification of Einstein gravity. The theory introduces two additional scalar fields and one vector field. The aim is to explain the dynamics of astronomical systems based only on their baryonic matter. The effect of the vector field in the theory resembles a Lorentz force where each mass has a charge proportional to the inertial mass. In this work, we obtain the weak field approximation of MOG by perturbing the metric and the fields around Minkowski space-time. We derive an effective gravitational potential which yields the Newtonian attractive force plus a repulsive Yukawa force. This potential, in addition to the Newtonian gravitational constant, $G_N$, has two additional constant parameters $α$ and $μ$. We use the THINGS catalog of galaxies and fix the two parameters $α$ and $μ$ of the theory to be $α=8.89 \pm 0.34$ and $μ=0.04 \pm 0.004 {\rm kpc}^{-1}$. We then apply the effective potential with the fixed universal parameters to the Ursa-Major catalog of galaxies and obtain good fits to galaxy rotation curve data with an average value of $\bar{χ^2} = 1.07 $. In the fitting process, only the stellar mass-to-light ratio $(M/L)$ of the galaxies is a free parameter. As predictions of MOG, our derived $M/L$ is shown to be correlated with the color of galaxies, and we fit the Tully-Fisher relation for galaxies. As an alternative to dark matter, introducing an effective weak field potential for MOG opens a new window to the astrophysical applications of the theory.

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