标题： 银河系旋转动力学在新的$f(\mathcal{R})$引力模型中 显示英文标题

标题： Galactic rotation dynamics in a new $f(\mathcal{R})$ gravity model

摘要： 我们提出测试最近引入的$f(\mathcal{R})$引力模型在星系尺度上的可行性。 为此，我们考虑在星系中心周围做稳定圆轨道运动的测试粒子。 我们通过Weyl变换研究$f(\mathcal{R})$引力的Palatini方法，这是从Jordan框架到Einstein框架的框架变换。 我们推导了新$f(\mathcal{R})$引力模型中测试粒子的旋转速度表达式。 对于高表面亮度和低表面亮度星系样本的观测数据，我们表明预测的旋转曲线与观测结果很好地吻合，从而表明该模型可以解释星系的平坦旋转曲线。 我们还研究了一个超弥散星系AGC$242019$，文献中声称它是一个类似于低表面亮度星系、具有缓慢上升旋转曲线的暗物质主导星系。 该星系的旋转曲线在我们的研究中也与模型预测很好地吻合。 此外，我们研究了整个星系样本的Tully-Fisher关系，并发现模型预测与数据一致。 显示英文摘要

摘要： We propose to test the viability of the recently introduced $f(\mathcal{R})$ gravity model in the galactic scales. For this purpose we consider test particles moving in stable circular orbits around the galactic center. We study the Palatini approach of $f(\mathcal{R})$ gravity via Weyl transformation, which is the frame transformation from the Jordan frame to the Einstein frame. We derive the expression of rotational velocities of test particles in the new $f(\mathcal{R})$ gravity model. For the observational data of samples of high surface brightness and low surface brightness galaxies, we show that the predicted rotation curves are well fitted with observations, thus implying that this model can explain flat rotation curves of galaxies. We also study an ultra diffuse galaxy, AGC $242019$ which has been claimed in literature to be a dark matter dominated galaxy similar to low surface brightness galaxies with a slowly rising rotation curve. The rotation curve of this galaxy also fits well with the model prediction in our study. Furthermore, we studied the Tully-Fisher relation for the entire sample of galaxies and found that the model prediction shows the consistency with the data.