It is shown that the foundational axioms of MOND alone predict a strong correlation between a bulk measure of the baryonic surface density, $Σ_B$, and the corresponding dynamical one, $Σ_D$, of an isolated object, such as a galaxy. The correlation is encapsulated by its high- and low-$Σ_B$ behaviors. For $Σ_B\ggΣ_M\equiv a_0/2πG$ ($Σ_M$ is the critical MOND surface density) one has $Σ_D\approxΣ_B$. Their difference -- which would be interpreted as the contribution of dark matter -- is $Σ_P=Σ_D-Σ_B\simΣ_M\llΣ_B$. In the deep-MOND limit, $Σ_B\llΣ_M$, one has $Σ_D\sim (Σ_MΣ_B)^{1/2}$. This is a primary prediction of MOND, shared by all theories that embody its basic tenets. Sharper correlations, even strict algebraic relations, $Σ_D(Σ_B)$, are predicted in specific MOND theories, for specific classes of mass distribution -- e.g., pure discs, or spherical systems -- and for specific definitions of the surface densities. I proceed to discuss such tighter correlations for the central surface densities of axisymmetric galactic systems, $Σ^0_B$ and $Σ^0_D$. Past work has demonstrated such relations for pure discs in the AQUAL and QUMOND theories. Here I consider them in broader classes of MOND theories. For most observed systems, $Σ^0_D$ can not be determined directly at present, but, in many cases, a good proxy for it is the acceleration integral $\mathcal{G}\equiv\int_0^\infty g_r d\ln~r$, where $g_r$ is the radial acceleration along a reflection-symmetry plane of a system, such as a disc galaxy. $\mathcal{G}$ can be determined directly from the rotation curve. I discuss the extent to which $\mathcal{G}$ is a good proxy for $Σ^0_D$, and how the relation between them depends on system geometry, from pure discs, through disc-plus-bulge ones, to quasi-spherical systems.
Testing Modified Gravity with Wide Binaries in GAIA DR2
最近的几项研究表明，非常宽的双星可以为试图模拟暗物质的修正引力理论提供一个有趣的测试;根据标准的暗物质理论，这些系统应该几乎是牛顿的，而MOND类理论的预测是明显不同的，如果各种观测问题可以克服的话。在这里，我们探讨了从最近的GAIA DR 2数据发布的测试的观测应用：我们选择了一个大样本的$\sim 24,000$候选宽双星距离$< 200$秒差距和大小$G < 16$从GAIA DR 2，估计组件质量使用的主序星质量-光度关系。然后，我们比较两两相对投影速度的频率分布，（相对于圆形轨道值）作为预计分离的函数;这些分布在接近牛顿预期的值处显示出明显的峰值，以及延伸到大得多的速度比的长“尾部”;“尾”比由具有随机位置的DR 2构建的对照样品中的“尾”多得多，因此其来源不清楚。将速度直方图与模拟数据进行比较，我们得出结论，没有外场效应的类似MOND的理论与观测数据强烈不一致，因为它们预测的峰移与数据明显不一致;用外场效应检验MOND类理论目前还不是决定性的，但随着对高速尾翼的模拟或理解的改进，和额外的光谱数据。
Fornax dwarf spheroidal in MOND: its formation and the survival of its globular clusters
Astronomical Observatory of Belgrade（贝尔格莱德天文台）；Scottish Universities Physics Alliance, University of Saint Andrews（苏格兰大学物理联盟，圣安德鲁斯大学）；Imperial Centre for Inference and Cosmology (ICIC), Department of Physics, Imperial College（帝国理工学院物理系推断与宇宙学中心）；CAS Key Laboratory for Research in Galaxies and Cosmology, Department of Astronomy, University of Science and Technology of China（中国科学院星系与宇宙学重点实验室，中国科学技术大学天文学系）；Department of Astronomy, University of Science and Technology of China（中国科学技术大学天文学系）
Dark Coincidences: Small-Scale Solutions with Refracted Gravity and MOND
广义相对论及其牛顿弱场极限不足以解释宇宙中观察到的现象，从大尺度结构的形成到星系的动力学，只有重子物质存在。研究最多的宇宙学模型$Λ$ CDM通过引入暗能量和暗物质这两个暗分量来解释大部分观测结果，这两个暗分量代表了宇宙质量-能量预算的95%，即$\sim$。然而，$Λ$ CDM模型在星系尺度上面临着重要的挑战。例如，盘星系中暗物质和重子物质的性质之间的一些非常紧密的关系，如重子Tully-Fisher关系（BTFR）、质量离散-加速度关系（MDAR）和径向加速度关系（RAR），它们见证了加速度标度$a_0 \simeq 1.2 \times 10^{-10}$ m s $^{-2}$的出现，不能用CDM范式直观地解释，宇宙结构通过随机合并过程形成。一个更突出的巧合是，星系动力学产生的加速度标度$a_0$似乎也与宇宙学常数$Λ$有关。另一个挑战是矮星系，它们比最里面的区域预期的要暗。这些证据可以更自然地解释，或者有时甚至预测，通过修改的引力理论，不引入任何暗流体。我用修改后的重力理论MOND来说明这些问题的可能解决方案，该理论在加速度小于$a_0$的情况下偏离牛顿重力，并用折射重力来说明这些问题，折射重力是2016年引入的一种新的经典重力理论，其中重力定律的修改由密度尺度来调节。
