Milgrom Mordehai
Department of Particle Physics and Astrophysics, Weizmann Institute, Rehovot 7610001, Israel.
Phys Rev Lett. 2016 Sep 30;117(14):141101. doi: 10.1103/PhysRevLett.117.141101. Epub 2016 Sep 27.
I derive a new modified Newtonian dynamics (MOND) relation for pure-disc galaxies: The "dynamical" central surface density, Σ_{D}^{0}, deduced from the measured velocities, is a universal function of only the true, "baryonic'' central surface density, Σ_{B}^{0}: Σ_{D}^{0}=Σ_{M}S(Σ_{B}^{0}/Σ_{M}), where Σ_{M}≡a_{0}/2πG is the MOND surface density constant. This surprising result is shown to hold in both existing, nonrelativistic MOND theories. S(y) is derived: S(y)=∫{0}^{y}ν(y^{'})dy^{'}, with ν(y) being the interpolating function of the theory. The relation aymptotes to Σ{D}^{0}=Σ_{B}^{0} for Σ_{B}^{0}≫Σ_{M}, and to Σ_{D}^{0}=(4Σ_{M}Σ_{B}^{0})^{1/2} for Σ_{B}^{0}≪Σ_{M}. This study was prompted by the recent finding of a correlation between related attributes of disc galaxies by Lelli et al.. The MOND central-surface-densities relation agrees very well with these results.
我推导出了适用于纯盘状星系的一种新的修正牛顿动力学（MOND）关系：从测量速度推导得出的“动力学”中心面密度Σ₀ᴰ，仅是真实的“重子”中心面密度Σ₀ᴮ的一个通用函数：Σ₀ᴰ = ΣₘS(Σ₀ᴮ / Σₘ)，其中Σₘ ≡ a₀ / 2πG是MOND面密度常数。这一惊人结果在现有的非相对论MOND理论中均成立。推导出了S(y)：S(y) = ∫₀ʸ ν(y')dy'，其中ν(y)是该理论的插值函数。对于Σ₀ᴮ ≫ Σₘ，该关系渐近于Σ₀ᴰ = Σ₀ᴮ；对于Σ₀ᴮ ≪ Σₘ，渐近于Σ₀ᴰ = (4ΣₘΣ₀ᴮ)¹/²。这项研究是由莱利等人最近发现盘状星系相关属性之间的相关性所引发的。MOND中心面密度关系与这些结果非常吻合。
