标题： 快速旋转的星系并不偏离MOND质量-渐近速度关系 显示英文标题

标题： Fast-rotating galaxies do not depart from the MOND mass-asymptotic-speed relation

摘要： 奥格尔等人最近错误地认为，快速旋转的盘状星系违背了MOND（修改牛顿动力学）的预测：在他们样本中的23个星系里，有6个自转速度最快的星系似乎显示出比星系的重子质量 $M$ 和其“自转速度” $V$ 之间的MOND关系所允许的更高的自转速度。他们将这一偏离解释为观测到的 $M-V$ 关系从接近MOND预测的对数斜率 $4$，变为一个较浅的斜率 $\approx 0$。然而，奥格尔等人…… 使用星系的最大旋转速度$V_{max}$，而不是出现在 MOND 预测中的渐近速度$V_\infty$$V_\infty^4=MGa_0$。 当他们将这些数据点的$M$对$V_{max}$绘制在 Lelli 等人（2016）给出的$M$对$V_\infty$图表上时，他们错误地得出了与 MOND 的上述矛盾。 Ogle 等人使用的 $H_\alpha$ 旋转曲线远不足以探测渐近态，并确定 $V_\infty$。然而，对于具有观测到的扩展 HI 旋转曲线的快速自转星系，已有充分记录表明它们可以具有远大于 MOND 相关的 $V_\infty$ 的 $V_{max}$ [Noordermeer 和 Verheijen (NV) (2007) 及其他人]。例如，NV 样本中自转最快的星系具有 $V_{max}\approx 490{\rm ~km/s}$，但 $V_\infty\approx 250{\rm ~km/s}$。 NV 还表明，在一个（与MOND无关的）$M-V_{max}$图中，高速星系偏离了由低速星系定义的幂律线，从而在$M$与$V$的关系中造成了断裂，正如Ogle等人所声称的那样。 但是，当绘制与MOND相关的$M$与$V_\infty$的关系时，所有星系都接近相同的幂律关系，而没有出现断裂。 显示英文摘要

摘要： Ogle et al. have fallaciously argued recently that fast-rotating disc galaxies break with the predictions of MOND: the 6 fastest rotators of the 23 galaxies in their sample appear to have higher rotational speeds than is consistent with the MOND relation between the baryonic mass of a galaxy, $M$, and its `rotational speed', $V$. They interpret this departure as a break in the observed $M-V$ relation from a logarithmic slope near the MOND-predicted $4$, to a shallow slope of $\approx 0$. However, Ogle et al. use the MAXIMAL rotational speed of the galaxies, $V_{max}$, not the ASYMPTOTIC one, $V_\infty$, which appears in the MOND prediction, $V_\infty^4=MGa_0$. Plotting their $M$ vs. $V_{max}$ pairs on an $M$ vs. $V_\infty$ plot from Lelli et al. (2016), they arrive erroneously at the above tension with MOND. The $H_\alpha$ rotation curves used by Ogle et al. are far too short reaching to probe the asymptotic regime, and determine $V_\infty$. However, it is well documented for fast rotators with observed, extended, HI rotation curves, that they can have $V_{max}$ considerably larger than the MOND-relevant $V_\infty$ [Noordermeer and Verheijen (NV) (2007) and others]. E.g., the fastest rotator in the NV sample has $V_{max}\approx 490{\rm ~km/s}$, but $V_\infty\approx 250{\rm ~km/s}$. NV also show that in a (MOND-irrelevant) $M-V_{max}$ plot the high-speed galaxies fall off the power-law line defined by the lower-speed ones, creating a break in the $M$ vs. $V$ relation, in just the way claimed by Ogle et al. But, when plotting the MOND-relevant $M$ vs. $V_\infty$ all galaxies fall near the same power-law relation, without a break.