快速旋转的星系不偏离MOND质量-渐近-速度关系
Fast-rotating galaxies do not depart from the MOND mass-asymptotic-speed relation
摘要：
Ogle等人最近错误地认为，快速旋转的盘状星系与MOND的预测不符：在他们的样本中，23个星系中6个最快的旋转星系的旋转速度似乎高于MOND关系，该关系与星系的重子质量$M$和它的“旋转速度”$V$之间的关系相一致。他们将这种偏离解释为观测到的$M-V$关系从接近MOND预测的$4$的对数斜率到$\approx 0$的浅斜率的中断。然而，奥格尔等人使用的是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$V_\infty$，$V_\infty^4=MGa_0$。在Lelli等人（2016）的$M$与$V_\infty$图上绘制$M$与$V_{max}$对，他们错误地得出了上述与MOND的张力。Ogle等人使用的$H_α$旋转曲线太短，无法探测渐近状态并确定$V_\infty$。然而，对于具有观察到的、延长的HI旋转曲线的快速旋转体，有充分的证据表明，它们的$V_{max}$可以显著大于MOND相关的$V_\infty$ [Noordermeer和Verheijen（NV）（2007）等]。例如，在一个示例中，NV样本中最快的旋转器具有$V_{max}\approx 490{\rm ~km/s}$，但具有$V_\infty\approx 250{\rm ~km/s}$。NV还表明，在（与MOND无关的）$M-V_{max}$图中，高速星系从由低速星系定义的幂律线上跌落，在$M$与$V$的关系中产生了一个中断，就像Ogle等人所声称的那样。但是，当绘制与MOND相关的$M$与$V_\infty$时，所有星系都落在相同的幂律关系附近，没有中断。
英文摘要：
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 $H_α$ 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.
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