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

Abstract

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.