[Paper Review] High-redshift rotation curves and MOND

Mordehai Milgrom|arXiv (Cornell University)|Mar 17, 2017

Advanced Numerical Analysis Techniques17 citations

TL;DR

This paper demonstrates that the high-redshift rotation curves (RCs) of six galaxies from Genzel et al. (2017) are well explained by Modified Newtonian Dynamics (MOND) with the standard local value of the MOND acceleration constant $a_0$, without requiring $z$-dependence. The observed baryon dominance, low asymptotic speeds, and RC declines are all consistent with MOND predictions, strongly constraining any time variation of $a_0$—particularly ruling out values as high as $4a_0$ at $z \sim 2$. This supports MOND as a universal law independent of cosmic epoch.

ABSTRACT

Genzel et al. have recently published the rotation curves of six high-redshift disc galaxies ($z\sim 0.9-2.4$), which they find to be `baryon dominated' within the studies radii. While not up to the standard afforded by data available for analysis in the nearby Universe, these data are valuable in constraining cosmological evolution of either DM scenarios, or -- as I discuss here -- $z$-dependence of MOND. Indeed, these results, if taken at face value, teach us useful lessons in connection with MOND. a. The dynamical accelerations at the half-light radii, found by Genzel et al., are rather high compared with the MOND acceleration constant, as measured in the nearby Universe: $g(R_{1/2})= (3-11)a_0$. MOND then predicts fractions of `phantom matter' at $R_{1/2}$ of at most a few tens of percents, which, galaxy by galaxy, agree well with what Genzel et al. find. b. The asymptotic rotational speeds predicted by MOND from the baryonic-mass estimates of Genzel et al. are substantially lower ($0.55-0.75$) than the maximal speeds of the RCs. MOND thus predicts a substantial decline of the RCs beyond the maximum. This too is in line with what Genzel et al. find. c. Arguably, the most important lesson is that the findings of Genzel et al. cast very meaningful constraints on possible variation of $a_0$ with cosmic time. For example, they all but exclude a value of the MOND constant of $\sim 4a_0$ at $z\sim 2$, excluding, e.g., $a_0\propto (1+z)^{3/2}$.

Motivation & Objective

• To test whether Modified Newtonian Dynamics (MOND) with the standard local value of the MOND acceleration constant $a_0$ can explain the rotation curves of high-redshift disc galaxies.
• To assess whether the observed baryon dominance and declining rotation curves in high-$z$ galaxies are consistent with MOND predictions.
• To constrain possible time evolution of the MOND constant $a_0$ using high-redshift data, particularly ruling out $a_0 \propto (1+z)^{3/2}$ or values as high as $4a_0$ at $z \sim 2$.
• To evaluate whether MOND's prediction of low 'phantom matter' fractions at accelerations above $a_0$ holds at high redshift, reinforcing its status as a fundamental law.
• To distinguish MOND's mass-asymptotic-speed relation (MASR) from empirical Tully-Fisher relations, emphasizing the need for asymptotic speeds in testing $a_0$ evolution.

Proposed method

• Applying the MOND formula $g_N = g_{ m N} \mu(a_0/g_N)$ to compute dynamical accelerations from observed baryonic masses and rotation speeds.
• Using the MOND mass-asymptotic-speed relation (MASR) $V_{\infty}^4 = a_0 G M_b$ to predict asymptotic rotational speeds from baryonic mass estimates.
• Calculating the fraction of 'phantom matter' at half-light radius via $x_{1/2} = g(R_{1/2}) / a_0$, where $g(R_{1/2})$ is the dynamical acceleration.
• Comparing observed rotation curve shapes and maximum speeds with MOND-predicted declines beyond the maximum, based on $V_{\infty}/V_{\rm max}$ ratios.
• Assessing the impact of external field effects and inclination uncertainties on RC interpretation, while assuming isolation to minimize such effects.
• Evaluating the consistency of observed $V_{\infty}/V_{\rm max}$ ratios with MOND predictions to infer constraints on $a_0$ evolution.

Experimental results

Research questions

• RQ1 Can the high-redshift rotation curves of six disc galaxies from Genzel et al. (2017) be explained by MOND using the standard local value of $a_0$?
• RQ2 To what extent do the observed baryon dominance and declining RCs at $z \sim 0.9-2.4$ align with MOND predictions for accelerations above $a_0$?
• RQ3 What constraints do these data place on the possibility that $a_0$ varies with cosmic time, particularly for $a_0 \propto (1+z)^{3/2}$ or $a_0 \sim 4a_0$ at $z \sim 2$?
• RQ4 Do the observed $V_{\infty}/V_{\rm max}$ ratios of 0.55–0.75 support MOND’s prediction of a substantial RC decline beyond the maximum, or do they indicate a need for $a_0$ evolution?
• RQ5 Can the observed RC behavior be distinguished from empirical Tully-Fisher relations, and does it support the MOND-predicted MASR as a fundamental relation?

Key findings

• The dynamical accelerations at half-light radii in the six high-redshift galaxies range from $3a_0$ to $11a_0$, indicating they are well above the MOND transition scale.
• MOND predicts that the fraction of 'phantom matter' at $R_{1/2}$ is at most a few tens of percent, which is consistent with the observed baryon dominance in the data.
• The observed $V_{\infty}/V_{\rm max}$ ratios of $0.55 \pm 0.1$ to $0.7 \pm 0.1$ are consistent with MOND’s prediction of a substantial decline beyond the maximum rotation speed.
• A MOND constant as high as $4a_0$ at $z \sim 2$ is strongly excluded, as it would predict $x_{1/2} \sim 1$ and $\zeta_{1/2} \sim 0.5$, conflicting with the observed low 'phantom matter' fractions.
• The data rule out $a_0 \propto (1+z)^{3/2}$, as such a model would require $a_0 \sim 4a_0$ at $z \sim 2$, which is inconsistent with the observed dynamics.
• The consistency of the data with MOND using the standard $a_0$ value—without $z$-dependence—strengthens the case for MOND as a universal law independent of cosmic evolution.