Mass-asymptotic speed relation

The mass-asymptotic speed relation, or MASSR, is a predicted relation between the total mass of a disk (or spiral) galaxy, and its large-radius rotation speed. The relation was first predicted by Mordehai Milgrom in 1983; it was confirmed in a number of observational studies about twenty years later. The observed form of the relation is usually called the baryonic Tully-Fisher relation, or BTFR.

The MASSR is not predicted by the standard cosmological model. In that theory, the rotation speed of a spiral galaxy is determined almost entirely at large radii by the gravitational force from the galaxy's dark matter. Milgrom's theory does not postulate the existence of dark matter. Confirmation of Milgrom's prediction lends support to the idea that dark matter does not exist.

The prediction

Milgrom's theory, called MOND or Milgromian dynamics, predicts that a test body moving in a circular orbit in the outskirts of a galaxy disk will have a speed $V$ given by $(a_{0}GM_{\rm {gal}})^{1/4}$ where

• $M_{\rm {gal}}$ is the total mass of the galaxy
• $G$ is the constant of gravitation
• $a_{0}$ is Milgrom's constant.

The predicted relation has a number of notable features. (1) The mass that appears in the relation, $M_{\rm {gal}}$, contains no contribution from dark matter (dark matter does not exist in Milgrom's theory); it is defined as the mass in stars, gas and dust. (2) The relation between $M_{\rm {gal}}$ and $V$ is predicted to be "functional", that is, exact; there should be no variance or "scatter". (3) A galaxy is predicted to fall on the relation regardless of its mode of formation or its evolutionary history. (4) The normalization of the relation is determined entirely by the product of $a_{0}$ and $G$, both of which are constants of nature, hence the same for every galaxy. (5) The "slope" of the predicted relation (on a log–log plot) is precisely $1/4$.

Observational verification

The fact that disk galaxies obey a relation of the form $V\propto M_{\rm {gal}}^{1/4}$ was not known at the time of Milgrom's prediction in 1983. Milgrom's prediction was confirmed in a number of observational studies starting around 2005. In these studies, the asymptotic rotation speed, $V$, is extracted from the measured rotation curve of a galaxy; this requires that the data extend to large enough radii that the "flat", or asymptotic, part of the curve is reached. The total mass, $M_{\rm {gal}}$, is inferred via a set of well-established techniques: the mass in stars is inferred from the galaxy's luminosity at visual or infrared wavelengths, together with a prescription for relating stellar mass to light; while the mass in gas is inferred from observations at radio wavelengths.

A plot that is constructed from data obtained in this way is usually called the "baryonic Tully-Fisher relation", or BTFR. The BTFR may be seen as the observable manifestation of the theoretically-predicted MASSR.

The most recent studies have verified that the observed BTFR has all the properties predicted by Milgrom's MASSR: its slope is $1/4$, its scatter is negligible and consistent with zero, and disk galaxies of all types (e.g. gas poor vs. gas rich; high vs. low surface brightness) respect it.

The predicted normalization of the MASSR is determined by the value of Milgrom's constant, $a_{0}$. This means that one can experimentally determine the value of $a_{0}$ from the BTFR. One finds:

$a_{0}\approx$ 1.2×10⁻⁸ cm s⁻²,

consistent with the values of $a_{0}$ determined by other techniques.

Significance

According to many philosophers of science, a hypothesis that is proposed to explain some phenomenon is only acceptable if, in addition to explaining that phenomenon, it successfully predicts some new facts that it was not designed to explain. Milgrom's explanation of the rotation curve anomaly satisfies this condition by virtue of successfully predicting the MASSR/BTFR. By contrast, explanation of the rotation-curve anomaly under the standard cosmological model is ad hoc: it simply states that dark matter is present, in whatever quantity or spatial distribution required to explain the observed motions. The prediction under the standard model that dark-matter particles are passing through the earth has not been confirmed.

External links

• The MOND paradigm of modified dynamics, Mordehai Milgrom
• "The Dark Matter Crisis" blog, Pavel Kroupa, Marcel Pawlowski

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