Figure 10: The mass discrepancy in spiral galaxies. The mass discrepancy is defined [270] as the
ratio where is the observed velocity and is the velocity attributable to visible
baryonic matter. The ratio of squared velocities is equivalent to the ratio of total-to-baryonic enclosed
mass for spherical systems. No dark matter is required when , only when . Many
hundreds of individual resolved measurements along the rotation curves of nearly one hundred spiral
galaxies are plotted. The top panel plots the mass discrepancy as a function of radius. No particular
linear scale is favored. Some galaxies exhibit mass discrepancies at small radii while others do not
appear to need dark matter until quite large radii. The middle panel plots the mass discrepancy
as a function of centripetal acceleration , while the bottom panel plots it against the
acceleration predicted by Newton from the observed baryonic surface density .
Note that the correlation appears a little better with because the data are stretched out
over a wider range in than in . Note also that systematics on the stellar mass-to-light
ratios can make this relation slightly more blurred than shown here, but the relation is nevertheless
always present irrespective of the assumptions on stellar mass-to-light ratios [270]. Thus, there is a
clear organization: the amplitude of the mass discrepancy increases systematically with decreasing
acceleration and baryonic surface density.
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