Figure 10

Figure 10: The mass discrepancy in spiral galaxies. The mass discrepancy is defined [270] as the ratio V 2∕V 2b where V is the observed velocity and Vb 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 V = V b, only when V > V b. 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 2 a = V ∕r, while the bottom panel plots it against the acceleration 2 gN = V b ∕r predicted by Newton from the observed baryonic surface density Σb. Note that the correlation appears a little better with gN because the data are stretched out over a wider range in gN than in a. 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.