Figure 13: Surface density profiles (top) and rotation curves (bottom) of two galaxies: the HSB
spiral NGC 6946 (Figure 12, left) and the LSB galaxy NGC 1560 (right). The surface density of
stars (blue circles) is estimated by azimuthal averaging in ellipses fit to the -band ( m)
light distribution. Similarly, the gas surface density (green circles) is estimated by applying the same
procedure to the 21 cm image. Note the different scale between LSB and HSB galaxies. Also note
features like the central bulge of NGC 6946, which corresponds to a sharp increase in stellar surface
density at small radius. In the lower panels, the observed rotation curves (data points) are shown
together with the baryonic mass models (lines) constructed from the observed distribution of baryons.
Velocity data for NGC 6946 include both HI data that define the outer, flat portion of the rotation
curve [66] and H data from two independent observations [54, 114] that define the shape of the
inner rotation curve. Velocity data for NGC 1560 come from two independent interferometric HI
observations [28, 163]. Baryonic mass models are constructed from the surface density profiles by
numerical solution of the Poisson equation using GIPSY [472]. The dashed blue line is the stellar
disk, the red dot-dashed line is the central bulge, and the green dotted line is the gas. The solid
black line is the sum of all baryonic components. This provides a decent match to the rotation curve
at small radii in the HSB galaxy, but fails to explain the flat portion of the rotation curve at large
radii. This discrepancy, and its systematic ubiquity in spiral galaxies, ranks as one of the primary
motivations for dark matter. Note that the mass discrepancy is large at all radii in the LSB galaxy.
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