Flat Rotation Curves

Most galaxies have rotation curves that show solid body rotation in the very center, following by a slowly rising or constant velocity rotation in the outer parts.

The rotation curve to the right was obtained using red camera the Double Spectrograph in the 5m Hale Telescope at the Palomar 0bservatory. Shown is the variation in the observed rotation velocity along the major axis. The radial velocities are derived from the doppler shifted H-alpha lines (rest wavelength 6563 Angstroms). Click here to see an example of how the rotation curve appears in the spectral image.

What does the fact that V(R) is nearly flat (or rises slowly) at large radius imply about the mass distribution?

Consider a star or gas cloud in circular orbit at radius R. The acceleration of gravity must be balanced by the centrifugal acceleration:

Therefore, a flat rotation curve implies that the mass increases linearly with the radius.

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