Due: Feb 24
1. More dynamical timescale stuff
2. Numerically show that for a galaxy with an exponential mass density profile:
where a = scale length, that the maximum circular velocity is reached at 2.2 scale lengths.
3. The functional form of the velocity curve that can be generated by dark matter halos of the form which produces flat rotation curves (question 5 in the second homework assignment can be found in
Kent, 1986 Astronomical Journal 91 1301
Kent, 1987 Astronomical Journal 93 816
Below are links to some real data that you now get to fit with your own mass models. For each galaxy there is a luminosity distribution and a rotation curve. For the luminosity distribution the radius coordinate is in units or arcseconds while the intensity coordinate is in units of magnitudes per square arcsecond. In astronomy a mangitude is defined as
where I = intensity.
The rotation curve data represents is such that columns 2-4 contain the radius, the circular velocity at that radius and the error in the circular velocity
For the six galaxies whose data can be retrieved below, try to make a mass model using two components (the luminous component and the dark component) that approximately reproduces the observed rotation curve. Only do this for two of the six galaxies!
There are many ways to approach this problem. The empirical way may be the best. That is, use the luminosity profile to determine the mass distribution by either assigning a constant M/L or a M/L which varies with radius. In this way the luminosity profile can be turned into a mass profile from which the circular velocity at that radius can be computed. Any observed excess in circular velocity is due to a dark matter halo.
This exercise is not easy as these rotation curves have a variety of bumps and wiggles in them. Just do the best you can.