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Physics 410/510 First Homework Assignment
Due: Feb 24

1. More dynamical timescale stuff

2. Numerically show that for a galaxy with an exponential mass density
profile:

* M(r)=M(o)exp*^{(-r/a)} * *
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

* M = -2.5 log (I) *
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.

get luminosity distributions for galaxy 1-3
get luminosity distributions for galaxy 4-6
get rotation curve for galaxy 1
get rotation curve for galaxy 2
get rotation curve for galaxy 3
get rotation curve for galaxy 4
get rotation curve for galaxy 5
get rotation curve for galaxy 6