- For each galaxy, calculate the total mass of the galaxy (measured out
to the last datapoint). A useful number is the gravitational constant, G.
If you measure distances in parsecs, masses in solar masses, and velocities
in kilometers per second, G = 4.43 × 10-3.
- Now try and fit a "maximum disk" model to each galaxy. Do this by
raising the disk mass-to-light ratio as far as you can (remember: your
curve should fit as close to the data points as possible, but never above).
You'll find NONE of the galaxies can be fit by a disk rotation curve alone.
Now change the halo parameters until you get a good fit.
- what are the parameters of your best "maximum disk" models for each galaxy?
- how unique are your solutions? ie, can you find other solutions
which fit equally well in each case?
- using the luminosities of the galaxies given below, calculate the
disk mass for each system. Then from your answer to (1) above,
figure out how much dark matter there is in each system. Also
calculate the ratio of dark-to-luminous mass.
| Galaxy || Luminosity (in Lsun)|
|NGC 2403 || 2.45 × 109|
|UGC 128 || 1.95 × 109|
|M33 || 1.75 × 109|
|F563-1 || 1.35 × 109|
- One outside constraint can be applied to the problem. For "normal"
stellar populations, it's hard to imagine a mass-to-light ratio for
a spiral galaxy which is much higher than about 2. Redo your fits in
problem (2), this time not allowing the disk mass-to-light ratio to be
larger than 2.
- what are the parameters of your best fit models?
- how much dark matter is in each system, and what are
the dark-to-luminous mass ratios for each galaxy?
- Two of the galaxies are "low surface brightness" (LSB) galaxies: UGC 128
and F563-1. The other two -- M33 and NGC 2403 -- are normal spiral
galaxies. How do your derived properties differ between the LSBs and
the normal spirals?