# Lab Exercises

1. 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.

2. 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.

 Luminosities Galaxy Luminosity (in Lsun) NGC 2403 2.45 × 109 UGC 128 1.95 × 109 M33 1.75 × 109 F563-1 1.35 × 109

3. 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?

4. 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?