Astr327 HW #4

due Friday April 7, 5pm

1. Globular Cluster Dynamics, Dammit!

(Re)do Problem #3 from HW #3.

2. Stability of Disk Galaxies

(with your partner) Go to the rotation curve fitting applet. It currently has rotation curve data for the following 4 galaxies:

Galaxy	Central SurfB	Exp scale length
	Lsun/pc**3	kpc
M33	140	2.0
NGC2403	175	2.1
F563-1	23	4.3
UGC128	13	6.8

By fitting the data, you will get

the disk mass-to-light ratio,
the central density of the halo (rhoh0), and
the scale radius of the halo (haloa)

Assume one astrophysical constraint: the M/L of the disk can't be greater than 2. This is about as large as one could reasonably expect from stellar populations. Anything else must be dark matter.

show me these parameters no later than Wednesday April 5!

The Halo model is that of an isothermal sphere, with Vc=4*PI*G*haloa*haloa*rhoh0*(1-(haloa/r)*arctan(r/haloa))

The disk model is an exponential disk (i.e., Bessel functions). Use your model fits for these four galaxies to calculate the stability parameters Q and X as a function of position in the disk. You'll need to assume something for velocity dispersions, so assume Milky Way parameters hold (ie at 50 Msun/pc**2 the velocity dispersion is about 30 km/s), and that vdisp scales as sqrt(surfd).

Describe and compare the stability parameters for the different galaxies.
Now look at a picture of them, and describe how their morphology relates to the stability parameters you calculate.

(where do you get a picture? either try looking at the Digital Sky Survey or the NASA Extragalactic Database. The former will show you a picture, the latter will show you pictures and also give you scads of other data you may find useful...).

3. The Decay of the LMC's Orbit

(with your partner) Use the Chandrasekhar formula to model the decay of the Large Magellenic Cloud's orbit. That is, set up a test-body integration of the Magellenic Cloud in the halo of the Milky Way (like you for part 1 of HW #2). Then add the dynamical friction term to the acceleration. This term should depend on position in the galaxy and the velocity of the LMC, so it will change throughout the orbit. Use a Miyamoto-Nagai potential for the disk (see BT p44), and a Hernquist model for the halo.

Things to think about:

What are good parameters for the Miyamoto-Nagai and Hernquist potentials?
What are good initial conditions for the mass of the LMC and the LMC's orbit? (you may be interested in reading Lin etal, ApJ, 439, 652 (1995)).

show me these parameters no later than Wednesday April 5!

Then, I want

X-Y and X-Z plots of the orbit,
a plot of r(t), showing how quickly the orbit decays,
a discussion of how reliable your result is, where your error sources are, and what you would do (and why) to improve your estimate.

Finally, rerun your simulation with the disk "turned off" (ie set the disk mass to zero). How and why does that affect your answer?

4. Project Design

tell me (in some detail) what simulations you will be doing for your project, and what parameters you will be varying. How will these simulations address the "big picture" result you are interested in?