| You have a choice of three(!) projects: project A involving
numerical N-body simulation using fast Poisson solver and project
B
on dynamics of galactic gas disks (spiral density waves in ISM forced
and resonantly excited by bars and spiral density waves in stellar component,
2-D).
Within proj. A there is even a choice of 2 problems: A-3D and A-2D, using 3-D and 2-D codes to investigate two separate phenomena. In previous years, there was another problem suggested, now called C. It was never satisfactorily completed by anyone. If you like the challenge, you still could be the first one to master it. It involves theory and the solution of at most 1-D equations. Project formulations below are rather general. You yourself, after the study of BT and literature, are supposed to find out not just the answers to the questions I have posed but, more importantly, to formulate your own questions (and answers). The idea is to explore the subject from all possible angles, and to use a given numerical (or other) technique to the fullest extent possible, i.e. to describe the processes in physical terms as best you can, leaving no stones unturned. For instance, an N-body collapse calculation can be looked at not just to plot the positions of particles (which would be insufficient, even if your code computes beautiful collapses), but to study their distributtion in E and J space, allowing you to say something interesting and quantitative about relaxation mechanisms, etc. |
Formulate the equations of motion in a non-dimensional form and
explain the units of mass, length and time (give specific examples). Demonstrate
the performance and accuracy of the code in a simple case of your choice
(e.g., 2-body problem, or restricted 3-body problem). Find out the numerical
limits on resolution and particle number you can achieve.
Use your code to study the dynamical evolution of a stellar system collapsing from the initial state of a uniform density sphere with and without initial: (i) velocity dispersion; (ii) clumpiness (cf. BT), (iii) slight overall rotation.
Which of the relaxation mechanisms: violent relaxation, phase mixing, or 2-body relaxation is mainly responsible for the fast intial restructuring of the object? (Give quantitative evidence.)
How does the collapsed object look depending on (e.g., does it resemble de Vaucouleur's law?) What is its DF (distribution function)? How many free-fall times did you have to wait for a stationary solution? Is it truly stationary or not (estimate the relaxation time(s) in your simulation)? Compare your results with literature on the subject, found via the ADS database.
Use your code to study the dynamical evolution of two interacting and
possibly merging stellar systems:
1. a Milky Way-type, large disk galaxy with an exponential stellar
disk and isothermal spherical halo (rigid; i.e. use analytical formula
for its potential/forces)
2. a small spherical object (dwarf galaxy, or giant intergalactic globular
cluster) whose potential is that of a Plummer sphere. This object can be
treated as a unit.
Assign a realistic rotation curve and velocity disparsion to your disk galaxy. (You can use NGC666 for that purpose.)
Configure your host galaxy's velocity dispersion such that Toomre stability parameter is Q=2..3 throughout (experiment a little). Make sure your unperturbed host galaxy is stable agains bar-forming or rapid spiral SWING instability. (Can you find empirically the minimum Q for stability? How does the numerical potential softening affect Q?)
Start the satellite system on a circular orbit in the outer part of the host galaxy.
Plot the semi-major axis and eccentricity evolution of your object, depending on its mass. (Use at least 3 different mass ratios between 1:100 and 1:10.)
Find and read BT and at least 1 relevant paper in the literature (consult
with me your choice) on the dynamical friction in disk galaxies, a topic
known also as the sinking satellites. Compare their results with yours
and interpret the differences if any.
"B" here means "B patient" (I'll describe it "soon").
Your objective is to understand the procedure and reproduce the main results of Young's paper: radial distributions of the stellar density and velocity dispersion inside and outside the initial King core radius, in a series of models with different BH masses. Express all masses according to BT's, not Young's definition of core mass.
Chose parameters to represent a real galactic nucleus with a BH and a cusp (from a review by Kormendy and Richstone 1995, ARA&A or other) and calculate the stellar density profile in dimensional units. Estimate the relaxation time and the collisional frequency (for actual physical collisions) between the average stars in the cusp. Is it large or small compared with the BH growth time scale of (more than 10 Myr but less than several Gyr)? What changes would you expect to happen on these two (relaxation and collisional) time scales?
The subsequent investigation will deal with an accretion disk through which gas flows onto the black hole. It is open-ended, i.e. you can do as little or as much about as you manage. Suggested course of action includes: