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\centerline{\medbf Astronomy 124, Winter 1992, Final Exam}
\bigskip
\centerline{\lilbf Due by midnight, March 18}
\bigskip
\bigskip

\noindent{\bf The boundary conditions:}~~ You can use your notes, but not any
books or review papers.  You can look up basic numerical values or physical
constants, but try to make your own estimates of the various astronomical
quantities where necessary.  There is no time limit, and you don't have to do
the exam in a single sitting.  Plan on about 1 hour and 2 pages for the problem
\#1, and up to half an hour and 1 page for the remaining problems (this is just
my guess, do as you see fit).  Please write clearly or type. 

\bigskip

\bigskip
{\bf 1.}~ 
What is the Eggen, Lynden-Bell, \& Sandage picture of the formation of our
Galaxy, and what are the more modern developments?  Do a quick estimate of the
potential energy of our Galaxy, and its mass (separately for the disk, bulge,
and the whole).  You can assume a flat rotation curve, and a cutoff at about 30
-- 50 kpc.  Then do the equivalent estimate for an average elliptical galaxy. 
Estimate the free-fall times.  If the binding energy is released during a
single free-fall time, what luminosity would that give to a protogalaxy?  What
if it happens on a 1 Gyr time scale? If a half of all baryonic mass is burned
in stars in these time intervals, how does the resulting nuclear-burning
luminosity compares with the release of the binding energy?  Can you guess the
wavelength region(s) in which the energy will be predominantly released (give
reasons)? 

\bigskip
{\bf 2.}~ 
Compare the kinetic energies of stars in a disk galaxy which correspond to the
random and ordered (rotation) motions; compare that with the ratio of disk
scale heights and scale lengths. What can you say about the importance of
mergers for galaxy disks? 

\bigskip
{\bf 3.}~ 
Define briefly the following time scales for a stellar system, and give
estimates for an open cluster, a globular cluster, and an elliptical galaxy: 
(a) crossing time; (b) relaxation time; (c) evolutionary time scale.  Which
dynamical processes are important for the evolution of the Galactic disk, open
clusters, globular clusters?  Give quantitative estimates of the relevant
physical quantities. 

\bigskip
{\bf 4.}~ 
Describe the physical reasoning behind the King models, including the relevant
time scales and approximations, and briefly outline the procedure for their
computation.  Are the multi-mass King models in a: thermal equilibrium? 
hydrostatic equilibrium?  both?  neither?  How can King models be generalized
to account for integrals other than the energy? 

\bigskip
{\bf 5.}~ 
What is the core collapse, and why and when does it happen?  How can it be
arrested and reversed?  What are the binary formation mechanisms? Mention at
least two relevant astrophysical situations in which core collapse plays an
important role. 

\bigskip
{\bf 6.}~ 
Define the following: (a) Integrals of motion; (b) Jeans' theorem; (c)
Boltzmann eq.; (d) Liouville's eq.; (e) Vlasov eq.; (f) Fokker-Planck eq. 

%\vfill
\eject 
\end
