GRAVITATIONAL DYNAMICS (AST 381C)
              	   http://www.as.utexas.edu/~sj/a381c-sp07/
	  	    Instructor: Prof. Shardha Jogeee
                  

	      MAIN TOPICS TO "TAKE HOME"  FROM THIS CLASS


======== Overview 1 : Important Timescales and Stages of evolution of a stellar system 


--  Stages of evolution of a stellar system: Assembly, virialization, collisionless 
    evolution under CBE; 2 body relaxation;  evolution under Boltzmann eq; equipartition, 
    mass segregation, runaway core collapse, binary formation....BH formation.

-- 3 types of stellar encounters/collisions 
   contact collisions, strong encounters, weak encounters

-- Timescales = dynamical, collision, crossing,  relaxation, dynamical friction
 
-- Table 1:  Dynamical stages of globular cluster cores, open clusters, galaxies 
-  Table 2:  Dynamical stages of groups, compact groups, clusters, superclusters



======== Basic Newtonian Dynamics    (Read Ch 2)

-- For arbitrary density distribution: expression for force, potential, GPE
   				     : Poisson's equation 

-- For Spherically symmetric systems : Newton's theorems, Circular speed, Escape Speed 

-- Observational constraints on mass density: 
   surface brightness profiles (Sersic, Exponential, Devaucouleurs)


-- Astrophysical Applications: 
- 4 useful potential-density pairs 
   Power law density profile 
   Logarithmic axisymmetric potential Phi(R,z) 
   Plummer Kuzmin axisymmetric potentials Phi(R,z) 
   Ferrer's potential for non-axisymmetric bar potential  Phi(R,phi,z)
- Deriving extent of Milky Way using escape speed

  
========  Virial Theorem

-- VT  for any finite bound self-gravitating systems.  
   Derivations can de done w/o CBE and applies even when CBE not valid.
   Read alternative derivation in Ch 4

-- Generalized tensor VT  (see HWK 4-9)
    d^2I_jk/dt^2 = W_jk + 2K_jk + surface term S1

-- Astrophysical Applications
- Binding energy of a galaxy & energy released during its assembly
- Negative heat capacity and its implications
    Nuclear reactions in core of a star 
    Runaway Core collapse in Globular Clusters (gravothermal  catastrophe)
- The v/sigma diagram for E 
- Scaling laws and Fundamental Plane Relations of E

STACY; ATHENA RANICE
Virial Shocks in the Early Universe


======== Evolution of A Classical System Before Stellar Encounters Become Important 
         (Read Ch 4)

-- Boltzmann Equation and  Collisionless Boltzmann Equation (CBE)

-- Moments of CBE : m0= continuity equation; m1= Jeans equation (cf Euler's eq of motion)

-- Astrophysical Applications
- Local Mass density and Implications for Dark Matter in Milky Way
- External Galaxies: Disk Heating Problem
- External Galaxies: Dark matter of Disk component vs DM in halo 

JEONG; DONGHUI
From Boltzmann equation to CMB anisotropy: primordial dance of baryon-photon fluid

DIMASTROGIOVANNI; E.
Classical and Relativistic Analysis of the evolution of density inhomogeneities

SHOJI; MASATOSHI
Linear perturbation analysis of the Large-Scale structure

MURPHY; JEREMY DAVID
Probing the Structure of Dark Matter Halos in Elliptical Galaxies




========  Evolution of A Classical System When Stellar Encounters Become Important 
          (Review class lectures 1-4 ; class lecture on Virial Theorem;Read Ch 8)

-- Boltzmann Equation revisited
-- Fokker Planck Approximation to solve Boltzmann Equation
-- Equipartition
-- Tidal Evaporation
-- Runaway Core Collapse  (see class lecture on application of Virial Theorem)

COUCH; SEAN MICHAEL
Numerical Applications of the Fokker Planck Approximation

BAYLESS; AMANDA JO
Formation and evolution of X-ray binaries.

BLUM; JOHN ROBERT H. JR.
Production and Orbital Decay of IMBH binaries in Globular Cluster Cores



========  Orbits and Disk Dynamics (Read Ch 3) 

(I)  Non-rotating potentials

--  Acceleration a = (a_R, a_Phi, a_z) =  - grad Phi(R, phi, z) 

-- Isolating Integrals of Motion, Surface of Section, and Nature of Orbits in 
    Spherical potential Phi (r) ;  Planar  closed or open rosette;  E, L
    Axisymmetric potential Phi(R,z) ; quasi-planar loop rosette; E, L_z and 3rd IIOM~L
    2-D non-axisymmetric potential Phi(R, phi); Loop and Box orbits 
    3-D triaxial potential Phi(R, phi, z)

(II) Rotating potential

-- Acceleration a =  - grad Phi(R, phi, z) + acceleration due to 3 fictitious forces
   where  3 fictitious forces = inertial force of rotation depending on d/dt(Omega_b)
                        + Coriolis  force   + Centrifugal forces

-- IIOM =  Jacobi's integral
-- Lagrange points L1 to L5;  L2 L2 L4 L5 define region of corotation 

-- Astrophysical Applications
- 2D slowly rotating non-axisymmetric potential :Periodic,Non Periodic, and Chaotic orbits 
- More applications under  "Dynamics and Stability of Disks"

======= Dynamics and Stability of Disks (Read Ch 5+6)

-- Bars,  Spirals and Warps in galactic disks (and in debris/proto-planetary disks)

- 2D slowly rotating non-axisymmetric potential 
   IIOM=Jacobi's integral; Lagrange points L1 L2 L4 L5 define CR
   Periodic,Non Periodic, and Chaotic orbits in SOS
   x_1 and x_2 family of periodic orbits
- Dynamical resonances (ILRs, UHR, CR, OLR) in strong and weak bars 
- The epicyclic approximation and angular frequency diagram for weak bars
- Why does a bar drive gas inflow ?(shocks + gravitational torques)
- Why does gas pile up near ILRS ?

-- Stability Analysis 
- Dispersion relations for differentially rotating, infinitely thin axisymmetric disk
- Instabilities in gas and stellar disks: the Safronov-Toomre Q parameter
- Condition for star formation in galactic disks
- Swing Amplifier

-- Fueling of starburst and Black holes 
-  The Angular momentum problem
-  Galaxy-Galaxy interactions: Minor mergers; Major mergers


GRAY; CANDACE LEAH
Gravitational dynamics of moons

MARINOVA; IRINA STOILOVA
Bar evolution and dissolution in present-day disk galaxies

WORHATCH; RANDI RENAE
Gas Dynamics in the Central Region of AGN

WEINZIRL; TIMOTHY MICHAEL
Loss Cone Feeding in AGN 

HWANG; SEHYUN
Toomre instability criterion applied to SF in galactic disks.


======== - Dynamics of Interacting systems

-- Dynamical Friction  
   Apply to satellite and GCs in halo, galaxy minor mergers, fueling of gas into BH
-- Galaxy-Galaxy interactions: Minor + Major mergers (See review 'Fueling starbursts and AGN')
-- Galaxy-Galaxy interactions: Tidal interactions, Harassment

BARENTINE; JOHN CALEB
Tidal disruption of accreted dwarf satellites and formation of globular clusters

HEIDERMAN; AMANDA LEA
How to mess up a galaxy : dynamical friction, harassment, ram pressure stripping

KIM; HYO JEONG
Dark matter in galaxies


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BLANC; GUILLERMO: Modified Newtonian Dynamics