Course Outline for Gravitational Dynamics Astro 381c (Unique 49090)/Prof. Shardha Jogee Class website = http://www.as.utexas.edu/~sj/a381c-sp10/ Below is an outline of the course. I will follow this outline, but there may be small changes, and the online version on the class website will be updated. See the class website for details of the textbook, grading scheme, assignments, etc. ==== (I) Overview of the Course -- READING: Ch 1 is partly relevant -- Overview of Stages of evolution of a stellar system === (II) Important Timescales -- Different types of stellar encounters: contact collisions, strong encounters, cumulative effects of weak interactions -- Important Timescales: t_coll, t_relax, t_cross, t_ff -- Astrophysical Applications ==== (III) Newtonian Dynamics and Potential Theory -- READING: Ch 2 -- For Arbitrary density distribution Expressions for Potential Phi, Gravitational force F, circular speed Vc, Escape speed Ve, and total Potential energy W -- For Spherically symmetric systems Expressions for Potential Phi, Gravitational force F, circular speed Vc, Escape speed Ve, and total Potential energy W -- NFW profile for virialized DM halos -- For Axisymmetric Potential Phi(R,z) for flattened systems -- Astrophysical Applications - Estimating lower limit on size of DM halo; - Equation for dynamical heating of a thin locally isothermal disk; - Estimating M/L ratio for matter in the disk plane. ==== (IV) Stellar Orbits -- READING: Ch 3 -- Orbits for a spherically symmetric potential Phi(r) Closed ellipses and rosettes -- Orbits for axisymmetric potential Phi(R,z) Isolating Integrals of Motion, Surfaces of Section Quasi-planar loop orbits For Near-circular orbits close to z=0 plane: epicyclic approximation -- Orbits for 2D non-axisymmetric potential Phi(R,phi) Isolating Integrals of Motion, Surfaces of Section Box and Loop orbits -- Orbits for 2D non-axisymmetric rotating potential Eq of motion in terms Coriolis force, Centrifugal force Jacobi Integral, Lagrange points ==== (V) Evolution of a Classical System Before Stellar Encounters Become Important -- READING: Ch 4 -- Boltzmann Equation & Collisionless Boltzmann Equation (CBE) -- Moment 0 of CBE = Continuity equation on n and v -- Moment 1 of CBE = Jean's equation (cf Euler's equation) -- 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 === (VI) Virial Theorem for any finite bound self-gravitating system -- Tensor Virial theorem -- Scalar Virial theorem -- Astrophysical Applications of Virial Theorem - 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 ==== (VII) Evolution of A Classical System Once Stellar Encounters Become Important -- READING: Ch 8 in Ed1, Ch 7 in Ed2 -- Boltzmann Equation revisited -- Fokker Planck Approximation (not for exam) -- Equipartition -- Tidal Evaporation -- Runaway Core Collapse how to stop it ==== (VIII) Dynamics and Stability of Disks -- READING: Ch 5+6 -- Bars - Equation of motion in 2D Non Axisymmetric Rotating Potential Jacobi Integral, Lagrange points - Orbital structure of bars: mainly x1 and x2 family of orbits - Dynamical resonances (IILR, OILR, Ultra Harmonic resonance, CR, OLR) and their relation to stellar orbits - Why does a bar end between UHR and CR? - Why does a bar drive gas inflow ?(shocks + gravitational torques) - Why does gas pile up near ILRS ? - Locating dynamical resonances with epicyclic approximation and angular frequency diagram for a weak bar - How to destroy a bar? - How to form bars? Swing Amplifier (just FYI, not for exam) -- Local and Global Stability of disks - Stability of a razor thin differentially rotating disk against local axisymmetric instabilities : The Safronov-Toomre Q parameter. - Application to the Solar Neighbourhood - Existence of a threshold density for SF in outer disks of spirals - Is onset of gravitational instabilities as characterized by Q relevant for SF in center of spirals? ===== (IX) Collisions and Encounters of Stellar Systems -- READING: Ch 7 in Ed1, Ch 8 in Ed2 1) Overview of galaxy-galaxy interactions - Which type of interactions lead to mergers? - What controls timescale of and structural damage inflicted in a merger? - 3 regimes for dealing with galaxy-galaxy interactions Dynamical friction, High Speed Encounters, Mergers 2) Dynamical friction -- Chandrasekhar formula -- Applications - Decay of globular cluster Orbits - Satellite sinking in halo (galaxy minor mergers) - Impact of t_DF on theoretically predicted merger rates - Fueling of gas into BH via dynamical friction 3) Galaxy Mergers - Major mergers - Minor mergers