1. Alice Quillen University of Rochester in collaboration with Ivan Minchev Observatoire de Strassbourg Aug, 2009

2. Motivation Hercules stream Sirius group Pleiades group Hyades stream Coma Berenices group The Milky Way has only rotated about 40 times (at the Sun’s Galacto-centric radius).  Little time for relaxation! Diffusive approximations are inappropriate for large and precise data sets Stellar velocity distribution Dehnen 98 Radial velocity Tangential velocity Structure in the motions of the stars can reveal clues about the evolution and formation of the disk.

3. Non equilibrium processes Resonances in the uv plane and Precision Galactic measurements –Libration timescales are likely to be long so evolution may be near or in non-adiabatic limit –Resonances are often narrow, so when identified they give a strong constraint on pattern speed Resonant trapping and heating –Constraints on evolution and growth of patterns Phase wrapping –Giving clues to ages since disturbances Perturbations to the disk caused by mergers –Can we tell the difference between merger remnants and perturbations to the existing populations?

4. Interpreting the U,V plane In terms of resonances Coma Berenices group Orbit described by a guiding radius and an epicyclic amplitude On the (u,v) plane the epicyclic amplitude is set by a 2 ~u 2 /2+v 2 The guiding or mean radius is set by v Gap due to 2:1 resonance with bar (e.g., Dehnen 2000) Hercules stream

5. Near the 4:1 Lindblad resonance. Orbits excited by resonances can cross into the solar neighborhood (Quillen & Minchev 2005) UU vv Each region on the u,v plane corresponds to a different family of closed/periodic orbits

6. Hamiltonian including a perturbation This is time independent, and is conserved.

7. First order Lindblad Resonances with bar or spiral Increasing radius Closed orbits correspond to fixed points BAR Outside OLR only one type of closed orbit. Inside OLR two types of closed orbits Growing bar Φ angle R=2I 1 Radius related to eccentricity

8. Precision Measurements of the Galactic Bar Both pattern speed and angle can be constrained using both streams and simulated Oort function measurements. C functions in hot and cold populations can only be matched for bar pattern speed +- a few % Bar angle  Oort C (Minchev et al. 2007) Why does the hot population have a higher C? Model hot: dotted Model cold: solid

9. Bar and Spiral arm Growth Near resonance there are no circular orbits --- accounts for deficits of particles in certain regions in uv plane Bar/spiral arm growth  resonance capture Depending on whether pattern slows down or speeds up –causes resonance capture, eccentricity related to pattern speed change –causes a jump in eccentricity as particles must jump across the resonance. Jump depends on bar/spiral strength.

10. Transient structure during and after bar growth Diversity in morphology in barred galaxies may be explained by recent bar growth (Bagley et al. 09) Explanations for some low velocity streams; Minchev et al. in preparation During bar growth Long lived R1,R2 rings following bar growth as long as pattern speed and strength does not vary

11. Bar Evolution bar sped up R1 destroyed bar slowed down resonant capture into R2 bar slows down during growth effect on initially cold test particle population

12. Heating mechanisms Transient spiral arms --- also leads to migration (DeSimone et al. 2004; Sellwood & Binney 2002) Resonant and chaotic (e.g., multiple patterns; Quillen 2003; Minchev & Quillen 2006; Chakrabarty 2007) Merger induced (e.g., Villalobos & Helmi 2009) All three leave signatures in phase space

13. An example of chaotic heating later times  starting with stars in a circle If integrable then eventually they would remain in a thin but twisted loop rather than a smooth distribution heating larger near a separatrix of one resonance and when there is a second perturbation Minchev & Quillen 2006

14. Analogy to the forced pendulum Controls center of first resonance and depends on radius Controls spacing between resonances and also depends on radius Strength of first perturbation Strength of second perturbation A model for chaotic resonant heating

15. Spiral structure at the BAR’s Outer Lindblad Resonance Oscillating primarily with spiral structure Perpendicular to spiral structure Oscillating primarily with the bar Perpendicular to the bar Poincare map used to look at stability. Plot every Orbits are either oscillating with both perturbations or are chaotic  heating (Quillen 2003)

16. Vertical resonances with a bar Banana shaped periodic orbits OR 1:1 anomalous orbits Increasing radius Orbits in the plane

17. As the bar grows stars are lifted Resonance trapping Growing bar Extent stars are lifted depends on the radius. An explanation for sharp edge to the peanut in boxy- peanut bulges.

18. Phase wrapping in the disk v u Semi-analytical model constructed by weighting with radial angle time following uneven distribution in epicylic oscillation angle, the thick disk can exhibit streams(Minchev et al. 2009)

19. Is the Milky Way Ringing? Proposed model for High Eccentricity Disk Streams Alternative model to merger remnants for high velocity streams in the disk

20. Mock Pencil Beam Surveys “getting out of the solar neighborhood’’ mean radial velocity velocity dispersion mass surface density galactic longitude distance from Sun Ω s =0.6Ω 0 Ω s =0.9Ω 0 4 arm steady spiral pattern Mean subtracted (Minchev & Quillen 2008)

21. Disk perturbed by a low mass satellite passing through the disk u v streams induced over short timescales as well as heating (Quillen et al. 2009)

22. Migration and mixing in the outer disk caused by multiple perturbations from a low mass satellite galaxy After 1 passageAfter 3 passages change in mean radius eccentricity Outer disk Mid disk Inner disk Quillen et al. 2009

23. Summary Rich dynamics! Dynamical structures and events leave signatures in velocity field Precise measurements will be made as observations becomes more comprehensive Time dependent models could be better explored Unveiling current and past structure and evolution of Milky Way will be very exciting