Galaxy/Stellar Dynamics and the Evolution of Galaxies

1. Galaxy/Stellar Dynamicsand the Evolution of Galaxies Hans-Walter Rix Max Planck Institute for Astronomy Heidelberg Jerusalem, January 2004

2. Goals • Most Empirical: • What is the (total) mass distribution? • On what orbits do the constituent mass elements, or the tracer masses, move? • Going a bit deeper: • What are the mass components: stars, gas, dark matter, etc… • Is the mass budget accounted for by the known/identified mass constituents? • Are (most) systems in (approximate) steady state on a “dynamical timescale”. • Finally: • to which extent is the range of observed galaxy structures determined by • Stability? • Initial conditions? • What can be learned about the formation process of galaxies from their dynamical state? • Any slow (“secular”) internal re-shaping?

3. ..Goals.. • But, let’s not forget the practical question: • How do we use observable information to get these answers? • Observables: • Spatial distribution and kinematics of “tracer population(s)”, which may make up • all (in globular clusters?) • much(stars in elliptical galaxies?) or • little(ionized gas in spiral galaxies) • of the “dynamical” mass. • In external galaxies only 3 of the 6 phase-space dimensions, xproj,yproj,vLOS, are observable! • Note: since tdynamical ~ 108 yrs in galaxies, observations constitute an instantaneous snapshot. • …the Galactic Center is an exciting exception..

4. Gas vs. Stars or Collisionless vs. Collisional Matter How often do stars in a galaxy „collide“? • RSun 7x1010 cm; DSun-Cen  1019 cm! => collisions extremely unlikely! …and in galaxy centers? Mean surface brightness of the Sun is  = - 11mag/sqasec, which is distance independent. The central parts of other galaxies have ~ 12 mag/sqasec. Therefore, (1 - 10-9) of the projected area is empty. • Even near galaxy centers, the path ahead of stars is empty.

5. Dynamical time-scale(=typical orbital period) Milky Way: R~8kpc v~200km/s torb~240 Myrs  torb~tHubble/50 Stars in a galaxy feel the gravitational force of other stars. But of which ones? • consider homogeneous distribution of stars, and force exerted on one star by other stars seen in a direction d within a slice of [r,rx(1+e)] • => dF ~ GdM/r2 = Gρ xr(!)xdΩ • - gravity from the multitude of distant stars dominates!

6. What about (diffuse) interstellar gas? • continuous mass distribution • gas has the ability to lose (internal) energy through radiation. • Two basic regimes for gas in a potential well of ‚typical orbital velocity‘, v • • kT/m  v2  hydrostatic equilibrium • • kT/m << v2, as for atomic gas in galaxies • in the second case: • supersonic collisions  shocks  (mechanical) heating (radiative) cooling  energy loss • For a given (total) angular momentum, what‘s the minimum energy orbit? • A (set of) concentric (co-planar), circular orbits. • => cooling gas makes disks!

7. Overview • Disks in Galaxies: • self-gravity and stability • Modeling Spheroids • Techniques: • Jeans-Equation • Schwarzschild Modeling • Some applications • Overall M/L’s of Spheroids • Black Hole Masses • Extracting the orbit distributions • Outlook • Resolved populations, proper motions • Sub-structure

8. Are Galaxy Disks Dynamically Stable? Let’s start with familiar ground, the Jeans Instability(1909/1929) • De-stabilizing agent: gravity • Stabilizing agent: pressure / vel. dispersion Equating the time-scales:  Collapse will occur for L>LJ What changes when considering disks? Geometry: flat Differential rotation: new stabilizing agent

9. Non-rotating disks: • tgrav.collapse ~ tdisperse: Rotating Disk(say, vc=const) A circular patch of size Lrot in the co-rotating frame seems to be rotating at WxLrot. If it wants to shrink, it needs to conserve its angular momentum Wx(Lrot)2=const.  centrifugal acceleration Balancing increased centrifugal acceleration and increased self-gravity under shrinking the patch leads to a maximal unstable radius: So, in disks are stable for L<LJ and L>Lrot  if LJ=Lrot, everything is stable! This is the essence of the Toomre (1964) criterion. Proper math, for arbitrary rotation curves gives: Stability for k: epicycle frequency, comb. of W and dW/dr

10. How self-gravitating are disks? • Milky Way at the Solar radius has Q~1.5. OK. • Traditional “maximum disk fits • But: you can’t extract two 1-D functions vc(disk) and vc(halo) from one measured function vc(obs)  Need independent estimate of stellar mass

11. Measuring the Self-Gravity of Disks I: Stellar Evolution Physics and IMF prior II: Disks are flat (at least, flatter than the halo) III: Disks have spiral arms (halos do not) Great for relative M/L, poor absolute calibrations

12. Bell and de Jong 2001 Great for relative M/L, poor absolute calibrations  Use colors to get a (perhaps still un-normalized) “stellar mass image”

13. Exploiting Spiral Arms Spiral galaxies, in their “mass images” show spiral arms. These mass perturbations should induce non-circular motions in the gas  velocity wiggles Their amplitude depends on the fraction of the rotation velocity (=mass) that comes from the disk (not DM) Kranz, Slysz and Rix, 2001, 2002

14. Fraction of the rotation speed at 2 Rexp from disk? 20% 85% Spirals with vc>200km/s are nearly maximal?

15. Bar-formation • Disks are prone to bar formation, even if only partially self-gravitating! Athanassoula 2002

16. Disks Upshot • Massive disks appear to be nearly self-gravitating (where did all the DM go?) • Many (stellar) disks are observed to be marginally stable, according to Toomre • Disks are being re-shaped by instabilities, even without any mergers

17. Modeling Collisionless Matter: Approach I (see Appendix) Phase space: dx, dv We describe a many-particle system by its distribution functionf(x,v,t) = density of stars (particles) within a phase space element Starting point: Boltzmann Equation(= phase space continuity equation) It says: if I follow a particle on its gravitational path (=Lagrangian derivative) through phase space, it will always be there. A rather ugly partial differential equation! Note: we have substituted gravitational force for accelaration! To simplify it, one takesvelocity moments: i.e. n = 0,1, ... on both sides

18. Moments of the Boltzmann Equation mass conservation Oth Moment 1st Moment “Jeans Equation” The three terms can be interpreted as: momentum change pressure force grav. force r: mass density; v/u: indiv/mean particle velocity

19. Let‘s look for some familiar ground ... If has the simple isotropic form as for an „ideal gas“ and if the system is in steady state , then we get simple hydrostatic equilibrium Before getting serious about solving the „Jeans Equation“, let‘s play the integration trick one more time ...

20. Virial Theorem Consider for simplicity the one-dimensional analog of the Jeans Equation in steady state: After integrating over velocities, let‘sintegrate over : [one needs to use Gauss’ theorem etc..]

21. Application of the Jeans Equation • Goal: • Avoid “picking”right virial radius. • Account for spatial variations • Get more information than “total mass” • Simplest case • spherical: static: Choose spherical coordinates: sris the radial andstthe tangential velocity dispersion for the „isotropic“ case!

22. Note: Isotropy is a mathematical assumption here, not justified by physics! Remember: is the mass density of particles under consideration (e.g. stars), while  just describes the gravitational potential acting on them. How are  and  related? Two options: 1. „self-consistent problem“ 2. with other = dark matter + gas + ... Black Hole

23. An Example:When Jeans Equation Modeling is Good EnoughWalcher et al 2003, 2004 The densest stellar systems sitting in very diffuse galaxies.. Spectra s (s(r)) Images r(r)

24. Mean Mass Density Nuclei in Late Type Galaxies G.C. Galaxies • Jeans Equation is great for estimating total masses for systems with limited kinematic data

25. from Rix et al 1997 “Orbit-based” ModelsSchwarzschild Models (1978) • What would the galaxy look like, if all stars were on the same orbit? • pick a potential F • Specify an orbit by its “isolating integrals of motion”, e.g. E, J or Jz • Integrate orbit to calculate the • time-averaged • projected properties of this orbit (NB: time average in the calculation is identified with ensemble average in the galaxy at on instant) • Sample “orbit space” and repeat

26. Figures courtesy Michele Capellari 2003

27. Observed galaxy image images of model orbits Vline-of-sight Projected density

28. Predict observables: spatial and velocity distribution for each individual orbit

29. Data s v h3 h4 Model Example of Schwarzschild ModelingM/L and MBH in M32Verolme et al 2001 Ground-based 2D data from SAURON Central kinematics from HST

30. Determine: inclination, MBH and M/L simultaneously NB: assumes axisymmetry

31. This type of modeling (+HST data) have proven necessary (and sufficient) to determine MBH dynamically in samples of nearby massive galaxies

32. MBH vs M*,Bulge seems just as good Haering and Rix 2003 See also Marconi and Hunt 2003

33. Stellar Kinematics and Clues to the Formation History of Galaxies Mergers scramble the dynamical structure of galaxies, but do not erase the memory of the progenitor structures completely. In equilibrium, phase space structure (E,J/Jz,+) is preserved. However, observations are in xproj,yproj,vLOS space! Connection not trivial!

34. Emsellem et al. 2003, MNRAS, submitted Let’s look at spheroids(data courtesy of the SAURON teamCo-PIs: de Zeeuw, Davies, Bacon)

35. SAURON versus OASIS(total body vs. center) • Cores often have different (de-coupled) kinematics! NGC 4382 McDermid et al. (2003) astro-ph/0311204

36. E S0 S0 S0 E S0 E S0 S0 S0 S0 E S0 S0 S0 S0 E S0 E S0 S0 S0 S0 E S0 E E S0 S0 S0 S0 S0 E E E E 40% classified by RC3 as ellipticals SAURON disk-like fast rotators

37. Let’s now look at the orbit structure Axisymmetric Galaxy meridional plane images of model orbits

38. Example 1: NGC4550 2D-binned data • Axisymmetric dynamical model fits up to h5-h6 • M/L very accurate Symmetrized data Axisymmetric model M/L = 3.4 ± 0.2 V  h3 h4 h5 h6

39. NGC 4550: orbital structure • Two counterrotating components • Double-peaked absorption lines (Rix et al. 1992, ApJ, 400, L5) • SAURON: accurate decomposition, in phase space • Both components are disks • Same mass • Different scale height

40. NGC 4473: data-model 2D-binned data Symmetrized data Axisymmetric model Are the V-shaped velocity and high major-axis dispersion produced by a counter rotating stellar component?

41. NGC 4473: orbital structure Main galaxy rotation Counter-rotating stars

42. `Metallicity' maps • Fit stellar population models to the data • Contours flatter than isophotes • `metallicity' enhanced in counter-rotating disks • The disks are coeval and old point symmetrized maps NGC 4550 NGC 4473

43. NGC 4660 V  h3 h4 NGC 4570

44. Kinematics and line strengths Seven E/S0 galaxies from the SAURON survey Velocity fields: stellar motions reveal disks and decoupled cores Maps of magnesium line strength: age and metal abundance of stars

45. Do such streams exist? • Stars with similar kinematics and chemical abundance • Assess their mass, orbits distribution • Is the whole spheroid a collection of streams?

46. Finding streams by selecting stars with a particulat color/luminosity(Odenkirchen et al 2001, from SDSS Data) Pal 5: Globular cluster in the process of disruption!

47. The disrupted Sagittarius dwarf Galaxy in the Milky Way (Ibata et al 1994, 2001) Project giant stars from 2MASS survey that are not near the disk plane onto great circles. Each great circle on the sky is defined by a pole

48. Tracing the recent accretion history in M31 Ibata et al 2001; Ferguson et al 2002 Star count map for stars on the blue (metal-poor) edge of M31’s giant branch Same, but for metal richer giants Direct evidence for different unbound (disrupted?) “bits” of diff. metallicity being incorporated in the stellar halo of the Milky Way.

49. Summary • Galaxy disks are re-shaped by (internal) instabilities; • Hot systems reflect their formation history • Schwarzschild modeling is the tool of choice to solve for • Gravitational potential • Orbital distribution • Kinematic (sub-)structure even of ellipticals reflect multiple (=? multi-epoch) formation events • Sub-structure in the Milky Way and M31 abounds