Kinematics of Dwarf Spheroidal Galaxies

1. Kinematics of Dwarf Spheroidal Galaxies Matthew Walker – U. Michigan Collaborators Mario Mateo – U. Michigan Edward Olszewski – U. Arizona, Steward Observatory Bodhisattva Sen – U. Michigan (Statistics) Xiao Wang - U. Michigan (Statistics) Michael Woodroofe – U. Michigan (Statistics) Rebecca Bernstein – U.C. Santa Cruz Oleg Gnedin – U. Michigan Data from Magellan/MMFS and MMT/Hectochelle The Globular Clusters - Dwarf Galaxies Connection Ann Arbor, Aug. 27, 2007

2. Introduction:Globular Clusters vs. dSphs • Globulars • Pressure supported • 105-6 L_sun • No gas • <v> ~ 10-20 km/s • Single age • Rhalf ~ 10 pc • dSphs • Pressure supported • 105-6 L_sun • No gas • <v> ~ 10-20 km/s • Extended Star formation • Rhalf ~ 100 pc DSS image of Fornax

3. Introduction: Dwarf Spheroidal Galaxies • Why study dSphs? • Smallest systems with dark matter • Dominated by dark matter (baryons negligible!) • Nearby • Dark Matter – want to know M(r) • M/L • Cusps or cores? • Halo mass function • Galaxy Evolution – want to understand complex stellar populations • Star formation histories • Metallicities/ages • Stellar kinematics • Galactic tides Diemand, Kuhlen and Madau (2007)

4. MMT + Hectochelle 240 fibers over 30 arcmin 5150 – 5300 A (R ~ 30000) +/- 1-2 km/s velocities for V~20.5 stars in 2 hours exposure time 600 spectra per night! Magellan + MMFS 256 fibers over 20 arcmin 5140-5180 A (R ~ 20000-25000) +/- 1-2 km/s velocities for V~20.5 stars in 2 hours exposure time 600 spectra per night! Observations & Data:Magellan/MMFS and MMT/Hectochelle

5. Observations & Data: Magellan & MMT Samples ~6800 stars, ~5000 members

6. Kinematics • 2 tests of Lambda-CDM • Inner Density profile: cusps vs. cores • DM halo mass function • Jeans Equation

7. Kinematics: Velocity Dispersion Profiles

8. Kinematics:Jeans Equation If β=0, If β=0 and constant velocity dispersion,

9. Kinematics:Mass from Jeans Estimator ASSUMPTIONS -Spherical symmetry -Dynamic equilibrium -Plummer Model for Stars -Anisotropy=0 -σV(R)=constant RESULTS Central cores, but necessarily so

10. Kinematics: NFW Profiles(Navarro, Frenk & White 1995, 1996, 1997) ASSUMPTIONS -Spherical symmetry -Dynamic equilibrium -Constant anisotropy RESULTS

11. Kinematics: Non-Parametric Mass Estimation(Wang et al. 2005) ASSUMPTIONS -Spherical symmetry -Dynamic equilibrium -Anisotropy=0 -shape restrictions -M(r) is non-negative and nondecreasing -M(r=0)=0 -ρ(r) is non-increasing

12. Kinematics: Non-Parametric Estimate, Quadratic vs. Cubic Spline P=2 (quadratic spline) P=3 (cubic spline) P=2 implies M(r) α r2 as r  0. Thus ρ(r) α r-1 (NFW cusp). P=3 implies M(r) α r3 as r  0. Thus ρ(r) =const. (core).

13. Kinematics: Robust Measure of M(~2rcore)see also Strigari et al. (2007); Penarrubia et al. (2007)

14. Kinematics: Robust Measure of M(~2r_core)

15. Kinematics:Summary of Mass Profiles • Mass-follows-light models fail. • Dark Matter dominates even the central mass density regardless of model. • Cores vs. cusps? Neither is ruled out by σV(r). • Isotropy, constant velocity dispersion, Plummer models  cores • But, cuspy NFW profiles fit the velocity data. • We don’t know the anisotropy. • Halo Mass Function? • M(600pc) = (2-5) x 107 M_sun regardless of model!

16. Chemo-dynamics

17. Chemo-dynamics:[Fe/H] Distributions and Gradients

18. Chemo-dynamics:Stellar Populations

19. Chemo-dynamics:spatially, chemically, kinematically distinct populations?(see also Tolstoy et al. 2004; Battaglia et al. 2006)

20. Chemo-dynamics:spatially, chemically, kinematically distinct populations?(see also Tolstoy et al. 2004; Battaglia et al. 2006)

21. Chemo-dynamics: “Tidal Stirring” as Evolutionary Mechanism • Distance-morphology relation • D= 0 -50 kpc  Sgr and streams • D= 50 -250 kpc  dSph • D> 250 kpc  dIrr • Tidal stirring (Mayer et al. 2001, 2005) • Remove gas • Convert rotation to pressure support • Tidal stripping mass lossbar instability decrease in v_rot/sigma  gas funneled toward center  star formation • Convert dIrr to dSph in 2-3 perigalactic passages (~5-10) Gyr • Implies dIrr are the pristine galactic building blocks

22. Summary • New spectra of ~ 8000 dSph targets, ~ 5000 members • Flat velocity dispersion profiles • Neither core/cusp ruled out • M(600pc) ~ 2-5 x107 M_sun • Metallicity gradients, metal-rich at center, metal-poor outward, correlated with kinematics

24. 4. Galactic Tides • Tidal disruption simulations: • Velocity Gradient Along Major Axis (Apparent rotation about minor axis) • Major axis aligned with proper motion vector • Rising velocity dispersion profile Read et al. (2006) Piatek & Pryor. (1995)

25. Galactic Tides:Kinematic Evidence of Tides? Rising Velocity Dispersion? Velocity Gradient? Magellan/MMT data

26. Galactic Tides: Apparent Rotation? Magellan/MMT data

27. Galactic Tides: Apparent Rotation? Magellan/MMT data

28. Galactic Tides: The Case of Leo I

29. Galactic Tides: The Case of Leo I

30. 5. Fun with Surfaces

31. Surfaces: Carina

32. Surfaces: Fornax

33. Surfaces: Sculptor

34. Surfaces: Sextans

35. 5. A Couple of Interesting Things

37. strigari07

38. penarrubia07

39. MoNDian scale length

40. Substructure Coleman et al. (2004; 2005)

41. Nonparametric Mass Estimation (Wang et al. 2005) • Assumptions • Spherical symmetry • Dynamical equilibrium • Velocity isotropy • Parametric model • Mass follows light • Jeans Equation where • Estimate f(r) and μ(r) separately • f(r)as a step function, recover from star count data • M(r) as a cubic spline subject to shape restrictions

42. Recovering f(r) from its Projection • Let • projected density gS(s) relates to 3-D density by • Let • We estimate GS directly from star counts: • Treat f as step function: for

43. Kormendy 1985 There is a size gap between globular clusters and dE gals, at similar Mv, and similar central velocity dispersion ``ellipticals/bulges, dwarf spheroidal galaxies and globular clusters are three very different kinds of stellar systems’’

44. Fundamental Plane Relations(from Zaritsky et al. 2006)

45. The Fundamental Manifold(from Zaritsky et al. 2006)

46. Jeans Equation (spherical symmetry) Solution: Projection:

47. Kinematics: Constant-Density Core(c.f. Strigari et al. 2006) ASSUMPTIONS -Spherical symmetry -Dynamic equilibrium -Constant Anisotropy RESULTS

49. Kinematics: Robust Measure of M(rcore) Penarrubia et al. 2007