1. Modelling the Ultra-Faint Dwarf Galaxies and Tidal Streams of the Milky Way M. Fellhauer Universidad de Concepcion in collaboration with N.W. Evans 1, V. Belokurov 1, D.B. Zucker 1, M.I. Wilkinson 2, G. Gilmore 1, M. Irwin 1 1 Institute of Astronomy; 2 Univ. Leicester

2. Ladies and gentleman SDSS Proudly presents: The ‘Field of Streams’

3. The SDSS survey 60 million stars are catalogued in SDSS in 5 colours

4. All stars of the Milky Way in SDSS: And then we apply a simple colour-cut And are left with only the halo stars…

5. “Field of Streams” Belokurov et al. 2006

6. A gallery of SDSS dwarfs D = 220 kpc r h = 550 pc M V = -7.9 D = 60 kpc r h = 220 pc M V = -5.8 D = 150 kpc r h = 140 pc M V = -4.8 D = 44 kpc r h = 70 pc M V = -3.7 CVn IBooCVn IICom

7. Some Implications Numbers: 10 new MW dwarfs (including UMa I, Leo V & Boo II) have been found to date, in SDSS data covering ~20% of the sky  tens more likely remain undiscovered Properties: Ultra-low luminosities (-3.8 ≥ M V ≥ -7.9) and surface brightnesses (µ V < 27 mag arcsec -2 ), odd morphologies  are these truly dwarf galaxies or fuzzy star clusters? Are these a distinct class of object? Hobbit Galaxies?

8. M V vs. Log(r h ) Mind the Gap?

9. But there is even more:

10. Leo T: A New Type of Dwarf? M V ~ -7.1, µ V ~ 26.9 mag arcsec -2 (m - M) 0 ~ 23.1, ~420 kpc Recent < 1 Gyr star formation - -blue loop/MS stars SDSS data INT Data Irwin et al. 2007

11. The Smallest Star-Forming Galaxy? Not dead yet: stars formed within past few x 10 8 yr HIPASS: Coincident H I RV  ~ 35 km/s if @ 450 kpc, ~ 2  10 5 M  in H I (M H I /M  ~ 1, cf. Local Group dIrrs) Is Leo T the tip of a Local Group “free floating” iceberg? HIPASS HI  3°  INT g,r Ryan-Weber et al. 2007

12. But now to some modelling…

13. Ursa Major II and the Orphan Stream

15. Complex A UMa II Gal. latitude   Ursa Major II Gal. longitude Orphan Stream M V = -3.8 ± 0.6 mag (approx. 6000 M sun )  ~6.7 km/s Mass estimate: 8 x 10 4 M sun Zucker et al. 2006 Belokurov et al. 2007 Muñoz et al. 2007 Martin et al. 2007 Simon & Geha 2007

16. Finding an orbit which connects UMa II with the Orphan Stream

17. Galactic Model: analytic potential for the MW Logarithmic Halo: –v 0 = 186 km/s –R g = 12 kpc –q  = 1 Miamoto-Nagai Disc: –M d = 10 11 M sun –b = 6.5 kpc, c = 0.26 kpc Hernquist Bulge: –M b = 3.4x10 10 M sun –a = 0.7 kpc Insert UMa II as a point mass and look for matching orbits

18. Possible Orbit: connecting UMa II & Orphan Stream UMa II: –RA: 132.8 deg. –DEC: +63.1 deg. –D sun : 30 ± 5 kpc Prediction for this orbit: –v helio : -100 km/s –   : -0.33 mas/yr –   : -0.51 mas/yr

19. Observational Data (to date) UMa II: –v helio = -115 ± 5 km/s (agrees well enough with our prediction) –  los = 7.4 +4.5 -2.8 km/s Orphan Stream: –Position known over 40 deg. –Distances between 20 (low DEC) and 32 kpc (high DEC) –v helio = -35 km/s (low DEC); +105 km/s (high DEC) Martin et al. 2007 Belokurov et al. 2007

20. Constraining the progenitor of UMa II and the Orphan Stream Initial model for UMa II: use simple Plummer spheres to constrain parameter space in initial mass & scale- length

21. Constraining the Progenitor: I. Length of the Tails Tails as function of progenitor mass and simulation time Progenitor must be >10 5 M sun & <10 7 M sun Simulation time must be longer than 7.5 Gyr

22. Constraining the Progenitor: II. Morphology of UMa II Progenitors with more than 10 5 M sun must be almost destroyed to account for the patchy structure, the low mass of the remnant and the high velocity dispersion of UMa II Progenitors with more than 10 6 M sun do not get sufficiently disrupted to account for the substructure

23. Comparing 2 UMa II models: One component model Plummer sphere: –R pl = 80 pc –M pl = 4 x 10 5 M sun Two component model Hernquist sphere: –R h = 200 pc –M h = 5 x 10 5 M sun NFW halo: –R NFW = 200 pc –M NFW = 5 x 10 6 M sun inserted at the position of UMa II 10 Gyr ago

24. Orphan stream UMa II 1-comp. 2-comp. Comparison of the 2 models - Reproduction of Orphan Stream & UMa II

25. Comparing the appearance & the kinematics of the two models: One component (B) Before(A), while (B) & after dissolution [c] Two component (D) A B C D Patchy structure (B) vs. round, bound, sound & massive (D) Both models show high velocity dispersion Mean v rad is patchy with gradient (B) vs. constant within object (D) A: before dissolution  is low and v rad constant B: patchy structure, high , patchy v rad with gradient C: no density enhancement, low , gradient in v rad

26. Conclusions: It is possible that UMa II is the progenitor of the Orphan Stream If UMa II is a massive star cluster or a dark matter dominated dwarf galaxy ? Decide for yourself… or wait for better data. But then we have some predictions:

27. If better data will be available: Predictions from our models: –At the Orphan Stream: if the progenitor was more massive than 10 6 M solar than we should see the wrap around of the leading arm at the same position but at different distances & velocities –At UMa II: if the satellite is DM dominated the contours should become smoother; if UMa II is the progenitor of the Orphan Stream the satellite is not well embedded in its DM halo anymore (otherwise there would be no tidal tails) –A disrupting star cluster will show a patchy structure in the mean line-of-sight velocities with a gradient through the object; a DM dominated bound satellite will have a constant v rad within the object Latest News: Simon & Geha (2007): Seem to confirm gradient in radial velocity

28. New unpublished data searching for tidal tails around UMa II show no sign of tidal tails - Solution: a) Connection between UMa II and the Orphan Stream does not exist b) Tails are still to faint to detect

29. Bootes

30. The Boötes Dwarf Galaxy

31.  = 14 h 00 m 06 s,  = +14 o 30’ 00” m-M = 18.9 mag  D sun = 62 ± 3 kpc M V = -5.8 mag (M/L=2)  M ≈ 37,000 M sun  0 = 28 mag/arcsec 2 R pl = 13’ (230 pc) v rad,sun =+95.6 ± 3.4km/s   6.6 ± 2.3km/s [Fe/H] = -2.5 v rad,sun =+99.9 ± 2.1km/s   6.5 ± 2.0 km/s [Fe/H] = -2.1 Boötes: Observational Facts Belokurov et al. 2006 Munoz et al. 2006 Martin et al. 2007

33. The Contours or what is real ? Is there an S-shape in the contours, i.e. is Boo tidally disturbed ?

34. Some simple maths… r tidal = 250 pc (0.2 o ) D GC = 60 kpc M MW (D GC ) = 6 x 10 11 M sun  M sat = 70,000 M sun  agrees with luminous matter R pl = 200 pc   los,0 = 0.5 km/s ???  los,0 = 7 km/s, M sat = 70,000 M sun  R pl = 20 pc  Boo too bright in the centre (20 mag/arcsec 2 ) NO BUT:  los,0 = 7 km/s, R pl = 200 pc  M sat = 1.5 x 10 7 M sun  Boo heavily dark matter dominated, r tidal = 1.2 kpc (1 o ) or Boo is elongated along the line of sight ???

35. Finding an Orbit We assume the orbital path from the on-set of the possible tails:   R peri R apo e (1)-0.53-0.621.866.20.95 (2)-0.54-0.704.766.20.87 (3)-0.58-0.9014.867.20.64 (4)-0.63-1.2036.976.60.35 (5)-0.66-1.4048.8104.30.36

36. Model A (TDG) M/L = 17 (unbound stars) Assuming a non-extreme orbit (e=0.35, R peri =37kpc, R apo =77kpc) Plummer Sphere: R pl = 202 pc ; R cut = 500 pc M = 8.0 x 10 5 M sun

37. Model B (mass follows light) M/L = 620 (DM dominated) (keeping the same orbit) Plummer Sphere: R pl = 200 pc ; R cut = 2000 pc M = 1.6 x 10 7 M sun

38. Model C (small DM halo) M/L 0 = 550 ( =1800) Stars: Hernquist Sphere R sc = 300 pc ; R cut = 300 pc M = 3.0 x 10 4 M sun DM: NFW-Profile R sc = 300 pc ; R cut = 1200 pc M = 4.5 x 10 7 M sun

39. Model D(extended DM halo) M/L 0 =800 ( =3400) Stars: Hernquist Sphere R sc = 250 pc ; R cut = 500 pc M = 4.0 x 10 4 M sun DM: NFW-Profile R sc = 1000 pc ; R cut = 2500 pc M = 3.0 x 10 8 M sun

40. Model E (radial orbit e=0.87 (2)) M/L = 1400 Stars: Hernquist Sphere R sc = 250 pc ; R cut = 400 pc M = 5.0 x 10 4 M sun DM: NFW-Profile R sc = 250 pc ; R cut = 1000 pc M = 1.25 x 10 8 M sun

41. We also run models on orbit (3) which is similar to orbits of sub-haloes in cosmological simulations: Initial models have to be more massive to get a similar remnant Final models have a higher central M/L-ratio and a lower average M/L- ratio

42. Conclusions Tidally disrupted models could be ruled out by means of numerical simulations and later by improved contours. The S-shape of Boo (tidal distortion) might not be real or is due to rotation. The velocity dispersion is now robust, so Boo is an intrinsically flattened system which is heavily DM dominated. OR: Low-number sampling of stars mimics elongation and fuzzy structure.

43. or (?)

44. Model A projected along the tails:  gauss = 0.8 km/s (red)  all distances = 5.7 km/s (black)  d<500pc = 5.0 km/s (green)

45. Some advertisement:

46. Formation of Dwarf Galaxies: (PhD project of P. Assmann (Concepcion)) Consider star formation in a DM halo Stars form in star clusters, which suffer from gas-expulsion Star clusters inside the DM halo merge and form a dwarf galaxy Aim: Constrain the parameter space of successful progenitors (halo shapes, SFEs, profile of star cluster distribution) Look for fossil records of the formation in velocity space

48. The Sagittarius Tidal Stream

49. Some words about Tidal Tails…

50. How does the ‘Field of Streams’ connect with the tidal tails of the Sagittarius dwarf galaxy ?

51. The Bifurcation (overlap of at least two branches of the tails) Upper Stream (B) Lower Stream (A) Stream (A) and (B) have almost the same distance Stream (C) is located behind stream (A)

52. “Houston - we have a Problem”: How can the two streams be so close in position and distance –Is there no peri-centre shift ? –Is there almost no shift of the plane of the orbit ? –Is it caused by two objects orbiting each other ? No, see LMC & SMC –Did Sagittarius collide with another object ? Maybe, but that’s not causing a bifurcated stream

53. Model for Sagittarius: Plummer sphere with 1M particles –R pl = 0.35 - 0.5 kpc ; R cut = 1.75 - 3.0 kpc –M pl = 10 8 - 10 9 M sun Position today –  = 18 h 55 m.1 ;  = -30 o 29’ –D sun = 25 kpc ; v rad = 137 km/s Proper motions –HST, Schmidt plates, Law et al. fit & variations Orbit followed from -10 Gyr until today

54. Galactic Models: 1. - ML Logarithmic Halo: –V 0 =186 km/s –R g =12 kpc Miamoto-Nagai Disc: –M d =10 11 M sun –b=6.5 kpc, c=0.26 kpc Hernquist Bulge: –M b =3.4x10 10 M sun –a=0.7 kpc

55. Galactic Models: 2. - DB Dehnen & Binney model (1998) 3 discs (ISM, thin, thick) double exponential 2 spheroids (bulge, halo) power law

56. ‘young’ leading arm ‘old’ trailing arm ‘old’ leading arm ‘’young’ trailing arm

57. Distances:

58. Sequence of increasing initial mass of Sagittarius Strength of the Bifurcation decreases with increasing mass M Sgr > 7.5 x 10 8 M sun  No Bifurcation visible

59. Increasing the mass matches the measured distances better

60. So is this just a YASS (yet another Sagittarius simulation) or can we actually learn something from it ?

61. What’s your result ? You should have spotted 7 simulations which show a bifurcation and maybe a few very weak ones. All simulations with bifurcation have 0.95 ≤ q ≤ 1.05

62. q=0.9 q=0.95 q=1.05 q=1.0 q=1.11 Miamoto-Nagai + logarith. halo - Dehnen-Binney model

63. Conclusions Bifurcation only appears in spherical or almost spherical halos Q   kpc  ≈ 0.95 - 0.97 Higher masses blur out the bifurcation but decrease the distance error M Sgr ≤ 7.5x10 8 M sun HST proper motion does not reproduce the bifurcation in any Galactic model Bifurcation only appears in spherical or almost spherical halos Q   kpc  ≈ 0.95 - 0.97 Higher masses blur out the bifurcation but decrease the distance error M Sgr ≤ 7.5x10 8 M sun HST proper motion does not reproduce the bifurcation in any Galactic model