How spherical is the invisible cow?

1. Arizona TAP Colloquium October 2007 How spherical is the invisible cow? ? Jeremy Bailin (McMaster) Collaborators: Chris Power, Peder Norberg, Josh Simon, Dennis Zaritsky, Alberto Bolatto, Brad Gibson, Stéphane Herbert-Fort, Geraint Lewis, Tim Hendtlass

2. Consider A Cow Sphere is the first approximation we always make. But we can see that the cow is not really a sphere… …it’s an ellipsoid. “How Spherical Is The Invisible Cow?” Jeremy Bailin, Arizona TAP Colloquium, Oct 2007

3. Consider An Invisible Cow If we can’t see the cow, how can we figure out its shape? ? ? “How Spherical Is The Invisible Cow?” Jeremy Bailin, Arizona TAP Colloquium, Oct 2007

4. Galactic Dark Matter Halos • We believe galaxies inhabit halos of dark matter (DM) that doesn’t interact with (emit/absorb) light. • Evidence: Rotation Curves, Stellar Velocity Dispersions, Satellite Velocity Dispersions, X-ray Gas, Cosmological Structure Formation, Gravitational Lensing • We see the gravitational effects of DM on visible matter (stars, gas) but the DM itself is invisible. “How Spherical Is The Invisible Cow?” Jeremy Bailin, Arizona TAP Colloquium, Oct 2007

5. Galactic Dark Matter Halos • Other possibility: incorrect theory of gravity (eg. MOND) • Inferred dark matter halo may have different properties than those of halo truly made of dark matter “How Spherical Is The Invisible Cow?” Jeremy Bailin, Arizona TAP Colloquium, Oct 2007

6. Properties of Dark Matter Halos • To determine the predictions of dark matter theory, we must run expensive cosmological N-body simulations. • Method: • Begin with almost-smooth distribution of dark matter particles (with fluctuations from CMB) • At each timestep, move each particle in gravitational field of other particles, within expanding spacetime • See what happens after 13.7 Gyr! “How Spherical Is The Invisible Cow?” Jeremy Bailin, Arizona TAP Colloquium, Oct 2007

7. Cosmological Simulations “How Spherical Is The Invisible Cow?” Jeremy Bailin, Arizona TAP Colloquium, Oct 2007

8. Prediction: Halos (Like Cows) Are Flattened “How Spherical Is The Invisible Cow?” Jeremy Bailin, Arizona TAP Colloquium, Oct 2007

9. Prediction: Halos are Flattened Spherical Extremely Flattened Baryon cooling results in somewhat more spherical halos (c/a~0.8). (Dubinski 1994; Kazantzidis et al. 2004; Bailin et al. 2005) Bailin & Steinmetz (2005) “How Spherical Is The Invisible Cow?” Jeremy Bailin, Arizona TAP Colloquium, Oct 2007

10. Inferred Halos in MOND • If theory of gravity is wrong (eg. MOND), only gravitational source is baryonic material. • In order to fit observational data, monopole (spherically-symmetric) term of baryon mass distribution must dominate in “halo” • Inferred halo is spherical! • Measurement of flattened halo distinguishes between DM and modified gravity. “How Spherical Is The Invisible Cow?” Jeremy Bailin, Arizona TAP Colloquium, Oct 2007

11. How Can We Measure Flattening of Invisible Halos? Using its gravitational effect on visible things! Some previous methods: • X-ray isophotes (Buote et al. 2002) • Weak lensing (Hoekstra et al. 2004; Mandelbaum et al. 2006) • Polar ring galaxies (Sackett et al. 1994) • Flaring of outer gas disk (Olling & Merrifield 2000) “How Spherical Is The Invisible Cow?” Jeremy Bailin, Arizona TAP Colloquium, Oct 2007

12. How Can We Measure Flattening of Invisible Halos? Using its gravitational effect on visible things! New methods: • Satellite galaxy locations • Satellite galaxy kinematics • Elliptical orbits from 2D velocity fields • Tidal streams “How Spherical Is The Invisible Cow?” Jeremy Bailin, Arizona TAP Colloquium, Oct 2007

13. Introduction to Satellite Galaxies • Small galaxies in the vicinity of and dynamically dominated by larger parent galaxies “How Spherical Is The Invisible Cow?” Jeremy Bailin, Arizona TAP Colloquium, Oct 2007

14. Introduction to Satellite Galaxies • Small galaxies in the vicinity of and dynamically dominated by larger parent galaxies • Around Milky Way: • LMC, SMC Roger Smith/NOAO “How Spherical Is The Invisible Cow?” Jeremy Bailin, Arizona TAP Colloquium, Oct 2007

15. Introduction to Satellite Galaxies • Small galaxies in the vicinity of and dynamically dominated by larger parent galaxies • Around Milky Way: • LMC, SMC • Sgr dSph Majewski et al. 2006 “How Spherical Is The Invisible Cow?” Jeremy Bailin, Arizona TAP Colloquium, Oct 2007

16. Introduction to Satellite Galaxies • Small galaxies in the vicinity of and dynamically dominated by larger parent galaxies • Around Milky Way: • LMC, SMC • Sgr dSph • Fornax dSph Phillip Keller “How Spherical Is The Invisible Cow?” Jeremy Bailin, Arizona TAP Colloquium, Oct 2007

17. Introduction to Satellite Galaxies • Small galaxies in the vicinity of and dynamically dominated by larger parent galaxies • Around Milky Way: • LMC, SMC • Sgr dSph • Fornax dSph • Scl, Car, UMi, UMa I + II, Boo I + II… Belokurov et al. 2006 “How Spherical Is The Invisible Cow?” Jeremy Bailin, Arizona TAP Colloquium, Oct 2007

18. Introduction to Satellite Galaxies • Small galaxies in the vicinity of and dynamically dominated by larger parent galaxies • Around M31: • M32 • NGC205 Robert Gendler “How Spherical Is The Invisible Cow?” Jeremy Bailin, Arizona TAP Colloquium, Oct 2007

19. Introduction to Satellite Galaxies • Small galaxies in the vicinity of and dynamically dominated by larger parent galaxies • Around M31: • M32 • NGC205 • And I - XVI (minus IV, VIII?) And VI Armandroff et al. 1998 And XVI Ibata et al. 2007 And II Da Costa et al. 2000 “How Spherical Is The Invisible Cow?” Jeremy Bailin, Arizona TAP Colloquium, Oct 2007

20. Halos Contain Substructure Subhalos “How Spherical Is The Invisible Cow?” Jeremy Bailin, Arizona TAP Colloquium, Oct 2007

21. Method 1: Locations of Satellites • Subhalos in cosmological halos are more common along halo major axis (Knebe et al. 2004; Zentner et al. 2005) • If satellites are associated with subhalos and if there are no dynamical biases, then so do satellites! • We can study anisotropic distribution of satellite galaxies to detect halo flattening! • Complications: • anisotropic infall from filaments • visible satellites may be biased subset of subhalos • dynamical timescales may be different for satellites on different orbits “How Spherical Is The Invisible Cow?” Jeremy Bailin, Arizona TAP Colloquium, Oct 2007

22. Locations of Satellites • Previous conflicting results: • Holmberg, Zaritsky et al., Milky Way, M31: Satellites of spirals lie perpendicular to disk • Studies using 2dFGRS, SDSS: Satellites of ellipticals lie along elliptical major axis, satellites of spirals are isotropic • Conundrum: largest samples give one answer, but best samples give another! • Small number statistics or systematic error? “How Spherical Is The Invisible Cow?” Jeremy Bailin, Arizona TAP Colloquium, Oct 2007

23. Selecting Satellites of Isolated Galaxies • Our goal: Use mock catalogues from cosmological simulations to evaluate how well previous studies have selected true satellites of isolated galaxies • Conclusion: Almost all previous studies have been dominated by galaxy groups, where primary does not dominate the environment, instead of satellites of isolated dominant primary galaxies • Exceptions: Zaritsky et al., Milky Way, M31 - these are the ones that show polar distribution of satellites! • With our criteria, we expect ~10% contamination. Most previous studies had >50%. “How Spherical Is The Invisible Cow?” Jeremy Bailin, Arizona TAP Colloquium, Oct 2007

24. Angular Distribution of Satellite Galaxies in SDSS All primaries Early-type primaries Late-type primaries Cumulative Fraction N 90o Disk Angle [°] Disk Angle [°] 0o Bailin et al., submitted “How Spherical Is The Invisible Cow?” Jeremy Bailin, Arizona TAP Colloquium, Oct 2007

25. Angular Distribution of Satellite Galaxies • Satellites of isolated spirals lie near minor axis, of isolated ellipticals lie near major axis! • Previous conflicting results due to looking at galaxy group members vs. true satellites, confusion between ellipticals and spirals. • Indication of halo shape? Maybe! But hard to disentangle from complications (ie. dynamical selection effects), especially around disk galaxies. • Possible solution: use kinematics of satellites, which are dominated by shape of potential Satellite Galaxies: Where are they located? “How Spherical Is The Invisible Cow?” Jeremy Bailin, Arizona TAP Colloquium, Oct 2007

26. Method 2: Kinematics of Satellite Galaxies • Satellite velocity dispersions have been used to measure extent, radial profile of halos (eg. Zaritsky et al. 1993; Klypin & Prada 2007) • In non-spherical halo, velocities along major axis are higher than along minor axis at a given radius • Compare velocities of satellites along visible major, minor axes to detect halo shape! • Avoids complications associated with satellite locations • Requires more satellites than available in SDSS! • Future work: Add 6dF satellites. “How Spherical Is The Invisible Cow?” Jeremy Bailin, Arizona TAP Colloquium, Oct 2007

27. Kinematics of Satellite Galaxies • Satellites of disk galaxies tend to orbit prograde to disk • Also a sharp mildly retrograde peak! Interpretation? Herbert-Fort et al., submitted “How Spherical Is The Invisible Cow?” Jeremy Bailin, Arizona TAP Colloquium, Oct 2007

28. Method 3: 2D Velocity Fields • Disk galaxies contain stars and gas on (nearly) closed orbits. In spherical potential, these are circular. • If potential in plane of disk is elliptical, closed orbits are also elliptical. • Measure ellipticity of orbits to infer ellipticity of potential. • 2D Velocity Fields from Integral Field Units or radio (HI, CO) data cubes (eg. Simon et al. 2005) • Projected shape distributions (eg. Ryden 2006) • May also help resolve cusp-core discrepancy (Hayashi et al. 2007) “How Spherical Is The Invisible Cow?” Jeremy Bailin, Arizona TAP Colloquium, Oct 2007

29. Disk Self-Gravity • Disk is deformed by elliptical potential, becomes elliptical. • Elliptical disk contributes to (dilutes) ellipticity of potential. • Must self-consistently solve for ellipticity of potential and shape of disk! • Previous attempts (Jog 2000) did not take radial variation of ellipticity into account. We do! “How Spherical Is The Invisible Cow?” Jeremy Bailin, Arizona TAP Colloquium, Oct 2007

30. Disk Self-Gravity • Must iteratively solve: Bailin et al. (2007) “How Spherical Is The Invisible Cow?” Jeremy Bailin, Arizona TAP Colloquium, Oct 2007

31. Effect of Disk Self-Gravity Bailin et al. (2007) “How Spherical Is The Invisible Cow?” Jeremy Bailin, Arizona TAP Colloquium, Oct 2007

32. Disk Ellipticity in Triaxial Halo b/a=0.7 b/a=0.8 b/a=0.9 Bailin et al. (2007) “How Spherical Is The Invisible Cow?” Jeremy Bailin, Arizona TAP Colloquium, Oct 2007

33. Detection of Disk Ellipticity • In progress: Test observational techniques of measuring halo profile, ellipticity: • Generate mock 2D velocity field from halo of a given shape. • Analyze mock observations using same method as real observations. • How well do inferred halo profile, ellipticity compare to input parameters? • Tentatively looks like ellipticity is recovered well, but cusps can be hidden for certain configurations. “How Spherical Is The Invisible Cow?” Jeremy Bailin, Arizona TAP Colloquium, Oct 2007

34. Method 4: Tidal Streams • If we could watch one star orbit around a galaxy for several Gyr, we could infer the shape of the potential. • Next best thing: tidal streams of disrupting satellite galaxies contain lots of stars at different phases of similar orbits! “How Spherical Is The Invisible Cow?” Jeremy Bailin, Arizona TAP Colloquium, Oct 2007

35. Tidal Streams • Compare velocity, position of Sgr tidal stream stars to models in halos with different flattenings, see which one reproduces observations. • Conflicting answers! • Flattened, like disk (Martinez-Delgado et al. 2004; Johnston et al. 2005) • Spherical (Ibata et al. 2001; Fellhauer et al. 2006) • Elongated perpendicular to disk (Helmi 2004) • Depends on which part of the stream is used! (Law et al. 2005) “How Spherical Is The Invisible Cow?” Jeremy Bailin, Arizona TAP Colloquium, Oct 2007

36. Self-Consistent Models of Tidal Streams • Because of current mass of Sgr, previous studies assumed MW does not react to its presence. But Sgr was more massive before disruption, so this is probably not a good assumption. • Our goal: model the MW-Sgr stream self-consistently, constrain halo shape and orbital history of Sgr. “How Spherical Is The Invisible Cow?” Jeremy Bailin, Arizona TAP Colloquium, Oct 2007

37. Self-Consistent Models of Satellite Disruption “How Spherical Is The Invisible Cow?” Jeremy Bailin, Arizona TAP Colloquium, Oct 2007

38. Self-Consistent Models of Tidal Streams • Self-consistent treatment of both Milky Way and Sagittarius makes a dramatic difference! • Much more difficult to derive initial conditions that place Sgr at present position and velocity after 5 Gyr of evolution, requires algorithims that explore parameter space very efficiently. • Still in progress! “How Spherical Is The Invisible Cow?” Jeremy Bailin, Arizona TAP Colloquium, Oct 2007

39. Conclusions • Prediction: Dark matter halos are elliptical (c/a~0.65 to 0.8 depending on effects of baryons), whereas modified gravity predicts that inferred “halos” are spherical. • Satellite galaxies of disks are distributed perpendicular to disk, of ellipticals are distributed along major axis. May be indication of halo shape. • We will be able to test this using the kinematics of satellite galaxies along major vs. minor axis once we increase our sample by combining SDSS with 6dF. “How Spherical Is The Invisible Cow?” Jeremy Bailin, Arizona TAP Colloquium, Oct 2007

40. Conclusions • Elliptical halo potential causes disk ellipticity that is measurable in 2D velocity fields. But must take disk self-gravity into account to interpret correctly! • May help resolve cusp-core debate. • Sgr stream can be used to measure shape of our halo, but requires simulating “live” Milky Way. The first such simulations are in progress. The flattening of dark matter halos is a testable prediction of the dark matter paradigm. “How Spherical Is The Invisible Cow?” Jeremy Bailin, Arizona TAP Colloquium, Oct 2007

41. Extra Slides

42. Disk/Halo Alignment in Simulations Bailin et al. 2005