1. Dark Matter and Baryons on Small Spatial Scales Rosemary Wyse Johns Hopkins University Gerry Gilmore, Mark Wilkinson, Vasily Belokurov, John Norris Wyn Evans, Dan Zucker, Andreas Koch, Eva Grebel

2. Ostriker & Steinhardt 03 Galaxy mass function depends on DM type Inner DM mass density depends on the type(s) of DM ΛCDM cosmology extremely successful on large scales. Galaxies are the scales on which one must see the nature of dark matter & galaxy formation astrophysics

3. GHALO (Stadel et al 09) MW Dark Halo in ΛCDM In ΛCDM the first scales to form are small, and galaxies like the Milky Way evolve through merging and assimilation of smaller systems. Highest resolution N-body simulations (gravity only) show persistent small-scale substructure, with many more dark- matter subhaloes surviving to the present-day than we see as satellite galaxies around the Milky Way or Andromeda Galaxy  `feedback’ to match mass function of CDM to galaxy luminosity function, on all scales

4. Dark-matter halos in ΛCDM have `cusped’ density profiles ρ α r -1.2 in inner regions Diemand et al 2008 Main halo Sub-halos Lower limits here

5. Galaxy-scale Challenges for CDM On galaxy scales there is an opportunity to learn some (astro)physics: On galaxy scales there is an opportunity to learn some (astro)physics: Large galaxies of old stars, small galaxies of young (plus old) stars  ‘downsizing’ Massive pure-thin-disk galaxies exist: None should since mergers heat and puff-up disks, create bulges The MWG has a thick disk, and these stars are old, as in the bulge. This seems common but implies little merging since early times, to build them up Sgr dSph in the MWG proves late minor merging happens, but is clearly not dominant process in evolution of MWG except the outer halo, R GC > 25 kpc The ‘feedback’ requirement: otherwise gas cools and stars form too efficiently, plus angular momentum transported away from gas in mergers: stellar disks are too massive and compact The substructure problem – how to hide them? ~

6.  Spatial distribution of stars contains clues as to dark matter scale length  Minimum scale length of dark matter, suggests not CDM  Motions of stars constrain the (dark) matter density profile  Most straightforward analysis  all have similar dark matter halos, with cores not cusps, suggests not standard CDM  Beware claimed masses for the `ultra-faint’ systems, too uncertain  Full distribution function modelling for luminous dwarfs  Astrophysical constraints:  Chemical abundances of dwarf galaxies show trends, not consistent with severe tidal stripping as in CDM models  Fossil record constrains `feedback’ – each dwarf galaxy has own star formation history, but similar dark halo The smallest galaxies as probes of Dark Matter:

7. Dwarf Spheroidals  Low luminosity, low surface-brightness satellite galaxies, ‘classically’ L ~ 10 6 L ,  V ~ 24 mag/  (~10 L  /pc 2 )   plus ultra-faint galaxies discovered in SDSS  Extremely gas-poor  No net rotation, supported by stellar ‘pressure’, velocity dispersion, measured by line-of-sight velocities of members  Apparently dark-matter dominated   velocity dispersion ~ 10km/s, 10 < M/L < 1000  Metal-poor, mean stellar metallicity < 1/30 solar value  Extended, low-rate star-formation histories typical, all from early epochs, perhaps before reionization  Most common galaxy in nearby Universe  Crucial tests for models of structure formation and star formation ~ ~ ~

8. Field of Streams (and dots) SDSS data, 19< r< 22, g-r < 0.4 colour-coded by mag (distance), blue (~10kpc), green, red (~30kpc) Belokurov et al (inc RW, 2006) Outer stellar halo is lumpy: but only ~15% by mass (total mass ~ 10 9 M  ) and dominated by Sgr dSph stream  Segue 1  Boo I

9. Add ~20 new satellites, galaxies and star clusters - but note low yield from Southern SEGUE/SDSS imaging : only Segue 2 and Pisces II as candidate galaxies (Belokurov et al 09,10) Dark matter, galaxies Self-gravitating Star clusters Update from Gilmore et al 07 ~ 10 7 L  ~ 10 3 L  ~ 10 9 L 

10. Minimum scale-length not just in Local Group: nearby (<10Mpc; M81 group, Sculptor group..) low-luminosity dwarfs do not lie on scale-length scaling of larger disks: scale-lengths are larger – consistent with same minimum Exponential fits to surface photometry from HST Sharina et al 08 Open: gas rich Filled: gas poor

11. There is a well-established size bi-modality: ♦ ♦ all equilibrium systems with size < 35pc are purely stellar −16 < M v < −1, M/L < 4; e.g. globular clusters, nuclear star clusters.. ♦ ♦ all systems with size greater than ~120pc have dark- matter halo : minimum scale of dark matter? Expect dark matter scale length to be at least equal to stellar scale length (gas dissipates prior to star formation) Extreme baryon loss in dSph – expand to new equilibrium (?) Stars could not have formed at the extremely low surface densities observed today ~ Minimum Dark Matter Length Scale

12.   No confirmed (equilibrium) galaxies with half-light radius less than ~ 120pc Exceptions are faint and closer than ~50kpc to Galactic center – regime of Sgr tidal tails/streams, may be associated (e.g. Segue 1, Niederste-Ostholt et al inc. RW 2009) – and on deep images often appear tidally disturbed systems Membership uncertainties due to difficulty of modelling field contamination plus small number statistics, together with expected low intrinsic velocity dispersion hampers mass determinations  Focus on more luminous dwarf spheroidals for masses, mass profiles

13. From kinematics to dynamics: Jeans equation, then full distribution function modelling Jeans equation relates spatial distribution of stars and their velocity dispersion tensor to underlying mass profile Jeans equation relates spatial distribution of stars and their velocity dispersion tensor to underlying mass profile Either (i) determine mass profile from projected dispersion profile, with assumed isotropy, and smooth functional fit to the light profile Or (ii) assume a parameterised mass model M(r) and velocity dispersion anisotropy β(r) and fit dispersion profile to find best forms of these (for fixed light profile) Jeans’ equation results allow objective comparisons among galaxies: isotropy is simplest assumption, derive mass profile Jeans’ equation results allow objective comparisons among galaxies: isotropy is simplest assumption, derive mass profile Only possible for large sample sizes  more luminous dSph Mass-anisotropy degeneracy

14. Mass density profiles: Jeans’ equation with assumed isotropic velocity dispersion: All consistent with cores (independent analysis agrees, Wu 07, plus gas-rich systems, Oh et al 08) These Jeans’ models are to provide the most objective comparison among galaxies, which all have different baryonic histories and hence different ‘feedback’  CDM predicts slope of −1.2 at 1% of virial radius, asymptotes to −1 (Diemand et al. 04) as indicated in plot Gilmore et al, inc RW 2007

15. Enclosed mass Very dark-matter dominated. Constant mass within optical extent for more luminous satellite galaxies. Gilmore RW et al 07; Mateo et al 93; Walker et al 07, 09; Strigari et al 08

16. Blue symbols: ‘classical’ dSph, velocity dispersion profiles to last modelled point, reproduces our results Red symbols: Ultra-faint dSph, data only in central region, extrapolation in radius by factor of at least 100  reflects approximately constant velocity dispersions Strigari et al 2008 Extension to lowest luminosities?

17. Beware underestimated errors….and non-members Wil 1 not a bound system (Geha); Segue 1 status unclear: cluster or galaxy ?

18. Segue 1: Most dark-matter dominated, faintest galaxy or star cluster? Segue 1 is at location of debris from the Sgr dSph -- line-of-sight, distance and velocity (Niederste- Ostholt et al inc RW, 2009), and radial-velocity members very extended on sky Segue 1 is at location of debris from the Sgr dSph -- line-of-sight, distance and velocity (Niederste- Ostholt et al inc RW, 2009), and radial-velocity members very extended on sky Cannot exclude contamination and spuriously high velocity dispersion – plausibly star cluster of Sgr dSph Cannot exclude contamination and spuriously high velocity dispersion – plausibly star cluster of Sgr dSph Available metallicity distribution based on four stars: two radial-velocity members at ~ 0.01 solar (Norris, RW et al. 2010), equal to that of the field halo, and of Sgr debris, two others very metal-poor, at 0.0003 solar ([Fe/H] ~ -3.5) Available metallicity distribution based on four stars: two radial-velocity members at ~ 0.01 solar (Norris, RW et al. 2010), equal to that of the field halo, and of Sgr debris, two others very metal-poor, at 0.0003 solar ([Fe/H] ~ -3.5)

19. Chemical abundances: Mean iron abundance of member stars against total luminosity of host system: clear trend, hard to maintain if significant loss of stars through tidal stripping of host Dispersion in metallicity increases as luminosity decreases – consistent with inhomogeneous stochastic enrichment but need more data!! Segue 1 (filled red star) based on 4 stars, 2 at 0.0003 solar iron value ([Fe/H] = -3.5), 2 at 0.01 solar iron: all members?? Norris, RW et al 2010

20. Full velocity distribution functions: breaking the anisotropy-mass profile degeneracy Same dispersion profile Different radial velocity distribution Abandon Jeans x

21. Members: Fornax: 2737 Sculptor: 1368 Sextans: 441 Carina: 1150 Plus new VLT Yield: Car, Sext ~50% For, Scl ~80% Non-members: Wyse et al 2006 Magellan (Walker data) +VLT (Gilmore, RW et al)  Very large samples with precision kinematics now exist. Good data in inner parts for density profiles on small scales, outer regions for total masses. Focus on Fornax: largest dataset, turndown in dispersion, well-behaved kurtosis

22. Comparing models with kinematic data Surface brightness profile determined from stars with good velocity data Surface brightness profile determined from stars with good velocity data Two-integral velocity distribution function models Two-integral velocity distribution function models Generalized Hernquist/NFW halo (Zhao 1996) Generalized Hernquist/NFW halo (Zhao 1996)  Parameters: 3 velocity distribution parameters (anisotropy); 5 halo parameters (density profile) Markov-Chain-Monte-Carlo used to scan parameter space Markov-Chain-Monte-Carlo used to scan parameter space  Multiple starting points for MCMC used - chains run in parallel and combined once “converged” Error convolution included - using only data with Error convolution included - using only data with Wilkinson

23. Tests with spherical models Cusp Core Artificial data sets of similar size, radial coverage and velocity errors to observed data set in Fornax Excellent recovery of input profiles (solid black), even in inner regions; green dashed is most likely, black dashed enclose 90% confidence limits Log r (kpc) Log ρ (M  /kpc 3 )

24. Tests with (anisotropic) triaxial models Axis ratios 0.6 and 0.8, similar to projected 0.7 of Fornax dSph; ~2000 velocities, to match data Models have discriminatory power even when modelling assumptions not satisfied CuspCore Log ρ (2e5 M  /kpc 3 ) Log r (kpc)

25. We build 2-integral, spherical anisotropic distribution function general models, and match data by Markov Chain Monte Carlo - half of the chains start with γ > 0.5, but converge to γ < 0.5  favour cores Left: Accepted radially anisotropic models, right: tangentially anisotropic Fornax dSph Sanity check only

26. Fornax - PRELIMINARY profiles 3 MCMC chains combined: total of ~5000 models M/L ~ 10, stars important, but yet to be subtracted Clear constraints on profile – flatter than cusp Very large dataset for Carina just obtained (VLT) Density Mass Stars Log ρ (M  /kpc 3 ) Log r (kpc) Log M/M  ρ α r -1.2

27.  Spatial distribution of stars contains clues as to dark matter scale length  Minimum scale length of dark matter, suggests not CDM  Motions of stars constrain the (dark) matter density profile  Most straightforward analysis  all have similar dark matter halos, with cores not cusps, suggests not standard CDM  Beware claimed masses for the `ultra-faint’ systems, too uncertain  Full distribution function modelling for luminous dwarfs  Astrophysical constraints:  Chemical abundances of dwarf galaxies show trends, not consistent with severe tidal stripping as in CDM models  Fossil record constrains `feedback’ – each dwarf galaxy has own star formation history, but similar dark halo The smallest galaxies as probes of Dark Matter:

28. Summary: A minimum physical scale for galaxies: A minimum physical scale for galaxies: half-light radius >100pc half-light radius >100pc Reflects characteristic minimum scale for dark matter? Reflects characteristic minimum scale for dark matter? Cored mass profiles preferred, with similar mean mass densities ~ few 0.1M  /pc 3, ~10GeV/cc Cored mass profiles preferred, with similar mean mass densities ~ few 0.1M  /pc 3, ~10GeV/cc An apparent characteristic (minimum) mass dark halo in all luminous dSph, mass ~10 7 M  within half-light radius An apparent characteristic (minimum) mass dark halo in all luminous dSph, mass ~10 7 M  within half-light radius Approx constant density plus scale, not new info Approx constant density plus scale, not new info masses for the lowest luminosity systems more uncertain masses for the lowest luminosity systems more uncertain Wide range of stellar populations (age distributions, chemical evolution) despite similar dark matter haloes – constrains ‘feedback’ and effects on DM Wide range of stellar populations (age distributions, chemical evolution) despite similar dark matter haloes – constrains ‘feedback’ and effects on DM Adds to challenges for CDM: need to consider a variety of DM candidates e.g. STERILE NEUTRINOS Adds to challenges for CDM: need to consider a variety of DM candidates e.g. STERILE NEUTRINOS

30. Formation of a (bulge-dominated) disk galaxy in  CDM: mergers dominate Abadi et al 2003 Stars are colour-coded by age: red = old, blue = young Face-onEdge-on

31. Norris, RW et al 2010

32. ‘ Things’ survey -- low-mass gas-rich spirals consistent Oh et al 2008 de Blok et al 2008 dSph Inner density slope Log Core density 10 -3 M  /pc -3 But see Kuzio de Naray et al 2010 for alternative : 9 gas-rich low- surface brightness galaxies, argue core fits do not show proper scalings or agree with Lyman-α forest bounds

33. Plausible orbits of Sgr Radial velocities of Blue Horizontal Branch stars from SDSS show streams, match Segue 1 (dot) Wide-area data from AAT/AAΩ (Gilmore, Wyse, Norris) plus stellar contours Easy to inflate velocity dispersion with Sgr stream contaminants

34. Little evolution in dark matter profile in models of dwarf spheroidals A, B denote star-formation prescriptions; B includes feedback from supernovae `weak’ wind has average speed 222km/s Dark solid line is dark-matter only simulation Read et al 2006 Small-scale ~1Mpc N-body/SPH simulations High resolution (10 3 M  ), 199 < z < 10 10 8 M 

35. Leo I, classical dSph Three fainter discoveries from SDSS (Belokurov et al, inc RW 06a) – all require confirmation with deeper imaging, then spectroscopy dSph (?) d=45kpc dSph d=150kpc glob (?) d=25kpc Governato et al 2010

36. The next step 2-integral distribution functions F(E,L) constructed using scheme of Gerhard; Saha Models projected along line of sight and convolved with velocity errors Data analysed star-by-star: no binning More general halo profile:

37. 2-Integral Distribution function Gerhard (1991)

38. Constructing the line of sight velocity distributions Fit surface brightness profile Fit surface brightness profile Use method by P. Saha to invert integral equation for DF: Use method by P. Saha to invert integral equation for DF: Project to obtain LOS velocity distribution on a grid of and Project to obtain LOS velocity distribution on a grid of and Spline to required radii for observed stars, and convolve with individual velocity errors Spline to required radii for observed stars, and convolve with individual velocity errors

39. Fitting to kinematic data Surface brightness profile determined from observations Surface brightness profile determined from observations Markov-Chain-Monte-Carlo scheme used to scan parameter space Markov-Chain-Monte-Carlo scheme used to scan parameter space Parameters: 3 velocity distribution parameters ( ); Parameters: 3 velocity distribution parameters ( ); 5 halo parameters ( ) 5 halo parameters ( ) Multiple starting points for MCMC used - chains run in parallel and combined once “converged” Multiple starting points for MCMC used - chains run in parallel and combined once “converged” Error convolution included - using only data with Error convolution included - using only data with

40. Belokurov et al 2010 Contours of stellar density from red giants and main sequence stars, with red ellipses being 1,2 x half-light radii. Black dots are blue horizontal branch star candidates (very likely members) (distant, 180kpc)(near, 16kpc) Star cluster

41. Velocity anisotropy profiles: isotropic input Reassuring, but need to test with models that do not satisfy our modelling assumptions.....e.g. triaxial Radius (kpc) ß(r)  Data 

42. Walker et al (2009): similar results to us from Jeans analysis on his data for classic dSph (constant mass within half-light radius), obtain trends when add ultra-faints – but concerns about data interpretation (membership?) and robustness for these. Blue curve: fixed NFW halo, scale radius 795pc, Vmax = 15km/s Red curve: fixed cored halo, scale radius 150pc, Vmax = 13km/s

43. Leo I Hernandez, Gilmore & Valls-Gabaud 2000  Intermediate-age population dominates in typical dSph satellite galaxies – with very low average SFR over long periods (~5M  /10 5 yr), until recently  Different baryonic histories, same dark matter halos (Gilmore et al, inc RW 07): not strong feedback from baryons to dark halo (cf Read et al 06, Fellhauer et al 08) UMi dSph Atypical SFH dSph Star-formation histories are measured (CMDs)

44. Grcevich & Putman 09 Dwarf spheroidals all only upper limits on atomic hydrogen content Log Distance to parent galaxy (kpc) Log mass HI/M 

45. Linear power spectrum at z ~ 300, showing influence of WIMP microphysics: Physical scales of interest correspond to smallest galaxies Anticipated DM effects on scales of pc up  first systems Green, Hofmann & Schwarz 2005

46. Adding velocity dispersion anisotropy: Leo II Fixed βRadially varying β Koch et al, inc RW 2007 Cores slightly favoured, but not conclusive

47. Fornax - surface brightness profile

48. Fornax - dispersion profile NB: Dispersion data not used to constrain models