1. Cosmological structure formation: models confront observations Andrea V. Maccio’ Max Planck Institute for Astronomy Heidelberg A. Boyarsky (EPFL),A. Dutton (Univ. Victoria), B. Moore (Zurich), A. Boyarsky (EPFL), A. Dutton (Univ. Victoria), B. Moore (Zurich), H.W. Rix (MPIA)O. Ruchayskiy (EPFL), F. van den Bosch (Yale) H.W. Rix (MPIA), O. Ruchayskiy (EPFL), F. van den Bosch (Yale)

2. Is (L)CDM the right model? Theory-Models Observations How to compare these two pictures?

3. Overview 1) Why CDM? 2) How to study DM distribution -> Nbody Simulations 3) DM haloes properties: density profile 4) Comparison with observations I: Rotation Curves 5) A new Universal quantity: DM column density 6) Comparison with observations II New method -> new evidence for DM 7) Conclusions

4. Why CDM? Explains flat rotation curves of spiral galaxies Van Albada+ 1985 Reproduces Large scale structure Springel+ 06 (C)DM required by Virial Theorem in galaxy clusters. and by Strong Lensing Analysis

5. CMB WMAP mission

6. Universe’s ingredients Non relativistic Matter: CDM + baryons (85% -15%) Radiation: today negligible (ρ~a -4 ) Dark Energy: ~70-75% Does not cluster (at least on scales <10-100 Mpc) Curvature: likely to be zero (CMB + Inflation) Structure formation ruled by DM with DE setting the background

7. How to study/follow the Universe: why numerical simulations? Initial conditions from the CMB 10 orders of magnitude (break down of linear theory) -> Numerical simulations

8. The N-body: Pure Gravity We want to solve the equations of motions of N particles directly. The N particles are a Monte-Carlo realization of the true initial conditions. Cold Dark Matter: non relativistic, collisionless fluid of particles Boltzmann collisionless equations (Vlasov Equation) in an expanding Universe Phase Space density Matter density

9. Particles for a numerical cosmologist Modern computer can handle more than 10 8 particles Simulation Volume: Our particles have the same mass of a dwarf galaxy… High resolution simulation of a single halo object: Galaxies (recent simulations m p ~1000 Msun) Clusters

10. Initial Conditions (ICs) z~1000

11. Zel’dovich Approximation Initial Conditions The Power Spectrum evolves according linear theory untill: T(k,z) provided by linear theory Then we should obtain a realization of this P(k) using particles:

12. Density wave Zeldovich Velocities and Positions are linked together

13. Maccio’+06,07 50 Mpc – 300 3 part z=25 z=0

14. Structure Formation in the WMAP5 cosmology (comoving coordinates - www.mpia.de/~maccio/movies)

15. Formation of a cluster in the WMAP5 cosmology (comoving coordinates www.mpia.de/~maccio/movies )

16. Distribution of particles of different masses (i.e. different symbols) at z=10. (figure from Klypin+01) High-Res Simulation of a single object

17. Refinement: Re-simulating one halo with better mass resolution

19. 36.000 DM satellites (within 300 kpc) 25 Millions part Highest res simulation ever made (Diemand+08 Maccio’+10)

20. Finding Halos: Spherical Over-density algorithm: Virial density contrast fixed by linear theory: Dvir = 220*background 180 Mpc

21. M vir R vir For each halo:

22. Radius Density Density profiles of CDM structures NFW 1997 Concentration C=R vir /r s 2 free parameters: r s and δ c or c and M vir. NFW1997: Works for all cosmological models Shape is preserved only the fitting parameters change Navarro, Frenk & White 1997

23. NFW profile II NFW velocity profile Circular velocity profile Rotation curve

24. Mass and concentration are related. Concentration is linked to the density of the universe at time of formation. Small haloes form earlier -> the universe was denser at high z -> small haloes are more concentrated Concentration Mass relation Maccio’+07 Maccio’+08 This relation strongly depends on the cosmological model

25. Inner density slope Navarro, Frank & White (1997) : Moore et al. (1999) : Moore+ 1999 CDM predicts Cuspy density profiles Springel+08 No asymptotic slope detected so far Springel+08

26. Observational Results Observations provide velocity profiles that are then converted in density profiles LSB: Dark matter dominated, stellar population make only a small contribution to the observed rotation curve Low Surface Brightness Galaxies Swaters+ 2001 Rotational velocity proportional to enclosed mass Rotational velocity from HI and H α

27. de Block+ 2001 30 LSB/Dwarf galaxies analyzed

28. de Blok+ 2001a 30 LSB/Dwarf galaxies analyzed Concentrations distribution NWF gives a poor fit Concentrations too low or too low mass to light ratio Theoretical prediction Ω m=0.3 σ 8 =0.95

29. de Blok+ 2001b Density profile of LSB galaxies NFW Moore Core Swaters+ 01

30. Observing Simulations Spekkens+05 Density slope determined by 2-3 points They tried to recover the density profile slope of DM haloes with the same pipeline used for observations All the possible “observational” biases favor a cored profile

31. Is the question solved? Not at all High resolution observations of single objects do show deviations from NFW C=3 NGC3741 Gentile+05Gentile+06 DDO47 Burkert profile

32. Matter surface density: New problems for CDM? Burkert profile Donato+09 Gentile+09 Nature MOND!! Is this constant surface density a problem for CDM? Can we learn something from it?

33. Dark Matter surface column density S is insensitive to the details of the density profile We can compute S for real galaxies and for DM haloes

34. S: a new universal quantity Donato+09 We collected from literature profiles for 372 (295) objects (Burkert, NFW and ISO) Spirals M DM instead of M B no restriction to use only (spiral) galaxies Spirals Clusters Spirals Clusters Elliptical Groups Spirals Clusters Elliptical Groups Let’s think Bigger Boyarsky+09

35. Spirals Clusters Elliptical Groups 25,000 DM haloes from WMAP5 simulations (Maccio’+08) M DM : 10 10 – 10 15 Msun Spirals Clusters Elliptical Groups DM haloes Let’s think even bigger!! Satellites are more concentrated than isolated haloes (Maulbetsch+06, Springel+ 08) Spirals Clusters Elliptical Groups dSphs (MW) DM haloes c/M toy model M+08 Spirals Clusters Elliptical Groups dSphs (MW) DM haloes c/M toy model M+08

36. Spirals Clusters Elliptical Groups dSphs DM haloes c/M toy model M+08 Aquarius sim. satellites 9 orders of magnitude!!! NO constant surface density, artifact of log/log New quantity: S allows direct comparison of theory and data CDM reproduces obs. on 9 (nine) orders of magnitude Only CDM works on all scales (no MOND for cluster) One more evidence for the presence of DM This is definitely a Nature plot Boyarsky et al. 2009, arXiv:0911.1774

37. Conclusions 1) Nbody sims best tool to study DM distribution 2) Solid predictions for CDM distribution. 3) To compare obs and sims unbiased quantities are needed 4) Rotation curves seems to prefer cored profiles (?) What is the effect of baryons (see Governato+09 Nature) 5) We present a new, fully unbiased parameter S. Astonishing agreement between obs and sims, 6) We do need CDM!