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Cosmological structure formation: models confront observations

This study explores the comparison between cosmological structure formation models and observations, with a focus on dark matter distribution. Topics covered include N-body simulations, properties of dark matter haloes, rotation curves, and a new universal quantity, among others.

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Cosmological structure formation: models confront observations

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

  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 Cold Dark Matter: non relativistic, collisionless fluid of particles Boltzmann collisionless equations (Vlasov Equation) in an expanding Universe Phase Space density Matter density 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.

  9. Particles for a numerical cosmologist Modern computer can handle more than 108 particles Simulation Volume: Our particles have the same mass of a dwarf galaxy… High resolution simulation of a single halo object: Galaxies (recent simulations mp~1000 Msun) Clusters

  10. Initial Conditions (ICs) z~1000

  11. 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: Zel’dovich Approximation

  12. Density wave Zeldovich Velocities and Positions are linked together

  13. 50 Mpc – 3003 part z=25 Maccio’+06,07 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. High-Res Simulation of a single object Distribution of particles of different masses (i.e. different symbols) at z=10. (figure from Klypin+01)

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

  18. 36.000 DM satellites (within 300 kpc) 25 Millions part Highest res simulation ever made (Diemand+08 Maccio’+10)

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

  20. For each halo: Mvir Rvir

  21. Concentration C=Rvir/rs • 2 free parameters: • rs and δc • or • c and Mvir. NFW 1997 Density NFW1997: Works for all cosmological models Shape is preserved only the fitting parameters change Radius Density profiles of CDM structures Navarro, Frenk & White 1997 NFW 1997

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

  23. Concentration Mass relation Maccio’+08 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 This relation strongly depends on the cosmological model Maccio’+07

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

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

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

  27. de Blok+ 2001a 30 LSB/Dwarf galaxies analyzed NWF gives a poor fit Concentrations too low or too low mass to light ratio Theoretical prediction Ωm=0.3 σ8=0.95 Concentrations distribution

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

  29. 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

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

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

  32. 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

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

  34. Spirals Clusters Elliptical Groups dSphs (MW) Spirals Clusters Elliptical Groups dSphs (MW) DM haloes c/M toy model M+08 DM haloes c/M toy model M+08 Spirals Clusters Elliptical Groups DM haloes 25,000 DM haloes from WMAP5 simulations (Maccio’+08) MDM: 1010 – 1015 Msun Spirals Clusters Elliptical Groups Let’s think even bigger!! Satellites are more concentrated than isolated haloes (Maulbetsch+06, Springel+ 08)

  35. DM haloes c/M toy model M+08 Aquarius sim. satellites Spirals Clusters Elliptical Groups dSphs 9 orders of magnitude!!! This is definitely a Nature plot • 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 Boyarsky et al. 2009, arXiv:0911.1774

  36. 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!

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