Cosmological structure Cosmological structure formation:formation:

models confront observationsmodels confront observations

Andrea V. Maccio’Andrea V. Maccio’

Max Planck Institute for AstronomyMax Planck Institute for AstronomyHeidelbergHeidelberg

A. Boyarsky (EPFL),A. Boyarsky (EPFL), A. Dutton (Univ. Victoria), B. Moore (Zurich), A. Dutton (Univ. Victoria), B. Moore (Zurich), H.W. Rix (MPIA)H.W. Rix (MPIA), O. Ruchayskiy (EPFL), F. van den Bosch (Yale)O. Ruchayskiy (EPFL), F. van den Bosch (Yale)

Is (L)CDM the right model?

Theory-Models

Observations

How to compare thesetwo pictures?

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

Why CDM?Explains flat rotation curves of spiral galaxies

Van Albada+ 1985

Reproduces Large scale structure

Springel+ 06

(C)DM required by Virial Theoremin galaxy clusters.and by Strong Lensing Analysis

CMB

WMAP mission

barm

Universe’s ingredientsNon 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 Structure formation ruled by DM with DE setting the backgroundwith DE setting the background

How to study/follow the Universe: why numerical simulations?How to study/follow the Universe: why numerical simulations?

Initial conditions from the CMB

510

T

T

510) (

centercluster

10 orders of magnitude10 orders of magnitude(break down of linear theory)

-> Numerical simulations

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

02

p

fmf

ma

p

t

f Boltzmann collisionless equations(Vlasov Equation)

in an expanding Universe

)](),([4),(

),,(),(

22

3

ttxGatx

pdtpxftx

),,( tpxff Phase Space density

Matter density

Particles for a numerical cosmologistParticles for a numerical cosmologist

Modern computer can handle more than 108 particles

Simulation Volume:

3211107755.2 MpcM suncr h

Mpc1200 h

91066.6 mcrpN

V pm

Our particles have the same mass of a dwarf galaxy…

High resolution simulation of a single halo object:

sunp

sun

Mm

Mm7

5p

10

10

Galaxies (recent simulations mp~1000 Msun)

Clusters

Initial Conditions (ICs)

z~1000

Zel’dovich Approximation

kkk kqbkqaq

qqS

qStbqtatqr

)sin()cos()(

)()(

)()()(),(

0

0

Initial ConditionsInitial Conditions

The Power Spectrum evolves according linear theory untill:

T(k,z) provided by linear theoryT(k,z) provided by linear theory

Then we should obtain a realization of this P(k) using particles:

5020~ 2.0 z),()( 2 zkTAkkP n

2

)1,0()(,

k

GausskPba kk

Density wave

Zeldovich

Velocities and Positionsare linked together

kkk kqbkqaq

qqS

qStbqtatqr

)sin()cos()(

)()(

)()()(),(

0

0

2

)1,0()(,

k

GausskPba kk

Maccio’+06,0750 Mpc – 3003 part z=25 z=0

]0:1[log

]5:2[log

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

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

Distribution of particles of different masses (i.e. different symbols) at z=10.(figure from Klypin+01)

High-Res Simulation of a single objectHigh-Res Simulation of a single object

Refinement:Re-simulating one

halo with better mass resolution

300 Mpc

3 M

pc

36.000DM satellites(within 300 kpc)

25 Millions part

Highest ressimulationever made(Diemand+08Maccio’+10)

Finding Halos:

Spherical Over-density algorithm: Virial density contrast fixed by linear theory: Dvir = 220*background

180 Mpc

Mvir

Rvir

For each halo:

Radius

Densi

ty

Density profiles of CDM structuresDensity profiles of CDM structures

NFW 1997NFW 1997

2)/1)(/(

)(

ss

c

cr rrrr

r

Concentration Concentration

C=RC=Rvirvir/r/rss

2 free parameters: • rs and δc

or • c and Mvir.

NFW1997:NFW1997:Works for all cosmological modelsWorks for all cosmological modelsShape is preserved only Shape is preserved only the fitting parameters changethe fitting parameters change

Navarro, Frenk & White 1997

NFW profile II

NFW velocity profile

R

RGMRVc

)()(

Circular velocity profileCircular velocity profile

Rotation curve

Mass and concentration are related.Concentration is linked to the densityof the universe at time of formation.

Small haloes form earlier-> the universe was denser at high z-> small haloes are more concentrated

Concentration Mass relationConcentration Mass relation

Maccio’+07Maccio’+08

This relation strongly dependson the cosmological model

Inner density slopeInner density slope

Navarro, Frank & White (1997) :

Moore et al. (1999) :

0.1

5.1

2)/1)(/(

)(

ss

c

cr rrrr

r

Moore+ 1999

CDM predict

s Cusp

y density p

rofiles

Springel+08

No asymptotic slope detected so far

Springel+08

Observational ResultsObservational ResultsObservations provide velocity profiles that are then converted in density profiles

LSB: Dark matter dominated, stellarpopulation make only a small contributionto the observed rotation curve

Low Surface Brightness Low Surface Brightness GalaxiesGalaxies

Swaters+ 2001

Rotational velocity proportional to enclosed mass

R

RGMRVc

)()(

Rotational velocity from HI and Hα

de Block+ 200130 LSB/Dwarf galaxies analyzed

de Blok+ 2001a30 LSB/Dwarf galaxies analyzed

Concentrations distributionConcentrations distribution

NWF gives a poor fitNWF gives a poor fit

Concentrations too lowConcentrations too low

or too low mass to light ratioor too low mass to light ratio

Theoretical predictionΩm=0.3σ8=0.95

de Blok+ 2001bDensity profile of LSB galaxies

NFW

Moore

Core

Swaters+ 01Swaters+ 01

Observing Simulations Spekkens+05Density slope determined by 2-3 points

They tried to recover the density profile slope of DM haloes with thesame pipeline used for observations

All the possible “observational” biasesfavor a cored profile

Is the question solved? Not at allHigh resolution observations of single objects do show deviations from NFW

C=3

NGC3741

Gentile+05 Gentile+05 Gentile+06Gentile+06

DDO47))((

)(2

02

0

300

rrrr

rr

Burkert profile

Matter surface density: New problems for CDM?

))(()(

20

20

300

rrrr

rr

Burkert profileDonato+09Gentile+09 Nature

MOND!!MOND!!

Is this constant surface density a problem for CDM?Can we learn something from it?

Dark Matter surface column density

S is insensitive to the detailsof the density profile

We can compute S for real galaxies and for DM haloes

))(()(

20

20

300

rrrr

rr BURK

S: a new universal quantity

Donato+09

We collected from literature profiles for 372 (295) objects(Burkert, NFW and ISO)

SpiralsSpirals

MDM instead of MB

no restriction to use only(spiral) galaxies

SpiralsClusters

SpiralsClustersEllipticalGroups

SpiralsClustersEllipticalGroups

Let’s think Bigger

drrrMR

DMDM )(4200

0

2

Boyarsky+09

SpiralsClustersEllipticalGroups

25,000 DM haloes fromWMAP5 simulations (Maccio’+08)MDM: 1010 – 1015 Msun

SpiralsClustersEllipticalGroups

DM haloes

Let’s think even bigger!!

Satellites aremore concentratedthan isolatedhaloes (Maulbetsch+06,Springel+ 08)

SpiralsClustersEllipticalGroupsdSphs (MW)

DM haloes c/M toy model M+08

SpiralsClustersEllipticalGroupsdSphs (MW)

DM haloes c/M toy model M+08

SpiralsClustersEllipticalGroupsdSphs

DM haloes c/M toy model M+08Aquarius 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 definitelya Nature plot

Boyarsky et al. 2009, arXiv:0911.1774

Conclusions1) Nbody sims best toolto study DM distribution

2) Solid predictions forCDM distribution.

3) To compare obs and simsunbiased 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!