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)
Is (L)CDM the right model?
Theory-Models
Observations
How to compare these
two 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
Reproduces Large scale structure
Van Albada+ 1985
(C)DM required by Virial Theorem
in galaxy clusters.
and by Strong Lensing Analysis
Springel+ 06
CMB
WMAP mission
 m   bar
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
How to study/follow the Universe: why numerical simulations?
Initial conditions from the CMB
T
T


( cluster center )  10
5
10 orders of magnitude
(break down of linear theory)
-> Numerical simulations



 10
5
The N-body: Pure Gravity
Cold Dark Matter: non relativistic, collisionless fluid of particles
f

t
p
ma
2
f  m
f
p
f  f (x, p, t)
 ( x, t ) 

0
Boltzmann collisionless equations
(Vlasov Equation)
in an expanding Universe
Phase Space density
3
f ( x, p, t )d p
  ( x , t )  4 Ga [  ( x , t )   ( t )]
2
2
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.
Particles for a numerical cosmologist
Modern computer can handle more than 108 particles
1
Simulation Volume: 200 h Mpc
 cr  2 . 7755  10 11 h 2 M
mp 
V
Np
Mpc
sun
  cr   m  6 . 66  10
3
9
Our particles have the same mass of a dwarf galaxy…
High resolution simulation of a single halo object:
m p  10 M sun Galaxies (recent simulations mp~1000 Msun)
5
m p  10 M sun Clusters
7
Initial Conditions (ICs)
z~1000
Initial Conditions
The Power Spectrum evolves according linear theory untill:

P ( k ) Ak T ( k , z )
n
2

 0 . 2 z ~ 20  50
T(k,z) provided by linear theory
Then we should obtain a realization of this P(k) using particles:
Zel’dovich Approximation
r ( q , t )  a ( t ) q  b ( t ) S ( q ) 
S (q )   0 (q )
0 (q ) 
a
k
cos( kq )  b k sin( kq )
k
a k , bk 
P( k )
Gauss ( 0 ,1)
k
2
Density wave
Zeldovich
Velocities and Positions
are linked together
r ( q , t )  a ( t ) q  b ( t ) S ( q ) 
S (q )   0 (q )
0 (q ) 
a
k
k
cos( kq )  b k sin( kq )
a k , bk 
P( k )
Gauss ( 0 ,1)
k
2
50 Mpc – 3003 part
 
log    [  1 : 0 ]
 
z=25
Maccio’+06,07
z=0
 
log    [ 2 : 5 ]
 
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)
High-Res Simulation of a single object
Distribution of particles of
different masses (i.e. different
symbols) at z=10.
(figure from Klypin+01)
Refinement:
Re-simulating one halo
with better mass
resolution
3 M pc
300 M pc
36.000
DM satellites
(within 300 kpc)
25 Millions part
Highest res
simulation
ever made
(Diemand+08
Maccio’+10)
Finding Halos:
Spherical Over-density algorithm:
Virial density contrast fixed by linear theory: Dvir = 220*background
180 Mpc
For each
halo:
Mvir
Rvir
Density profiles of CDM structures
 (r )
 cr

c
( r / rs )( 1  r / rs )
2
NFW1997
1997
NFW
Concentration
C=Rvir/rs
Density
Navarro, Frenk & White 1997
2 free parameters:
• rs and δc
Radius
or
• c and Mvir.
NFW1997:
Works for all cosmological models
Shape is preserved only
the fitting parameters change
NFW profile II
NFW velocity profile
Rotation curve
Circular velocity profile
V c (  R )
GM (  R )
R
Concentration Mass relation
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
Maccio’+07
Maccio’+08
This relation strongly depends
on the cosmological model
 (r )
Inner density slope
Navarro, Frank & White (1997) : 
Moore et al. (1999) :
  1 .0
 cr

c
( r / rs )( 1  r / rs )
   1 .5
Moore+ 1999
Springel+08
Springel+08
No asymptotic slope detected so far
2
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
V c (  R )
GM (  R )
R
Swaters+ 2001
de Block+ 2001
30 LSB/Dwarf galaxies analyzed
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
de Blok+ 2001b
Density profile of LSB galaxies
Core
NFW
Moore
Swaters+ 01
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
Is the question solved? Not at all
High resolution observations of single objects
do show deviations from NFW
Gentile+05
Gentile+06
NGC3741
C=3
 (r ) 
 0 r0
3
( r  r0 )( r  r )
2
Burkert profile
2
0
DDO47
Matter surface density: New problems for CDM?
Burkert profile
 (r ) 
 0 r0
Donato+09
Gentile+09 Nature
3
( r  r0 )( r  r0 )
2
2
MOND!!
Is this constant surface density a problem for CDM?
Can we learn something from it?
Dark Matter surface
column density
 ( r ) BURK 
 0 r0
3
( r  r0 )( r  r0 )
2
2
S is insensitive to the details
of the density profile
We can compute S for
real galaxies and for DM haloes
S: a new universal quantity
Boyarsky+09
We collected from literature profiles for 372 (295) objects
(Burkert, NFW and ISO)
Donato+09
M
DM


R 200
0
4  r  DM ( r ) dr
2
Let’s think Bigger
MDM instead of MB
no restriction
to use only
(spiral) galaxies
Spirals
Spirals
Spirals
Spirals
Clusters
Clusters
Elliptical
Clusters
Elliptical
Groups
Groups
Spirals
Spirals
Clusters
Clusters
Elliptical
Elliptical
Groups
Groups
Let’s think
even bigger!!
Satellites are
more concentrated
than isolated
haloes (Maulbetsch+06,
Springel+ 08)
DM haloes
25,000 DM haloes from
WMAP5 simulations (Maccio’+08)
MDM: 1010 – 1015 Msun
Spirals
Clusters
Elliptical
Groups
dSphs (MW)
DM haloes
c/M toy model M+08
Spirals
Clusters
Elliptical
Groups
dSphs
DM haloes
c/M toy model M+08
Aquarius sim. satellites
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
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!