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!