Transcript Diapositiva 1

THE NATURE OF DARK ENERGY FROM N-BODY
COSMOLOGICAL SIMULATIONS
Paola Solevi
Università Milano - Bicocca
1
A.A. 2003/2004
Overview of the talk
• What is Dark Energy?
• About n-body cosmological simulations
• How to constrain different DE models by n-body
cosmological simulations
Halos Profile

Halos Mass function
VPF
ICL
2
What is Dark energy?
The best fit model of WMAP:
tot  1.02  0.02
b  0.044 0.004
~70% dark energy
 dm  0.27  0.04
The cosmological constant is described by energy-momentum
tensor:
p
T  g 
w 


 1
Problems of LCDM cosmology
•Coincidence problem: why just now
,0
1
•Fine tuning:
 54
 , EW 10
,0  cr,0
?
3
Solution: Dynamical Dark energy
We have a real self-interactive scalar filed
 (t ) with a potential
V ( ) .
  2 a   a 2 dV  0

•Equation of motion
a
d
 
•Energy density
 2
2

 V ( )
2a
 2
p 
 V ( )
2a 2
•Pressure
 2
2
 V ( )
2
 V ( )
w  2a2

2a
Potentials which admit a tracker solution:
RP
V ( ) 
Where
4


SUGRA
V ( ) 
 is the energy scale parameter.
4



e
 
4 
 mp





2
4
The evolution of the DE density
wde  1
de  0.7
dt
da
& of time vs. the scale factor
5
Collision less n-body cosmological simulations
All our simulations are performed using ART, a PM adaptive code
(Klypin & Kratsov) and QART, modification of ART (by Andrea
Macciò) for models with DDE.
PM (particle-mesh) calculation:
1. Assign “charge” to the mesh (particle mass
grid density)
2. Solve the field potential equation ( Poisson’s) on the mesh
3. Calculate the force field from the mesh-defined potential
4. Interpolate the force on the grid to find forces on the particles
5. Integrate the forces to get particle velocities and positions
6. Update the time counter
6
Basic ingredients
Initial conditions: power spectrum of density perturbations
depends on the cosmological parameter & inflationary model
n=1 for scale-free HZ spectrum
T (k , z )
is the transfer function
(from CMBfast)
P(k) at z=40 for different
kind of Dark Energy.
7
Growing of perturbation depends on the background evolution
Analytic formula for m (a) in Friedmann eq.
for resolving equations used in simulation:
2x   4 Ga2    



d p
dx
p
  x  ,
 2
dt
dt
a
 m,0
a
 H0
a
a 3 m ( a )
(eq. of Poisson )
(eq. of motion)
FITTING FORMULAE
 m z   1 
1    ,
m,0
1  z 
  a  bz2
a  a1 log   a2
b  b1 log   b2
c  c1 log   c2
8
 c ( z, m )
 vir ( z, m )
Linear features of the model
 8 ( z,  m )
Periodic boundary conditions (homogeneity & isotropy), we need
a large box for a good representation of the universe
Mass & force resolution increase with decreasing box size
m part
 Lbox
  m , 0  cr , 0 
 N row
 Lbox
  
 N grid
 1 n
2





3
Nrow number of particles in one dimension
Lbox box size
Ngrid number of cells in one dimension
n number of refinment levels
9
Density profiles
RP
SUGRA
LCDM
All NFW profiles…
c
 r 

cr r rc 1  r rc 2
…but with different concentrations
C103  R103 / rc
FEATURES OF
SIMULATED
CLUSTERS
RP3
LCDM
SU3
Virial Radius
(Mpc)
0.663
(149.8)
0.730
(103.1)
0.709
(118.3)
Virial Mass
5.01e13
4.44e13
4.53e13
Cvir
10.1
7.2
8.84
10
The best way for test different central concentration is via Strong
Gravitational Lensing
Formation of Giants Arcs
More Arcs for RP
model
11
LCDM
Z=0.3
Z=0.5
Z=1.0
RP
Z=1.5
12
Mass function evolution
No differences predicted because
of the same σ8 normalization at
z=0
But different evolution expected
13
Void probability function
Simulations run at HITACHI MUNCHEN MPI 32 Node,32x256 Pr.
Three simulations: LCDM, RP (Λ=103GeV), SU (Λ=103GeV)
Cosmologies
Simulations features
Ωm
0.3
LBox
100 h-1Mpc
ΩDE
0.7
Npart
2563
h
0.7
Mp
5.0x109 Mʘh-1
σ8
0.90
є
3.0 h-1kpc
(7 refinement levels)
14
VPF is a function of all the correlation terms :
  ( N R ) i

P0 ( R)  exp
ki ( R ) 
 i 1 i!

-
kn
reduced n-point correlation function mean value
-
NR
mean galaxy number in VR
Why do we expect that VPF depend on the cosmological model?
Different evolution rate
Different halo #
PLCDM(R)> PSU(R) > PRP(R)
15
Z=0
VPF, M > 1x1012Mʘh-1
Just as for halos MF no
differences predicted at z=0
Z=0.9
But different evolution
expected
16
VPF, M > 1x1012Mʘh-1
Z=1.5
VPF, M > 5x1012Mʘh-1
Notice the dependences on the mass limit, significant differences but halo
number getting low
17
Intracluster light
ICL (intracluster light) is due to a diffuse stellar component
gravitationally bound not to individual galaxies but to the cluster
potential.
First ICL Observations :
Zwicky 1951 PASP 63, 61
The fraction of ICL depends on the dynamical state of the cluster
and on its mass so studying ICL is important to understand the
evolution of galaxy clusters.
ICL tracers: Red Giants, SNIa, ICG’s,PNe
Direct estimations of ICL surface brightness are difficult because it
is less than 1% of the sky brightness and because of the diffuse
light from the halo of the cD galaxy.
Origin: -Tidal stripping
18
-Infall of large groups
Why PNe as ICL tracers?
PN is a short (~104 years) phase in stellar evolution
between asymptotic giant branch & WD
(HR diagram)
Luminosity
Because of a so short life,
studying PNe’s properties is
just like investigating mean
local features.
The diffuse envelope of a PN
re-emits part of UV light from
the central star in the bright
optical O[III] (λ = 5007 Å) line.
Surface T
19
Hot central star
T~5x104K
UV
Shell of gas from the
envelope of central
star
(Arnaboldi et al 2003)
O[III] emission
20
If metallicity is large
emission on many lines, scarce
efficiency
Average efficiency 15%
RELATIONSHIP
O[III] intensity
metallicity
age of formation
mass
Pop I, disk population
poor emitters
Pop II, bulge population
strong emitters
Progenitor’s birth
PN type
>0.64Mʘ
1 Gyr
Type I
1.2-2.4Mʘ
0.58-0.64Mʘ
3 Gyr
Type II
1.0-1.2Mʘ
~0.56Mʘ
6 Gyr
Type III
0.8-1.0Mʘ
~0.555Mʘ
10 Gyr
Type IV
Progenitor M
Central Star M
2.4-8Mʘ
21
Studying PNe, very low intensity stellar objects are found
Cluster materials outside galaxies can be inspected
Current studies concentrate on Virgo
Results: - ICPNe not centrally
concentrated
- 10% < ICL < 40%
Main danger in studying PNe: background emitters at λ = 5007 Å
contributing ~25% of fake objects (interlopers)
22
Numerical simulations aiming to reproduce the observed PN
distribution
1 – Napolitano, Pannella, Arnaboldi, Gehrardt,Aguerri, Freeman,
Capaccioli,Ghigna, Governato, Quinn, Stadel
2003 ApJ 594, 172
PKDGRAV n-body cosmological simulation,
NO HYDRO
Model: ΛCDM, Ωm=0.3, σ8=1, h=0.7
Cluster of 3x1014Mʘ (cluster magnified, still n-body)
Np(<Rv)
~ 5x105
mp
5.06x108Mʘ
є
2.5kpc
23
How to use DM to reproduce star formation?
Particle in overdensity
- points with

hits
becomes a star
 1.2  104 at z = 3, 2, 1, 0.5, 0.25, 0

Now for ICL must trace unbound stars
- trace points down to z = 0, reject those in subhalos & cD
What did they do?
- Phase space distribution analysis in 30’x30’ areas at
0.2, 0.4, 0.5, 0.6 Mpc from cluster center
- 2-p angular correlation function
- Velocity distribution along l.o.s
Consistency with observational data
24
2 – Murante, Arnaboldi, Gehrardt, Borgani, Cheng, Diaferio,
Dolag, Moscardini, Tormen, Tornatore, Tozzi
ApJL 2004, 607, L83
HYDRO +
GADGET (treeSPH) used for LSCS, includes: radiative cooling,
SNa feedback, star formation
Model: ΛCDM, Ωm=0.3, Ωb=0.019h-2, σ8=0.8, h=0.7
117 clusters with M > 1014Mʘh-1
mp,gas
6.93x108Mʘh-1
mp,DM
4.62x109Mʘh-1
є
7.5 h-1kpc
25
Bound and free stars have been selected by SKID, fraction
depends on  , optimal  ~ 20 h-1kpc
Problems with spatial resolution: numerical overmerging causes
apparently unbound stars
increasing resolution
(Diemand et al 2003)
Fraction of unbound stars > 10%
26
3 – Willman, Governato, Wadsley, Quinn
astro-ph/0405094 and MNRAS 2004 (in press)
GASOLINE (treeSPH) includes: radiative+Compton cooling,
HYDRO +
SNa feedback, star formation,
UV background (Haardt&Madau 1996)
Cosmological simulation (n-body)
1 cluster magnified
Model: ΛCDM, Ωm=0.3, Ωb not given, σ8=1, h=0.7
27
Coma-like galaxy cluster M ~ 1.2x1015Mʘh-1
(Willman et al 2004)
Two large groups ranging in size from Fornax to Virgo
28
NDM
N*
mp,DM/Mʘ mp,* /Mʘ Є / kpc
C2
6.9x105 8.5x105 1.5x109
C2,low
8.6x104 1.4x105 1.2x1010 8.3x108 7.5
Murante
et al
Comparison of C2 with C2,low
6.6x109
7.2x107 3.75
10.8
C2,low not enough resolution
29
Bound and free stars were detected by SKID using
  18kpc
&
  9kpc
20% of stars found in intracluster medium
Problem: stellar baryon fraction ~ 36% in simulation vs. 6-10%
from 2MASS & SDSS data (Bell et al 2003).
COOLING CRISIS: not enough effects to slow down star
formation
Claim: distribution of stars still OK
TRUE? Neglected effects could be star-density dependent
Is the sophisticated star formation machinery really better
than searching for overdensity regions?
30
Various conclusions
- Unbound stars fraction depends on dynamical status of
cluster
Two peaks at z~0.55
and z~0.2 correspond to
the infall of large groups
Variation of IC stars
fraction from 10% at z~1
to 22% at z~0
(Willman 2004)
31
IC fract.from halos M<M
-More IC stars from large galaxies but more star/unit-mass
from small galaxies
Mass M
-85% of stars forms at z < 1.1
(Willman et al 2004)
32
What did we do so far?
ART & it’s generalization QART (modified for DE models)
Models: ΛCDM
RP(Λ=103GeV)
Ωm=0.3, σ8=0.75, h=0.7
Ωm=0.3, σ8=0.75, h=0.7
Cluster with M =2.92x1014Mʘh-1
Lbox
Npart
mpart
є
80 Mpc h-1
5123
3.17x108Mʘh-1
1.2 h-1kpc
1.05x109Mʘh-1
2.6 h-1kpc
Willman et al
Napolitano et al
3.54x108M
-1
h
ʘ
1.7 h-1kpc33
LCDM
z=0
34
RP3
z=0
35
LCDM
z=1
36
RP3
z=1
37
LCDM
z=2
38
RP3
z=2
39
Conclusions: What are we doing?
- Star formation in iperdensities (SMOOTH), density
contrast to be gauged to reproduce observed star amount
- Star formation z’s at Δz ~ 0.1
- Dynamical status of candidate-star particle monitorized
Extra aim
Searching for cosmological model dependencies due to:
- different formation history
- concentration of dark matter halos
40