1 THE NATURE OF DARK ENERGY FROM N-BODY COSMOLOGICAL SIMULATIONS Paola Solevi Università Milano - Bicocca A.A. 2003/2004
Dec 30, 2015
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THE NATURE OF DARK ENERGY FROM N-BODY COSMOLOGICAL SIMULATIONS
Paola Solevi
Università Milano - Bicocca
A.A. 2003/2004
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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
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What is Dark energy?
The best fit model of WMAP:
04.027.0
004.0044.0
02.002.1
dm
b
tot
~70% dark energy
The cosmological constant is described by energy-momentum tensor:
Problems of LCDM cosmology
•Coincidence problem: why just now ?
•Fine tuning:
gT 1
pw
54,
0,
10
1
EW
0,0, cr
4
Solution: Dynamical Dark energy
We have a real self-interactive scalar filed with a potential
.
•Equation of motion
•Energy density
•Pressure
Potentials which admit a tracker solution:
RP SUGRA
)(t)(V
02 2
d
dVa
a
a
)(2 2
2
Va
)(2 2
2
V
ap
)(
2
)(2
2
2
2
2
Va
Vaw
4
)(V
2
44
)(
pmeV
Where is the energy scale parameter.
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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) calculationPM (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
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Basic ingredients
Initial conditionsInitial conditions: power spectrum of density perturbations depends on the cosmological parameter & inflationary model
n=1 for scale-free HZ spectrum
),( zkT is the transfer function (from CMBfast)
P(k) at z=40 for different kind of Dark Energy.
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FITTING FORMULAE
20, , 1
11 bza
zz m
m
21
21
21
log
log
log
ccc
bbb
aaa
for resolving equations used in simulation: )(3
0,0 aa
Ha
a
m
m
)(amAnalytic formula for in Friedmann eq.
,
2a
p
dt
xd
dt
pdx
22x 4 Ga (eq. of Poisson )
(eq. of motion)
Growing of perturbation depends on the background evolutionbackground evolution
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Linear features of the modelLinear features of the model
Periodic boundary conditionsPeriodic boundary conditions (homogeneity & isotropy), we need a large box for a good representation of the universe
Mass & force resolution Mass & force resolution increase with decreasing box size
3
0,0,
row
boxcrmpart N
Lm
),(
),(
),(
8 m
mvir
mc
z
z
z
Nrow number of particles in one dimension
Lbox box size
Ngrid number of cells in one dimension
n number of refinment levels
n
grid
box
N
L
12
10
All NFW profiles…
RPSUGRALCDM
21 cc
c
cr rrrr
r
crRC /103103
Density profiles
…but with different concentrations
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
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The best way for test different central concentration is via Strong Gravitational Lensing
Formation of Giants Arcs
More Arcs for RP
model
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No differences predicted becauseof the same σ8 normalization at But different evolution expectedz=0
Mass function evolution
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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
Ωm0.3 LBox 100 h-1Mpc
ΩDE0.7 Npart 2563
h 0.7 Mp 5.0x109 Mʘh-1
σ80.90 є 3.0 h-1kpc
(7 refinement levels)
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VPF is a function of all the correlation terms :
- reduced n-point correlation function mean value
- 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)
10 )(
!
)(exp)(
ii
iR Rki
NRP
nk
RN
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VPF, M > 1x1012Mʘh-1
Just as for halos MF no
differences predicted at z=0
Z=0.9Z=0
But different evolution expected
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VPF, M > 1x1012Mʘh-1 VPF, M > 5x1012Mʘh-1
Notice the dependences on the mass limit, significant differences but halo number getting low
Z=1.5
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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,PNeDirect estimations of ICLDirect 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.
OriginOrigin: -Tidal stripping -Infall of large groups
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Why PNe as ICL tracers?Why PNe as ICL tracers?
PN is a short (~104 years) phase in stellar evolution
between asymptotic giant branch & WD
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
Lum
ino
sity
(HR diagram)
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Shell of gas from the envelope of central star
Hot central star T~5x104K
O[III] emission
UV
(Arnaboldi et al 2003)
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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 M Central Star M Progenitor’s birth PN type
2.4-8Mʘ >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
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Studying PNe, very low intensity stellar objects are found
Cluster materials outside galaxies can be inspected
Current studies concentrate on Virgo
Main danger in studying PNe: background emitters at λ = 5007 Å
contributing ~25% of fake objects (interlopers)
Results: - ICPNe not centrally concentrated
- 10% < ICL < 40%
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Numerical simulations aiming to reproduce the observed PN Numerical simulations aiming to reproduce the observed PN distributiondistribution
1 – Napolitano, Pannella, Arnaboldi, Gehrardt,Aguerri, Freeman, Capaccioli,Ghigna, Governato, Quinn, Stadel
2003 ApJ 594, 172
PKDGRAV n-body cosmological simulation,
Model: ΛCDM, Ωm=0.3, σ8=1, h=0.7
Cluster of 3x1014Mʘ (cluster magnified, still n-body)
Np(<Rv) mp є
~ 5x105 5.06x108Mʘ 2.5kpc
NO HYDRO
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How to use DM to reproduce star formation?
Particle in overdensity hits becomes a star
- points with 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
4102.1
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2 – Murante, Arnaboldi, Gehrardt, Borgani, Cheng, Diaferio, Dolag, Moscardini, Tormen, Tornatore, Tozzi
ApJL 2004, 607, L83
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 mp,DM є
6.93x108Mʘh-1 4.62x109Mʘh-1 7.5 h-1kpc
HYDRO +
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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
Fraction of unbound stars > 10%
(Diemand et al 2003)
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3 – Willman, Governato, Wadsley, Quinn
astro-ph/0405094 and MNRAS 2004 (in press)
GASOLINE (treeSPH) includes: radiative+Compton cooling,
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
HYDRO +
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Coma-like galaxy cluster M ~ 1.2x1015Mʘh-1
Two large groups ranging in size from Fornax to Virgo (Willman et al 2004)
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NDM N*mp,DM/Mʘ mp,* /Mʘ Є / kpc
C2 6.9x105 8.5x105 1.5x109 7.2x107 3.75
C2,low 8.6x104 1.4x105 1.2x1010 8.3x108 7.5
Murante et al
6.6x109 10.8
Comparison of C2 with C2,low C2,low not enough resolution
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Bound and free stars were detected by SKID using
&
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?
kpc18 kpc9
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Various conclusionsVarious 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)
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-More IC stars from large galaxies but more star/unit-mass from small galaxies
-85% of stars forms at z < 1.1
(Willman et al 2004)
Mass M
IC f
ract
.fro
m h
alos
M<
M
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What did we do so far?What did we do so far?
ART & it’s generalization QART (modified for DE models)
Models: ΛCDM Ωm=0.3, σ8=0.75, h=0.7 RP(Λ=103GeV) 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
Willman et al 1.05x109Mʘh-1 2.6 h-1kpc
Napolitano et al 3.54x108Mʘh-1 1.7 h-1kpc
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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