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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

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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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The evolution of the DE density

7.0de

1dew

da

dt

& of time vs. the scale factor

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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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Z=0.3 Z=0.5 Z=1.0 Z=1.5

LCDMLCDM

RPRP

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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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LCDM

z = 0

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RP3

z = 0

36

LCDM

z = 1

37

RP3

z = 1

38

LCDM

z = 2

39

RP3

z = 2

40

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