THE NATURE OF DARK ENERGY FROM N-BODY COSMOLOGICAL SIMULATIONS

Paola SoleviUniversit Milano - Bicocca A.A. 2003/2004

Overview of the talk

What is Dark Energy?About n-body cosmological simulationsHow to constrain different DE models by n-body cosmological simulations Halos Profile Halos Mass functionVPFICL

What is Dark energy?The best fit model of WMAP:

~70% dark energyThe cosmological constant is described by energy-momentum tensor:

Problems of LCDM cosmologyCoincidence problem: why just now?Fine tuning:

Solution: Dynamical Dark energyWe have a real self-interactive scalar filed with a potential .Equation of motionEnergy densityPressurePotentials which admit a tracker solution:RPSUGRAWhere is the energy scale parameter.

The evolution of the DE density& of time vs. the scale factor

Collision less n-body cosmological simulationsAll our simulations are performed using ART, a PM adaptive code (Klypin & Kratsov) and QART, modification of ART (by Andrea Macci) for models with DDE.PM (particle-mesh) calculation: Assign charge to the mesh (particle mass grid density) Solve the field potential equation ( Poissons) on the mesh Calculate the force field from the mesh-defined potential Interpolate the force on the grid to find forces on the particles Integrate the forces to get particle velocities and positions Update the time counter

Basic ingredients

Initial conditions: power spectrum of density perturbations depends on the cosmological parameter & inflationary model

n=1 for scale-free HZ spectrumis the transfer function (from CMBfast)P(k) at z=40 for different kind of Dark Energy.

for resolving equations used in simulation: Analytic formula for in Friedmann eq. (eq. of Poisson )

(eq. of motion)Growing of perturbation depends on the background evolution

Linear features of the model

Periodic boundary conditions (homogeneity & isotropy), we need a large box for a good representation of the universe

Mass & force resolution increase with decreasing box sizeNrow number of particles in one dimensionLbox box size

Ngrid number of cells in one dimensionn number of refinment levels

All NFW profilesDensity profilesbut with different concentrations

FEATURES OF SIMULATED CLUSTERSRP3LCDMSU3Virial Radius (Mpc)0.663 (149.8)0.730 (103.1)0.709 (118.3)Virial Mass 5.01e134.44e134.53e13Cvir10.17.28.84

The best way for test different central concentration is via Strong Gravitational LensingFormation of Giants Arcs

More Arcs for RP model

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

No differences predicted becauseof the same 8 normalization at But different evolution expectedz=0Mass function evolution

Void probability functionSimulations run at HITACHI MUNCHEN MPI 32 Node,32x256 Pr.Three simulations: LCDM, RP (=103GeV), SU (=103GeV)

CosmologiesSimulations featuresm0.3LBox100 h-1MpcDE0.7Npart2563h0.7Mp5.0x109 Mh-180.903.0 h-1kpc(7 refinement levels)

VPF is a function of all the correlation terms :

- reduced n-point correlation function mean value-mean galaxy number in VRWhy do we expect that VPF depend on the cosmological model? Different evolution rateDifferent halo # PLCDM(R)> PSU(R) > PRP(R)

VPF, M > 1x1012Mh-1Just as for halos MF nodifferences predicted at z=0Z=0.9Z=0But different evolution expected

VPF, M > 1x1012Mh-1VPF, M > 5x1012Mh-1Notice the dependences on the mass limit, significant differences but halo number getting low Z=1.5

Intracluster lightICL (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, 61The 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, ICGs,PNeDirect 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 -Infall of large groups

Why PNe as ICL tracers?PN is a short (~104 years) phase in stellar evolutionbetween asymptotic giant branch & WDBecause of a so short life, studying PNes 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] ( = 5007 ) line. Surface TLuminosity(HR diagram)

Shell of gas from the envelope of central starHot central star T~5x104KO[III] emissionUV(Arnaboldi et al 2003)

If metallicity is large emission on many lines, scarce efficiency Average efficiency 15% RELATIONSHIPO[III] intensity metallicity age of formation massPop I, disk population poor emittersPop II, bulge population strong emitters

Progenitor MCentral Star MProgenitors birthPN type2.4-8M>0.64M1 GyrType I1.2-2.4M0.58-0.64M3 GyrType II1.0-1.2M~0.56M6 GyrType III0.8-1.0M~0.555M10 GyrType IV

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 = 5007 contributing ~25% of fake objects (interlopers)Results: - ICPNe not centrally concentrated - 10% < ICL < 40%

Numerical simulations aiming to reproduce the observed PN distribution

1 Napolitano, Pannella, Arnaboldi, Gehrardt,Aguerri, Freeman, Capaccioli,Ghigna, Governato, Quinn, Stadel2003 ApJ 594, 172PKDGRAV n-body cosmological simulation, Model: CDM, m=0.3, 8=1, h=0.7Cluster of 3x1014M (cluster magnified, still n-body)

NO HYDRO

Np(

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, 0Now for ICL must trace unbound stars- trace points down to z = 0, reject those in subhalos & cDWhat did they do?- Phase space distribution analysis in 30x30 areas at0.2, 0.4, 0.5, 0.6 Mpc from cluster center- 2-p angular correlation function- Velocity distribution along l.o.sConsistency with observational data

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 formationModel: CDM, m=0.3, b=0.019h-2, 8=0.8, h=0.7

117 clusters with M > 1014Mh-1

HYDRO +

mp,gas mp,DM 6.93x108Mh-1 4.62x109Mh-1 7.5 h-1kpc

Bound and free stars have been selected by SKID, fraction depends on , optimal ~ 20 h-1kpcProblems with spatial resolution: numerical overmerging causes apparently unbound stars increasing resolution

Fraction of unbound stars > 10%(Diemand et al 2003)

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: CDM, m=0.3, b not given, 8=1, h=0.7

HYDRO +

Coma-like galaxy cluster M ~ 1.2x1015Mh-1

Two large groups ranging in size from Fornax to Virgo (Willman et al 2004)

Comparison of C2 with C2,low C2,low not enough resolution

NDM N*mp,DM/Mmp,* /M / kpc C26.9x1058.5x1051.5x1097.2x1073.75 C2,low8.6x1041.4x1051.2x10108.3x1087.5Murante et al6.6x10910.8

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 formationClaim: distribution of stars still OKTRUE? Neglected effects could be star-density dependentIs the sophisticated star formation machinery really better than searching for overdensity regions?

Various conclusions- Unbound stars fraction depends on dynamical status of clusterTwo 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)

-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 MIC fract.from halos M

What did we do so far?

ART & its generalization QART (modified for DE models)

Models: CDMm=0.3, 8=0.75, h=0.7 RP(=103GeV)m=0.3, 8=0.75, h=0.7

Cluster with M =2.92x1014Mh-1

Lbox Npart mpart 80 Mpc h-151233.17x108Mh-1 1.2 h-1kpcWillman et al1.05x109Mh-12.6 h-1kpcNapolitano et al3.54x108Mh-1 1.7 h-1kpc

LCDM z = 0

RP3 z = 0

LCDM z = 1

RP3 z = 1

LCDM z = 2

RP3 z = 2

Conclusions: What are we doing?- Star formation in iperdensities (SMOOTH), density contrast to be gauged to reproduce observed star amount- Star formation zs at z ~ 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