1. 1 THE NATURE OF DARK ENERGY FROM N-BODY COSMOLOGICAL SIMULATIONS Paola Solevi Università Milano - Bicocca A.A. 2003/2004

2. 2 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

3. 3 What is Dark energy? The best fit model of WMAP: ~70% dark energy The cosmological constant is described by energy-momentum tensor: Problems of LCDM cosmology Coincidence problem: why just now? Fine tuning:

4. 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: RPSUGRA Where is the energy scale parameter.

5. 5 The evolution of the DE density & of time vs. the scale factor

6. 6 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 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

7. 7 Basic ingredients Initial conditions Initial conditions: power spectrum of density perturbations depends on the cosmological parameter & inflationary model n=1 for scale-free HZ spectrum is the transfer function (from CMBfast) P(k) at z=40 for different kind of Dark Energy.

8. 8 FITTING FORMULAE for resolving equations used in simulation: Analytic formula for in Friedmann eq. (eq. of Poisson ) (eq. of motion) background evolution Growing of perturbation depends on the background evolution

9. 9 Linear features of the model Periodic boundary conditions Periodic 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 N row number of particles in one dimension L box box size N grid number of cells in one dimension n number of refinment levels

10. 10 All NFW profiles… RP SUGRA LCDM Density profiles …but with different concentrations FEATURES OF SIMULATED CLUSTERS RP3LCDMSU3 Virial Radius (Mpc) 0.663 (149.8) 0.730 (103.1) 0.709 (118.3) Virial Mass 5.01e134.44e134.53e13 C vir 10.17.28.84

11. 11 The best way for test different central concentration is via Strong Gravitational Lensing Formation of Giants Arcs More Arcs for RP model

12. 12 Z=0.3 Z=0.5 Z=1.0 Z=1.5 LCDM RP

13. 13 No differences predicted because of the same σ 8 normalization at But different evolution expected z=0 Mass function evolution

14. 14 Void probability function Simulations run at HITACHI MUNCHEN MPI 32 Node,32x256 Pr. Three simulations: LCDM, RP (Λ=10 3 GeV), SU (Λ=10 3 GeV) CosmologiesSimulations features ΩmΩm 0.3L Box 100 h -1 Mpc Ω DE 0.7N part 256 3 h 0.7MpMp 5.0x10 9 M ʘ h -1 σ8σ8 0.90 є 3.0 h -1 kpc (7 refinement levels)

15. 15 VPF is a function of all the correlation terms : - reduced n-point correlation function mean value -mean galaxy number in V R Why do we expect that VPF depend on the cosmological model? Different evolution rate Different halo # P LCDM (R)> P SU (R) > P RP (R)

16. 16 VPF, M > 1x10 12 M ʘh -1 Just as for halos MF no differences predicted at z=0 Z=0.9Z=0 But different evolution expected

17. 17 VPF, M > 1x10 12 M ʘh -1 VPF, M > 5x10 12 M ʘh -1 Notice the dependences on the mass limit, significant differences but halo number getting low Z=1.5

18. 18 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 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 Origin: -Tidal stripping -Infall of large groups

19. 19 Why PNe as ICL tracers? PN is a short (~10 4 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 Luminosity (HR diagram)

20. 20 Shell of gas from the envelope of central star Hot central star T~5x10 4 K O[III] emission UV (Arnaboldi et al 2003)

21. 21 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 MCentral Star MProgenitor’s birthPN type 2.4-8M ʘ >0.64M ʘ 1 GyrType I 1.2-2.4M ʘ 0.58-0.64M ʘ 3 GyrType II 1.0-1.2M ʘ ~0.56M ʘ 6 GyrType III 0.8-1.0M ʘ ~0.555M ʘ 10 GyrType IV

22. 22 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%

23. 23 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, Model: ΛCDM, Ω m =0.3, σ 8 =1, h=0.7 Cluster of 3x10 14 M ʘ (cluster magnified, still n-body) N p (<R v ) m p є ~ 5x10 5 5.06x10 8 M ʘ 2.5kpc NO HYDRO

24. 24 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

25. 25 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, Ω m =0.3, Ω b =0.019h -2, σ 8 =0.8, h=0.7 117 clusters with M > 10 14 M ʘ h -1 m p,gas m p,DM є 6.93x10 8 M ʘ h-1 4.62x10 9 M ʘ h -1 7.5 h -1 kpc HYDRO +

26. 26 Bound and free stars have been selected by SKID, fraction depends on, optimal ~ 20 h -1 kpc Problems with spatial resolution: numerical overmerging causes apparently unbound stars increasing resolution Fraction of unbound stars > 10% (Diemand et al 2003)

27. 27 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, Ω m =0.3, Ω b not given, σ 8 =1, h=0.7 HYDRO +

28. 28 Coma-like galaxy cluster M ~ 1.2x10 15 M ʘ h -1 Two large groups ranging in size from Fornax to Virgo (Willman et al 2004)

29. 29 N DM N * m p,DM / M ʘ m p, * / M ʘ Є / kpc C 2 6.9x10 5 8.5x10 5 1.5x10 9 7.2x10 7 3.75 C 2,low 8.6x10 4 1.4x10 5 1.2x10 10 8.3x10 8 7.5 Murante et al 6.6x10 9 10.8 Comparison of C 2 with C 2,low C 2,low not enough resolution

30. 30 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?

31. 31 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)

32. 32 -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 fract.from halos M<M

33. 33 What did we do so far? ART & it’s generalization QART (modified for DE models) Models: ΛCDMΩm=0.3, σ8=0.75, h=0.7 RP(Λ=10 3 GeV)Ωm=0.3, σ8=0.75, h=0.7 Cluster with M =2.92x10 14 M ʘ h -1 L box N part m part є 80 Mpc h -1 512 3 3.17x10 8 M ʘ h -1 1.2 h -1 kpc Willman et al 1.05x10 9 M ʘ h -1 2.6 h -1 kpc Napolitano et al 3.54x10 8 M ʘ h -1 1.7 h -1 kpc

34. 34 LCDM z = 0

35. 35 RP3 z = 0

36. 36 LCDM z = 1

37. 37 RP3 z = 1

38. 38 LCDM z = 2

39. 39 RP3 z = 2

40. 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