Numerical simulations of cosmic structure formation

1. Numerical simulations of cosmic structure formation Liang Gao NAOC

2. Plan • A basic overview of Cosmological simulations. • Dark side of the Universe • Simulations of visible side of the Universe • Available numerical data in NAOC

3. Simulations need to account for the full cosmic matter-energy contentMATERIAL IN THE UNIVERSE tot= 1flat space-time Cosmological Constant“Dark Energy” 3  Dark Matter 85% 27 Matter  15% Baryons

4. Recreating the Universe in a computer • Creating initial matter distribution of the Universe according to the observed Microwave background. • Start evolution from a time shortly after big bang • Follow the matter in an expanding cubic region

7. Cosmological N-body simulations have grown rapidly in size over the last three decades"N" AS A FUNCTION OF TIME • Computers double their speed every 18 months (Moore's law) • N-body simulations have doubled their size every 16-17 months • Recently, growth has accelerated further.

8. The large N-body dark matter with uniform mass resolution like the MS may be not ideal to study internal structure of galaxy size halo ~1e12 solar masses. To reliably revolve inner structure of dark halo, one needs least million particles. We need a simulation 1000 times bigger than the Millennium simulation! A resimulation will help here!

9. 4 stages: • (1) Identify object of interest in existing simulation • (2) Create high resolution smooth mass distribution • of the region the object originates from. • Add old power keeping phases/amplitudes the • same +add extra power • (4) Feed initial conditions to n-body code

10. 10^9 particles simulation of a galaxy sized halo Springel et al. 2008

11. 10^9 particles simulation of a cluster sized halo Gao et al. 2010

12. Structure of dark matter halos • Halos extend to more than 10 times the visible radius of galaxies and contain more than about 10 times the mass in the visible regions • Halo are not spherical but approximate triaxial ellipsoids • Cuspy density profiles with outwardly increasing slopes. • Substantial number of self-bound subhalos contain about 10% of the halo mass.

13. Small scale structure in halos A ‘Milky halo’ Springel et al. 2008 A rich galaxy cluster halo Gao et al. 2010

14. Dark halo tests of LCDM • Measures of the shape and density profile of halos from Lensing and dynamics of visible tracers (stars, satellite galaxies) • Limits on the central cusps from galaxy rotation curves • Limits on amount of substructure from Observed satellites number counts and image distortion of background lensed objects. • Predictions for all these properties require simulations.

15. Density profiles of dark matter halos

16. Density profile slope Slope evolves much slower as radius for clusters than galaxies. Inner slopers are quite noisy for clusters A couple of Phoenix clusters tentatively have asymptotic inner slopes up to the numerically trusted scales.

17. Einasto versus NFW Some Phoenix cluster are better fitted with Einasto profile, while some are better with NFW, still some can not be well fitted with both fits.

18. Subhalo abudance (Gao et al. 2010) • There are more subhalos in clusters than in galactic halos. The subhalo mass function is close to N(m)~m^(-1.9x). Most mass of dark halos are not in subhalos. Cluster have higher abundance of subhalos (in terms of mass) and more mass in subhalos.

19. Subhalo spatial distribution Subhalo radial distribution is almost identical for cluster and galaxy. subhalo mass fraction is higher everywhere in clusters than in galaxies, especially in the innermost regions.

20. But we need to carefully interpret dark matter only simulation Missing satellites? Miss-distributed galaxies? Diemand, Moore & Stadel 2005 Moore et al 1999

21. By taking into account of baryon physics, there is indeed no crisis for radial distribution of cluster galaxies Gao et al. 2004 with SA model

22. Towards a realistic simulation of the Universe Can we simulate the astrophysical objects from the first principle?

23. The baryons in the universe can be modelled as an ideal gas BASIC HYDRODYNAMICAL EQUATIONS Euler equation: Continuity equation: First law of thermodynamics: Equation of state of ideal monoatomic gas:

24. Towards ideal cosmological simulation! We need to integrate more physics For example: Radiative cooling, UV background--is relatively well defined, but do we really understand UV background? Modelling star formation and subresolution multiphase model for the ISM --we have to put by hand. Phenomenological model for galactic winds--physics is not clear yet. Detailed chemical enrichment--relying on feedback model. Growth of supermassive black holes and AGN feedback--physics is not yet clear. Blackhole formation, feeding, feedback? Radiative transfer--computational challenge. A function of 6 variables, position, photo frequency, And direction.

25. 1. First stars • The cleanest simulation we can do from the first principle because of • 1. Very clean initial conditions • 2. Very clear physics.

26. What are needed to make the first stars • Assembly of dark matter structures to provide potential well to constrain gas. CDM --------dark halo WDM ---dark halo, filaments and pancakes. • Primordial Gas collapse to high density to make a proto-star seed (central density reach stellar density 10^22 cc).

27. What we have known • At T<10000k, H2 is the main coolant to dispose primordial gas entropy: • Formation of H2 • channel , dominates at z>200 • H- channel, dominates at z<200 and • 3 body reaction, very rapid reaction, dominates

28. Gas density Dark matter The first star will be formed in two density peak

29. Self-gravitating cloud 0.3Mpc 5pc 0.01pc A new born proto-star with T* ~ 20,000K r ~ 10 Rsun! Fully-molecular core

30. First stars in WDM Gao & Theuns,2007, Science

31. Status of current cosmological hydro-dynamical simulation • Even the most sophisticated hydro-dynamical simulation failed to reproduce a right shape luminosity function seen today. • Disk formation is still an problem. (too small is disk size) • Many simulation results are resolution dependant. • Overcooling problems. • Nevertheless it is promising in future!

32. Why hydro-dynamical simulation still fails? <> Unclear subgrid physics and how to integrate subgrid Physics to numerical code. Star formation, AGN, Blackhole… <>Feedback is vital in galaxy formation. It heat baryons, redistribute metals where gas cooling rate is sensitive to the metalicity. <> Feedback--winds, supernova explosion in real galaxy. Different implementations of feedback often lead to very different results (see Thacker et al. 2001).

33. Different implement Of star formation and Associated feedback Recipe lead to different Morphology of galaxies. Okomoto et al. 2002

34. Available simulations in NAOC

35. Phoenix Project • A brother project of the Aquarius. Collaborating with Simon White, Carlos Frenk, Volker Springel and Adrian Jenkins • A set of simulations of 9 rich clusters sized halo with mass about 1e15 Msun/h with unprecedented resolution • Pure dark matter only, but will run with whole physics in future • For the most expensive simulation, it takes more than 2 months on 1024 computing cores • Simulations have been performed at Supercomputer center, CAS

36. 10^9 particles inside virial radius; Mp=5e5 Msun/h resolves 200,000 substructures. 5Mpc/h across

37. Unit Mpc/h across

38. Phoenix simulation overview • 9 clusters (Ph-[A-I]) with masses great than 5e14 Msun randomly selected from the MS • 9 clusters have been simulated with 10^8 particles inside their R200. Per DM particles ~5e6 Msun/h , force resolution 320 pc/h • The PhA halo has been simulated with 4 different resolutions. The PhA-1 has 10^9 particles inside its viral radius. Mass resolution 5e-5 Msun/h, softenning=150pc/h • Stored 71 snapshots for all simulations. • We now already have all halo/subhalo catalogues and merging trees for the level-4 and 2 simulations, but only have catalogues for z=0 for the Ph-A-1.

41. Ongoing research projects • The dark side of rich clusters. Properties of dark matter component of rich clusters, i.e. density profiles, velocities profiles, shapes, substructures etc. • Dark matter annihilation signal from clusters • Strong lensing--Perturbation of giant arcs by DM halos of cluster galaxies • Intra-cluster light • Galaxy formation in rich clusters • Tidal disruption of subhalos • And many others

42. C4 Project • One of the largest Cosmological simulations in the world. 1Gpc/h Boxsize and 3072^3 particles. Mass resolution 2.4 e9Msun/h • Run with the WMAP 5 Cosmological parameters. • Collaborators: Ming Li, Longlong Feng, Yipeng Jing, Xiaohu yang, pengjie Zhang, Xi Kang, Jun Pan, Liang Gao etc. • Two weeks running on 2048 Cores at Super computer center, CAS

43. Science program for the C4 project • Make good mocks for Large observational surveies in China, for example, LAMOST, Sub millimeter survey of Dome-A. • Large scale structure of the Universe • Study earlier massive galaxy formation • Weak lensing studies

44. Other Available simulation data of the Virgo consortium at NAOC • Millennium simulation (Dark matter density, halos, subhalos, merging tree, the latest galaxy catalogue) • MS2 – 125 time higher resolution than MS but with 125 time less volume. • Aquarius Project—6 galactic halos with resolution up to 1000 Msun/h

45. What are simulations good for? • They compress cosmic evolution into human timescales • They can follow complex structures and complex physics in order to learn origin of cosmic systems • They can be observed in exactly similar ways to the real sky, enabling direct comparison of theory and observation • Keep computer busy.