Cosmological Fluid Dynamics with AMR

1. Cosmological Fluid Dynamics with AMR Michael L. Norman Laboratory for Computational Astrophysics, UCSD

2. Baryons + Radiation + Magnetic fields Under the gravitational influence of dark matter Interacting galaxies Coma cluster in X-ray

3. Cosmological Fluid Dynamics • Definition • Fluid/plasma dynamics on cosmic scales driven by the clustering of cold dark matter • Goals • understand origin and evolution of cosmic structure from the Big Bang onward across all physical length, mass & time scales • understand interplay between different mass constituents (dark matter, baryons, radiation), self-gravity, and cosmic expansion • predict earliest generation of cosmic structures which have not yet been observed

4. Outline • Cosmological standard model (LCDM) and hierarchical structure formation • Baryonic physics in structure formation • Enzo: numerical methods and tests • adaptive particle-mesh • cosmological PPM • comparison with SPH • additional physics • Applications • Future plans

5. The Universe Exhibits a Hierarchy of StructuresDynamic Range > 109 galaxy superclusters dwarf galaxies galaxy groups star clusters galaxy clusters galaxies 109 100 101 102 103 104 105 106 107 108 Parsecs

6. Large Scale Structure 11-13.7 Gyr ABB

7. Cosmic Microwave BackgroundTemperature Fluctuations 380,000 yr ABB NASA WMAP DT/T ~ Dr/r ~ 10-4

8. CMB Angular Power Spectrum

9. Mass-Energy Budget of the Universe (WMAP) WL Wb Wcdm Wcdm+ Wb+ WL=1

10. Matter Power Spectrum P(k) LCDM http://www.hep.upenn.edu/~max

11. Linear evolution • Decompose density perturbations into Fourier components d(k) • In linear regime, every wave mode grows independently, due to gravitational instability, at the same rate:

12. Nonlinear scale in LCDM z4 z3 clusters galaxies first objects nonlinear z2 linear z1 LSS Log D2 5 orders of magnitude Log k

13. Nonlinear evolution • Plane waves become Zel’dovich pancakes • Quasi-spherical overdensities become gravitationally bound, virialized objects • Because of shape of CDM power spectrum, a vast range of scales go nonlinear nearly simultaneously for M<~M(dwarf galaxy), followed by hierarchical merging • adaptive high resolution methods in 3D • Dynamics depends on the mass constituent • collisionless dark matter: violent relaxation • baryons: shock thermalization

14. Cold Dark Matter • Dominant mass constituent: Wcdm~0.23 • Only interacts gravitationally with ordinary matter (baryons) • Collisionless dynamics governed by Vlasov-Poisson equation • Solved numerically using N-body methods* (*equivalent only if 2-body relaxation is absent)

15. Hierarchical Clusteringof Cold Dark Matter LCDM 2563 AMR comoving frame 16 Mpc/h

16. Hierarchical Merging • large galaxies form from mergers of sub-galactic units • Galaxy groups form from merger of galaxies • Galaxy clusters form from merger of groups • Where did it begin, and where will it end? Lacey & Cole (1993)

17. Baryonic Physics and Structure Formation

18. A S T R O N O M I C A L U N I V E R S E

19. baryonic universe radiative transfer radiation background self-shielding photo-ionization photo-heating photo-evaporation ionizing flux absorption infall galaxies IGM feedback (energy, metals) SF-recipe multi-species hydrodynamics N-body dynamics cosmic expansion self-gravity dark matter dynamics

20. Algorithms requirements posed by cosmological structure formation • Must be resolution-matched to the dark matter • adaptive, multiresolution methods • High order-accurate • Need to follow perturbation growth accurately from linear to nonlinear regime • CDM exhibits power on all scales, including grid scale • Monotonic • Gravity amplifies density perturbations; numerical oscillations disastrous • Shock capturing • virialization of collapsing perturbations involve very strong shocks (M>100)

21. Greg Bryan et al. http://cosmos.ucsd.edu/enzo

22. Structured Adaptive Mesh Refinement (Berger and Colella 1989)

23. Enzo Vlasov-Poisson Solver:AMR-Particle Mesh (Dark matter, stars) • [1] Mass assignment • Mass assigned at every level of the mesh hierarchy with TSC cloud whose size is proportional to Dx(level) • [2] Field solve • Root grid: 3D FFT • Subgrid: local multigrid with boundary potentials interpolated from parent grid, or copied from sibling grids • [3] Particle push • Particle belongs to the finest grid which contains it • TSC force interpolation: resolution ~2Dx(level) • Leapfrog integration with local timestep Dt(level)

24. Enzo Euler Solvers • Piecewise Parabolic Method (Colella & Woodward 1984; Bryan et al. 1995) • Comoving frame equations • DE, LR formulations • Directionally split • Dual energy formalism • Self-gravity • variety of Riemann solvers • ZEUS hydro (Stone & Norman 1992a) • Staggered finite difference • Van Leer monotonic advection • Artificial viscosity

25. Baryons: The Tail of the Dog Dark matter Gas

26. Just Shocking!: Temperature Evolution

27. Comparison with GADGET: Tree+SPH (O’Shea et al. 2005)

28. Dark Matter: Tree vs. AMR-PM

29. Power spectrum

30. Halo mass function

31. Baryons: SPH vs. AMR-PPMnonradiative gas “adiabatic”

32. Halo baryon mass function

33. Baryon fractions in halos Enzo GADGET

34. Entropy distribution functions

35. Code Comparison: Conclusions • DM quantities agree over entire range of halo masses if AMR uses low overdensity threshold and 2x finer force grid • Baryonic properties agree somewhat less well; sensitive to resolution and method • Preheating in AV methods modifies entropy distributions, baryon fractions • PPM asymptotes to ~ 1.0 cosmic mean • SPH asymptotes to ~ 0.9 cosmic mean

36. Enzo Additional Physics • multi-species Euler solver for cosmic gas • stiff nonequilibrium chemistry solver for H, H+, He, He+, He++, e-, H-, H2+, H2 • UV radiation backgrounds • radiative heating and cooling (inverse Compton, line and continuum, etc.) • parameterized star formation/feedback recipes • metallicity fields

37. Sample Applications radiative cooling star formation ionization dark matter molecules rad. Xfer feedback gas

38. X-Ray Clusters • Hot, x-ray emitting gas bound to a cluster of galaxies • Extremely luminous in x-ray • T easily measured • T and M tightly correlated • n(T,z)n(M,z) • Cosmological probes of P(k), Wm,Wb andWL Coma Cluster ROSAT (Boehringer et al)

39. Idealized Cluster ICM virialization shock R~Rvir T~108 K adiabatic halo: tcool>tHubble supernovae heating << gravitational heating R~0.1Rvir non-adiabatic core: tcool<=tHubble radiative cooling modifies entropy profile T<108 K

40. Formation of an X-ray Cluster2563 AMR (adiabatic) Temperature X-ray surface brightness 16 Mpc (comoving)

41. C1 z=0 log(Sx) log(Tx) back Motl et al. (2002)

42. The Intergalactic Medium Source: M. Murphy

43. Physical Origin of Ly a Forest quasar N=10243 L=54 Mpc/h Simulated HI absorption spectrum Earth Baryon Overdensity, z=3

44. Precision cosmology using the Lyman a forest • Absorption spectrum is a 1D map of neutral hydrogen along LOS • Assuming gas is in ionization equilibrium with known UV background, have 1D map of baryons along LOS • Baryons closely follow dark matter, hence have 1D map of total mass density along LOS • Many LOS sample matter power spectrum P(k) • Simulations provide mapping between absorption spectra and P(k) back

45. Simulating the Formation of the First Star in the Universe Feb. 2003 Nov. 2002 Tom Abel, Greg Bryan & MN http://www.TomAbel.com

46. Formation of First StarsAbel, Bryan & Norman (2001) 1 x 10 x 100 x 1000 x Cosmic scales 104 x 105 x 107 x 106 x Solar system scales

47. Impact of the First Stars • The first stars are massive, extremely luminous, and short lived • The either explode as supernovae or collapse to form the first black holes, or both • Early reionization and reheating of the intergalactic medium (WMAP) • Chemical enrichment of the intergalactic medium back

48. Formation and Evolution of Galaxies

50. Hydrodynamic Simulation of Galaxy Formation M. Norman, G. Bryan & B. O’Shea