1. Structures Formation in Extragalactic Astrophysics and Cosmology: numerical approaches G. Murante SAIT, Pisa, May 7th

2. Why Non linear evolution of Dark Matter density fluctuations (gravitational instability): no general analitic solution..adding baryons: hydrodynamics required, even worse Subgrid astrophysical processes (radiative cooling, star formation, Sne energy feedback, AGN feedback…): not even understood in full details

3. Where Cosmology: LSS Cosmology: high redshift structures (Damped Ly , high Z galaxies, protoclusters..) Galaxy cluster formation, evolution, properties; AGN/cluster connection Early type galaxy formation and evolution; DSC Disk galaxy formation

4. How N-Body (particle) codes for following gravitational instability from CMB on.. Vlasov-Poisson (Boltzsmann) equations Hydro codes for the gas evolution Euler equations Subgrid parametric models for a number of astrophysical processes HPC required!

5. N-Body codes A density field is sampled with massive particles Gravitational forces evaluated in a newtonian way General relativity enters in the background evolution ( cosmological model a(t) )

6. N-Body methods Direct summation Particle-Mesh Particle-Particle/ Particle-Mesh Tree Codes Adaptive P 3 M, Tree-PM…..

7. Hydrodynamical methods Eulerian (grid-based) methods: evolution of hydrodynamical quantities at fixed spatial (grid) position, by directly solving the Euler equation. Disadvantage: limited resolution (overcome with AMR codes) Advantage: Euler equation directly solved Lagrangian methods (SPH): hydrodynamical quantities attached to gas particles; evolution followed along the particle orbits; hydro forces exchanged along with gravitational forces Disadvantage: it’s a mimic to true hydrodynamics Advantage: high resolution achievable thanks to Lagrangian treatment (not bounded to the mesh size).

8. SPH

9. Other (astro)physical processes Star formation/feedback – subgrid, but: bruteforce Chemical enrichment / SNIa - subgrid Metal/Atomic/Molecular cooling - exact Magnetic field – exact (simpler cases) BH/AGN feedback - subgrid Cosmic rays - subgrid Thermal conduction - exact Navier-Stokes - exact Radiative transport – approximate! …..

10. Available codes GADGET (Springel 2001, 2005) HYDRA (Couchman & Pearce 1995) FLASH (Fryxell et al 2000) ENZO (O’Shea et al 2004) GASOLINE (Wadsley, Stadel, Quinn 2004) RAMSES (Teyssier, 2002) ART (Klypin, 1997; Kravtsov 1999) …and many others…

11. An example (GADGET2)

12. Code validation Standard gravity/hydro tests Code comparison (e.g. Santa Barbara Cluster Comparison, Frenk et al, 1999, ApJ, 525, 554) Eulerian Lagrangian

13. Open questions GRAVITY: ok, except softening/resolution (BUT: full GR treatment, probably not needed; modified gravities..) …60 order of magnitude in mass approx… Boltzsmann codes?? SPH: artificial viscosity; turbulence not well resolved EULERIAN: not Galilean invariant? Numerical viscosity/mixing not well controlled..and of course, SUBGRID processes…

14. FLASH PPM moving FLASH ppm not moving Wadsley, Veeravally & Couchman 2008

15. SPH SPH, turbulent diffusion SPH, turbulent diffusion HR SPH, reduced visc

16. Mixed schemes: AREPO (Springel 2009) Voronoi tassellation, centered on gas particles

17. Mixed schemes: AREPO (Springel 2009) Fluxes evaluated through the cell interfaces, resolving the corresponding Riemann problems KH instability: comparison between AREPO and an Eulerian code (ATHENA) Note: SPH would perform miserably here

18. Mixed schemes: GPH Riemann problem solved between all particle couples P*, v* found and put in SPH equations (can be derived..) Artificial viscosity dropped Imaeda & Inutsuka 2002 Inutsuka 1994, 2002 Inutsuka & Imaeda 2001 Cha 2002 Cha & Withworth 2003 Fluid mixing!

19. GPH in GADGET: SOD tube test (Murante, Borgani, Brunino,..in prep?) “blip” “whiggles” No whiggles! Blip reduced! mixing

20. Star formation, feedback… simpler schemes Dark Matter Gas Stars Star formation Gravity only Gravity + hydrodynamics Density/temperature threshold UV heat. SN Radiative Cooling Kinetic FB

21. Star formation, feedback… MultiPhase schemes Dark Matter Hot gas Cold gas Stars Radiative Cooling Star Formation Gravity SN UV heat. Gravity only Gravity + Hydro

22. MOLECULAR GAS = = = MUPPI MUPPI Murante, Monaco, Giovalli, Borgani, Diaferio STAR FORMATION RESTORATION COOLING EVAPORATION M H2 -> SF On hot phase! On cold phase!

23. Conclusions Simpler the physics, more robust the code …gravity:  OK …hydro: quite ok, but work in progress …subgrid: phenomenological, many recipes, something missing As always: more computing power needed!