Structures Formation in Extragalactic Astrophysics and

Cosmology: numerical approaches

G. Murante

SAIT, Pisa, May 7th

WhyWhy

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

WhereWhere

Cosmology: LSSCosmology: high redshift structures (Damped Ly, high Z galaxies, protoclusters..)Galaxy cluster formation, evolution, properties; AGN/cluster connectionEarly type galaxy formation and evolution; DSCDisk galaxy formation

HowHow

N-Body (particle) codes for following gravitational instability from CMB on..Vlasov-Poisson (Boltzsmann) equationsHydro codes for the gas evolutionEuler equationsSubgrid parametric models for a number of astrophysical processesHPC required!

N-Body codesN-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) )

N-Body N-Body methodsmethods

Direct summationParticle-MeshParticle-Particle/Particle-MeshTree Codes

Adaptive P3M, Tree-PM…..

F i

Gm2(x i

x j )

2 x i

x j

2 3 / 2j

Hydrodynamical methodsHydrodynamical 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).

SPHSPH

AS(r ) mb

Ab

bb

W(r -

r b;h)

x/hq ;

2q ; 0

2q1 ; q)(24

1

1q0 ; q4

3q

2

3-1

h

h)W(x, 3

32

Other (astro)physical processesOther (astro)physical processes

Star formation/feedback – subgrid, but: bruteforceChemical enrichment / SNIa - subgridMetal/Atomic/Molecular cooling - exactMagnetic field – exact (simpler cases)BH/AGN feedback - subgridCosmic rays - subgridThermal conduction - exactNavier-Stokes - exactRadiative transport – approximate!…..

Available codesAvailable 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…

An An exampleexample

(GADGET2)(GADGET2)

Code validationCode validationStandard gravity/hydro tests

Code comparison (e.g. Santa Barbara Cluster Comparison, Frenk et al, 1999, ApJ, 525, 554)

Eulerian

Lagrangian

Open questionsOpen 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 resolvedEULERIAN: not Galilean invariant? Numerical viscosity/mixing not well controlled..and of course, SUBGRID processes…

FLASH PPM moving

FLASH ppm not moving

Wadsley, Veeravally & Couchman 2008

SPH

SPH, turbulentdiffusion

SPH, turbulent diffusion HR

SPH, reduced visc

Mixed schemes: AREPO Mixed schemes: AREPO (Springel 2009)(Springel 2009)

Voronoi tassellation, centeredon gas particles

Mixed schemes: AREPO Mixed schemes: AREPO (Springel 2009)(Springel 2009)

Fluxes evaluated through thecell interfaces, resolvingthe corresponding Riemann problems

KH instability: comparison between AREPOand an Eulerian code (ATHENA)Note: SPH would perform miserably here

Mixed schemes: GPHMixed schemes: GPH

Riemann problem solved between all particle couplesP*, v* found and put in SPH equations (can be derived..)Artificial viscosity dropped

Imaeda & Inutsuka 2002Inutsuka 1994, 2002Inutsuka & Imaeda 2001Cha 2002Cha & Withworth 2003

Fluid mixing!

GPH in GADGET: SOD tube test (Murante, Borgani, Brunino, ..in prep?)

“blip” “whiggles”No whiggles!Blip reduced!mixing

Star formation, feedback…Star formation, feedback…simpler schemessimpler schemes

Dark Matter

Gas

StarsStar formation

Gravity only

Gravity + hydrodynamics

Density/temperaturethreshold

UV heat.

SN

RadiativeCooling

Kinetic FB

Star formation, feedback…Star formation, feedback…MultiPhase schemesMultiPhase schemes

Dark Matter

Hot gas

Cold gas

Stars

RadiativeCooling

StarFormationGravity

SN

UV heat.

Gravity only

Gravity + Hydro

MOLECULAR GASMOLECULAR GAS

cMcM

M

M

hM

hM

=

= =

MUPPIMUPPIMurante,

Monaco,

Giovalli,

Borgani,

Diaferio

sfM

sfM

STAR

FO

RM

ATIO

Ndyn

Hstarsf t

f MM 2

restM

RESTORATION

restM

sfrestrest MM f

coolM

coolM

CO

OLIN

G

cool

hcool t

MM

EVAPO

RATIO

N

evapM

evapM

dyn

Hevapevap t

f MM 2

MH2 ->SF

On hotphase!

On coldphase!

ConclusionsConclusions

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!