Hydrodynamical simulationsHydrodynamical simulationsof cosmic structuresof cosmic structures

Stefano BorganiDepartment of Astronomy

Inter-dept. Centre for Computational Sciences University of Trieste

Talk @ CISC Workshop, Trieste, June 15th 2005

Core group: Collaborators:

SB (DAUT) Francesca Matteucci (staff, DAUT)

Luca Tornatore (post-doc, SISSA) Cristina Chiappini (staff, INAF)

Silvia Ameglio (PhD, DAUT) Andrea Biviano (staff, INAF)

Alex Saro (undergrad., DAUT) Marisa Girardi (staff, DAUT)

Francesco Calura (post-doc, DAUT)

Paolo Tozzi (staff, INAF)

Basel:Ortwin Gerhard

Bologna: Stefano EttoriLauro Moscardini Mauro Roncarelli

Garching:Klaus DolagVolker Springel

Padova:Giuseppe Tormen Elena Rasia

Roma:Pasquale Mazzotta

Torino:Magda ArnaboldiAntonaldo Diaferio Giuseppe Murante

Who are we?Who are we?

Trieste: Silvia AmeglioStefano BorganiLuca TornatoreAlex Saro

Beijing:Ling-Mei Cheng

The initial conditionsThe initial conditions

The final stateThe final state

REFLEX survey2dF GRS

What does a LSS model What does a LSS model require?require?

(a) Parameters of the Friedmann background (m=0.3 ; =0.7 ; H0=70+/-5 km/s/Mpc).

(b) Initial fluctuation spectrum (P(k)kn with n=1).(c) Choice of fluctuation mode (adiabatic).(d) Statistical distribution of fluctuations (Gaussian).(e) Chemistry: density of baryons, cold and hot particles, number of relativistic species.(f) Tools to follow the evolution of perturbations: linear theory, approximate methods for non-linear evolution, numerical computations (N-body).(g) Relation between distributions of mass and light: evolution of gas, galaxy formation, star formation processes.

The equations of motionThe equations of motion

Density fluctuation field:(a) Continuity Equation:

(b) Euler Equation:

(c) Poisson Equation:

Evolution of hot Evolution of hot (T> 3 keV)(T> 3 keV) clustersclusters

BG ‘01

N-body approaches to gravitational instability

Method 1. Direct summation

Compute the force on a given particles by directly summing over the contributions of the other N-1 particles:

jji

jii

xx

xxGmF 2/322

2 )(

Parameters defining a simulation:1. Box size L: ~ 1 Mpc~ 1 Mpc for the formation of a single galaxy for the formation of a single galaxy ~ 500 Mpc~ 500 Mpc for the distribution of galaxies and clusters for the distribution of galaxies and clusters

2. Mass resolution: ~ 10~ 1055-10-1066 M Msunsun for the formation of a single for the formation of a single galaxy; galaxy;

101088 M Msunsun for the formation of a galaxy cluster for the formation of a galaxy cluster

3. Force resolution: ~ 0.1 kpc~ 0.1 kpc for the formation of a single for the formation of a single galaxy; galaxy;

~ 1-5 kpc~ 1-5 kpc for the formation of a galaxy cluster for the formation of a galaxy cluster

softening parameter (force resolution)

N(N-1)/2 operations!!!

N-body approaches to gravitational instability

Method 4. Tree codes (Barnes & Hutt 1986)

General strategy:

Consider a far-away group of particles as a single particle for the force computation

The limiting “aperture angle” =s/r regulates the accuracy of the long-range force.

Smoothed particle hydrodynamics (SPH)(Monaghan 1992, ARAA, 30, 543)

Use an interpolation method to express any function in terms of its values at a set of disordered points (i.e. particles):

Def.: Intergral interpolant of the function A(r): 'rd h);'r-r W()A(r')r(A I

W: interpolating kernel.

)'r-r( h);'r-r W(B.

1 'rd h);'r-rW( A.

D0h

When dealing with a discrete distribution of particles:

h);r-r W(A

m)r(A bb b

bbS

b: particle label

mb: mass of the b-th particle

b: density of the b-th particle

Ab: value of A(r) at the position rb

L=480 Mpc/h

Ngas=NDM=4803

8=0.8

zin=46

Tree + SPH GADGET2 (Springel et al .’01; Springel ‘05)

www.MPA-Garching.MPG.DE/gadget Explicit entropy conservation (Springel & Hernquist ‘02)

Radiative cooling + uniform evolving UV background

Multiphase model for self-regulated star-formation

Phenomenological model for galactic winds (Springel & Hernquist ‘03)

Chemical enrichment from Sn-Ia and II (Tornatore et al. ’04, ‘05)

Reduced-viscosity SPH scheme (Dolag et al. ‘05, in prep.)

fraction of mass in stars >8M (Salpeter IMF)

SN energy fraction powering winds (=0.5-1)amount of gas in wind, units of dM* (=2)

vvw w (300-500) km s(300-500) km s-1-1

The simulation code

The simulation box (z=0)Gas density Gas temperature

40,000 CPU hours on the IBM-SP4

70 GB RAM – 1.2 TB output

The biggest cluster (1.3 1015 h-1 M )

density field temperature field

9 h -1 Mpc

9 h

-1 M

pc

9 h

-1 Mpc

Sim

ulation

of a single h

aloS

imu

lation of a sin

gle halo

A Cluster Resimulation Champaign

Extract a few (4) clusters from the box and resimulate at higher resolution

Cl-1

1.4e15 M/h

Cl-2

2.9e14 M/h

Cl-4

1.6e14 M/h

Cl-3

2.7e14 M/h