Hydrodynamical simulations of cosmic structures
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Transcript of Hydrodynamical simulations of cosmic structures
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