Large, Single Realization N-body Simulations
Future Directions of N-Body Simulations for Cosmology
Jan Hartlap
Argelander-Institut für Astronomie
Universität Bonn
Nov 08, 2010
Current situation
◮
ongoing medium-size and large upcoming and planned
surveys (BAO/galaxy clustering, weak lensing, etc. )
◮
all predictions for these surveys rely on numerical
simulations (nonlinearity of structure formation)
◮
all of these are plagued by systematic effects requiring
numerical modelling
Large, single-realization simulations
◮
◮
usually push the limit of what is computationally feasible
usually for currently favoured cosmology
→
→
→
→
halo properties
galaxy formation
testing of methods
predictions/statistics for smaller surveys
Simulation ensembles
◮
◮
computationally cheaper
different cosmologies
→ predict cosmology-dependence of observables
→ get covariances, etc.
Some notable examples
Year
1998
2004
2006
2009
2009
2009
2010
2010
Name
Hubble Volume (Colberg et al. 2000)
Millennium Run (Springel et al. 2005)
MareNostrum (Gottlöber et al. 2006)
MillenniumII (Kolchin et al. 2009)
Horizon Run (Kim et al. 2009)
Teyssier et al. (2009)
Coyote Universe (Lawrence et al. 2010)
Millennium XXL
# Particles
1 × 109
1 × 1010
2 × 1 × 109
1 × 1010
7 × 1010
7 × 1010
1 × 109
3 × 1011
Box Size
[h−1 Mpc]
3000
500
500
100
6592
2000
1300
3000
Trade-off between
◮
volume
◮
small-scale resolution
(Semi-analytic) models of galaxy formation:
◮
large volume for rare objects, statistical analyses
◮
resolution for small objects, accurate merger histories,
satellite galaxies, etc..
Cluster counts, shear peak statistic, etc.:
◮
need to find rare objects (e.g. massive clusters at high z)
◮
need sufficient resolution to model the properties of the
luminous tracers (cluster galaxies/source galaxies)
BAOs
Baryonic Accoustic Oscillations:
◮
large volume for good sampling of large-wavelength modes
◮
resolution for modeling tracer population reliably
Millennium Simulation
(Springel et al. 2005)
0.20
log (∆2(k) / ∆2lin)
0.10
0.00
-0.10
-0.20
0.01
0.10
k [ h / Mpc ]
Horizon Run (2300× larger)
(Kim et al. 2009)
Weak lensing
Weak gravitational lensing:
◮
large volume for statistics, real space observables,
light-cone construction
◮
resolution for small scalle-correlations, modeling of
galaxies, higher-order statistics, intrinsic alignments, etc.
but: depends on how important baryons are...
Weak lensing: light cone construction
Lens plane
Simulation snapshot
Observer
z=0.02
z=0.04
z=0.06
z=0.09
Lens plane 1
Lens plane 2
z=0.02 z=0.02
z=0.02
Redshift
slice
z=0.04 z=0.04
Lens plane
Simulation
volume
...
z=0.04
z=0.12
Weak lensing: real space measures and projections
You cannot have a simulation that accurately models realand Fourier-space quantities simultaneously!
(e.g. Sirko 2005, Pen 1997 )
◮
most (if not all?) large simulations have initial conditions
set up in Fourier space
◮
modes with small |k | are sparsely sampled
◮
modes with |k | < 2π/L are not represented
⇒ real space statistics differ from their continous
counterparts (DFT 6= FT)
◮
also affects projections of the density field
(e.g. convergence)
Weak lensing: predicting the correlation functions
◮
remove all power from Pδ for k <
◮
sources at z = 1
2π
L
1.05
1
ξ+(L) / ξ+
0.95
0.9
0.85
L=6000 Mpc/h
L=3000 Mpc/h
L=1000 Mpc/h
L=500 Mpc/h
0.8
0.75
0.7
1
10
θ [arcmin]
100
Weak lensing: covariances
◮
Gaussian covariance of ξ+
◮
sources at z = 1, A = 150 deg2 , ngal = 21/arcmin2 , σǫ = 0.4
diag[Cov+(L)] / diag[Cov+]
1.05
1
0.95
0.9
0.85
L=6000 Mpc/h
L=3000 Mpc/h
L=1000 Mpc/h
L=500 Mpc/h
0.8
0.75
0.7
1
(see also Sato et al. 2010)
10
θ [arcmin]
100
Clustering of galaxy clusters
(S. Hilbert)
Weak lensing: modeling galaxies is important
Removal of close galaxy pairs biases correlation functions!
FIX criterion, rSDSS = 25
3
[%]
2
1
0
[%]
-1
-2
1
0
-1
-2
-3
-4
-5
θfix = 2.0′′
θfix = 3.7′′
θfix = 5.0′′
1
∆ξ+z+δ (θ)
∆ξ−z+δ (θ)
∆ξ+δ (θ)
∆ξ−δ (θ)
10
100
1
θ [arcmin]
(Hartlap et al. 2010)
10
100
Importance of baryons
(Rudd et al. 2008)
(Jing et al. 2006)
red: non-rad. baryons,
dashed: non-rad. baryons
blue:
rad. cooling/heating,
solid: rad. cooling/heating,
star formation, SN feedback,
star formation, SN feedback
sources at z = 1
Some conclusions
◮
large simulations important for testing methods,
understanding structure formation, halos, etc.
◮
trade-off between volume and resolution depends
somewhat on application, but:
◮
large volume important for almost all cosmological probes
◮
really need to model the observations, i.e. model the
observable tracers (galaxies, clusters)
Some questions
◮
◮
How meaningful is it to push small-scale resolution of DM
simulations (baryons...)?
What are the next steps?
◮
◮
◮
DM simulations with larger boxes/ higher resolution?
runs with baryons?
how well do we understand baryonic physics on the
relevant scales?
◮
How should predictions for surveys be made (fitting
formulae, emulation)?
◮
Should we start setting up simulations with real-space
applications in mind?