LCDM simulations:
A review of the state of the art
Carlton Baugh
Institute for Computational Cosmology
Durham University
Future Directions of N-Body Simulations for Cosmology
Edinburgh 8th November
The cosmological setting:
Primordial fluctuations + gravitational instability
in a Cold Dark Matter Universe
z ~ 1100
z~0
Sanchez et al. 2006, 2009
Moore’s law for simulations
From Volker Springel
The impact of simulations
Press & Schechter 1974
Why cold dark matter?
Cosmic web
galaxy
Ben Moore
COLD
WARM
HOT
The Large
Scale
Structure of the
Universe
Springel, Frenk & White 2006
Moore’s law for simulations
The Millennium Simulation
(courtesy Volker Springel)
Springel et al 2005 Millennium Simulation z=5.7
Springel et al 2005 Millennium Simulation z=1.4
Springel et al 2005 Millennium Simulation z=0
Billion particle simulations:
common for cosmological volumes
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Hubble Volume Runs (Evrard et al 2002) (1)
Millennium (Springel et al 2005) (10)
MICE (Fosalba et al. 2008) (8.5)
Horizon run (Kim et al 2009) (70)
Horizon project (Teyssier et al 2009) (70)
MXXL (Springel et al 2010) (300)
Baryonic Acoustic
Simulations at the ICC
BASICC
L = 1340/h Mpc V=2.4/h^3 Gpc^3
(20 x Millennium volume)
N=1448^3 (>3 billion particles)
Can resolve galactic haloes
130,000 hours CPU on Cosmology Machine
at ICC, Durham.
Combine with semi-analytical galaxy
formation model GALFORM
50 low-res BASICC runs for errors
(= 1000 Millenniums!)
Angulo et al. 2008
LCDM simulations:
Current state of the art
What have LCDM simulations done for us?
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The abundance of DM haloes
The clustering of DM
The structure and properties of DM haloes
Galaxy formation
Fraction of total mass in haloes of mass M
How many haloes of different mass?
Used a range of VIRGO
simulations:
different cosmology
different output redshifts
PS underpredicts high mass halo
abundance and overpredicts low
mass halo abundance ->
improved theoretical modelling:
ellipsoidal collapse (Sheth et al)
Universal fitting formula:
Accurate to 10-20%
low mass - common
high mass - rare
Jenkins et al. 2001
Improvements over PS mass function
Bhattacharya et al. (2010)
Results from GPC volume simulations
• MICE runs find more halos
>1.e+14/h Msun
• Transients due to starting
redshift and choice of initial
conditions generator?
• Improved fit
Crocce et al 2010
Redshift dependence of fit?
Crocce et al. 2010
Non-universality
Tinker et al 2008
Clustering of dark matter
32,768 particles
32.5/h Mpc
Davis et al. 1985
Clustering of
dark matter
Galaxies show power law
Correlation function
DM correlation function has
Curvature
Implies scale dependent bias
16 million particles 239.5/h Mpc
Jenkins et al. 1998
Halo clustering
Clustering depends on halo mass and a second parameter
Gao et al. 2005, 2007
Clustering of galaxies and DM
Springel, Frenk & White 2006
Scale-dependent bias
Deviation from unity is a deviation from linear theory
Deviation from dashed line = scale dependent bias
Dark matter
halos
Strength of scale dependence of bias depends on peak height M/M*
Angulo et al. 2008; see also Smith et al. , Crocce et al.
The
formation
of DM
haloes
Navarro, Frenk & White 1997
A universal density profile?
Navarro, Frenk & White 1997
Formation of a Milky Way like DM halo
Aquarius halo: Volker Springel et al. 2008
Via Lactea – II
1 billion particles
4100 Msun
1 million CPU hours
November 2007
Diemand et al 2008
Aquarius MW haloes
8 x resolution of Via Lactea II
Springel et al. 2008
Dark Matter Substructures
Springel et al 2008
Hierarchies of substructure
Springel et al 2008
The structure of DM haloes
Navarro et al. 2010
The properties of dark matter haloes
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Mass profiles are approximately universal
2 or 3 parameter density profile?
Strongly triaxial shapes
Abundant substructure (but small fraction of
total halo mass ~ 10%) – too many Milky Way
satellites?
• Cuspy inner density profiles: mass increases
with improving resolution – a problem for
galaxy rotation curves?
Navarro et al. 2010
Hierarchical Galaxy Formation
Dark matter plus baryonic physics
Gas dynamics simulations
Semi-analytical modelling
Structure formation in DM provides
context for galaxy formation
Images by Chris Power
Baugh 2006
Crain et al. 2009)
The OWLS simulations
• LOFAR IBM Bluegene/L (12k CPUs, PowerPC 440, 700 MHz,
500 MB per 2 CPUs)
• Cosmological (default: WMAP3)
• Hydrodynamical (SPH)
• Gadget III
• 2xN3 particles, N = 512 for most
• Two sets:
– L = 25 Mpc/h to z=2
– L = 100 Mpc/h to z=0
• Runs repeated many times with varying physics/numerics
• Status: runs nearly done, starting analysis
Joop Schaye et al.
Gas simulations vs.
Semi-analytic modelling
Gas simulations:
• More direct
• (Sometimes) more
information
• Challenged by
dynamic range
• Still use ‘sub-grid’
physics (=semianalytics)
Semi-analytic models:
• More generalised
calculation e.g.
Spherical symmetry
• Faster
• Flexible
• Modular
• Hybrid approach?
Populating DM haloes with galaxies
H-a selection
H-band selection
z=1
Orsi et al. 2009
Summary
• Simulations only way to follow collapse of
perturbations accurately
• Simulations have defined the CDM model
• Cosmological volumes/ resimulations of
individual haloes
• DM only: multi-billion particles standard
• DM + gas: multi-hundred million particles
• DM + semi-analytics: larger volumes than gas
• Databases: new paradigm for scientific publishing
• The future: beyond LCDM?