Download - Cosmological N-body Simulations
Cosmological N-body Simulations
Julian Adamek
The IFT School on Cosmology Tools
Madrid, 16/03/2017
Beyond the Linear Frontier
At late time (t & 1 Gyr) and on “not too large” scales (r . 100Mpc) the Universe is clumpy. A linear treatment is insufficient.
This so-called large-scale structure (LSS) contains a hugeamount of information that we want to harness with the nextgeneration of telescopic surveys.
Julian Adamek IFT School on Cosmology Tools 2017 1 / 16
Beyond the Linear Frontier
At late time (t & 1 Gyr) and on “not too large” scales (r . 100Mpc) the Universe is clumpy. A linear treatment is insufficient.
This so-called large-scale structure (LSS) contains a hugeamount of information that we want to harness with the nextgeneration of telescopic surveys.
Things we may be interested in:
• Non-linear power spectra / correlation functions
• Structure and evolution of dark matter halos
• Local and integrated projection effects (Doppler RSD,gravitational lensing . . . )
Julian Adamek IFT School on Cosmology Tools 2017 1 / 16
N-body Challenges
Cosmological N-body Simulation = full simulation of thenon-linear (gravitational) evolution of a N-body system
Challenges:
• Computationally expensive → parallelization
• Too much information → data reduction
• Competition between finite volume and finite resolution
• Validation of results → convergence studies, codecomparison. . .
• Systematics due to unmodelled astrophysics
Julian Adamek IFT School on Cosmology Tools 2017 2 / 16
Choose the Right Tool
gevolution Gadget-2 RAMSESparadigm particle-mesh tree / tree-PM particle-meshresolution fixed adaptive (tree) adaptive (AMR)
hydro no SPH Cartesian FVMgravity metric (GR) Newtonian F Newtonian ψ
neutrinos yes (no) nolanguage C++ ANSI C Fortran 90
release date 2016 2005 2008
There are many more N-body codes on the market (Enzo,pkdgrav, CubePM. . . )
Julian Adamek IFT School on Cosmology Tools 2017 3 / 16
Particle-Mesh (PM) Scheme
Julian Adamek IFT School on Cosmology Tools 2017 4 / 16
Particle-Mesh (PM) Scheme
Julian Adamek IFT School on Cosmology Tools 2017 4 / 16
Particle-Mesh (PM) Scheme
Julian Adamek IFT School on Cosmology Tools 2017 4 / 16
Particle-Mesh (PM) Scheme
Julian Adamek IFT School on Cosmology Tools 2017 4 / 16
Particle-Mesh (PM) Scheme
Julian Adamek IFT School on Cosmology Tools 2017 4 / 16
Adaptive Mesh Refinement (AMR)
Idea: by subdividing cells, increaseresolution of PM grid in “interesting”regions
• choose refinement criterion(e.g. density threshold)
• work out boundary conditionsat coarse/fine transition
• implement appropriatenumerical solvers (no FFT!)
• worry about load balance! credit: R. Teyssier
Julian Adamek IFT School on Cosmology Tools 2017 5 / 16
Tree Algorithm
Idea: speed up computation of two-body forces by “lumping together”clouds of particles
• choose “tree opening angle”
• still needs “softening length”
• worry about load balance!
credit: University of Texas / Austin
Julian Adamek IFT School on Cosmology Tools 2017 6 / 16
Initial DataSimulations are initialized at early time (typically redshift50–100) where perturbation theory is still valid
• initial fluctuation amplitudes can be computed with aBoltzmann code (e.g. CAMB or CLASS)
Julian Adamek IFT School on Cosmology Tools 2017 7 / 16
Initial DataSimulations are initialized at early time (typically redshift50–100) where perturbation theory is still valid
• initial fluctuation amplitudes can be computed with aBoltzmann code (e.g. CAMB or CLASS)
Procedure:• set up homogeneous particle ensemble• generate random realization of the perturbation field in
Fourier space• Fourier transform to obtain displacement• displace particles
Julian Adamek IFT School on Cosmology Tools 2017 7 / 16
Initial DataSimulations are initialized at early time (typically redshift50–100) where perturbation theory is still valid
• initial fluctuation amplitudes can be computed with aBoltzmann code (e.g. CAMB or CLASS)
Procedure:• set up homogeneous particle ensemble• generate random realization of the perturbation field in
Fourier space• Fourier transform to obtain displacement• displace particles
Radiation is usually ignored (often even in the background!)• compute linear transfer function at redshift z=0 and scale
back using the appropriate growth function• can use Newtonian 2LPTJulian Adamek IFT School on Cosmology Tools 2017 7 / 16
Post-processing: Power Spectra
Pδ cdm
+b(k)[M
pc3/h3]
Pδ ν(k)[M
pc3/h3]
gevolutionCLASS
z = 63z = 31z = 15z = 7z = 3z = 1z = 0
100
100
10
10
1
1
1
1
1
1
0.1
0.1
0.1
0.1
0.1
0.1
0.01
0.01
0.01
0.01
0.01
0.01
0.001
0.001
∑mν = 0 meV
∑mν = 200 meV
∑mν = 200 meV
∑mν = 200 meV
mν = 60 meV mν = 80 meV
Julian Adamek IFT School on Cosmology Tools 2017 8 / 16
Post-processing: Halo Finder
Break down particle ensembleinto halos using halo finder algo-rithm
• friends-of-friends
• spherical overdensity
Halo catalog = huge data reduc-tion
• halo distribution (e.g.two-point statistics)
• individual halo properties(e.g. density profiles)
Julian Adamek IFT School on Cosmology Tools 2017 9 / 16
Post-processing: Halo Finder
Break down particle ensembleinto halos using halo finder algo-rithm
• friends-of-friends
• spherical overdensity
Halo catalog = huge data reduc-tion
• halo distribution (e.g.two-point statistics)
• individual halo properties(e.g. density profiles)
Julian Adamek IFT School on Cosmology Tools 2017 9 / 16
Post-processing: Ray Tracing
Write output in form of a lightcone (as opposed to equal-timesnapshot) → one can constructobservables using ray tracing
Julian Adamek IFT School on Cosmology Tools 2017 10 / 16
A Brief Overview of gevolution
spin-1 metric perturbationwith gevolution
gevolution, a general relativistic N-body code
• based on weak-field expansion (inPoisson gauge)
• for any given T µν computes the six
metric d.o.f. (Φ, Ψ, Bi, hij)
• N-body particle ensemble evolved usingrelativistic geodesic equation
Julian Adamek IFT School on Cosmology Tools 2017 11 / 16
A Brief Overview of gevolution
spin-1 metric perturbationwith gevolution
gevolution, a general relativistic N-body code
• based on weak-field expansion (inPoisson gauge)
• for any given T µν computes the six
metric d.o.f. (Φ, Ψ, Bi, hij)
• N-body particle ensemble evolved usingrelativistic geodesic equation
Models beyond ΛCDM may have relativistic sources ofstress-energy perturbations
• Newtonian limit not always a good approximation
Julian Adamek IFT School on Cosmology Tools 2017 11 / 16
A Brief Overview of gevolution
spin-1 metric perturbationwith gevolution
gevolution, a general relativistic N-body code
• based on weak-field expansion (inPoisson gauge)
• for any given T µν computes the six
metric d.o.f. (Φ, Ψ, Bi, hij)
• N-body particle ensemble evolved usingrelativistic geodesic equation
Models beyond ΛCDM may have relativistic sources ofstress-energy perturbations
• Newtonian limit not always a good approximation
Increasing data quality imposes new challenge to take intoaccount relativistic effects (e.g. in modelling RSD, WL. . . )
• perturbations of spacetime geometry are signal, not noise!
Julian Adamek IFT School on Cosmology Tools 2017 11 / 16
A Brief Overview of gevolution
spin-1 metric perturbationwith gevolution
gevolution, a general relativistic N-body code
• based on weak-field expansion (inPoisson gauge)
• for any given T µν computes the six
metric d.o.f. (Φ, Ψ, Bi, hij)
• N-body particle ensemble evolved usingrelativistic geodesic equation
Models beyond ΛCDM may have relativistic sources ofstress-energy perturbations
• Newtonian limit not always a good approximation
Increasing data quality imposes new challenge to take intoaccount relativistic effects (e.g. in modelling RSD, WL. . . )
• perturbations of spacetime geometry are signal, not noise!
https://github.com/gevolution-code/gevolution-1.1.git
Julian Adamek IFT School on Cosmology Tools 2017 11 / 16
Strategy
• choose ansatz for the metric (perturbed FLRW)
ds2=a2(τ)[
−e2Ψdτ2+ e−2Φδijdxidxj+ hijdx
idxj− 2Bidxidτ
]
Julian Adamek IFT School on Cosmology Tools 2017 12 / 16
Strategy
• choose ansatz for the metric (perturbed FLRW)
ds2=a2(τ)[
−e2Ψdτ2+ e−2Φδijdxidxj+ hijdx
idxj− 2Bidxidτ
]
• metric components are evolved with Einstein’s equations
Gµν = 8πGT µ
ν
Julian Adamek IFT School on Cosmology Tools 2017 12 / 16
Strategy
• choose ansatz for the metric (perturbed FLRW)
ds2=a2(τ)[
−e2Ψdτ2+ e−2Φδijdxidxj+ hijdx
idxj− 2Bidxidτ
]
• metric components are evolved with Einstein’s equations
Gµν = 8πGT µ
ν
• stress-energy tensor is determined by solving the EOM’s ofall sources of stress-energy
Tµνm =
∑
nm(n)
δ(3)(x−x(n))√
−g
(
−gαβdxα
(n)
dτ
dxβ
(n)
dτ
)
−12 dxµ
(n)
dτ
dxν(n)
dτ
Julian Adamek IFT School on Cosmology Tools 2017 12 / 16
Design Principles
We use the LATField2 libraryas data handling / parallelizationback end.
• metric field represented ona regular lattice
• Fourier analysis possible(LATfield2 provides FFT)
dim=0
dim=1
dim=2
Julian Adamek IFT School on Cosmology Tools 2017 13 / 16
Design Principles
We use the LATField2 libraryas data handling / parallelizationback end.
• metric field represented ona regular lattice
• Fourier analysis possible(LATfield2 provides FFT)
dim=0
dim=1
dim=2
The front end / user interface borrows a lot from CLASS
• code can be directly interfaced with CLASS!
• use unified notation!
Julian Adamek IFT School on Cosmology Tools 2017 13 / 16
k [h/Mpc] k [h/Mpc] k [h/Mpc]
∆(k)
Φ
Φ-Ψ
hij
B
z = 3 z = 1 z = 0
10
10
10
10
10
10
10
10
1 1 10.1 0.1 0.10.01 0.01 0.01
-10
-12
-14
-16
-18
-20
-22
-24