View
1.203
Download
0
Category
Tags:
Preview:
DESCRIPTION
Citation preview
Simulating the Universe
Andreas Faltenbacher
Cape Town International Cosmology Summer School, 23. January 2012
Outline:
• Celestial peace
• Gravitation
• Initial conditions
• Background cosmology
• From dark to light
Celestial peace
Dunhuang Star Chart from Tang Dynasty (618 - 907)
Orion didn’t move much the last 1200 years
Dunhuang Star Chart from Tang Dynasty (618 - 907)
Orion didn’t move much the last 1200 years
We hardly see motion in astronomical observations
but if Big Bang Theory is correct
objects must have formed at some point
Simulations are the only tool to
directly investigate the evolution
of the Universe and it’s constituents
Gravitation
Erik Holmberg 1941: Replacing gravitation by light
Intensity (Power per unit Area): I = P2πr2
The 1/r2 law for ∼homogeneous distributions
Impact of individual spheres is ≈equal
The 1/r2 law for ∼homogeneous distributions
Impact of individual spheres is ≈equal
Simulations of gravitationally interacting N-body systems:
The long range nature of gravity requires a double sum over all
interacting objects ⇒ N2 problem
Can energy loss due to tides cause capture ?
hyperbolic orbits & tidal friction ⇒ capture
Initial conditions
how to get the fluctuation spectrum right
Aarseth 1963
How to simulate an irregular cluster ?
Peebles 1970: Top hat collapse
density profiles of clusters too steep
White 1976: expanding initial conditions
700 particles representing galaxies with different masses
White 1976: expanding initial conditions
O > M > H > ∗, too much mass segregation
Poisson (P (k) = const.) observed power spectrum
Aarseth, Gott & Turner 1979: Cosmic density field
In order to generate fluctuations with power spectrum,P (k) ∝ k−1, particles are placed along rods
Aarseth, Gott & Turner 1979: Cosmic density field
In order to generate fluctuations with power spectrum,P (k) ∝ k−1, particles are placed along rods
Aarseth, Gott & Turner 1979: Cosmic density field
In order to generate fluctuations with power spectrum,P (k) ∝ k−1, particles are placed along rods
Klypin & Shandarin 1983:
323 particle, 160 Mpc/h box, Zel’dovich approximation, FFT
Klypin & Shandarin 1983:
323 particle, 160 Mpc/h box, Zel’dovich approximation, FFT
Klypin & Shandarin 1983:
323 particle, 160 Mpc/h box, Zel’dovich approximation, FFT
Current approach:
• Compute initial power spectrum CMB-
FAST, CAMB, CMBeasy, ...
• Generate a random realization of the
density field in k-space
• Do Fourier transform to get real space
density fluctuations
• Apply Zel’dovich approximation to obtain
initial positions and velocities of simula-
tion particles
Initial power spectrum & transfer function
P (k) = 〈|δ(k)|2〉δ(r) =
∫δ(k) exp(−ikr)dk
δ(r) =ρ(r)− ρ
ρ
Bardeen, Bond, Kaiser & Szalay 1986
Zel’dovich approximation: r(q, t) = a(t)[q + b(t)s(q)]s(q) = ∇Φ0(q)
Edmund Bertschinger’s COSMICS package (http://web.mit.edu/edbert/)
Springel at al. 2005 :
as time went by ...
Background cosmology
Newtonian gravity on expanding background
The collosionless Boltzmann equation (Vlasov equation) for the
dark matter distribution function, f , in comoving coordinates x:
f = f(x, x, t)
∂f
∂t+ x
∂f
∂x− ∇φ
∂f
∂p= 0, p = a2x,
∇2φ = 4πGa2(ρ(x, t)− ρ) = 4πGa2Ωdmδρcr
The solution of the Vlasov equation can be written in terms ofequations for characteristics, which look like equations of parti-cle motion:
dp
da= −
∇φa,
dv
dt+ 2
a
av = −
∇φ′
a3
dx
da=
p
aa2,
dx
dt= v
∇2φ = 4πGΩ0δρcr,0/a, φ′ = aφ
a = H0
√1 + Ω0
(1
a− 1
)+ ΩΛ
(a2 − 1
)
Mare Nostrum Universe: 100 Mpc/h10243 particles, 500 Mpc/h, mDM = 8.24× 109h−1M
credit: Arman Khalatyan et al.
Mare Nostrum Universe: 20 Mpc/h10243 particles, 500 Mpc/h, mDM = 8.24× 109h−1M
credit: Arman Khalatyan et al.
Mare Nostrum Universe:10243 particles, 500 Mpc/h, mDM = 8.24× 109h−1M
credit: Arman Khalatyan et al.
From dark to light
adding baryons
Mare Nostrum Universe: Adiabatic Hydrodynamics10243 particles, 500 Mpc/h, mgas = 1.45× 109h−1M
credit: Arman Khalatyan et al.
Mare Nostrum Universe: Adiabatic Hydrodynamics10243 particles, 500 Mpc/h, mgas = 1.45× 109h−1M
credit: Arman Khalatyan et al.
Mare Nostrum Universe: Adiabatic Hydrodynamics10243 particles, 500 Mpc/h, mgas = 1.45× 109h−1M
credit: Arman Khalatyan et al.
Other recipes to take baryons into account:
• Full astro-hydrodynamics, including
cooling, feed back, etc.
• Semi-analytical approach
• Halo occupation distribution, abundance
matching
Guedes 2011: Succeeded to simulate a realistic disk
15 kpc 0.3 0.7
... how far are we from ...
Recommended