4. Dunhuang Star Chart from Tang Dynasty (618 - 907)
Orion didn’t move much the last 1200 years
5. Dunhuang Star Chart from Tang Dynasty (618 - 907)
Orion didn’t move much the last 1200 years
6. 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
8. Erik Holmberg 1941: Replacing gravitation by light
P
Intensity (Power per unit Area): I = 2πr2
9. The 1/r2 law for ∼homogeneous distributions
Impact of individual spheres is ≈equal
10. The 1/r2 law for ∼homogeneous distributions
Impact of individual spheres is ≈equal
11. Simulations of gravitationally interacting N-body systems:
The long range nature of gravity requires a double sum over all
interacting objects ⇒ N 2 problem
12. Can energy loss due to tides cause capture ?
hyperbolic orbits & tidal friction ⇒ capture
19. Aarseth, Gott & Turner 1979: Cosmic density field
In order to generate fluctuations with power spectrum,
P (k) ∝ k−1, particles are placed along rods
20. Aarseth, Gott & Turner 1979: Cosmic density field
In order to generate fluctuations with power spectrum,
P (k) ∝ k−1, particles are placed along rods
21. Aarseth, Gott & Turner 1979: Cosmic density field
In order to generate fluctuations with power spectrum,
P (k) ∝ k−1, particles are placed along rods
25. 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
26. Initial power spectrum & transfer function
P (k) = |δ(k)|2
δ(r) = δ(k) exp(−ikr)dk
ρ(r) − ρ
¯
δ(r) =
ρ
¯
Bardeen, Bond, Kaiser & Szalay 1986
30. The collosionless Boltzmann equation (Vlasov equation) for the
dark matter distribution function, f , in comoving coordinates x:
f = f (x, x, t)
˙
∂f ∂f ∂f
+ x
˙ − φ = 0, p = a2x,
˙
∂t ∂x ∂p
2 φ = 4πGa2 (ρ(x, t) − ρ) = 4πGa2 Ω
¯ dm δρcr
31. The solution of the Vlasov equation can be written in terms of
equations for characteristics, which look like equations of parti-
cle motion:
dp φ dv a
˙ φ
= − , +2 v = − 3
da a
˙ dt a a
dx p dx
= 2
, = v
da aa
˙ dt
2 φ = 4πGΩ δρ
0 cr,0 /a, φ = aφ
1
a = H0 1 + Ω 0
˙ − 1 + ΩΛ a2 − 1
a
32. Mare Nostrum Universe: 100 Mpc/h
10243 particles, 500 Mpc/h, mDM = 8.24 × 109h−1M
credit: Arman Khalatyan et al.
33. Mare Nostrum Universe: 20 Mpc/h
10243 particles, 500 Mpc/h, mDM = 8.24 × 109h−1M
credit: Arman Khalatyan et al.
36. Mare Nostrum Universe: Adiabatic Hydrodynamics
10243 particles, 500 Mpc/h, mgas = 1.45 × 109h−1M
credit: Arman Khalatyan et al.
37. Mare Nostrum Universe: Adiabatic Hydrodynamics
10243 particles, 500 Mpc/h, mgas = 1.45 × 109h−1M
credit: Arman Khalatyan et al.
38. Mare Nostrum Universe: Adiabatic Hydrodynamics
10243 particles, 500 Mpc/h, mgas = 1.45 × 109h−1M
credit: Arman Khalatyan et al.
39. Other recipes to take baryons into account:
• Full astro-hydrodynamics, including
cooling, feed back, etc.
• Semi-analytical approach
• Halo occupation distribution, abundance
matching