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 ...