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Simulating the Universe                                  Andreas FaltenbacherCape Town International Cosmology Summer Scho...
Outline:           • Celestial peace           • Gravitation           • Initial conditions           • Background cosmolo...
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 s...
Gravitation
Erik Holmberg 1941: Replacing gravitation by light                                               P         Intensity (Powe...
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 ...
Can energy loss due to tides cause capture ?        hyperbolic orbits & tidal friction ⇒ capture
Initial conditionshow 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 conditions700 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...
Aarseth, Gott & Turner 1979: Cosmic density field   In order to generate fluctuations with power spectrum,         P (k) ∝ k...
Aarseth, Gott & Turner 1979: Cosmic density field   In order to generate fluctuations with power spectrum,         P (k) ∝ k...
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 real...
Initial power spectrum & transfer function          P (k) =      |δ(k)|2           δ(r) =       δ(k) exp(−ikr)dk          ...
Zel’dovich approximation:           r(q, t) = a(t)[q + b(t)s(q)]                                    s(q) = Φ0(q)Edmund Ber...
Springel at al. 2005 :                    as time went by ...
Background cosmologyNewtonian gravity on expanding background
The collosionless Boltzmann equation (Vlasov equation) for thedark matter distribution function, f , in comoving coordinat...
The solution of the Vlasov equation can be written in terms ofequations for characteristics, which look like equations of ...
Mare Nostrum Universe: 100 Mpc/h10243 particles, 500 Mpc/h, mDM = 8.24 × 109h−1M                 credit: Arman Khalatyan e...
Mare Nostrum Universe: 20 Mpc/h10243 particles, 500 Mpc/h, mDM = 8.24 × 109h−1M                 credit: Arman Khalatyan et...
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−1Mcredit: Arman Khalatyan et ...
Mare Nostrum Universe: Adiabatic Hydrodynamics10243 particles, 500 Mpc/h, mgas = 1.45 × 109h−1Mcredit: Arman Khalatyan et ...
Mare Nostrum Universe: Adiabatic Hydrodynamics10243 particles, 500 Mpc/h, mgas = 1.45 × 109h−1Mcredit: Arman Khalatyan et ...
Other recipes to take baryons into account:       • Full   astro-hydrodynamics,   including         cooling, feed back, et...
Guedes 2011: Succeeded to simulate a realistic disk     15 kpc                 0.3             0.7
... how far are we from ...
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Faltenbacher - Simulating the Universe

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Faltenbacher - Simulating the Universe

  1. 1. Simulating the Universe Andreas FaltenbacherCape Town International Cosmology Summer School, 23. January 2012
  2. 2. Outline: • Celestial peace • Gravitation • Initial conditions • Background cosmology • From dark to light
  3. 3. Celestial peace
  4. 4. Dunhuang Star Chart from Tang Dynasty (618 - 907) Orion didn’t move much the last 1200 years
  5. 5. Dunhuang Star Chart from Tang Dynasty (618 - 907) Orion didn’t move much the last 1200 years
  6. 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
  7. 7. Gravitation
  8. 8. Erik Holmberg 1941: Replacing gravitation by light P Intensity (Power per unit Area): I = 2πr2
  9. 9. The 1/r2 law for ∼homogeneous distributions Impact of individual spheres is ≈equal
  10. 10. The 1/r2 law for ∼homogeneous distributions Impact of individual spheres is ≈equal
  11. 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. 12. Can energy loss due to tides cause capture ? hyperbolic orbits & tidal friction ⇒ capture
  13. 13. Initial conditionshow to get the fluctuation spectrum right
  14. 14. Aarseth 1963 How to simulate an irregular cluster ?
  15. 15. Peebles 1970: Top hat collapse density profiles of clusters too steep
  16. 16. White 1976: expanding initial conditions700 particles representing galaxies with different masses
  17. 17. White 1976: expanding initial conditions O > M > H > ∗, too much mass segregation
  18. 18. Poisson (P (k) = const.) observed power spectrum
  19. 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. 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. 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
  22. 22. Klypin & Shandarin 1983:323 particle, 160 Mpc/h box, Zel’dovich approximation, FFT
  23. 23. Klypin & Shandarin 1983:323 particle, 160 Mpc/h box, Zel’dovich approximation, FFT
  24. 24. Klypin & Shandarin 1983:323 particle, 160 Mpc/h box, Zel’dovich approximation, FFT
  25. 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. 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
  27. 27. 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/)
  28. 28. Springel at al. 2005 : as time went by ...
  29. 29. Background cosmologyNewtonian gravity on expanding background
  30. 30. The collosionless Boltzmann equation (Vlasov equation) for thedark 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. 31. The solution of the Vlasov equation can be written in terms ofequations 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. 32. Mare Nostrum Universe: 100 Mpc/h10243 particles, 500 Mpc/h, mDM = 8.24 × 109h−1M credit: Arman Khalatyan et al.
  33. 33. Mare Nostrum Universe: 20 Mpc/h10243 particles, 500 Mpc/h, mDM = 8.24 × 109h−1M credit: Arman Khalatyan et al.
  34. 34. Mare Nostrum Universe:10243 particles, 500 Mpc/h, mDM = 8.24 × 109h−1M credit: Arman Khalatyan et al.
  35. 35. From dark to light adding baryons
  36. 36. Mare Nostrum Universe: Adiabatic Hydrodynamics10243 particles, 500 Mpc/h, mgas = 1.45 × 109h−1Mcredit: Arman Khalatyan et al.
  37. 37. Mare Nostrum Universe: Adiabatic Hydrodynamics10243 particles, 500 Mpc/h, mgas = 1.45 × 109h−1Mcredit: Arman Khalatyan et al.
  38. 38. Mare Nostrum Universe: Adiabatic Hydrodynamics10243 particles, 500 Mpc/h, mgas = 1.45 × 109h−1Mcredit: Arman Khalatyan et al.
  39. 39. Other recipes to take baryons into account: • Full astro-hydrodynamics, including cooling, feed back, etc. • Semi-analytical approach • Halo occupation distribution, abundance matching
  40. 40. Guedes 2011: Succeeded to simulate a realistic disk 15 kpc 0.3 0.7
  41. 41. ... how far are we from ...

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