Monday, 07/24: Writing a pm-code - AIP

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Cosmological simulations 1 Cosmological simulations: the problem • The Universe is thought to be composed of dark matter and normal matter (the baryons), photons, neutrinos, etc. • There should be ∼ 10 80÷90 particles of dark matter and baryons in the observable Universe. • In our Galaxy, the Milky Way, alone there are ∼ 10 68 baryonic particles. • Simulations, of course, cannot follow evolution of all of these particles. • The evolution of a large number of particles of a given type can be described as evolution of a continuous field, characterized by the distribution function f(x, ẋ, t) — the density of particles in phase space.
equations I 2 Cosmological simulations: equations I • The evolution of f i is described by the Boltzmann equation: ∂f i ∂t + ẋ∂f i ∂x + ẍ∂f i ∂ẋ = C [f i, f j ] ; • C[f i , f j ] is the collision integral, describing possible particle collisions, which can scatter particles in and out of a phase-space volume. The form of C depends on the specific properties of particles in the system (i.e., how they scatter, whether they can be created or annihilated, etc.) • In general, a system of 6D Boltzmann equations (equations for each of the relevant components, i, of the Universe) needs to be solved. • This is indeed done in <strong>code</strong>s describing evolution of the primordial matter and linear perturbations to solve for the initial power spectrum and properties of the CMB temperature anisotropies. In this case, the matter distribution is close to uniform and no detailed information on the 3D distribution of matter is needed. The dimensionality of the problem can thus be reduced.
Page 1: Writing a PM code Andrey Kravtsov a
Page 5 and 6: N-body approach 4 Cosmological simu
Page 7 and 8: particle initial conditions 6 Cosmo
Page 9 and 10: equations of gasdynamics 8 Cosmolog
Page 11 and 12: equations summary 10 • Baryonic g
Page 13 and 14: dissipationless simulations 12 Part
Page 15 and 16: Model equations 14 Model equations
Page 17 and 18: Model equations 16 The quantities w
Page 19 and 20: Model equations 18 In dimensionless
Page 21 and 22: PM: main code blocks 20 Density Ass
Page 23 and 24: PM: main code blocks 22 In practice
Page 25 and 26: PM: main code blocks 24 Implementin
Page 27 and 28: PM: main code blocks 26 Solving the
Page 29 and 30: PM: main code blocks 28 ⇒ Given a
Page 31 and 32: PM: main code blocks 30 After n tim
Page 33 and 34: Zeldovich approximation (ZA) 32 Zel
Page 35 and 36: A test problem: 1D collapse of a pl
Page 41 and 42: Setting up cosmological ICs 40 The
Page 43 and 44: Setting up cosmological ICs 42 Appl
Page 45 and 46: project summary 44 Project summary
Page 47 and 48: References and links 46 PM in cosmo
Page 49 and 50: References and links 48 • Michael

Monday, 07/24: Writing a pm-code - AIP

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