Outline Simulating the Dark Universe and Cosmic Structure Formation Andreas Marek Max-Planck Institut for Astrophysics Advisor-seminar 2006 Outline Outline 1 A short overview of Structure Formation 2 Dark Matter properties 3 Simulations The need for simulations Simulation techniques Initial conditions 4 The Millennium Run The simulations setup A sub-sample of results 5 Outlook: Galaxy Formation Outline Outline 1 A short overview of Structure Formation 2 Dark Matter properties 3 Simulations The need for simulations Simulation techniques Initial conditions 4 The Millennium Run The simulations setup A sub-sample of results 5 Outlook: Galaxy Formation Outline Outline 1 A short overview of Structure Formation 2 Dark Matter properties 3 Simulations The need for simulations Simulation techniques Initial conditions 4 The Millennium Run The simulations setup A sub-sample of results 5 Outlook: Galaxy Formation Outline Outline 1 A short overview of Structure Formation 2 Dark Matter properties 3 Simulations The need for simulations Simulation techniques Initial conditions 4 The Millennium Run The simulations setup A sub-sample of results 5 Outlook: Galaxy Formation Outline Outline 1 A short overview of Structure Formation 2 Dark Matter properties 3 Simulations The need for simulations Simulation techniques Initial conditions 4 The Millennium Run The simulations setup A sub-sample of results 5 Outlook: Galaxy Formation Introduction Dark Matter Properties Simulations The Millennium Run Outlook: Galaxy Formation What means “Structure Formation”? From an almost uniform CMB (the earliest time we can observe) ... Introduction Dark Matter Properties Simulations The Millennium Run Outlook: Galaxy Formation What means “Structure Formation”? we see at later times clusters and galxies. This is called Structure Formation. Introduction Dark Matter Properties Simulations The Millennium Run Outlook: Galaxy Formation The Standard Model of Structure Formation the growth of structure originates from seed density fluctuations The fluctuations in the CMB are not big enough to explain Structure Formation density fluctuations grow approximately / scale factor a Compare: (baryonic) CMB fluctuations of 10−5 at a = 10−3 with current densities of order unity Introduction Dark Matter Properties Simulations The Millennium Run Outlook: Galaxy Formation The Standard Model of Structure Formation the growth of structure originates from seed density fluctuations The fluctuations in the CMB are not big enough to explain Structure Formation density fluctuations grow approximately / scale factor a Compare: (baryonic) CMB fluctuations of 10−5 at a = 10−3 with current densities of order unity Introduction Dark Matter Properties Simulations The Millennium Run Outlook: Galaxy Formation The Standard Model of Structure Formation the growth of structure originates from seed density fluctuations The fluctuations in the CMB are not big enough to explain Structure Formation density fluctuations grow approximately / scale factor a Compare: (baryonic) CMB fluctuations of 10−5 at a = 10−3 with current densities of order unity Introduction Dark Matter Properties Simulations The Millennium Run Outlook: Galaxy Formation The Standard Model of Structure Formation the growth of structure originates from seed (DM) density fluctuations δ these fluctuations were present before the decoupling of the photon-baryon fluid (CMB) DM strengthens the density contrast and after decoupling baryonic matter follows the gravitational wells in the linear regime (δ << 1) this can be calculated analytically Introduction Dark Matter Properties Simulations The Millennium Run Outlook: Galaxy Formation The Standard Model of Structure Formation the growth of structure originates from seed (DM) density fluctuations δ these fluctuations were present before the decoupling of the photon-baryon fluid (CMB) DM strengthens the density contrast and after decoupling baryonic matter follows the gravitational wells in the linear regime (δ << 1) this can be calculated analytically Introduction Dark Matter Properties Simulations The Millennium Run Outlook: Galaxy Formation The Standard Model of Structure Formation the growth of structure originates from seed (DM) density fluctuations δ these fluctuations were present before the decoupling of the photon-baryon fluid (CMB) DM strengthens the density contrast and after decoupling baryonic matter follows the gravitational wells in the linear regime (δ << 1) this can be calculated analytically Introduction Dark Matter Properties Simulations The Millennium Run Outlook: Galaxy Formation The Standard Model of Structure Formation the growth of structure originates from seed (DM) density fluctuations δ these fluctuations were present before the decoupling of the photon-baryon fluid (CMB) DM strengthens the density contrast and after decoupling baryonic matter follows the gravitational wells in the linear regime (δ << 1) this can be calculated analytically Introduction Dark Matter Properties Simulations The Millennium Run Outlook: Galaxy Formation Collisionless dynamics reviewed DM physics is important! Introduction Dark Matter Properties Simulations The Millennium Run Outlook: Galaxy Formation Collisionless dynamics reviewed DM only interacts gravitationally: thus only a non-saturating long-range force is important! Important for collisionless dynamics: Vlasov-equation @f + ~vr f − mr Φr f = 0 (1) @t q q p apply moments method: Jeans-Equations no pressure and viscous terms! but: How does relaxation then proceed ? how are objects stabilized against gravity ? Introduction Dark Matter Properties Simulations The Millennium Run Outlook: Galaxy Formation Collisionless dynamics reviewed: Governing equations DM only interacts gravitationally: thus only a non-saturating long-range force is important! Governing Equations −! Jeans equations: Continuity equation: @ρ + div(ρ~v) = 0 (2) @t momentum equation: @~v + (~vr)~v = −∇Φ − div(ρσ2) (3) @t with 2 σij = h~vi~vj i − h~vi ih~vj i (4) Introduction Dark Matter Properties Simulations The Millennium Run Outlook: Galaxy Formation Collisionless dynamics reviewed: Governing equations DM only interacts gravitationally: thus only a non-saturating long-range force is important! Governing Equations −! Jeans equations: Poisson equation: 4Φ = 4πGρ (5) closed system Introduction Dark Matter Properties Simulations The Millennium Run Outlook: Galaxy Formation Collisionless dynamics reviewed: Dynamical friction a particle moving through a cloud produces a wake Introduction Dark Matter Properties Simulations The Millennium Run Outlook: Galaxy Formation Collisionless dynamics reviewed: Dynamical friction behind the particle there is a density enhancement Introduction Dark Matter Properties Simulations The Millennium Run Outlook: Galaxy Formation Collisionless dynamics reviewed: Dynamical friction density enhancement breaks down particle velocity Introduction Dark Matter Properties Simulations The Millennium Run Outlook: Galaxy Formation Collisionless dynamics reviewed: Dynamical friction Ekin of particle =) unordered random motion Introduction Dark Matter Properties Simulations The Millennium Run Outlook: Galaxy Formation Collisionless dynamics reviewed: Dynamical friction used for describing capturing of objects Introduction Dark Matter Properties Simulations The Millennium Run Outlook: Galaxy Formation Outline 1 A short overview of Structure Formation 2 Dark Matter properties 3 Simulations The need for simulations Simulation techniques Initial conditions 4 The Millennium Run The simulations setup A sub-sample of results 5 Outlook: Galaxy Formation Introduction Dark Matter Properties Simulations The Millennium Run Outlook: Galaxy Formation The need for simulations / Simulation goals Gravitational instability leads to non-linear effects that are only track-able by direct simulations Thus (large) simulations are needed for theoretical predictions of the “Standard Model of Structure Formation” Simulations can test the consequences of different models (DM,inflation) Simulations of can be compared to observations and are helpful to determine experimental biases. Statistics important! Introduction Dark Matter Properties Simulations The Millennium Run Outlook: Galaxy Formation The need for simulations / Simulation goals Structure Formation simulations allow to investigate the time evolution of the hierarchical tree when (at which redshift) massive clusters and quasars were formed galaxy formation; additional input physics (e.g. semi- analytical models) needed! Introduction Dark Matter Properties Simulations The Millennium Run Outlook: Galaxy Formation Outline 1 A short overview of Structure Formation 2 Dark Matter properties 3 Simulations The need for simulations Simulation techniques Initial conditions 4 The Millennium Run The simulations setup A sub-sample of results 5 Outlook: Galaxy Formation Introduction Dark Matter Properties Simulations The Millennium Run Outlook: Galaxy Formation N-Body Codes DM is represented by particles of certain mass These particles move according evolution equations Advantage: resolution automatically increases where it is needed Introduction Dark Matter Properties Simulations The Millennium Run Outlook: Galaxy Formation Gravity: a heavy burden DM only interacts via gravity. Makes physics easier! =) Good Gravity is a long range force (every particle interacts with all other particles). Thus direct calculation of gravitational force scales with N2 =) Bad (Computational costs) Think of a clever way to circumvent the direct summation Introduction Dark Matter Properties