Simulating the Dark Universe and Cosmic Structure Formation

Home , Millennium Run

Outline

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 (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

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 + ~v∇ f − m∇ Φ∇ 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 + (~v∇)~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 Simulations The Millennium Run Outlook: Galaxy Formation

Gravity: a heavy burden

Gravity: a heavy burden and a way around

Part I: the Particle Mesh (PM) Method Compute the mass density on a Cartesian grid Solve Poisson equation Interpolate the gravitational ﬁeld from grid to particles This is a fast method (scales roughly O(N) with use of FFT) BUT: it creates large errors for close particles Introduction Dark Matter Properties Simulations The Millennium Run Outlook: Galaxy Formation

Gravity: a heavy burden and a way around

Part II: the Barnes-Hut (BH) Tree Method Divide space recursively into hierarchy of cells If appropriate calculate gravitational force by multipoles of these cells; else use direct summation (almost never needed) Fast algorithm (scales O(NlogN)) Force for near particles can be calculated quite accurate Introduction Dark Matter Properties Simulations The Millennium Run Outlook: Galaxy Formation

Part II: the Barnes-Hut (BH) Tree Method

Divide space recursively into hierarchy of cells Introduction Dark Matter Properties Simulations The Millennium Run Outlook: Galaxy Formation

Part II: the Barnes-Hut (BH) Tree Method

Calculate gravitational force by multipoles of the cells 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

Initial conditions: DM Powerspectrum, Theory

We need the initial DM fluctuations which act as seed for gravitational instability. These fluctuations come from inflationary models and are Gaussian random fields. Theory: P(k) ∝ k ns T (k)2 , with T (k) being a transferfunction, and ns = 1 Do measurements give the same? Introduction Dark Matter Properties Simulations The Millennium Run Outlook: Galaxy Formation

DM Powerspectrum, Measurements Introduction Dark Matter Properties Simulations The Millennium Run Outlook: Galaxy Formation

Initial conditions: the density ﬂuctuations

Once one has a chosen Powerspectrum one can calculate density fluctuations δ which are a Gaussian random field Introduction Dark Matter Properties Simulations The Millennium Run Outlook: Galaxy Formation Initial conditions: From the dark matter Powerspectrum to density fluctuations Introduction Dark Matter Properties Simulations The Millennium Run Outlook: Galaxy Formation

Initial conditions: Cosmological parameters

From CMB + SNIa measurements we obtain the cosmological parameters: ΩΛ, σ8, ns, h, Ωm, ΩB Introduction Dark Matter Properties Simulations The Millennium Run Outlook: Galaxy Formation

Initial conditions: Cosmological parameters Introduction Dark Matter Properties Simulations The Millennium Run Outlook: Galaxy Formation

The Millennium Run

produced by the Virgo Consortium (http://www.virgo.dur.ac.uk/new/) performed at MPA by V. Springel with Lean-Gadget-2 (http://www.mpa- garching.mpg.de/gadget/) on an IBM Power4 Regatta System (http://www.rzg.mpg.de) 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 simulation setup Introduction Dark Matter Properties Simulations The Millennium Run Outlook: Galaxy Formation

The simulation setup

Up to now the largest Structure Formation simulation 21603 particles (≈ 1010) L = 500 h−1 Mpc 5 h−1 kpc spatial resolution roughly 840 GByte memory needed 350000 CPU hours on 512 CPUs Introduction Dark Matter Properties Simulations The Millennium Run Outlook: Galaxy Formation

The computer system IBM REGATTA 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 universe in a box Introduction Dark Matter Properties Simulations The Millennium Run Outlook: Galaxy Formation

Some movies ... a) Formation of a cluster

(http://www.mpa-garching.mpg.de/galform/datavis/) Introduction Dark Matter Properties Simulations The Millennium Run Outlook: Galaxy Formation

Some movies ... b) Zooming into an cluster

(http://www.mpa-garching.mpg.de/galform/virgo/millennium/) Introduction Dark Matter Properties Simulations The Millennium Run Outlook: Galaxy Formation

Some movies ... c)Flying through the universe

(http://www.mpa-garching.mpg.de/galform/virgo/millennium/) Introduction Dark Matter Properties Simulations The Millennium Run Outlook: Galaxy Formation

The baryonic-acoustic oscillations

At the moment of decoupling the Baryon-Photon gas oscillates in the gravitational potential given by the DM and modulates this potential After decoupling the photon gas dilutes quickly (photon density scales with a−4 Baryons then follow (modiﬁed) Dark matter potential Galaxyformation is “modulated” on a 150 MPc scale (measured by SLOAN) Introduction Dark Matter Properties Simulations The Millennium Run Outlook: Galaxy Formation

The baryonic-acoustic oscillations Introduction Dark Matter Properties Simulations The Millennium Run Outlook: Galaxy Formation

Understanding galaxy formation

One has to consider baryonic matter: radiation processes and complicated hydro make life much harder A lot of unknown physics is involved: details of star formation, galactic winds, AGN feedback effects Thus phenomenological models are used Introduction Dark Matter Properties Simulations The Millennium Run Outlook: Galaxy Formation

Understanding galaxy formation Introduction Dark Matter Properties Simulations The Millennium Run Outlook: Galaxy Formation

References

Volker Springel, The cosmological simulation code GADGET-2,astro-ph/0505010 Volker Springel et. al., Nature, 435, 629 http://dsg.port.ac.uk/ schaeferb/teaching