Outline

Simulating the Dark Universe and CosmicStructure 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 SimulationsThe need for simulationsSimulation techniquesInitial conditions

4 The Millennium RunThe simulations setupA sub-sample of results

5 Outlook: Galaxy Formation

Outline

Outline

1 A short overview of Structure Formation

2 Dark Matter properties

3 SimulationsThe need for simulationsSimulation techniquesInitial conditions

4 The Millennium RunThe simulations setupA sub-sample of results

5 Outlook: Galaxy Formation

Outline

Outline

1 A short overview of Structure Formation

2 Dark Matter properties

3 SimulationsThe need for simulationsSimulation techniquesInitial conditions

4 The Millennium RunThe simulations setupA sub-sample of results

5 Outlook: Galaxy Formation

Outline

Outline

1 A short overview of Structure Formation

2 Dark Matter properties

3 SimulationsThe need for simulationsSimulation techniquesInitial conditions

4 The Millennium RunThe simulations setupA sub-sample of results

5 Outlook: Galaxy Formation

Outline

Outline

1 A short overview of Structure Formation

2 Dark Matter properties

3 SimulationsThe need for simulationsSimulation techniquesInitial conditions

4 The Millennium RunThe simulations setupA 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 canobserve) ...

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 calledStructure 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 densityfluctuations

The fluctuations in the CMB are not big enough to explainStructure 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 densityfluctuations

The fluctuations in the CMB are not big enough to explainStructure 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 densityfluctuations

The fluctuations in the CMB are not big enough to explainStructure 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) densityfluctuations δ

these fluctuations were present before the decoupling ofthe photon-baryon fluid (CMB)

DM strengthens the density contrast and after decouplingbaryonic matter follows the gravitational wells

in the linear regime (δ << 1) this can be calculatedanalytically

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) densityfluctuations δ

these fluctuations were present before the decoupling ofthe photon-baryon fluid (CMB)

DM strengthens the density contrast and after decouplingbaryonic matter follows the gravitational wells

in the linear regime (δ << 1) this can be calculatedanalytically

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) densityfluctuations δ

these fluctuations were present before the decoupling ofthe photon-baryon fluid (CMB)

DM strengthens the density contrast and after decouplingbaryonic matter follows the gravitational wells

in the linear regime (δ << 1) this can be calculatedanalytically

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) densityfluctuations δ

these fluctuations were present before the decoupling ofthe photon-baryon fluid (CMB)

DM strengthens the density contrast and after decouplingbaryonic matter follows the gravitational wells

in the linear regime (δ << 1) this can be calculatedanalytically

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-saturatinglong-range force is important!

Important for collisionless dynamics: Vlasov-equation

∂f∂t

+ ~v∇qf − m∇qΦ∇pf = 0 (1)

apply moments method: Jeans-Equations

no pressure and viscous terms! but: How does relaxationthen 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-saturatinglong-range force is important!Governing Equations −→ Jeans equations:

Continuity equation:

∂ρ

∂t+ div(ρ~v) = 0 (2)

momentum equation:

∂~v∂t

+ (~v∇)~v = −∇Φ − div(ρσ2) (3)

withσ2

ij = 〈~vi~vj〉 − 〈~vi〉〈~vj 〉 (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-saturatinglong-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 SimulationsThe need for simulationsSimulation techniquesInitial conditions

4 The Millennium RunThe simulations setupA 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 areonly track-able by direct simulations

Thus (large) simulations are needed for theoreticalpredictions 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 arehelpful to determine experimental biases. Statisticsimportant!

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 quasarswere 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 SimulationsThe need for simulationsSimulation techniquesInitial conditions

4 The Millennium RunThe simulations setupA 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 isneeded

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 withall other particles). Thus direct calculation of gravitationalforce 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

DM only interacts via gravity. Makes physics easier! =⇒Good

Gravity is a long range force (every particle interacts withall other particles). Thus direct calculation of gravitationalforce 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 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 ofthese cells; else use direct summation (almost neverneeded)

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 SimulationsThe need for simulationsSimulation techniquesInitial conditions

4 The Millennium RunThe simulations setupA 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 forgravitational instability. These fluctuations come frominflationary models and are Gaussian random fields.

Theory: P(k) ∝ kns T (k)2 , with T (k) being atransferfunction, 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 calculatedensity fluctuations δ which are a Gaussian random field

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

Initial conditions: From the dark matterPowerspectrum to density fluctuations

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

Initial conditions: Cosmological parameters

From CMB + SNIa measurements we obtain thecosmological 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 VirgoConsortium(http://www.virgo.dur.ac.uk/new/)

performed at MPA by V. Springelwith Lean-Gadget-2(http://www.mpa-garching.mpg.de/gadget/)

on an IBM Power4 RegattaSystem (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 SimulationsThe need for simulationsSimulation techniquesInitial conditions

4 The Millennium RunThe simulations setupA 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 SimulationsThe need for simulationsSimulation techniquesInitial conditions

4 The Millennium RunThe simulations setupA 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 gasoscillates in the gravitational potential given by the DM andmodulates this potential

After decoupling the photon gas dilutes quickly (photondensity 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

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 processesand complicated hydro make life much harder

A lot of unknown physics is involved: details of starformation, 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

Understanding galaxy formation

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

Understanding galaxy formation

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

References

Volker Springel, The cosmological simulation codeGADGET-2,astro-ph/0505010

Volker Springel et. al., Nature, 435, 629

http://dsg.port.ac.uk/ schaeferb/teaching