Computing the Universe

University of Durham

Carlos S. Frenk Institute for Computational Cosmology, Durham

Institute for Computational Cosmology The origin of cosmic structure University of Durham

Inflation (t~10-35 s) Simulations

CMB (t~3x105 yrs) Structure (t~13x109yrs) δρ/ρ~10-5

• Develop cosmological theory into ~1-105 non-linear regime δρ/ρ • Compare cosm. theory with astr. data • Establish connection between objects at different epochs • Design & interpret observational programmes Institute for Computational Cosmology • Discover new physics and astrophysics Rev Mod Phys 48, 1976

University of Durham

Institute for Computational Cosmology University of Durham

Rev Mod Phys 48, 1976

Institute for Computational Cosmology Modelling galaxy formation

Cosmological model

(Ωm, ΩΛ, h); dark matter

Standard model: Primordial fluctuations (O-) ΛCDM δρ/ρ(M, t)

• Material content: Cold dark matter (eg neutralino;21%), baryons (4%), dark energy (Λ; 75%)

Quantum fluctuations during inflation: 2 • Initial conditions: |δk| k; Gaussian amplitudes

• Growth processes: Gravitational instability Ω = 0.21, Ω = 0.04, Ω = 0.75, • Parameters: CDM b Λ h = 0.70,σ 8 = 0.9, ...

€ Cosmological model

(Ωm, ΩΛ, h); dark matter Well established Primordial fluctuations δρ/ρ(M, t)

Dark matter halos Well understood (N-body simulations)

Gas processes (cooling, star formation, feedback)

Gasdynamic simulations Semi-analytics

Formation and evolution of galaxies Non-baryonic dark matter University of Durham cosmologies

Neutrino dark CDM matter produces Ω=0.2 unrealistic clustering

Early CDM N-body simulations gave Neutrinos promising results HDM ΩΩ=1=1

In CDM CfA redshift structure forms survey Davis,Davis, Efstathiou,Efstathiou, hierarchically FrenkFrenk && WhiteWhite ‘85‘85

Institute for Computational Cosmology Moore's Law for Cosmological N-body Simulations University of Durham N AS A FUNCTION OF TIME • Computers Millennium double their speed every 18 months “Hubble Volume” • A naive N-body force calculation needs N2 op's • Simulations double their size every 16.5 months Simulation particles • N = 1010 should have been reached in 2008 • ..but was reached in 2004 Efstathiou & Jones 1979

yearInstitute for SpringelComputational Cosmologyet al 2005 University of Durham

MNRAS 1979

Institute for Computational Cosmology Efstathiou & Jones 1979 1000-particle simulation z = 0 Dark Matter

University of Durham 1010-particle simulation

Springel etal 05 Institute for Computational Cosmology Moore's Law for Cosmological N-body Simulations University of Durham N AS A FUNCTION OF TIME • Computers Millennium double their speed every 18 months “Hubble Volume” • A naive N-body force calculation needs N2 op's • Simulations double their size every 16.5 months Simulation particles • N = 1010 should have been reached in 2008 • ..but was reached in 2004

yearInstitute for SpringelComputational Cosmologyet al 2005 Virgo consortium for

University of Durham supercomputer simulations Core members and associates . Carlos Frenk – ICC, Durham (P.I.) . Adrian Jenkins – ICC, Durham . Tom Theuns – ICC, Durham . Gao Laing – ICC, Durham . Simon White – Max Plank Institut für Astrophysik (co-P.I.) . Volker Springel – Max Plank Institut für Astrophysik . Frazer Pearce – Nottingham . Naoki Yoshida – Tokyo . Peter Thomas – Sussex . Hugh Couchman – McMaster . John Peacock – Edinburgh . George Efstathiou – Cambridge . Joerg Colberg – Pittsburgh . Scott Kay – Oxford Simulation data available at: . Rob Thacker – McGill http://www.mpa-garching.mpg.de/Virgo . Julio Navarro – Victoria . Gus Evrard – Michigan Pictures and movies available at: . Joop Schaye – Leiden www.durham.ac.uk/virgo Virgo junior associates Institute for Computational Cosmology

Around 20 Phd students+postdocs The Millennium simulation University of Durham

Cosmological N-body simulation

• 10 billion particles

• 500 h-1 Mpc box

8 -1 UK, Germany, Canada, US • mp = 8×10 h Mo collaboration

• Ω =1; Ωm=0.25; Ω b=0.045; Simulation data available at: h=0.73; n=1; σ8 =0.9 http://www.mpa-garching.mpg.de/Virgo Carried out at Garching using 6 • 20 ×10 gals brighter than LMC Pictures and movies available at: L-Gadget by V. Springel www.durham.ac.uk/virgo (27 Tbytes of data) Institute for Computational Cosmology

The Millennium simulation

Springel et al Nature June/05 Halo mass function in Millennium Sim University of Durham

Solid curves are the empirical fitting formula of Jenkins et al 2001 with no Number density of halos well known from dn/dM

parameters / z = 10 - 0 2

adjusted M

At z = 0 half of all mass is in Jenkins etal 01 lumps of M > 2.1010MO -1 Mass (h Mo) Springel et al Institute for Computational Cosmology 2005 University of Durham

z = 0.0 Institute for Computational Cosmology •Jenkins & Frenk 2004 The Density Profile of Cold Dark

University of Durham Matter Halos

Halo density profiles are ) 3 independent of halo mass & cosmological parameters kpc o Galaxy clusters There is no obvious density M plateau or `core’ near the 10 centre. Dwarf galaxies (Navarro, Frenk & White ‘97) Log density (10

Log radius (kpc) Institute for Computational Cosmology 3 N=800 45 million particles inside rvir N=8003

NF W crit ρ (r)/ ρ

NFW profile is a good fit to ρ(r) down to ~0.1% rvir

r/h-1kpc Springel, Jenkins, Helmi, Navarro, Frenk & White ‘06 Convergence tests

University of Durham •Log r2 ρ(r )

Springel, Jenkins, Helmi,

Navarro, Frenk & White ‘06 Institute for Computational Cosmology University of Durham

Maximum inner slope < 0.7

Does nature make divergent density profiles?

Springel, Jenkins, Helmi,

Navarro, Frenk & White ‘06 Institute for Computational Cosmology Density profile of dark datter halos

University of Durham Millennium Simulation at z=0

LCDM cosmology L = 500 Mpc/h N = 1x1010

Mvir,r m = 8.6 x 108 vir eps = 5kpc/h

1.7x106 groups and 1.8x107 embedded substructures The most massive Fausti, Cole, structure with thousands ~106Navarro, halos Frenk, (Springel et al. 500of h substructures M>101White, 1.5Springel h-1M0 ‘06 -1Mpc 2005) Institute for Computational Cosmology Density profile of dark datter halos potential centre rvir r c = vir rs high fraction ofCentre of mass substructures offset 18% concentration 15%

vir • Fitting 2

r unrelaxed halos

crit € results in low ρ

/ concentrations; a relaxed halo2 (r)r

... ρ Unrelaxed halos

log have unstable

Fausti, Cole, density profiles; Navarro, Frenk, White, Springel ‘06 …and for fixed mass, expect log r/ large scatter in c rvir Relaxed halos Measuring c University of Durham Vary rs and rs Fit range [rconv,rvir] rconv avoid rs numerical r~1/r r~1/ r3 relaxation in nucleus c=r200/rs Minimize (Log r/ rfit)2 log10 Or abs(Log( r/rfit ))

Fausti, Cole, Navarro, Frenk, White, Springel ‘06

Institute for Computational Cosmology Distribution of concentrations at fixed mass

University of Durham Characterization of the Galaxies all scatter relaxe d Model for scatter in c at unrela fixed mass P(log c) unrelax xed relaxed Low mass halos ed Symmetric distribution Clusters for relaxed halos all relaxe More scatter for d unrelaxed halos unrela P(log c) xed Scatter decreases with High mass halos increasing mass Fausti, Cole, Navarro, log c Frenk, White, Springel ‘06

Institute for Computational Cosmology Halo Spins In the University of Durham Millennium Simulation

Philip Bett Carlos Frenk, Vince Eke, Adrian Jenkins, John Helly, Julio Navarro

June 2006 ICC, Durham Institute for Computational Cosmology The distribution of the spin parameter University of Durham JE1/ 2 Dimensionless λ = spin parameter GM 5 / 2

1.5 million halos 100 halos € λ ) P(log

Bett et al 06

Institutelog for λComputational Cosmology Cosmological model

(Ωm, ΩΛ, h); dark matter Well established Primordial fluctuations δρ/ρ(M, t)

Dark matter halos Well understood (N-body simulations)

Gas processes (cooling, star formation, feedback)

Gasdynamic simulations Semi-analytics

Formation and evolution of galaxies Modelling galaxy formation University of Durham • Aim: follow history of galaxy formation ab initio, i.e starting from a cosmological model for structure formation so as to predict observables • Main Physical processes: • Assembly of dark matter halos • Shock-heating and radiative cooling of gas within halos • Star formation and feedback • Production & mixing of metals • Evolution of stellar populations • Dust obscuration • Black hole format’n, AGN feedback • Galaxy mergers Institute for Computational Cosmology University of Durham Modelling galaxy formation

Galaxy formation involves complex processes spanning a dynamic range greater than 10 Mpc/0.1pc = 108

The largest dynamic range achievable in simulations is 104

⇒ Star formation, feedback, etc must be treated phenomenologically as “sub-grid physics’’ in simulations

Or through the technique of semi-analytic modelling

Sub-grid physics • Black hole format’n, AGN feedback • Galaxy mergers Institute for Computational Cosmology University of Durham

Simulations of disc galaxy formation

ΛCDM initial conditions Smooth Particle Hydrodynamics (SPH)

Takashi Okamoto (NAOJ/Durham) A. Jenkins, V.R. Eke, & C.S. Frenk (Durham)

See also Abadi, Navarro, Steinmetz 04,05 Governato et al 05, Sommer-Larsen et al 05 Springel et al 05 Institute for Computational Cosmology Simulations of disk galaxy formation University of Durham

Gadget2 (Parallel TreePM SPH code by V. Springel) – Multi-phase gas model – Phase decoupling (Okamoto et al. 2004) – Metallicity dependent cooling (Sutherland & Dopita 1993). – Photoionizing background at z<6 (Haardt & Madau 1996) – SNII • Chemical yield (Portinari et al. 1998) – SNIa (Greggio & Renzini 1983) • Chemical yield (W7 of Nomoto et al. 1997) – Stellar pop synthesis (Pegasse; Fioch & Rocca-Volmerange ‘02)

Institute for Computational Cosmology Simulations of disk galaxy formation University of Durham

Two star formation modes (from semianalytic model):

• Quiescent – Self-regulated star formation – Standard (Kennicutt) IMF

• Burst – High star formation efficiency – Top-heavy IMF ⇒ large feedback energy in merging galaxies

Institute for Computational Cosmology Shock- induced burst

stars

gas Stars: edge on

Stars: face on kpc -1 50 h

Gas: edge on

Okamoto etal 05 University of Durham Star formation history

No-burst z • SF peaks at high z and most of gas is used up No-burst Density-induced bursts /yr) • Similar to no-burst model until o gas density reaches threshold. • Once bursts occur, SF strongly suppressed. SFR (M • Almost no SF after z = 0.5 Shock-burst Shock-induced bursts • Burst fraction high at high-z → SF strongly suppressed. t (yr) • Burst fraction gradually  Institute for Computational Cosmology The luminosity function of Local Group satellites

University of Durham

ΛCDM semi-analytic ΛCDM simulations “Satellite problem” is a … non-problem

Local Group

resolution

Libeskind, Frenk, Cole, Okamoto & Jenkins 06 Institute for Computational Cosmology The luminosity function of Local Group satellites

University of Durham

Mgas/Mtot

The satellites in the simulations look a lot like the real satellites simulations LG data

Libeskind, Frenk, Cole, Okamoto & Jenkins 06 Institute for Computational Cosmology University of Durham

z = 0.0 Institute for Computational Cosmology The 2dF Galaxy Redshift Survey A collaboration between (primarily) UK and Australia 250 nights at the AAT

 221,000 redshifts

to bj<19.45 median z=0.11 Survey complete and catalogue released in July/03 The galaxy luminosity function University of Durham K-band

Key questions: • Why this shape? • What limits the number of faint galaxies? • What limits the number of bright galaxies?

Cole et al 01: (2MASS+2dFGRS) faint bright Kochanek etal: 01; Huang et al 03 (2MASS+SDSS) Institute for Computational Cosmology University of Durham

Institute for Computational Cosmology Modelling galaxy formation University of Durham • Aim: follow history of galaxy formation ab initio, i.e starting from a cosmological model for structure formation so as to predict observables • Main Physical processes: • Assembly of dark matter halos • Shock-heating and radiative cooling of gas within halos Semi-analytical model • Star formation and feedback – Parametrize physics • Production & mixing of metals – Set of coupled Evolution of stellar populations • differential equations • Dust obscuration – Parameters (5 in Sub-grid physics • Black hole format’n, AGN feedback simplest case) fixed empirically • Galaxy mergers Institute for Computational Cosmology Shock heating & cooling of University of Durham gas in halos

• Infalling gas shock-heated • Gas cools radiatively to form a disk • Disk size ↔ angular momentum of cooled gas

Key timescales: tcool ↔ tinfall

Institute for Computational Cosmology Gas cooling in SPH and semi-analytics University of Durham SPH Semi-analytics

Gas cooling only Helly, Cole, Frenk, Benson, Baugh, Lacey ’03 (see also Benson etal 00, Yoshida etal ’03) Institute for Computational Cosmology z = 0 Dark Matter

University of Durham Populating the MS with galaxies

Semi-analytic modelling • Find dark matter halos • Construct halo merger trees • Apply SA model (gas cooling, star formation, feedback)

Springel etal 04 Institute for Computational Cosmology AGN feedback in semi-analytic University of Durham models of galaxy formation Croton et al 2005; Bower et al 2006 1. Construct merger trees in MR and apply s-analytic GalF model

2. Model growth of central black holes (BH) –! accretion of gas triggered by mergers and disks instability –! by BH-BH megers when their host galaxies merge

cf Kauffmann & Haehnelt (2000) 3. “Radio mode” feedback from BHs at cooling flow centres – Croton etal: energy feedback from central BH depends on BH 1.5 mass, gas temp. and gas fraction E ∝ fgas mBH T

– Bower et al: cooling flow quenched if tcool>tff and Lcool< εed Led Institute for Computational Cosmology University of Durham

Black holes and galaxy formation ) o M -1

B-H mass vs bulge mass /h smbh Free parameter: fraction fBH of gas accreted by BH log (M

fBH fixes normalization; slope and scatter are free

BH growth during feeding phase Data:Haering & Rix steepens slope at large M Colour: halo mass

Bower et al 06 Institute for Computational-1 Cosmology log (Mbulge/h Mo) z = 0 Dark Matter

University of Durham

Springel etal 04 Institute for Computational Cosmology z = 0 Galaxy light

University of Durham

Croton etal 05 Institute for Computational Cosmology real

simulated ΛCDM Springel, Frenk & White Nature, May ‘06 Deconstructing the galaxy LF University of Durham

Faint end: SN feedback+photoionization Photoionization + reheating of cold AGN feedback disk gas by SN

Bright end: AGN feedback: energy transported by bubbles

Bower et al 05 Institute for Computational Cosmology Deconstructing the galaxy LF University of Durham

Faint end: Photoionization+SN feedback Photoionization + reheating of cold No AGN feedback disk gas by SN

Bright end: AGN feedback: energy transported by bubbles

Bower et al 05 Benson, Bower,Frenk, Lacey, Baugh & Cole ‘03 Institute for Computational Cosmology B-band University of Durham no AGN

Effect of AGN no feedback on lum fn dustwith dust

K-band

no AGN

Bower et al 05

Institute for Computational Cosmology AGN feedback and the properties of ellipticals University of Durham

The most massive With AGN heating galaxies are red, elliptical

With AGN heating

No AGN heating

and old!! log Mstars/Mo Croton et al 05 Institute for Computational Cosmology The broken hierarchy of University of Durham galaxy formation

Test the model against observations at high redshift

Institute for Computational Cosmology The broken hierarchy of University of Durham galaxy formation

Observations show:

• Massive galaxies were already in place at z>1 with number density similar to z=0. – An “anti-hierarchical” universe?

• Star formation rate in massive galaxies was higher in the past: – Star formation “downsizing” ?

Institute for Computational Cosmology University of Durham AGN Cole Evolution of rest- et al 00z=0 frame K-band LF AGN Bright galaxies are in place at high-z Baugh et al 05 At hi-z: no AGN AGN • Improved gas cooling model ⇒ more efficient star formatn • Halos less likely to be hydrostatic & have small BHs ⇒ no AGN feedback ⇒ Gals form efficiently at hi-z Bower et al 06 Institute for Computational Cosmology AGN AGN University of Durham Evolution of the z=0 stellar mass fn

Massive galaxies in place at z=4.5

⇒ AGN feedback breaks the hierarchy implicit in halo formation! Maclure etal 06

Data: Fontanot etal 04 Glazebrook etal 05 -2Institute for Computational Cosmology-2 Drory et al 05 (photom) log(M*/h Mo) log(M*/h Mo) dark matter z=8.5 galaxies z=8.5 5 5 University of Durham

Millennium Simulation z=5.7 z=5.7 2 2

At early times, the dark matter is smooth, but the z=1.3 z=1.3 galaxies are already 9 9 strongly clustered

z=0 z=0

Springel, Frenk & White Nature, May/06 150 Mpc/h 150 Mpc/h Institute for Computational Cosmology Conclusions University of Durham Inflation (t~10-35 s) CMB (t~3x105 yrs)

Structure (t~13x109yrs)

• Cosmological simulations → key role in development of ΛCDM Large scales Evolution of dark matter well understood • Halo structure • Gasdynamics → many uncertainties; large discs OK (feedback) • Semi-analytic models required to compare with observations • Gal lum fn (inc satellites of LG) can be understood within ΛCDM

Institute for Computational Cosmology • “Anti-hierarchical” gal formtn possible in ΛCDM (AGN feedback) CONCLUSIONS University of Durham 1. The galaxy luminosity function In CDM, it is determined by feedback processes • Faint end: photoionization & SNe feedback (Satellites of Local Group: not a problem for ΛCDM) • Bright end: feedback from bubbles generated by AGN jets 2. The mass-to-light ratio as a fn of halo mass • The predicted variation of M/L with halo M is seen in 2dFGRs 3. Galaxy clustering

• The power-law nature of ξ(r) is a coincidence due to the way in which galaxies populate halos of different mass

• ΛCDM agrees v well with 2dFGRS ξ(r) asInstitute a fn forof Computational lum and Cosmology type