The Millenium Simulation: our Universe in a supecomputer Simon White Max Planck Institute for Astrophysics Moore's Law for Cosmological N-body Simulations Springel et al 2005 Millennium Run ● Computers double their speed every 18 months ● A naive N-body force 2 calculation needs N op's ● Simulations double their size every 16.5 months ● Progress has been roughly equally due to hardware and to improved algorithms Millennium Run Statistics Springel et al 2005: The Virgo Consortium 3 10 ● DM particle number: N = 2160 = 10,077,696,000 ≈ 10 5 ● Box size: L = 500 Mpc/h, Softening: = 5 kpc/h L/ = 10 ● Initial redshift: z = 127 init ● Cosmology: =1, =0.25, =0.045, h =0.73, n=1, =0.9 tot m b 8 ● 343,000 processor-hours on 512 nodes of an IBM Regatta (28 machine days @ 0.2 Tflops using 1 Tbyte RAM) ● Full raw and reduced data stored at 64 redshifts 27 Tbytes of stored data A testbed for simulating the formation of ~107 galaxies Goals for simulations of galaxy/AGN evolution ● Explore the physics of galaxy formation ● Understand the links between galaxy and SMBH formation ● Clarify why galaxy properties are related to clustering ● Determine how environment stimulates galaxy activity ● Interpret new multi-wavelength surveys of galaxies ● Check if such surveys can provide precision tests of and parameter estimates for the standard CDM paradigm Simulating galaxies /AGN in the Millennium Run Springel et al 2005; Croton et al 2005, De Lucia et al 2005 ● Build and store merger trees which encode the detailed assembly history of every z=0 halo and of the substructure within it ● Implement models for the formation/evolution of galaxies to follow -- accretion, shock-heating and cooling of diffuse gas into disks -- star formation from the ISM in disks -- stellar evolution [After Springel et al (2001) -- SN feedback and stellar winds and De Lucia et al (2004)] -- chemical enrichment/dust formation -- galaxy merging/morphological transformation ● Implement models for the growth of central black holes to follow -- formation and growth from ISM gas during mergers [ A f t e r K a u f f m an n -- black hole mergers following galaxy mergers & Haehnelt (2000)] ● Include “radio mode” feedback from BH at cooling flow centres -- energy feedback from BH in the central dominant galaxy depends on 1.5 BH mass, gas temperature and gas mass fraction f m T ∝ gas BH z = 0 Dark Matter Halo Mass Functions in the MS Springel et al 2005 Solid curves are the empirical fitting formula from Jenkins et al 2001 with no parameters adjusted At z = 0 half of all mass is in lumps of M > 2 × 1010M ⊙ Does halo clustering depend on formation history? Gao, Springel & White 2005 The 20% of halos with the lowest formation redshifts in a 30 Mpc/h thick slice M ~ 1011M halo ⊙ Does halo clustering depend on formation history? Gao, Springel & White 2005 The 20% of halos with the highest formation redshifts in a 30 Mpc/h thick slice M ~ 1011M halo ⊙ Does formation history depend on environment? Gao, Springel & White 2005 An equal number of randomly chosen DM particles Halo bias as a function of M = 1011M /h halo ⊙ mass and formation time Gao, Springel & White 2005 ● Bias increases smoothly with formation redshift ● The dependence on formation redshift is strongest at low mass ● This dependence is consistent neither with excursion set M = 6×1012M /h * ⊙ theory nor with HOD models z = 0 Dark Matter z = 0 Galaxy Light Springel, Frenk & White 2006 Galaxy autocorrelation function Springel et al 2005 mass For such a large simulation the purely statistical error bars are o][ 2dFGRS negligible on even for the galaxies Precise estimates of autocorrelation functions Luminous red galaxies in the SDSS Masjedi et al 2005 Precise estimates of autocorrelation functions Luminous red galaxies in the M.S. From public Millennium Simulation data archive M > 1011M * ⊙ g – r > 0.8 A test of the HOD model Galaxy autocorrelations are compared between two models (a) a full simulation of galaxy formation (b) the same simulation but with galaxy popula- tions shuffled among halos of fixed mass The bias plotted is the square root of the ratio of the correlation func's All galaxies A test of the HOD model Galaxy autocorrelations are compared between two models (a) a full simulation of galaxy formation (b) the same simulation but with galaxy popula- tions shuffled among halos of fixed mass The bias plotted is the square root of the ratio of the correlation func's Blue galaxies A test of the HOD model Galaxy autocorrelations are compared between two models (a) a full simulation of galaxy formation (b) the same simulation but with galaxy popula- tions shuffled among halos of fixed mass The bias plotted is the square root of the ratio of the correlation func's Red galaxies Baryon galaxies wiggles in mass the galaxy distribution linear Springel et al 2005 Power spectra from the Millennium run divided by a baryon- free CDM spectrum Galaxy samples are matched to plausible large observational surveys at given z The effects of “radio mode” feedback on z=0 galaxies Croton et al 2005 ● In the absence of a “cure” for the cooling flow problem, the most massive galaxies are: too bright too blue disk-dominated ● With cooling flows suppressed by “radio AGN” these galaxies are less massive red elliptical Effect of feedback on the Luminosity Function Full model with reionisation, AGN and SN feedback Croton et al 2005 Effect of feedback on the Luminosity Function Full model with reionisation, AGN and SN feedback Croton et al 2005 Effect of feedback on the Luminosity Function Full model with reionisation, AGN and SN feedback Croton et al 2005 Effect of feedback on the Luminosity Function Full model with reionisation, AGN and SN feedback Croton et al 2005 Effect of feedback on the Luminosity Function Full model with reionisation, AGN and SN feedback Croton et al 2005 Croton et al Other galaxy properties at z=0 2005 Evolution of feedback sources Croton et al 2005 B-band luminosity function evolution Mass function evolution Kitzbichler et al 2006 Formation histories of ellipticals De Lucia et al 2005 M > 4 109 * Distribution of star formation times M > 1011 * Distribution of assembly times Evolution of mass and galaxy correlations Springel, Frenk & White 2006 M – 5 log h < -20 I I < 24 “COSMOS” 1.4º x 1.4º Kitzbichler et al 2006 A bright quasar and its surroundings at 1 billion years One of the most massive dark matter clumps, containing one of the most massive galaxies and most massive black holes. M = 5 × 1012M M = 1011M h ⊙ * ⊙ SFR = 235 M /yr M = 108M ⊙ BH ⊙ The quasar's descendant and its surroundings today, at t = 13.7 billion years One of the most massive galaxy clusters. The quasar's descendant is part of the central massive galaxy of the cluster. M = 2 × 1015M h ⊙ http://www.g-vo.org Local Group “Timing Argument” mass estimates with a ΛCDM prior Li & White 2006 M =M (MW)+M (M31) Find all isolated pairs of disk- true 200 200 dominated galaxies with: ● 150 km/s < V < 300 km/s max,halo ● - 80 km/s > V > -180 km/s rad ● 500 kpc < D < 1 Mpc Find ratio of the true mass to the “Timing Argument” estimate for each pair Multiply by the TA estimate for the Local Group.