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Numerical Galaxy Formation and Cosmology Simulating the Universe on a Computer Numerical galaxy formation and cosmology Simulating the universe on a computer Lecture 1: Motivation and Historical Overview Benjamin Moster 1 About this lecture • Lecture slides will be uploaded to www.usm.lmu.de/people/moster/Lectures/NC2018.html • Exercises will be lead by Ulrich Steinwandel and Joseph O’Leary 1st exercise will be next week (18.04.18, 12-14, USM Hörsaal) • Goal of exercises: run your own simulations on your laptop Code: Gadget-2 available at http://www.mpa-garching.mpg.de/gadget/ • Please put your name and email address on the mailing list • Evaluation: - Project with oral presentation (to be chosen individually) - Bonus (up to 0.3) for participating in tutorials and submitting a solution to an exercise sheet (at least 70%) 2 Numerical Galaxy Formation & Cosmology 1 11.04.2018 Literature • Textbooks: - Mo, van den Bosch, White: Galaxy Formation and Evolution, 2010 - Schneider: Extragalactic Astronomy and Cosmology, 2006 - Padmanabhan: Structure Formation in the Universe, 1993 - Hockney, Eastwood: Computer Simulation Using Particles, 1988 • Reviews: - Trenti, Hut: Gravitational N-Body Simulations, 2008 - Dolag: Simulation Techniques for Cosmological Simulations, 2008 - Klypin: Numerical Simulations in Cosmology, 2000 - Bertschinger: Simulations of Structure Formation in the Universe, 1998 3 Numerical Galaxy Formation & Cosmology 1 11.04.2018 Outline of the lecture course • Lecture 1: Motivation & Historical Overview • Lecture 2: Review of Cosmology • Lecture 3: Generating initial conditions • Lecture 4: Gravity algorithms • Lecture 5: Time integration & parallelization • Lecture 6: Hydro schemes - Grid codes • Lecture 7: Hydro schemes - Particle codes • Lecture 8: Radiative cooling, photo heating • Lecture 9: Subresolution physics • Lecture 10: Halo and subhalo finders • Lecture 11: Semi-analytic models • Lecture 12: Example simulations: cosmological box & mergers • Lecture 13: Presentations of test simulations 4 Numerical Galaxy Formation & Cosmology 1 11.04.2018 Outline of this lecture • Motivation for simulations and semi-analytic models ‣ Observations at high redshift (CMB) and low redshift (SDSS) ‣ Linear density perturbations • Historical Overview ‣ The foundations of cosmology ‣ The first simulations ‣ Simulations of Galaxy Clusters ‣ Simulations of Large-Scale Structure ‣ Properties of dark matter haloes ‣ State-of-the-art simulations of galaxies 5 Numerical Galaxy Formation & Cosmology 1 11.04.2018 Observing large scale structure • Cosmic structure can be observed at very high redshift (z>1000): CMB Very smooth, only small perturbations (10-5) • At low redshift: galaxies are very clustered forming a ‘cosmic web’. z > 1000 z ~ 0 Galaxies SDSS CMB - Planck 6 Numerical Galaxy Formation & Cosmology 1 11.04.2018 Observing large scale structure • Things to keep in mind: ‣ Structure formation process is dominated by gravity ‣ Galaxies are only tracers of cosmic structure (<3% of all mass) ‣ Galaxy formation depends on ‘baryonic physics’ z > 1000 z ~ 0 Galaxies How? SDSS CMB - Planck 7 Numerical Galaxy Formation & Cosmology 1 11.04.2018 What about linear perturbation theory? • How far can we push it? • A quick recap of cosmological perturbation theory: ~r = a~x ~x comoving position a˙ ~v = ~r˙ = ~u + ~r with ~u = a~x˙ ~u peculiar velocity a momentum conservation: comoving (1st order): @~v ~ ~ @~u a˙ 1 +(~v phys)~v = physφ + ~u = ~ φ @t r −r @t a −ar continuity equation: with @⇢ @ 1 ⇢ ⇢¯ + ~ (⇢~v)=0 + ~ ~u =0 δ = − @t rphys @t ar ⇢¯ Poisson equation: ~ 2 φ =4⇡G⇢ ~ 2φ =4⇡Ga2⇢¯ rphys r 8 Numerical Galaxy Formation & Cosmology 1 11.04.2018 Linear growth of structures • Combining this we get the evolution of the density contrast δ a˙ ⇢¯ δ¨ +2 δ˙ =4⇡G c δ solved by growth function D ( a ) : δ(a)=δ D(a) a a3 0 For a matter dominated universe we have D(a) a • ⇠ ˆ ~ i~k~x 3 • Can be decomposed into waves: δ(~x)= δ(k)e− d k Power spectrum is P ( k )= δˆ ( k ) 2 (whereZ : ensemble average) h| | i hi 2 and it grows like P (k)=P0D (a) Formalism works as long as δ 1 • ⌧ Breaks down when δ 1 (negative densities) • ⇠ • Either go to higher order (still no ‘baryonic physics’) or use simulations 9 Numerical Galaxy Formation & Cosmology 1 11.04.2018 From high to low redshift • Cosmological model + initial conditions + simulation code = galaxies Dark matter Galaxies 10 Numerical Galaxy Formation & Cosmology 1 11.04.2018 Outline of this lecture • Motivation for simulations and semi-analytic models ‣ Observations at high redshift (CMB) and low redshift (SDSS) ‣ Linear density perturbations • Historical Overview ‣ The foundations of cosmology ‣ The first simulations ‣ Simulations of Galaxy Clusters ‣ Simulations of Large-Scale Structure ‣ Properties of dark matter haloes ‣ State-of-the-art simulations of galaxies 11 Numerical Galaxy Formation & Cosmology 1 11.04.2018 The foundations of cosmology • 1905: Special Relativity Gµ⌫ =8⇡GTµ⌫ • 1915: General Relativity Albert Einstein • 1916: Slipher ➙ Local galaxies are receding from us • 1922: GR + Cosmological principle ➙ Friedmann equations Vesto Slipher a˙ 2 H2 = a ✓ ◆ 8⇡G kc2 ⇤ = ⇢ + 3 − a2 3 Alexander Friedmann 12 Numerical Galaxy Formation & Cosmology 1 11.04.2018 The foundations of cosmology • 1927: Lemaître ➙ Expansion of the Universe 1929: Hubble ➙ Velocity-Distance Relation (Big Bang?) • George Lemaître • 1933: Zwicky uses virial theorem for Coma Cluster ➙ Dark Matter Edwin Hubble Fritz Zwicky 13 Numerical Galaxy Formation & Cosmology 1 11.04.2018 1941 Erik Holmberg 14 Numerical Galaxy Formation & Cosmology 1 11.04.2018 1941 Erik Holmberg 14 Numerical Galaxy Formation & Cosmology 1 11.04.2018 1941 The first ‘simulations’ N = 2 x 37 • Experiment replaces gravity by light (same 1/r2 law) • Galaxies move closer to each other and merge • Formation of tidal arms Erik Holmberg • Gravity for each body: ¨ mi~ri = F~ (~ri) • For brute-force approach: summation over (N-1) particles ~ ~ri ~rj F (~ri)= Gmimj − 3 − (ri rj) i=j X6 − for all N particles ➙ number of operations ∝N (N-1) ∝N2 15 Numerical Galaxy Formation & Cosmology 1 11.04.2018 1963 Sverre Aarseth 16 Numerical Galaxy Formation & Cosmology 1 11.04.2018 1963 Sverre Aarseth 16 Numerical Galaxy Formation & Cosmology 1 11.04.2018 1963 One of the first N-body codes N = 25-100 • One of the first studies to apply an N-body code to galaxy clusters Groundworks for all particle codes • Sverre Aarseth • Nbody6 / Nbody7 is still one of the most prominent codes used for stellar clusters 17 Numerical Galaxy Formation & Cosmology 1 11.04.2018 1963 One of the first N-body codes N = 25-100 Sverre Aarseth 18 Numerical Cosmology & Galaxy Formation 1 13.04.2016 1963 One of the first N-body codes N = 25-100 Sverre Aarseth Wang+16 18 Numerical Cosmology & Galaxy Formation 1 13.04.2016 1970 Jim Peebles 19 Numerical Galaxy Formation & Cosmology 1 11.04.2018 1970 Jim Peebles 19 Numerical Galaxy Formation & Cosmology 1 11.04.2018 1970 Simulations with more particles N = 300 • Similar approach as Aarseth, but with more particles • Coma cluster is compared to results of computer model • Observed features are found consistent Jim Peebles 20 Numerical Galaxy Formation & Cosmology 1 11.04.2018 1972 Alar Toomre Juri Toomre 21 Numerical Galaxy Formation & Cosmology 1 11.04.2018 1972 Alar Toomre Juri Toomre 21 Numerical Galaxy Formation & Cosmology 1 11.04.2018 1972 Toomre & Toomre galaxy merger N = 120 • Restricted three-body equation of motions • Binary mergers of galaxies • Explains formation of tidal arms Alar Toomre (e.g. Antennae Galaxies) Juri Toomre 22 Numerical Galaxy Formation & Cosmology 1 11.04.2018 1974 William Press Paul Schechter 23 Numerical Galaxy Formation & Cosmology 1 11.04.2018 1974 William Press Paul Schechter 23 Numerical Galaxy Formation & Cosmology 1 11.04.2018 1974 Press & Schechter Theory N = 1000 • Analytic Theory to predict number of object with certain mass in given volume • Growth of density perturbations leads to collapse William Press • Mass fraction in objects above M is related to fraction of volume samples for which the smoothed density fluctuations are above some density threshold Theory tested with numerical N-body simulations • Paul Schechter in an expanding Universe 24 Numerical Galaxy Formation & Cosmology 1 11.04.2018 1974 Press & Schechter Theory N = 1000 • Excellent agreement of theory even with today’s state-of-the-art simulations William Press Paul Schechter 25 Numerical Galaxy Formation & Cosmology 1 11.04.2018 1974 Press & Schechter Theory N = 1000 • One of the most cited papers in astrophysics! William Press Paul Schechter 26 Numerical Galaxy Formation & Cosmology 1 11.04.2018 1976 Simon White 27 Numerical Galaxy Formation & Cosmology 1 11.04.2018 1976 Simon White 27 Numerical Galaxy Formation & Cosmology 1 11.04.2018 1974 Simulations with non-equal particle mass N = 700 • Hierarchical structure formation (bottom-up) Simon White 28 Numerical Galaxy Formation & Cosmology 1 11.04.2018 2005 More recent simulations N = 21603 ≈ 1010 Simon White • Millennium 2005 500 Mpc/h Millennium II 2006 • Volker Springel 100 Mpc/h • Millennium XXL 2011 3 Gpc/h 29 Numerical Galaxy Formation & Cosmology 1 11.04.2018 2005 More recent simulations N = 21603 ≈ 1010 30 Numerical Galaxy Formation & Cosmology 1 11.04.2018 1976 George Efstathiou 31 Numerical Galaxy Formation & Cosmology 1 11.04.2018 1976 George Efstathiou 31 Numerical Galaxy Formation & Cosmology 1 11.04.2018 1981 The P3M-Method N = 20 000 • Invention of the particle-particle/particle-mesh (P3M) method ➙ drastic speed-up • Number of particles up to 20 000 Einstein-de Sitter
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