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 = phys + ~u = ~ @t r r @t a ar continuity equation: with @⇢ @ 1 ⇢ ⇢¯ + ~ (⇢~v)=0 + ~ ~u =0 = @t rphys @t ar ⇢¯ Poisson equation: ~ 2 =4⇡G⇢ ~ 2 =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 a˙ ⇢¯ ¨ +2 ˙ =4⇡G c solved by growth function D ( a ) : (a)= 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: (~x)= (k)e d k Power spectrum is P ( k )= ˆ ( k ) 2 (whereZ : ensemble average) h| | i hi 2 and it grows like P (k)=P0D (a)
Formalism works as long as 1 • ⌧ Breaks down when 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 Universe with !0 = 1 George Efstathiou
32 Numerical Galaxy Formation & Cosmology 1 11.04.2018 1983
Anatoly Klypin
Sergei Shandarin
33 Numerical Galaxy Formation & Cosmology 1 11.04.2018 1983
Anatoly Klypin
Sergei Shandarin
33 Numerical Galaxy Formation & Cosmology 1 11.04.2018 1983 Cosmological Simulations N = 323 = 32 768 • Pure PM method • Cosmological initial conditions (Zeldovich approx.) • Filaments form (cosmic web)
Anatoly Klypin
Sergei Shandarin
34 Numerical Galaxy Formation & Cosmology 1 11.04.2018 2011 Cosmological Simulations N = 20483 = 8.6 109 • Bolshoi simulation with WMAP cosmology • MultiDark simulation suite with several boxes
Anatoly Klypin
35 Numerical Galaxy Formation & Cosmology 1 11.04.2018 1985
Marc Davis
George Efstathiou
Carlos Frenk
Simon White
36 Numerical Galaxy Formation & Cosmology 1 11.04.2018 1985
Marc Davis
George Efstathiou
Carlos Frenk
Simon White
36 Numerical Galaxy Formation & Cosmology 1 11.04.2018 1985 Gang of Four • Realistic initial conditions using Zeldovich approximation
• Detailed study of numerical effects Marc Davis
George Efstathiou
Carlos Frenk
Simon White
37 Numerical Galaxy Formation & Cosmology 1 11.04.2018 1985
Marc Davis
George Efstathiou
Carlos Frenk
Simon White
38 Numerical Galaxy Formation & Cosmology 1 11.04.2018 1985
Marc Davis
George Efstathiou
Carlos Frenk
Simon White
38 Numerical Galaxy Formation & Cosmology 1 11.04.2018 1985 Gang of Four • Invention of Friends-of-Friends halo finding algorithm
• Biased galaxy formation Marc Davis
George Efstathiou
FoF
Carlos Frenk
Simon White
39 Numerical Galaxy Formation & Cosmology 1 11.04.2018 1985 Gang of Four • Invention of Friends-of-Friends halo finding algorithm
• Biased galaxy formation Marc Davis
George Efstathiou
Carlos Frenk
Simon White
40 Numerical Galaxy Formation & Cosmology 1 11.04.2018 1985 Gang of Four
Marc Davis
George Efstathiou
Carlos Frenk
Simon White
41 Numerical Galaxy Formation & Cosmology 1 11.04.2018 1986
Josh Barnes
Piet Hut
42 Numerical Galaxy Formation & Cosmology 1 11.04.2018 1986
Josh Barnes
Piet Hut
42 Numerical Galaxy Formation & Cosmology 1 11.04.2018 1986 The Tree algorithm • Divide space into cubic cells hierarchically • Organise particles into tree structure • Compute forces directly only within sub-cell Josh Barnes
Piet Hut
43 Numerical Galaxy Formation & Cosmology 1 11.04.2018 1986 - now
• successive refinement of simulation techniques • allowing for more and more and more particles to be simulated • new field in astrophysics has emerged
44 Numerical Galaxy Formation & Cosmology 1 11.04.2018 1997
Julio Navarro
Carlos Frenk
Simon White
45 Numerical Galaxy Formation & Cosmology 1 11.04.2018 1997
Julio Navarro
Carlos Frenk
Simon White
45 Numerical Galaxy Formation & Cosmology 1 11.04.2018 1997 The NFW profile • Invented the re-simulation (zoom) technique
Julio Navarro
Carlos Frenk
Simon White
46 Numerical Galaxy Formation & Cosmology 1 11.04.2018 1997 The NFW profile
Julio Navarro
Carlos Frenk
Simon White
47 Numerical Galaxy Formation & Cosmology 1 11.04.2018 1997 The NFW profile
48 Numerical Galaxy Formation & Cosmology 1 11.04.2018 1997 The NFW profile
Julio Navarro
Carlos Frenk
Simon White
49 Numerical Galaxy Formation & Cosmology 1 11.04.2018 until 1999 Problems with CDM simulations • despite ever refined simulation methods… • despite advances in computer technology… • ...despite ever increasing resolution:
dark matter halos do not show substructure!
“overmerging crisis”
50 Numerical Galaxy Formation & Cosmology 1 11.04.2018 1987
Simon White
• noted already in 1987
51 Numerical Galaxy Formation & Cosmology 1 11.04.2018 1987
Simon White
• noted already in 1987
51 Numerical Galaxy Formation & Cosmology 1 11.04.2018 1996
Ben Moore • still a problem in 1996
52 Numerical Galaxy Formation & Cosmology 1 11.04.2018 1996
Ben Moore • still a problem in 1996
52 Numerical Galaxy Formation & Cosmology 1 11.04.2018 1999
Anatoly Klypin • still a problem in 1996
53 Numerical Galaxy Formation & Cosmology 1 11.04.2018 1999
Anatoly Klypin • still a problem in 1996
53 Numerical Galaxy Formation & Cosmology 1 11.04.2018 1999 Overmerging vs. resolution • Extremely high-resolution simulations (~250 000 particles per halo) • Detailed study of physical vs. numerical effects • New halo finder introduced (BDM) Anatoly Klypin
Brute force: lots of surviving substructure
54 Numerical Galaxy Formation & Cosmology 1 11.04.2018 1999
do we observe that much substructure?
55 Numerical Galaxy Formation & Cosmology 1 11.04.2018 1999
Anatoly Klypin
56 Numerical Galaxy Formation & Cosmology 1 11.04.2018 1999
Anatoly Klypin
56 Numerical Galaxy Formation & Cosmology 1 11.04.2018 1999 The missing satellite problem • Local group simulation shows many satellite haloes • Where are the galaxies?
Anatoly Klypin
57 Numerical Galaxy Formation & Cosmology 1 11.04.2018 1999 The missing satellite problem • Local group simulation shows many satellite haloes • Where are the galaxies?
Anatoly Klypin
58 Numerical Galaxy Formation & Cosmology 1 11.04.2018 1999
Ben Moore
59 Numerical Galaxy Formation & Cosmology 1 11.04.2018 1999
Ben Moore
59 Numerical Galaxy Formation & Cosmology 1 11.04.2018 1999 The missing satellite problem
Ben Moore
60 Numerical Galaxy Formation & Cosmology 1 11.04.2018 2012
Mike Boylan-Kolchin
61 Numerical Galaxy Formation & Cosmology 1 11.04.2018 2012
Mike Boylan-Kolchin
61 Numerical Galaxy Formation & Cosmology 1 11.04.2018 2012 Too big to fail?
Mike Boylan-Kolchin
62 Numerical Galaxy Formation & Cosmology 1 11.04.2018 now Problems with CDM? • Large scales: good match between observations and simulations • Small scales:
Observations Simulations
Shallow density cores Steep density cores
Few satellites Many satellites
Low total satellite masses Higher total satellite masses
• Failure of CDM?
63 Numerical Galaxy Formation & Cosmology 1 11.04.2018 now Possible solutions
• The cosmological model is wrong… • Maybe, but not much…
• The observations are wrong… • Better telescopes…
• The simulations are wrong… • Physics missing! Baryons… • Something else is wrong…
64 Numerical Galaxy Formation & Cosmology 1 11.04.2018 Cosmological simulations with baryons
• Unlike dark matter, gas can cool and fall to the centre • Feedback from forming stars will affect the galaxies on small scales • Relation between galaxies and haloes is not 1:1
65 Numerical Galaxy Formation & Cosmology 1 11.04.2018 Up next • 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
69 Numerical Galaxy Formation & Cosmology 1 11.04.2018