Outline

1. Outline Part II. Structure Formation: Dark Matter 5. Linear growth of fluctuations by gravitational Instability 6. Statistics of fluctuations: initial fluctuations and the cold-dark-matter scenario 7. Nonlinear growth of structure: spherical collapse, virial equilibrium, Zeldovich approximation and the cosmic web, N-body simulations 8. Hierarchical clustering: Press-Schechter halo distribution, EPS merger trees, galaxy/halo biasing, HOD and correlation function 9. Dark-matter halos: universal profile, the cusp/core problem, dynamical friction, tidal effects, halo shape 10. Substructure of dark-matter halos, phase-space density

2. Outline cont. Part III. Galaxy Formation: Including gas and Stars 11. Angular momentum: tidal-torque theory, halo spin, disk formation, the AM problem 12. Galaxy bimodality: observations, virial shock heating, star formation and quenching mechanisms, downsizing 13. Dwarf galaxies and supernova feedback 14. Formation of elliptical galaxies by mergers: missing dark matter? origin of scaling relations, origin of red sequence and downsizing 15. Galaxy formation at high redshift: cold streams, clumpy disks and compact spheroids 16. Massive black holes in galaxies: AGN feedback 17. Semi-analytic modeling of galaxy formation

3. Linear Growth of Fluctuations by Gravitational Instavility 2dF WMAP

4. 2dF Galaxy Redshift Survey ¼ M galaxies 2003 CFA Survey 1980

5. History Early Universe Cosmic Microwave Background Today time

6. Cosmological Epochs recombination last scattering 380 kyr z~1000 CMB transparent optical opaque: “dark ages” first stars reionization 180 Myr z=8.81.5 galaxy formation: optical transparent → see galaxies today 13.8 Gyr

7. Gravitational instability small-amplitude fluctuations:  gravitatinal instability: galaxy cluster  void 0

10. ימסוקה גראמה - תויצאוטקלפה לודיג

11. Gravitational Instability: linear, matter-era : equations Fluid    Continuity Euler Poisson   ) 1 ( ( )  0 V          (2) V ( V ) V P/ρ Φ           2 ) 3 ( 4 G      Uniform background : ( ) . r const     2 8 4 a  a  G a   G 3        ) 1 ( 0 r a x v r       3 2 3 a a a a   ) 1 ( / 3 H a  a H              Perturbati ons : ( , ) ( )[ 1 ( , )] ( ) r t t r t V H t r v P p          u u  st 1 order : 1 etc.              ) 1 ( ( )  0 H r v v                   2   ) 2 ( ( ) ( ) v H r v H v v v c             s     2 ) 3 ( 4 G     P  P  P  kT   2 u  ( ideal gas ) P c       s m   p

12.   r a      Comoving coordinate : s x r a         r x r a  t t a   t x r     / / w v a a         ) 1 ( ( ) 0  w w              2   1 ) 2 ( 2 (  )  w H w w w a c          s     2 2 ) 3 ( 4 [ / 3 (  ) 2 ] G H    u  1  ( eq. ) 2 / ( eq. ) 1  a  t       H 2      2 2 2 4  G a c     u s gravity pressure a     3 ( , ) ( ) ( ) ( )  x t a t H t t a   u a

13. a     H 2      2 2 2 4  G a c  3     ( ) ( ) ( )  a t H t t a   u u s a  Static background : 0 . 1 . a  a const  const    u  2      2 2 exp[ ( )] 4 i k x t k c G      s u pressure gravity / 1   2 / 3   2 2      / 3 2     4 2 k 4 G c T     Jeans scale : u s k M           J J J m   2 / 1 2 3 G c J s      t t ( ) 0  p Ae Be      J   stable oscilation s   J   Expanding background , :  J 4 2 t  / 2 3 1  At Bt       2 / 3   0 k a t       2 3 3 t 3 2 t t       . freezout const    0 0 1 k a t        3 2 t

14. Properties of the linear growing mode:      :  2 linear 2 / 3 (  ) 2 ( ) ( ) H H H t t     growing mode D(t) δ D  D   3 6 . 0 2 ( ) ( 2 ) f H f          2 HD D  1   continuity v      Hf  3 H 2      Poisson irrotation al v      v v f The Jeans scale in an expanding universe:     k i  x  k H In space  : ( ) k t e r ax    k       2     2 for each : 2 4 ( ) same Jeans scale k G k c     k k s k

15. Lecture Statistics of Fluctuations: The Cold Dark Matter Scenario

16. The Initial Fluctuations At Inflation: Gaussian, adiabatic a realization of an ensemble ensembe average ~ volume average   ( ) x     fluctuation field  ( ) x        k i x     ~   ( ) Fourier x ke  Power Spectrum 2| ) n ( ) | ( P k k k      k   ~ 2 / K K K rms      2 3 3 3 ~ exp[ ( ) ' ] ' ~ i k k  x d k d k d k   k 0   0          ' k k k k  ' 0 k k   ( ) ' k k  Dirac   2 /  2 3 ( 3 / ) 3  n     2| P d k M |           k k k k  0 k δ Pk  3 / 2  1 n M    / 1  2 0  n M    3 . n const   M k

17. Scale-Invariant Spectrum (Harrison-Zel’dovich) R  t mass  MH t Horizon 3 2   a t  H t m M time t 2 / 3 t   2 / 3 2 / 3     ( , ) M t M t        H ( ) t M H  . const H  1 n P k  k 2 / 3   M M

18. Cosmological Scales mass ~ R  ct MH t Horizon 3 2   a t  m  3  a matter  4  a rad t0 teq time zeq~104

19. CDM Power Spectrum MH t  mass H  growth when matter is self- gravitating  H  H   rad mass t time teq CDM 1  k Pk  2 / 3  3 M  k CDM HDM HDM free streeming mass k kpeak m h Meq

20. Formation of Large-Scale Structure Fluctuation growth in the linear regime: rms fluctuation at mass scale M: Typical objects forming at t:   ~ 1    / 2 t 6 3 1 a  / ) 3   M M   n  0  a 2    ( n    2 / 3     / 1   M a * example 6 M a   * HDM: top-down CDM: bottom-up / 1 2 / 1 2 2 2                     1 1 free streaming 0 0 M M

21. Micro-Macro Connection Cold Dark Matter Hot Dark Matter 

22. 2dF redshift survey

23. 2dF and Mocks

24. Power Spectrum

25. Success of the LCDM Power Spectum