Theory of galaxy formation

Transcription

1 Theory of galaxy formation Bibliography: Galaxy Formation and Evolution (Mo, van den Bosch, White 2011) Lectures given by Frank van den Bosch in Yale

2 Theory of Galaxy Formation ρ (x, t) = ρ0 (t)[1+ δ (x, t)] ρ x (t) δ (x, t) = δ x (t) = ρ0 (t)

3 Structure growth δ x (tcmb ) ~ 10 5 tcmb~350,000 y δ x (t0 ) ~ 10 6 t0= y (in DM, even more for gas and stars)

4 Galaxy formation (star formation) is an inefficient process!!

5 Galaxy Formation in a nutshell Formation of DM haloes Gas collapse into the DM haloes Gas cooling Conservation of angular momentum Star formation (and feedback)

6 Galaxy formation II White & Rees 1978

7 The program δ x (t) = ρ x(t) < ρ(t) > Evolution of the background density à Cosmology Evolution of a Dark Matter fluctuation, Numerical Simulations Gas cooling within DM haloes and Star Formation Stars and Galaxies

8 Exercises/Simulations δ x (t) = ρ x(t) < ρ(t) > Pure DM simulations Hydrodynamical Cosmological simulations: GAS Star Formation Feedback

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11 Cosmology in a nut shell FRW and expansion factor Density evolution and Ω i Linear theory and perturbation growth The CMB Beyond linear theory

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13 Big Bang: very hot and very dense; mostly photons; opaque; uniform but tiny quantum fluctuations Inflation: very brief (~10-35 sec), very rapid expansion, quantum fluctuations become real Cosmic Microwave Background: cooled to ~3,000K (due to expansion now into microwave regime), atoms (H and He) formed, transparent to photons Last Scattering Surface before recombination

14 FRW and Universe expansion Homogeneous and Isotropic Expanding

15 Expansion laws k= curvature (k=0 for a flat Universe) Λ = Cosmological constant p = pressure ρ= density First law of thermodynamics

16 Expansion Laws II (Dark) Matter w=0 Radiation w=1/3 Curvature w=-1/3 Cosmo Constant w=-1 ρ r (t) = ρ r (0)a 4 ρ K (t) = ρ K (0)a 2 Sooner or later DE will rule the expansion of the Universe

17 Expansion law

18 Density parameters! # "!a a $ & % 2 = 8 3 πgρ * c + Ω m a 3 + Ω r a 4 + Ω K a 2 + Ω Λ, -

19 Age of the Universe

20 Liner Evolution ρ(x,t) = ρ 0 (t)[1+δ(x,t)] δ<<1 What is the time evolution of δ(x) under the following assumptions Ideal Fluid Gravity No viscosity Linear regime Expanding Universe Jeans equation

21 [ ] > 0 Oscillation [ ] < 0 Collapse Jeans criterium

22 Perturbation growth in Dark Matter c s =0 in Dark Matter DM dominated Universe Ω m =1 DE dominated Universe Ω Λ >Ω m δ k a =1/ (1+ z)

23 Perturbation growth in Dark Matter c s =0 Radiation dominated Universe Ω r ~1 DM perturbations in the radiation era have a logarithm (very slow) growth?

24 Super-Horizon perturbations Particle horizon Radiation Matter Super horizon perturbation can growth even in the radiation domination era

25 Power Spectrum Historically R=8 Mpc/h Primordial and transmitted power spectrum T(k,z) = Transfer Function

26 Black board drawing

27 And the Baryons?

28 The CMB origin Dark Matter: provides potential well due to primordial perturbation Baryons: due to gravity are dragged at the bottom of the potential well Photons: tend to disperse any concentration of baryons Dynamical time vs Sound crossing time t dyn 1 Gρ t sc = λ c

29 if t dyn < t sc if t dyn > t sc Collapse Oscillation Jeans length Before recombination: Oscillation After recombination: Free to growth

30 The CMB spectrum First peak compression Second rarefaction

31 The Cosmic Microwave Background Sets the initial conditions of our Universe

32 Observed Power Spectrum

33 Beyond Linear theory Perturbation divided in shells No shell crossing Internal shells will re-collapse first

34 Beyond Linear theory Turn around Virialization E kin = -1/2 E pot ρ ta /ρ 0 =Δ ta = 5.5 ρ vir /ρ 0 =Δ vir = 178 (Ω m =1.0) Δ vir = 95 (Ω m =0.3 Ω Λ =0.7 )

35 Press and Schecter Linear threshold for collapsed objects: δ c = 1.69 Volume V with a given overdensity δ σ R σ M Fraction of mass in collapsed objects: Depends only on the transmitted PS

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37 Power Spectrum and DM? Will the PS continue to decrease linearly?

38 CMB Large scales (galaxy clusters) Small scales (dwarf galaxies) m HDM m WDM m CDM ~ ev ~ kev > GeV DM Particles are created with non zero Thermal velocity. This velocity is inverse proportional to their mass

39 $ k S 0.3 ' & ) % ( Ω X 0.15 $ & % m X kev ' ) ( 1.15 Mpc 1 The cut in the PS affects the mass of the objects that can form

40 Smit+2001 Smit+2001 M min =10 9 M sun CDM M min =10 9 M sun m X = 0.1 kev

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42 The end (for today) δ x (t) = ρ x(t) < ρ(t) > Evolution of the background density à Cosmology Evolution of a Dark Matter fluctuation, Numerical Simulations Galaxy formation is a young science In DM domination perturbations grow linear with a(t) There is a specific density contrast at which objects virialize DM candidate mass determines the size of the smallest object

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