ASTRO504 Extragalactic Astronomy
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13. Galaxy Formation Theory ASTRO504 Extragalactic Astronomy
Transcript of ASTRO504 Extragalactic Astronomy
13. Galaxy Formation Theory
ASTRO504Extragalactic Astronomy
Summary so far
• Before z=1100
• Baryon-photon tightly coupled
• DM perturbation grow logarithmically (RD) and linearly (MD) in a(t).
• After z=1100
• Baryons thermally coupled to CMB till z~150
• Baryons go into the gravitational potential (that DM made), form halos
• Halos (when spherical) collapse at ΔNL~200 [or 18π2!] (when δc=1.686).
From halos to galaxies
1010 1011 1012 1013 1014 1015 1016
Mass [M�]
10�8
10�7
10�6
10�5
10�4
10�3
10�2
10�1
100
Mas
sfu
nct
ion
dn(M
)/d
lnM
[Mpc�
3]
z=0
z=0.5
z=1
z=1.5
z=2
Sheth & Tormen (’99) mass function • How many 1015M halos at z<1?
• Relation between Mhalo to Mgalaxy?
• How many 1014M
galaxies must be there at z<1?
• How many observed?
Galaxy formation inside halos
• CDM(~5/6): no interaction. responsible for growth of structure
• Baryons(~1/6): interaction with photon, can radiate, cool down
I.C. = Virial shock and thermalizationBirnboim & Dekel (2003)
• line= Each shell of spherically collapsed gas in adiabatic case
• Inside = shock-heated gas
• Outside = newly collapsed shell gravitationally infalling
• Shock-heating continuously grow the shock radius, and it follows the viral radius.
• Shock thermalizes the kinetic energy
• At viral radius,
Accretion shock (adiabatic collapse)
Eshell,K =3
2NkBTsh =
1
2Mshellv
2in
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Tsh =1
3
Mshell
N
v2inkB
=µmp
3kBv2in
<latexit sha1_base64="8p3ZKEDAQowzjAFy1nv3Mv2mNbM=">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</latexit><latexit sha1_base64="8p3ZKEDAQowzjAFy1nv3Mv2mNbM=">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</latexit><latexit sha1_base64="8p3ZKEDAQowzjAFy1nv3Mv2mNbM=">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</latexit><latexit sha1_base64="8p3ZKEDAQowzjAFy1nv3Mv2mNbM=">AAACT3icbZFLSwMxFIUz9dXWV9Wlm2ARXJUZFXRTEN24UFGwKnTqkEkzNjTJDElGKCH/0I3u/BtuXChi2hnB14WQw3fuJclJnDGqtO8/e5Wp6ZnZuWqtPr+wuLTcWFm9UmkuMenglKXyJkaKMCpIR1PNyE0mCeIxI9fx8GjsX98TqWgqLvUoIz2O7gRNKEbaoaiRXEYmlByqgYVtGCYS4WCn2M3pl0UYs9ac2QLfF5gKe7ttzTA6tPV24YQ8hzzKrNkZ0+99UaPpt/xJwb8iKEUTlHUeNZ7CfopzToTGDCnVDfxM9wySmmJGbD3MFckQHqI70nVSIE5Uz0zysHDTkT5MUumW0HBCv08YxJUa8dh1cqQH6rc3hv953Vwn+z1DRZZrInBxUJIzqFM4Dhf2qSRYs5ETCEvq7grxALlotPuCugsh+P3kv+JquxX4reBit3lwUsZRBetgA2yBAOyBA3AMzkEHYPAAXsAbePcevVfvo1K2VrxSrIEfVal9AroRtPQ=</latexit>
v2in = ⇣GM
r⌘ ⇣V 2
vir<latexit sha1_base64="5Uol8m87DkL034Mdg3ubrx+wr2g=">AAACJXicbVDLSgMxFM34rPVVdekmWARXZaYIulAouNCFQgX7gE4tmfROG8xkxiRTqMP8jBt/xY0Liwiu/BXTdhbaeiBwOOdcbu7xIs6Utu0va2FxaXllNbeWX9/Y3Nou7OzWVRhLCjUa8lA2PaKAMwE1zTSHZiSBBB6HhvdwMfYbA5CKheJODyNoB6QnmM8o0UbqFM4GncSVAWYivS/jc+w+gSbY9SWhyeVNmsgUu/AYs0Hm1KfxAZMm3ykU7ZI9AZ4nTkaKKEO1Uxi53ZDGAQhNOVGq5diRbidEakY5pHk3VhAR+kB60DJUkABUO5lcmeJDo3SxH0rzhMYT9fdEQgKlhoFnkgHRfTXrjcX/vFas/dN2wkQUaxB0usiPOdYhHleGu0wC1XxoCKGSmb9i2iemIW2KzZsSnNmT50m9XHLsknN7XKxcZ3Xk0D46QEfIQSeogq5QFdUQRc/oFb2jkfVivVkf1uc0umBlM3voD6zvHyvwpRY=</latexit><latexit sha1_base64="5Uol8m87DkL034Mdg3ubrx+wr2g=">AAACJXicbVDLSgMxFM34rPVVdekmWARXZaYIulAouNCFQgX7gE4tmfROG8xkxiRTqMP8jBt/xY0Liwiu/BXTdhbaeiBwOOdcbu7xIs6Utu0va2FxaXllNbeWX9/Y3Nou7OzWVRhLCjUa8lA2PaKAMwE1zTSHZiSBBB6HhvdwMfYbA5CKheJODyNoB6QnmM8o0UbqFM4GncSVAWYivS/jc+w+gSbY9SWhyeVNmsgUu/AYs0Hm1KfxAZMm3ykU7ZI9AZ4nTkaKKEO1Uxi53ZDGAQhNOVGq5diRbidEakY5pHk3VhAR+kB60DJUkABUO5lcmeJDo3SxH0rzhMYT9fdEQgKlhoFnkgHRfTXrjcX/vFas/dN2wkQUaxB0usiPOdYhHleGu0wC1XxoCKGSmb9i2iemIW2KzZsSnNmT50m9XHLsknN7XKxcZ3Xk0D46QEfIQSeogq5QFdUQRc/oFb2jkfVivVkf1uc0umBlM3voD6zvHyvwpRY=</latexit><latexit sha1_base64="5Uol8m87DkL034Mdg3ubrx+wr2g=">AAACJXicbVDLSgMxFM34rPVVdekmWARXZaYIulAouNCFQgX7gE4tmfROG8xkxiRTqMP8jBt/xY0Liwiu/BXTdhbaeiBwOOdcbu7xIs6Utu0va2FxaXllNbeWX9/Y3Nou7OzWVRhLCjUa8lA2PaKAMwE1zTSHZiSBBB6HhvdwMfYbA5CKheJODyNoB6QnmM8o0UbqFM4GncSVAWYivS/jc+w+gSbY9SWhyeVNmsgUu/AYs0Hm1KfxAZMm3ykU7ZI9AZ4nTkaKKEO1Uxi53ZDGAQhNOVGq5diRbidEakY5pHk3VhAR+kB60DJUkABUO5lcmeJDo3SxH0rzhMYT9fdEQgKlhoFnkgHRfTXrjcX/vFas/dN2wkQUaxB0usiPOdYhHleGu0wC1XxoCKGSmb9i2iemIW2KzZsSnNmT50m9XHLsknN7XKxcZ3Xk0D46QEfIQSeogq5QFdUQRc/oFb2jkfVivVkf1uc0umBlM3voD6zvHyvwpRY=</latexit><latexit sha1_base64="5Uol8m87DkL034Mdg3ubrx+wr2g=">AAACJXicbVDLSgMxFM34rPVVdekmWARXZaYIulAouNCFQgX7gE4tmfROG8xkxiRTqMP8jBt/xY0Liwiu/BXTdhbaeiBwOOdcbu7xIs6Utu0va2FxaXllNbeWX9/Y3Nou7OzWVRhLCjUa8lA2PaKAMwE1zTSHZiSBBB6HhvdwMfYbA5CKheJODyNoB6QnmM8o0UbqFM4GncSVAWYivS/jc+w+gSbY9SWhyeVNmsgUu/AYs0Hm1KfxAZMm3ykU7ZI9AZ4nTkaKKEO1Uxi53ZDGAQhNOVGq5diRbidEakY5pHk3VhAR+kB60DJUkABUO5lcmeJDo3SxH0rzhMYT9fdEQgKlhoFnkgHRfTXrjcX/vFas/dN2wkQUaxB0usiPOdYhHleGu0wC1XxoCKGSmb9i2iemIW2KzZsSnNmT50m9XHLsknN7XKxcZ3Xk0D46QEfIQSeogq5QFdUQRc/oFb2jkfVivVkf1uc0umBlM3voD6zvHyvwpRY=</latexit>
Virial temperature of gas• Combining all, we find [ζ and μ?]
• Or, in terms of the collapsed halos (Δ=200) [make sense?]
Of course, in reality, inside the viral radius, temperature gradient builds up to maintain HSE, so virial temperature is a representative temperature.
Tvir = 7.8⇥ 105 K
✓⇣
0.6
◆⇣ µ
0.59
⌘✓⌦mh2
0.145
◆1/3 ✓1 + z
4
◆✓M
1012M�
◆2/3
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Tvir = ⇣µmp
3kBV 2vir =
✓⇣
0.6
◆⇣ µ
0.59
⌘✓Vvir
100 km/s
◆2
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The 106K is too hot!• 106K~86.18eV!
• Jeans mass [make sense?]
• What are the implications?
MJ =4⇡
3⇢̄m�3
J ' 1.87⇥ 1014M�(1 +�)�1/2
✓⌦mh2
0.147
◆�1/2 ✓T
106K
◆3/2
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Radiative Cooling processes• Thermal Bremsstrahlung (free-free)
• Recombination (free-bound)
• Collisional ionization (bound-free)
• Collisional excitation + radiative de-excitation
e- + X+ → X+ + e- + 𝞬
e- + X+ → X + 𝞬
e- + X → X+ + 2e-
e- + X → e- + X`→ e- + X`+ 𝞬
Atomic cooling function (H and He)
• Defined as 𝝠(T,Z) = 𝓒/nH2
• Free-free wins at T>106K (∝T1/2)
• Excitation not important for T>105K . Why?
• Ionization weak at T~104K, Why?
• No cooling at lower temperature T<104K. Why?
Atomic cooling function with metalSutherland & Dopita (1993)
Metal ContributionsWiersma, Schaye & Smith (2009)
Cooling function with MoleculesMaio+(2007)
Metalicity
Cooling time scale• Cooling time = time it takes for a hot, virialized gas to radiate
away its virial temperature:ℇ = specific internal energy per unit mass
tcool ⌘⇢"
C =3nkBT
2⇤(T )n2H
=3.3⇥ 106yrs
✓T
109 K
◆⇣ n
10�3 cm�3
⌘�1✓
⇤(T )
10�23erg cm3/s
◆�1
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Worked example: 1012M at z=3
• Tvir~8×105 K, 𝝠(T)~0.5×10-23 erg cm3/s
• If fully ionized (X = hydrogen mass fraction ~ 0.75),
• Therefore, cooling time is about 109 years. Enough time for cooling! Is that enough to form a galaxy?
n =27
12nH =
27
12
⇢X
mp
' 5.5⇥ 10�3cm�3
✓1 + z
4
◆3
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tcool = 3.3⇥ 109yrs
✓T
106 K
◆⇣ n
10�3 cm�3
⌘�1✓
⇤(T )
10�23erg cm3/s
◆�1
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Three time scales• Hubble time (tH) ~ age of the Universe
• Free-fall time (tff) ~ dynamical time to restore HSE (~ tH/10)
• Cooling time (tcool)
• Three cases [discuss!]
• tcool > tH :
• tH > tcool > tff :
• tff > tcool (Rees-Ostriker Criterion) :
Back to the example: 1012M at z=3
• Cooling time is about 109 years. Enough time for cooling!
• But, the free-fall time is (4×108 years) shorter than the cooling time, so the gas will be in the quasi-hydrostatic equilibrium state.
t↵ =
r3⇡
32G⇢'
s3⇡fgas
32Gnµmp' 2.1⇥ 109 yrsf�1/2
gas
⇣ n
10�3cm�3
⌘�1/2
<latexit sha1_base64="XQ5dtO2EobqO5LaK32vSV8LRi94=">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</latexit><latexit sha1_base64="XQ5dtO2EobqO5LaK32vSV8LRi94=">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</latexit><latexit sha1_base64="XQ5dtO2EobqO5LaK32vSV8LRi94=">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</latexit><latexit sha1_base64="XQ5dtO2EobqO5LaK32vSV8LRi94=">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</latexit>
Rees-Ostriker criterion• Cooling time is efficient when tcool < tff
• Therefore, cooling is more efficient at higher redshifts!
t↵ =
r3⇡
32G⇢'
s3⇡fgas
32Gnµmp' 2.1⇥ 109 yrsf�1/2
gas
⇣ n
10�3cm�3
⌘�1/2
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tcool = 3.3⇥ 109yrs
✓T
106 K
◆⇣ n
10�3 cm�3
⌘�1✓
⇤(T )
10�23erg cm3/s
◆�1
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Cooling and galaxy formation
Total gas mass
Density (Δ=200)
• Maximum mass of galaxy 1012M !
• Constant density, spherical distribution
• In hierarchical model, smaller Gs formed first.
• Over-cooling problem (White & Rees 1978)
Cooling radius• Relaxing the constant density assumption: ϱ=ϱ0(r/r0)-α
• Cooling is more efficient at the center than outskirt, so
• Cooling time shorter near the center, longer at larger radii.
• Cooling radius = tcool(r) = tage
• For isothermal case [ϱ=ϱ0(r/r0)-2], cooling radius increases in time, called “cooling wave”:
• rcool, Mcool ∝t1/2
Hot & Cold accretion• rcool < rshock : shock heated then cool
• rcool > rshock : “cold mode accretion” [unstable, why?]
• Isothermal sphere:
• rcool = 𝝠1/2t1/2 , rshock = vct
• Shock radius grows faster than cooling radius
Hot mode & Cold mode
• Halos with M<1010M /h always accrete in cold mode.
• Halos with M>1012M /h have a stable accretion shock close to the viral radius (hot mode).
Effect of photoionization• At lower redshifts, we do have UV radiation background that
can photo-ionize the gas.
• Two effects:
• Severely suppress the cooling rate of the low-density gasBecause photoionization reduces the number of neutral atoms and shut off the collisional excitation and collisional ionization
• It heats the gas
M/L ratio
• Lower mass (M<1012M ) :SN feedback is important!
• Higher mass (M>1012M ):AGN feedback is important!
Formation of disk galaxies• While the gas sink
toward the center, it is hard to loose the angular momentum (radiation is isotropic).
• Initial angular momentum from “tidal torque” (see figure).
• Spin parameter:
• Simulation find that distribution of λi = log-normal with mean=0.05, variance=0.5
• Exponential disk : λnow = 0.425, need (0.425/0.05)2~72-fold shrink without DMhalo, would take 43Gyr!
• With halo, only 7-fold, took 1.4 Gyr.
Need dark halo to explain spin!� =
J |E|1/2
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