radiative transfer in a clumpy universe: the uvbhipacc.ucsc.edu/html/hipacclectures/uvb.pdf ·...
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Radiative Transfer in a Clumpy Universe: the UVB
Piero MadauUC Santa CruzWednesday, August 4, 2010
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The cosmic UVB originates from the integrated emission of star-forming galaxies and QSOs. It determines the thermal and ionization state of the IGM, the repository of most of the baryons in the Universe at high redshift.
It is a crucial yet most uncertain input parameters for cosmological simulations of LSS and galaxy formation, for interpreting QSO absorption-line data and derive information on the distribution of primordial gas -- traced by HI, HeI, HeII transitions -- and of the nucleosynthetic products of star formation -- CIII, CIV, SiIII, SiIV, OVI, etc.
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Outline
Hydrogen recombinationThe dark agesCosmic structure formationThe reionization equationQuasars or galaxies?The Gunn-Peterson troughQuasar absorbers along the LOSEffective optical depth of the UniverseCosmological radiative transferCUBA (the code)
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Hydrogen recombination
Two factors delay recombination:(1) η-1
=1.5x109≫1(2) inability to mantain equilibrium as H!1
! trec " x/x
e-+p→H+γ @ z=1100marks the end of the plasma era
But the baryon-photon ratio is very small, ! =nB/n"=6.5# 10-10 .
Recalling that for a blackbody n" =20.2 T3 cm-3, and eliminating T
and nH in favor of n" and !, the Saha equation becomes:
!
x2
1" x= 2.5 #106$"1 I
kBT
%
& '
(
) *
3 / 2
exp "I
kBT
%
& '
(
) *
big coefficient
kBT=1/3 eV (T=3870) $ x=0.72
kBT=0.3 eV (T=3500) $ x=0.14
Recombination is further delayed by inability to maintain
equilibrium. Two main routes to the production of HI are: a) two-
photon decay from metastable 2s level to the ground state; and b)
loss of Lyman-alpha resonant photons by the cosmological redshift
(Peebles 1968).
equilibrium (Saha) eq. for x≡ne/nH
I=13.6eV η-1≡nγ/nb
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Hydrogen recombination (a digression)
When an e- is captured to the ground state of HI, it produces a photon that immediately ionizes another atom, leaving no net change.
When it is captured to an excited state, the allowed decay to the ground state produces a resonant Lyman series photon, which has a large capture cross-section → puts another atom in a high energy state that is easily photoionized again, thereby annulling the effect.
Two main routes to the production of atomic hydrogen:
1) two-photon decay from the 2s level to 1s.2) loss of Lyα resonance photons by the cosmological redshift.
Zeldovich, Kurt, Sunyaev 1968Peebles 1968
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The “dark ages”...
Timescale for relaxation of matter temperature is
➔
tcomp =3mec
4!T aBT 4
1+x
2x
zth ! 580(!bh2)2/5
! 130.TV !!1
= const
..and their end
➞ Universe becomes semi-opaque after reionization!T (z) =
! z
0ne(z)"T |cdt/dz|dz = 0.087
WMAP
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The “dark ages”...
Timescale for relaxation of matter temperature is
➔
tcomp =3mec
4!T aBT 4
1+x
2x
zth ! 580(!bh2)2/5
! 130.TV !!1
= const
..and their end
➞ Universe becomes semi-opaque after reionization!T (z) =
! z
0ne(z)"T |cdt/dz|dz = 0.087
WMAP
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QSOCosmic structure formation: I
Example: ionized gas of density ne filling uniformly a fraction f of the available volume, rest is empty space. Then
ne
nene
ne
ne
Clumpiness boosts H recombination rate:
!n2e" = fn2
e; !ne" = fne
# !n2e" = !ne"2/f # C = 1/f
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Cosmic structure formation: II
nHdVdt
= N! ! V !Bn2
H
HII region in homogeneous ISM (Stromgren analysis):
HII region in expanding clumpy IGM (Shapiro & Giroux 1987):
nH(t)(dVdt
! 3HV ) = N! ! V !B"nH(t)#2C
V = N!trecnH
(1 ! e!t/trec)➞
V=proper volume
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Reionization @ milliFLOP speed (PM, Haardt, & Rees 1999)
QI(t)= volume filling factor of HII regions at t
The reionization equation
QI(t) =! t
0n!(t!)
!nH(t!)"dt# !! t
0QI (t!)
trecdt#
source sink
(no redshifting, ionizing photons assorbed locally). Differentiating:
dQI
dt=
n!
!nH" !QI
trec
simple diff. eq. statistically describes transition from a neutral Universe to a
fully ionized one!Contrary to the static case, cosmological HII regions will always percolate in an expanding universe with constant comoving ionizing emissivity....
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The reionization equation
trec ! t " QI #n!
!nH" trec
Because of hydrogen recombinations, only a fraction trec/t of the photons emitted above 13.6 eV is actually used to ionize new IGM material.
The universe is completely reionized when QI=1, i.e. when Numerical simulation of stellar
reionization (Gnedin 2000)
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(Bright) QSOs are not responsible for the reionization of cosmic hydrogen!
Quasars or galaxies?
Text
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radiation emitted at νe and ze becomes resonant (Lyα) at (1+z) = (1+ze) να/νe ➔ scattered off the los with cross-section:
total optical depth for resonant scattering (Gunn-Peterson)
!(") = !e2
mecf #(")
Hydrogen is highly ionized at z<5.7
!GP(ze) =! ze
0"nHI(z)|cdt/dz|dz =
"
!e2fme"!
#
nHI
H.
The Gunn-Peterson trough
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f(NHI,z) defined by the probability dP that a los intersects an absorber with column density NHI in the range dNHI, at redshift z in the range dz,
dP = f(NHI, z)dNHIdz
We can now quantify the degree of attenuation of UV radiation in a clumpy Universe by introducing the concept of an effective continuum optical depth τeff along the line-of-sight to redshift z: where the average is taken over all lines-of-sight.
!e!! " = e!!eff
Quasar absorbers along the LOS
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➔ Poissonian probability of encountering a total optical depth kτ0 is:
Assume random distribution of absorbers in column density and redshift space, then:
!e!("o, zo, z) =!
z
zo
dz!!"
0f(NHI, z)(1! e#! )
Effective optical depth
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The equation of cosmological radiative transfer describes the timeevolution of the space- and angle-averaged monochromatic intensity Jν:
*
!e!("o, zo, z) =!
z
zo
dz!!"
0f(NHI, z)(1! e#! )
observed must be modeled
☛equation * must be solved by iteration since NHI
Cosmological radiative transfer
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1) absorbers are not only sinks but also sources of ionizing radiation. In particular, HeII reprocesses soft X-rays He-ionizing photons into UV H-ionizing ones.
Two important effects must be included:
• recombinations to ground state of HI,HeI, HeII
• HeII Balmer and 2-photon continuum
• HeII Lyman-alpha
Ionizing recombination radiation includes:
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2) besides photoelectric absorption, resonant absorption by H and He Lyman series will produce a sawtooth modulation of the spectrum.
ν=ναν=νβ
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HI distribution QSO/GAL LF SED
J-solution flow chart
ABSORBERS SOURCES
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HI distribution
cosmological radiative transfer ➔ J
QSO/GAL LF SED
J-solution flow chart
ABSORBERS SOURCES
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HI distribution
local radiative transfer ➔H/He ionization state
cosmological radiative transfer ➔ J
QSO/GAL LF SED
J-solution flow chart
ABSORBERS SOURCES
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HI distribution
local radiative transfer ➔H/He ionization state
τeff, εreccosmological radiative transfer ➔ J
QSO/GAL LF SED
J-solution flow chart
ABSORBERS SOURCES
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HI distribution
local radiative transfer ➔H/He ionization state
τeff, εreccosmological radiative transfer ➔ J
QSO/GAL LF SED
J-solution flow chart
ABSORBERS SOURCES
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HI distribution
local radiative transfer ➔H/He ionization state
τeff, εreccosmological radiative transfer ➔ J
UVB
QSO/GAL LF SED
J-solution flow chart
ABSORBERS SOURCES
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HI distribution
local radiative transfer ➔H/He ionization state
τeff, εreccosmological radiative transfer ➔ J
UVB
QSO/GAL LF SED
CUBA
J-solution flow chart
ABSORBERS SOURCES
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z=0 z=1
z=3 z=5
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THE END
Haardt & PM 1996, ApJ, 461, 20 PM, Haardt, & Rees 1999, ApJ, 514, 648 PM et al, 2004 ApJ, 604, 484PM & Haardt 2009, ApJ, 693, L100Gilmore et al. 2009, MNRAS, 399, 1694Haardt & PM 2020, in preparationhttp://pism.ucolick.org/CUBA
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