1. Constraint on Cosmic Reionization from High-z QSO Spectra
Kumiko Hiroi
(Univ. of Tsukuba)
Collaborators :
Masayuki Umemura, Taishi Nakamoto
(Univ. of Tsukuba)

2. Requirements for Reionization History
There are two independent observations related to cosmic reionization.
Observation of High-z QSO
(R. H. Becker et al. 2001, Fan et al. 2001)
DA increases steeply at z >4
Observation by WMAP
(Spergel et al. 2003, Kougut et al. 2003)
The optical depth of Thomson scattering is te=0.17±0.04
Reionization history must satisfy these observational results.

3. Observation of High-z QSO
Continuum Depression (Oke & Korycansky 1982)
decrease of the average flux by absorption of neutral hydrogen
QSO at z=6.28
DA=0.93
Fan et al. 2001 J
z=6.28
Lyα
Continuum Depression
Flux (μJy)
fνcon
Strong absorption
Lyß
Wavelength (Å)
DA increases steeply at z >4

4. Observation by WMAP (D.N.Spergel et al. 2003)
Polarization cross-power spectra
The solid line is the predicted signal based on temperature power spectra.
The excess power at large angular scale was caused by Thomson scattering.
te=0.17±0.04

5. The Purpose of Research
We simulate the cosmic reionization by solving 3D radiative transfer of ionizing photons in an inhomogeneous universe.
By comparing the calculation results with observational data, we attempt to estimate
the evolution of UV radiation intensity
the epoch of cosmic reionization

6. Models and Methods 1. A LCDM cosmology(WMAP) is assumed.
i.e. Wm=0.3, WL=0.7,Ωbh2=0.02, H0=70km s-1 Mpc-1
2. Random Gaussian density fields are generated by the Truncated Zel’dovich approximation at each redshift from z=4 to z=20.
3. Isotropic UV background spectrum is assumed to be
I0=I (ν/νL)-1 erg cm-2 s-1 Hz-1 str-1
4. The Ionization structures are calculated by solving 3D radiative transfer at each redshift.
The ionization degrees are calculated assuming ionization equilibrium.

7. Ionization by UV Background Radiation
N3＝643 in (8Mpc) 3, Nangle = 642 -2 -3 -4 -5 -6 -1
log XHI
Ionization Structure (z=6, I21=0.1)
-26
-27
-26.5
-27.5
-28
log rg [cm-3]
Density Field at z=6
UV background radiation
10-3≤ I21 ≤1
Neutral fraction

8. Evolution of Ionization Structure
(in the case of I21=0.1)
z=12 -2 -3 -4 -5 -6 -1
log XHI
Central part of over dense regions are neutral because of the self-shielding effect.
z=6
The neutral fraction decreases with redshift.
z=4
All regions are highly ionized.

9. Generation of Absorption Line System
result of z=6 and I21=0.1
QSO
at zQSO -2 -3 -4 -5 -6 -1
log XHI
observer
1. We place a QSO at zQSO.
2. A line of sight is randomly selected.
3. We calculate the amount of neutral hydrogen at each point on a line of sight. Then absorption lines are generated.
line profile：Voigt profile(Tg=104K)

10. Lya Absorption Line Systems
zQSO=4 and I21=1
zQSO=5 and I21=0.1
normalized flux
zQSO=6 and I21=0.1
wavelength [Å]

11. Continuum Depression and Ionization Degree
Continuum Level
zQSO=6 and I21=0.1 1
normalized flux
0.6
0.2
8500
8100
8200
8300
8400
wavelength [Å]
continuum depression of this spectrum :
spatial mean of the neutral hydrogen fraction :
Large value of DA does not indicate a high fraction of neutral hydrogen.

12. Evolution of Continuum Depression
The observed trend of DA between z=4 and z=6
requires the evolution of UV background intensity.
I21=10-2
I21=0.1
continuum depression DA
I21=1
The observational results of DA require the UV intensity to be
I21 ≈ 1 at z ≈ 4
I21 ≈ 0.1 at 4<z<6
redshift z

13. Redshift Evolution of <XHI>
The difference of the results between RT and optically thin increases with redshift. -1
0.9 -2
0.99
I21=10-2
log<XHI>
<Xe>
I21=0.1 -3
0.999
This mean that the self -shielding effect is prominent at higher redshift.
: RT -4
0.9999
: optically thin -5 4 6 8 10 12 14 16 18
redshift z
The self-shielding effect can reduce the electron optical depth significantly!!

14. The Electron Optical Depth
The self-shielding is prominent at z>14 in the case of I21=0.1.
0.2
If the UV intensity keeps constant at I21=0.1,
the optical depth can’t achieve the WMAP result.
0.1
optical depth τe(z)
0.04
：I21=0.1
The UV intensity needs to be stronger at z>14.
：I21=10-2
0.02
：optically thin
10-2 4 8 12 16 20
i.e.
redshift z
I21 > 0.1 at z >14

15. Reionization Redshift
The self -shielding is prominent above
a critical number density of hydrogen
ncrit=1.410-2cm-3(M/108 Msun)-1/5I213/5
for 104 K gas
(Tajiri and Umemura 1998)
0.2
Reionization redshift can be predicted by <nH(z)> = ncrit .
optically thin
0.1
optical depth τe(z)
0.04
This condition gives,
1+zr≈22(R/8Mpc)-1/5I211/5
0.02
I21=0.1
I21=1
WMAP optical depth requires I21 ≥1 at z≈20.
10-2 5 10 15 20 25
redshift z
Reionization epoch is assessed to be zr≈21

16. Evolution of UVB Intensity
Redshift
z<4
z≈4
4<z<6
z>14
z≈20
Method
proximity effect DA te
I21
0.5±0.1
Giallongo et al. 1996
I21≈1
I21≈0.1
I21 > 0.1
I21 ≥ 1
I21
free 1
0.1
0.5 4 6 14 20
Redshift

17. Summary
The observed trend of DA at z>4 requires the evolution of the UV background intensity.
The observational results of DA require the UV intensity to be I21≈1 at z≈4 and I21≈0.1 at 4<z<6 .
The optical depth by free electrons requires that the UV background intensity needs to keep I21>0.1 at z>14 and I21≥1 at z≈20 .
If the UV background intensity keeps I21≈1 at z>14 , the cosmic reionization epoch is assessed to be zr≈21.