3D RT calculation on Escape ofionizing photons from forming

galaxies

★Hidenobu Yajima（University of Tsukuba）M. Umemura(Univ. of Tsukuba), M. Mori（Univ. of Tsukuba）

T. Nakamoto（Tokyo Institute of Technology）

Outline● Intro

・ Our scheme (Authentic Ray Tracing method)・ Cosmic reionization, Escape fraction・ Previous works

● Model&Method● Results

・ Ionization structure・ Escape fraction

● Discussion・ Can LAEs and LBGs ionize IGM at z=3~7 ?

● Summary

ART methodAuthentic Ray Tracing Method

!!! "# +$= Ids

dIabs

(point source version)

●Radiation meshes are arranged radiallyfrom each sources independently of fluidmeshes.

●The radiation field on fluid meshes areestimated by interpolating from nearradiation meshes.

●The order of calculation amount

!

Nsource " N# " N$ " Npath

!

Nsource " Nx " Ny " Nz " NpathLong characteristic method:

Basic equation:

ART-type 1(type2→Chizuru’s talk!)

Test calculation

Hydrogen only

Uniform density　→　nHI= 1 /cm3

Uniform temperature　→　T = 104 Kluminosity : 6.9×1045 /s photon/s

!

XHII

・Stromgren sphere

(ART)(Long)

!

N" =4

3#$BnH

2rs

3

rs% 3.0pc

Analytical solution

SED：Black body (105K)

R (pc)

Analytical!

XHII

Test calculation

Hydrogen + dust(dust-to-gas ratio = 0.01)

Uniform density　→　nHI= 1 /cm3

Uniform temperature　→　T = 104 Kluminosity : 5.5×1053 /s photon/s

!

XHII

・Effect of dust in HII region

!

rs " 2.6kpc

# sd =10

y =ri

rs= 0.37

ri = 0.95kpc

Analytical estimation

SED：Black body (105K)

R (kpc)Analytical

!

XHII

H only H+dust y~0.35

(Spitzer1977)

10kp

c

!

XHII

Applicationto

ionization structure in forming galaxies

Cosmic Reionizationneutral

HII

Ionization by QSOs

What are the ionizing sources at z>4?

The major candidates of ionizing sources are Lyman alphaemitters(LAEs) and Lyman break galaxies(LBGs).

Escape fraction　Escape fraction(fesc)　 ・・・　The ratio of photon numberescaped from a galaxy to photon number radiated by stars.

Escaped photons→ Ionization of the IGM

HII region

The escape fraction of ionizing photons can control the UVbackground intensity and hence has a close relation to the cosmicreionization process.

!

fesc

=Nint

" # Nabs,HI

" # Nabs,DUST

"

Nint

"

Previous works(Observation)

The typical value of escape fraction of high-zgalaxis has not been understood yet.

There are some observational estimations of escape fraction at z~3.

However detected young galaxies with ionizing photons are few.(Shapley et al. 2006, Iwata et al. 2008)

(Steidel et al. 2001)

(Inoue et al. 2005)

(Shapley et al. 2006)

(Giallongo et al. 2002)

%60~escf

%5esc!f

%38esc!f

%14~escf

(Iwata et al. 2008)

!

fesc"15%

(stack data)

(no detection → upper limit)

(no detection → upper limit)

(2 object)

(16 object)

Previous works(Simulation)&Objective

Previous works(simulation)

!

fesc" 3%

Gnedin et al. 2008

Their model galaxies are diskgalaxies (see also Lazoumovet al. 2006, 2007).

Our objectiveWe calculate the escape fraction to LAEs and LBGs withprecise radiation transfer calculation.

Disk Irregular

!

fesc ~3% ?

LAEs and LBGs may be irregulargalaxies(Mori&Umemura2006).

Model galaxyIMF:Salpeter IMF

（Mori&Umemura2006）

z=7.0 z=5.8 z=5.0 z=3.7Stars

gas

Metals

LAE phase LBG phase

Evolution by multiple SNe

MDM=1011Msun

Method

!

dI"

ds= #($abs,HI +$abs,DUST )I"

Radiative transfer equation

!

I" : intensity

#abs : absorption cofficient

$" : emissivity

HIIerecHIe

C

HI0 nnnnn !!"!!#+!#= $%

Equation of ionization degree inequilibrium state.

!

"# : photo ionization ratio , "C : collisional ionization ratio

nHI : number density of hydrogen, ne : number density of electron

$ rec : recombination cofficient(caseB)

The calculation box iscomposed of １２８３ cells.

●Calculation scheme

：ART method

●on-the-spot approximation(Osterbrock 1989)

(Nakamoto et al. 2001, Iliev et al. 2006)

!

mdust

= fdust

Z

Zsun

mH

●Dust distribution

!

fesc

=Nesc

"

Nintrinsic

"

The number of angular bins is 1282 per source.

z=5.0

z=7.0

z=3.7

z=5.8

0- 8 - 4

Ionization StructureIonization Structure

log10XHI

130kpc

Escape fraction

No dust extinction case

dust extinction case

Dust-sublimated case△

LAE phaseLBG phase

Are LAEs and LBGs ionizing sources ?

Can LAEs and LBGs ionize IGM?

① Necessary photon number to ionize the IGM

② Photon number radiated by LAEs and LBGs

VS!

N ion (z) = (1051.2s-1Mpc-3)C30

1+ z

6

"

# $

%

& '

3(bh50

2

0.08

"

# $

%

& '

2

(Madau et al. 1999)

!

N ion (z) = 1053.1s-1Mpc-3( ) " SFRD(z) " fesc (Madau et al. 1999)

Observation data Our results！

(C30:clumpiness factor)

SFRD : star formation rate density fesc : escape fraction

Photon number radiated by LAEs and LBGs

z

log 1

0Nio

n ( s

-1 M

pc-3

)

Reionization limit(C=30)

(C=1)

QSOs

Our results(Median value) : fesc= 35%(LAEs),18%(LBGs)

LBGs

LAEs

SUMMARY

● LAEs and LBGs have a large escape fraction (17% ~ 47%). (theoretical previous works → ~3%)

● Escape fraction can largely vary by considering dustextinction.

● LBGs can ionize the IGM at z=3~5. However only LAEs andLBGs can not ionize the IGM at z≧6.

ENDEND