“The Stromgren sphere” around the highest redshift QSOs

Qingjuan Yu

UC Berkeley

April 7, 2005

Highest redshift QSOs (z>6.1)

• Gunn-Peterson absorption troughs– Hydrogen in the early universe

significantly neutral (>1% in mass average)

• Flux transmission between the absorption trough and the Ly line center:– Hydrogen in the vicinity of the

QSO highly ionized

– Highly ionized region idealized as spherical (Stromgren sphere, stellar astronomy)

(Fan et al. 2004)

Apparent shape of the Stromgren sphere• May not be a sphere

– Ionization front relativistically expanding

– Time-delay effect

– rotationally symmetric along OC– r decreases with increasing theta

(Yu, astro-ph/0411097, ApJ in press)

ti : nuclear activity triggered,

τQ =t(zQ)−ti , QSO age at t(zQ),

τ =tO −ti ,

OA + AD =c(τQ −τ),r(τ )(1−cosθ) =c(τQ −τ), 0 ≤θ ≤π

D

Light reaches theobserver at thesame moment.

Comparison on geometry• Apparent shape of the

Stromgren sphere• Apparent shape of a relativistically

expanding radio shell with vel. v:

r(τ )(1−cosθ) =c(τQ −τ) r(1−vc

cosθ) =vt spheroid

4π3

d(xHI nH r3)dτ

= &Nphs(τ )−4π3BC nH

2 r3

evolution QSO recombination

emission

(Rees, 1967, MNRAS; Studies in radio source structure: I. A relativistically expanding model for variable quasi-stellar radio sources)C ≡ nHII

2 nH2

Possible observational tests

Proper distance: |OC| ~ 5 Mpc ~ 7 arcmin

• Spectra of background sources (e.g., Ly emitters)

• Tomography of 21 cm HI emission

Apparent shapes may be used to constrain:

• QSO intrinsic properties: age, luminosity evolution

• QSO environment, re-ionization history

– clumping factor C

– neutral hydrogen fraction

• Cosmological parameter: (Alcock-Paczynski test)

r(τ )(1−cosθ) =c(τQ −τ)

4π3

d(xHI nH r3)dτ

= &Nphs(τ )−4π3BC nH

2 r3

evolution QSO recombination

emission C ≡ nHII2 nH

2

Apparent shapes may be used to constrain:

• QSO age

r(τ )(1−cosθ) =c(τQ −τ)

4π3

d(xHI nH r3)dτ

= &Nphs(τ )−4π3BC nH

2 r3

evolution QSO recombination

emission

r(τ )(1−cosθ) =c(τQ −τ)

τQ > r(θ =π / 2) c

τQ > 2r(θ =π) c

C ≡ nHI2 nH

2

Evolution of the ionization front

for

for

4π3

d(xHI nH r3)dτ

= &Nphs(τ )−4π3BC nH

2 r3

evolution QSO recombination

emission C ≡ nHII2 nH

2

(Yu & Lu 2005)

r

(Hubble expansion ignored)

Constraining QSO intrinsic properties and environment

• QSO age increases from inward to outward.

• r(τ=10τrec)/(cτrec)= 4, 8 (left, right).

Shape evolution

• Study of the environment and re-ionization around the highest redshift QSOs: x(HI)~0.1, C~35;

• recombination timescale << QSO lifetime (>4x107 yr).

The observational Stromgren radii along the line of sight are consistent the expected sizes rS.

(Yu & Lu 2005)

Constraining QSO intrinsic properties and environment

• re-ionization:

C=35, x(HI)=0.1,τQ >> τrec

C=1,x(HI)=1

x(HI)=0.3

x(HI)=0.1

Constraining

(Alcock-Paczynski test)• |OC|, redshift difference

– affected little by at high redshift.

• R=dA, Angular diameter distance:

– depends on

H (z) ≡&aa

=H0 M (1+ z)3 +k(1+ z)2 +

dA =c

(1+ z)d ′z

H( ′z ),

0

z

∫ k =0

Anisotropic emission1) Obscuration by a torus (analogous

to the [OIII] ionization cone observed in nearby Seyfert II galaxies)

2) Disk emission e.g., 1+2|| (limb-darkening effect)

different cross sections

Comparison• Time-delay effects

– Decreasing r with increasing theta

• Anisotropic effects (QSO emission and structure perturbations)– May depend on the detailed

geometric configuration between the disk and observer;

– Dominated if the QSO age is significantly long compared to the hydrogen recombination process and the QSO luminosity evolution is significantly slow;

– Could be statistically averaged out in a large sample.

Summary • The apparent shape of the ionization fronts around the highest

redshift QSOs may systematically deviate from a spherical shape because of the time-delay effect.

• The apparent shape of the Stromgren sphere may be mapped by transmitted spectra of background sources behind or inside the ionized regions or by surveys of the hyperfine transition (21 cm) line emission of neutral hydrogen.

• Measurements of the apparent shapes may be used to constrain the QSO intrinsic properties and environment (e.g., the re-ionization history of the universe).

• The apparent shape could also be used to constrain the cosmological parameter by the Alcock-Pacynski test if the QSO intrinsic properties and environment are well constrained.