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Lecture 27 – The Intergalactic Medium

1. Cosmological Scenario2. The Ly Forest 3. Ionization of the Forest4. The Gunn-Peterson Effect5. Comment on HeII Reionization

ReferencesJ Miralda-Escude´, Science 300 1904 2003M Rauch, ARAA 36 267 1998A Loeb & R Barkana, ARAA 39 19 2001X Fan et al. ARAA 44 415 2006X Fan AJ 132 117 2006

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1. Cosmological Scenario

z+1

Big BangNow

10 100 10001

log t 10 9 7 6

J. Miralda-Escude´, Science, 300, 1904 2003

The universe recombined at z ~ 1100 (300,000 yr) andwas re-ionized much later (10-20 Gyr) by the radiation from the first stars and galaxies.

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Cosmological Formulae Redux

i = i

cr

= + DM + B

cr =3H0

2

8 G= h2 1.88 10 29 gr cm 3 H0 = h 100 km s 1Mpc 1

h = 0.70 = 0.73 DM = 0.22 B = 0.04

Concordance Cosmological Parameters

= 0(1+ z)

t =tn

(1+ z)32

tn 13.73Gyr

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2. Lyman- Forest

PKS 0454+0339, z = 1.34PSS 0209+0517

1. The huge number of Ly absorbers dominates the massof the IGM: If Ñ is the number distribution function of Lyclouds and N is the column density of atomic hydrogen,then Ñ(N,z) has the following properties:• Ñ(z) increases rapidly with z, roughly as (1+z)2.5

• Ñ(N) decreases rapidly with N, roughly as N-1.5

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More on the Ly Forest

2. Since Ly Forest clouds are defined as optically thinto Lyman continuum photons (log N < 17.2), they areionized, and most of their mass is not detected by Lyabsorption.3. Upper limits to the temperature come from the modestline widths, bD ~ 20 - 25 km s-1 or T ~ 30,000 K.*4. The IGM ionizing radiation field and ionization ratecan be estimated from a “proximity effect”, i.e., fromthe variation in Ñ near quasars: J ~ 10-21 erg cm-2 s-1 sr-1 Hz-1 G ~ 10-12 s-1

5. Photoionization-simulation models give x(H) ~ 10-5.6. Flat structures for small columns, ~ 50 kpc thick and~ Mpc wide are suggested by a few lensed quasars andquasar pairs.

* bD = 22.5 km/s corresponds to FWHM = 53 km/s

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Comparison with the Diffuse ISMThe Ly- forest arises from quasi-distinct features, althougha smooth background distribution is not ruled out.

Compare the IGM at z ~ 3 with the closest ISM phases*: WIM* n ~ 0.375 cm-3 T ~ 8000 K

HIM n ~ 0.003 cm-3 T ~ 106 K

IGM (z ~ 3) n ~ 10-5 cm-3 T ~ 3x104 K

The thermal pressure of the IGM is tiny.

• The ISM gas of the Milky Way is bound by gravity andbalanced in hydrostatic equilibrium with several sourcesof pressures.• The IGM is governed largely by the gravity of CDM halosplus self-gravity and shocks in a highly clustered medium.

*The numbers for the WIM refer to its denser parts (Lec08)

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3. Photoionization Modeling

We provide the elementary basis for these models by considering the physical conditions at a typical location in a uniform and flat cosmological model. Of course, current understanding of the Ly forest is based on non-uniform structures that arose from primordial fluctuations and evolved dynamically according to the

CDM cosmology (with the parameters given earlier).

a. Post-recombination Density

HH

H

HHeH

)1()1(

mY

mYn

Y

cr

B

B

BB

==

+=+=

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3373

H

H )1(cm106.1)1()1( zzm

YnB

cr ++=

e.g., at recombination (z ~1000): nH ~ 200 cm-3

at reionization (z ~ 7): nH ~ 10-4 cm-3

b. Local Photoionization Balance

The basic physics was covered in Lec03. The controllingparameter is the ionization parameter, in this caseG/nH . Although surely variable, typical parameters forthe IGM might be (see Sec. 3d below): G ~ 10-12 s-1 T ~ 30,000 K x(H) ~ 10-5

With ~ 2 x 10-13 cm3 s-1,

G

n= 2.5 107 (1+ z) 3

>>1 for z 10

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)He()He()H()H()H(

)H()H()H()H(

eH

e

+++++

++

++=+=

=

nNnnnnn

nGnn

This large value means that the photoionization time is

much shorter than the recombination time,

e

recph

11

nG=<<=

and implies that the IGM is fully ionized: ne = nH.

c. Atomic Hydrogen Abundance

The chemical balance equations are:

Again using ne = nH, the abundance of H is:

1)1(1041)H( 38

1

H

1

H

<<+=+= zn

G

n

Gx

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d. The Ionization Flux of a Quasar

The IGM radiation field is clearly basic for understandingthe Ly- forest. It depends on cosmic time through the history of star, galaxy, and quasar formation. We give just one estimate, that due to a luminous quasar, analogous tothose made for O & B stars in earlier lectures. For furtherdiscussion, see Loeb & Barkana, ARAA 39 19 2001.

311111 ))(()()(

4

1

==h

JdG

We use an empirical SED for quasars (Madau astro-ph 0005106 2001) with 1 the frequency at theLyman edge

L L1(1 )2 L1 =1030 erg s-1 Hz-1 4 J

L

4 r2

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The result for the ionization rate at Mpc distances is

2

1

1-12 )Mpc

(s102rL

LG =

This is the same order of magnitude found in simulations (where G is assumed to be same everywhere).

The problem is complicated because one has to include the contributions of all relevant quasars, especially those close to the line of sight and also do the radiative transfer.

As for H II regions, one can evaluate the heating rate, or equivalently the mean photo-electron energy, as,

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4. Gunn Peterson Effect

Almost immediately after the discovery of quasars, Gunnand Peterson (ApJ 142 1633 1965) considered the effectof a distribution of intervening atomic H on quasar spectraarising from the “resonant scattering” of Ly photons ofthe quasar continuum (shortward of Ly ). Resonantscattering is closely related to the photo-absorptionprocess responsible for the absorption lines; it refers tothe photon emitted following absorption:

h + H(n =1) H(n = 2) H(n =1) + h

In the following diagram of the GP effect,(Q) = wavelength of the photon absorbed at redshift z(O) = the observed wavelength(Ly ) = rest wavelength of the Lyman line

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O H Q redshift

z = 0 z z = zem

observer absorber/scatterer quasar

The observed and emitted wavelengths satisfy therelations (1+zem) (Q) = (O) and (1+z) (Ly ) = (O)

or,(Q) =

1+ z

1+ zem(Ly ) < (Ly )

i.e., the absorbed continuum photon has a wavelengthshorter than the Lyman line

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GP Optical Depth

d = f12e2

mec[(1+ z) (O) v12] n1(z)dl

Gunn and Peterson (GP) calculate the observed absorptionoptical depth at frequency (O) in terms of the optical depthin the emitting frame where = (1+z) (O) :

GP = f12 12

e2

mecn(H)

c

H0

(1+ z)32

where is the lineshape function and 12= (Ly ). Since the range in z is very much larger than the linewidth, the integration is easily carried out on using

dl

dz= m

c

H0

(1+ z) 5 / 2

Setting n1=n(H), the GP optical depth is

Note the dependence on f .

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Estimate of the GP Optical Depth

Combining this result with the expression for nH on slide8, with n(H) = x(H) nH, and using the cosmological parameters on slide 3, yields:

GP 2.6 104 x(H) (1+ z)32

• Even for a small neutral H fraction ~ 10-4, the opticaldepth for z ~ 6 is large. Of course photoionization models show that x(H) is sensitive to the ionization rate G (as 1/G); GP is large from the recombination epoch until re-ionization.• Although there had been evidence for a finite GP in the spectra of high-z quasars, truly convincing data only became available from the z ~ 6 quasars found by the Sloan Digital Sky Survey (SDSS).

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Onset of GP Troughs for High-z Quasars

z = 5.80

z = 5.82

z = 5.99

z = 6.28

Q 1030+0524 hasno detectable flux short of Ly & Ly .

Pre-SDSS Q 1422+23 (zem=3.62)c.f, Rauch ARAA 36 267 1998

High-z SDSS Quasars, Becker etal., ApJ 122 2850 2001

High red-shift quasar showing richLy forest plus absorption linesystems for Ly , Si IV, and CIV,but no strong evidence for a GPtrough between the lines.

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Close Up of SDSS 1030+0524 (zem - 6.28)Becker et al. (2001)

20)Ly(5)Ly( GPGP >>

HI Reionization occurs at z ~ 6 or before

Keck/ESI Ly spectrum8200-8810 Å

Keck/ESI Ly spectrum6920-7440 Å

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Ly & Ly Troughs and Reionization

Since GP ~ f , the Ly and Ly troughs are even moresensitive than Ly to the start of reionization.

.41621215.67Ly

.079101025.72Ly

0.02899972.54Ly

fluwavelengthtransition

• Consideration of the first ionizing stars (to be discussed in Lec28) leads to the idea that their HII regions grow and multiply, and merge, producing a clumpy universe. • The development of the GP near z ~ 6 involves both an increase in the density of L forest lines but also the diminution of the ionizing flux.

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Growth of the GP Trough Towards z = 6.42

6.426.486.226.206.136.076.056.016.005.995.955.935.855.855.835.825.805.795.74

Detailed examinationof GP troughs indicates

that GP varies with direction, suggestiveof variations in the re-Ionizing radiation.

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Troughs for the Two Highest-z Quasars

z = 6.28

z = 6.42

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Transmitted Flux in the GP Trough

Tiny fluxes for z 6Songaila AJ 127 2598 2004

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Increase of GP Optical Depth With z

Fan et al.AJ 132 117 2006

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HI Fraction for 19 High-z Quasars

Fan et al.AJ 132 117 2006

Lower limits to the HI fraction for z = 5.0 - 6.2 Based on models of the ionizing radiation (dashed lines are numerical simulations)

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5. Reionization of He II

Basic facts about He II: IP = 54.418 eV (227.8 Å)

E(Ly ) = 40.81 eV (303.8 Å)which imply:1. Much harder UV radiation is needed to ionize He IIthan H I (maybe quasars rather than stars).2. Detecting He II in high-z quasars requires UVobservations, e.g., for HeII Ly is shifted to 1215Åfor z = 3 .3. HST has UV capability down to 1150 Å and FUSEprovides high resolution from 905-1195 Å.4. Five examples known (as of 2005)He II Ly observations provides unique informationabout the spectrum of ionizing radiation in the IGM.

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He II in the IGM With FUSE

Q 2347-4342 z = 2.885

Green: HST STIS spectrumRed: extrapolated STIS continuum

Kriss et al. Science, 293 1112 2001 (FUSE + STIS)See Zheng et al. ApJ 2004 (FUSE + VLT) for a re-

analysis of He II Ly clouds in the spectrum of this quasar.

He II reionization

occurred near

z = 3, i.e. later than

H reionization

detector gap