Determining the Redshift of Reionization from the Spectra Of

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Determining the Redshift of Reionization From the Sp ectra of High{Redshift

Sources

1;2 1

Zoltan Haiman and Abraham Lo eb

ABSTRACT

The redshift at which the universe was reionized is currently unknown. We

examine the optimal strategy for extracting this redshift, z , from the sp ectra of

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early sources. For a source lo cated at a redshift z beyond but close to reionization,

(1 + z ) < (1 + z ) < (1 + z ), the Gunn{Peterson trough splits into disjoint

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Lyman , , and p ossibly higher Lyman series troughs, with some transmitted ux

in b etween these troughs. We show that although the transmitted ux is suppressed

considerably by the dense Ly forest after reionization, it is still detectable for

suciently bright sources and can b e used to infer the reionization redshift. The Next

Generation Space Telescop e will reach the sp ectroscopic sensitivity required for the

detection of such sources.

Subject headings: cosmology: theory { quasars: absorption lines { galaxies: formation

{intergalactic medium { radiative transfer

Submitted to The Astrophysical Journal, July 1998

1. Intro duction

The standard Big Bang mo del predicts that the primeval plasma recombined and b ecame

predominantly neutral as the universe co oled b elow a temp erature of several thousand degrees at

a redshift z 10 (Peebles 1968). Indeed, the recent detection of Cosmic Microwave Background

(CMB) anisotropies rules out a fully ionized intergalactic medium (IGM) beyond z 300 (Scott,

Silk & White 1995). However, the lack of a Gunn{Peterson trough (GP, Gunn & Peterson 1965)

in the sp ectra of high{redshift quasars (Schneider, Schmidt & Gunn 1991) and galaxies (Franx et

al. 1997) implies that the IGM is highly ionized at low redshifts, z 5. Taken together, these

< <

two observations indicate that the IGM was reionized in the redshift interval 5 z 300.

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The epoch of reionization marks the end of the \dark ages" during which the cosmic radiation

background was dominated by the ever-fading CMB at all wavelengths. During this ep o ch, ionized

Astronomy Department, Harvard University, 60 Garden Street, Cambridge, MA 02138, USA

NASA/Fermilab Astrophysics Center, Fermi National Accelerator Lab oratory,P.O. Box 500, Batavia, IL 60510, USA

{2 {

hydrogen (HI I) started to o ccupy again most of the volume of the universe. Most likely, the phase

transition from HI to HI I was triggered by the emission from the rst stars and quasars in the

universe (see Lo eb 1998, and references therein).

The characteristic distance b etween the sources that ionized the universe was much smaller

than the Hubble scale, and the overlap of the HI I regions surrounding these sources was completed

on a timescale much shorter than the Hubble time. The resulting reionization redshift, z ,

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is therefore sharply de ned and serves as an imp ortant milestone in the thermal history of the

universe. Measurement of this parameter would also constrain the small-scale p ower of primordial

density uctuations that pro duced the rst ob jects. Theoretical mo dels and three{dimensional

< <

simulations predict that reionization o ccurs at 7 z 20, just b eyond the horizon of current

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observations (Haiman & Lo eb 1997, 1998; Gnedin & Ostriker 1997). Forthcoming instruments,

suchasthe Space Infrared Telescope Facility (SIRTF), and the Next Generation Space Telescope

(NGST) are exp ected to reach the sensitivity required for the detection of sources beyond the

reionization redshift. It is therefore timely to ask: how could one infer z from the observed

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sp ectra of these sources?

The sp ectrum of a source at a redshift z > z should show a GP trough due to

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absorption by the neutral IGM at wavelengths shorter than the lo cal Ly resonance at the

source, < (1 + z ). By itself, the detection of sucha trough would not uniquely establish

obs

the fact that the source is lo cated beyond z , since the lack of any observed ux could be

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equally caused by (i) ionized regions with some residual neutral fraction, (ii) individual damp ed

Ly absorb ers, or (iii) line blanketing from lower column densityLy forest absorb ers (see, e.g.

the sp ectrum of a z =5:34 galaxy taken by Dey et al. 1998). An alternative approach prop osed

by Miralda-Escude (1998) is to study the detailed shap e of the damping wing of the GP trough.

Although a measurement of this shap e could ideally determine the optical depth of the absorbing

HI slab between the source redshift and reionization, it is also likely to be compromised by

contaminating e ects such as: (i) redshift distortions due to p eculiar velo cities; (ii) uncertainties

in the absorption pro le due to the unknown intrinsic shap e of the Ly emission line from the

source; (iii) ionization of the IGM in the vicinity of the source due to the source emission; and (iv)

the existence of a damp ed Ly absorb er outside or inside the source.

In this pap er we consider a di erent approach for measuring z . Our metho d relies on the

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existence of some transmitted ux b etween the Ly and Ly absorption troughs in the sp ectra of

sources which are lo cated just b eyond the reionization redshift. For such sources, the GP troughs

due to di erent Lyman series resonances do not necessarily overlap, and the transmitted ux

between these troughs is only a ected by the p ost-reionization Ly forest. In x2, we simulate the

absorption by the dense Ly forest (or \Ly jungle") and demonstrate that the transmitted ux

features are detectable. In x3, we estimate the numb er of sources which are suciently brightto

allow detection of these features with NGST. Finally, x4 summarizes the main conclusions of this

work.

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2. Sp ectra of High Redshift Sources

The phase transition from HI to HI I o ccurs almost simultaneously throughout the IGM

volume, when the expanding HI I regions around the separate ionizing sources overlap (Arons &

Wingert 1972). This pro cess is nearly instantaneous (Haiman & Lo eb 1998; HL98) and de nes

a corresp onding redshift, z . However, at z each individual HI I region could still have

overlap overlap

a non{negligible Ly optical depth due to its residual HI fraction. The GP trough from the

uniform IGM disapp ears only at a somewhat later redshift, z , when the average Ly optical

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depth of the smo oth IGM drops b elow unity. (We distinguish b etween this GP absorption and the

absorption pro duced due to IGM clumpiness by the p ost-reionization Ly forest). In this pap er,

we assume that the delaybetween z and z is small and set z = z , based on the

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overlap overlap

following reasoning.

The Ly optical depth across a stationary HI I sphere is as large as 10 (Osterbro ck 1974),

but cosmological HI I regions are much thinner b ecause of the cosmological redshifting of the

Ly photons away from resonance. If z 7 and the HI I regions are driven by quasars or

overlap

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star{clusters in Cold Dark Matter halos of virial temp erature of 10 K(M 1:5 10 M ),

halo

then the typical prop er radius of an HI I region is R 0:05 Mp c (HL98). When two such

HI I

HI I regions rst overlap, the neutral fraction x = n =n at their intersection is x 2 10 ,

HI H

assuming photoionization equilibrium . Taking this value as representative for the IGM, the

resulting Ly optical depth of the smo oth IGM is 3. The GP trough disapp ears as so on as

the neutral fraction is reduced by another factor of 3, i.e. when the lo cal UV ux is increased

by the same factor. Such an increase o ccurs shortly after the overlap epoch, since it requires the

cumulative contribution from sources in a region as small as 3 0:05 Mp c =0:15 Mp c, i.e.

0:1% the lo cal Hubble length. Therefore, the resulting breakthrough redshift, z is only

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slightly lower than z . The short redshift delay distorts the shap e of the damping wings at

overlap

wavelengths extending by a few tenths of a p ercent ( tens of A) b elow the blue edge of the

GP trough near the observed wavelength of (1 + z ). Our simplifying assumption of sudden

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ionization is therefore justi ed to this level of sp ectral resolution. Note that the Ly optical depth

is 3.5 times b elow that of Ly , so that the Ly and higher GP troughs are even more sharply

de ned.

We now consider the sp ectrum of a source lo cated at a redshift z >z . Ly absorption

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by neutral hydrogen between z and z suppresses the ux in the observed wavelength

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interval, (1 + z ) < < (1 + z ) ; Ly absorption causes a second trough at

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obs

(1 + z ) < < (1 + z ) , and higher Lyman series lines pro duce analogous troughs at

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obs

shorter wavelengths. In the absence of other e ects, the resulting sp ectrum would consist of a

generic sequence of troughs separated by blo cks of transmitted ux, as depicted in Figure 1. In

Note that the neutral fraction would b e 100 times higher near the edge of a steady-state Stromgren sphere.

However, at redshifts z 10 the recombination time exceeds the Hubble time, and our short-lived ( 10 years)

sources do not reach a steady state.

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this illustration we assumed that reionization o ccured suddenly as discussed ab ove, at z =7,

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but included the damping wings of the Lyman lines at b oth edges of the absorption troughs

(see the App endix in Miralda-Escude 1998). Note that a Ly photon emitted by the source can

escap e from its host's HI I region and travel across the uniform IGM only if the HI I region has

an unusually large radius of at least 1Mpc. The emitted Ly photons are much more likely to

b e absorb ed by the IGM. Below we consider observations on a telescop e with a suciently high

angular resolution, so that the di use Ly re-emission by the IGM can b e ignored.

The top panel of Figure 1 shows that the closer z gets to z , the narrower the GP troughs

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b ecome and the more similar they lo ok to individual Ly absorb ers. Equation (1) b elow predicts a

20 2

few damp ed Ly systems with neutral hydrogen column densities N 10 cm in the sp ectra

20 2 1

of a source at redshifts z 5. A single absorb er with N =10 cm and b =35kms would

s H

have a rest{frame equivalent width of 7:7A. In order to avoid confusion with such an absorb er,

the width of the GP troughs must be 8(1 + z )A. Note also that p eculiar velo cities could

shift the lo cation of the narrow troughs by 10A. The b ottom panel of Figure 1 also indicates

that as the source redshift approaches the limiting value (1 + z )=(1 + z )= = =32=27,

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only a single narrow blo ck of transmitted ux remains between the Ly and Ly troughs. At

still higher redshifts this window disapp ears, leaving a continuous GP trough at wavelengths

< (1 + z ) which carries no information ab out the reionization redshift.

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obs

Reionization also leaves a distinct mark in the soft X-ray regime. The source sp ectrum would

be strongly suppressed at the Lyman edge, = 912(1 + z )A, due to the large continuum

obs

optical depth in from H and He ionizations ( 10 ). The optical depth drops at shorter

cont

wavelengths due to the sharp decline in the ionization cross{sections, / . The ux recovers

its intrinsic amplitude at E 0:1 keV, where the optical depth falls b elow unity. The observed

photon energy where this o ccurs provides a measure of the reionization redshift, as long as the

value of h is indep endently measured. Would AXAF b e able to detect this sp ectral signature?

For a source whose observed ux at E =0:1keV is 100 nJy, the AXAF count rate in the 0.08-0.15

3 4 5

keV band would b e 10 p er second , suciently large to collect 100 photons in 10 seconds. The

abilityof AXAF to determine z relies on the existence of suciently bright sources b eyond the

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reionization redshift. In the case where these sources are early quasars, their required infrared ux

is 10Jy. As illustrated by Figure 4 b elow, such sources are exp ected to b e very rare at z>5.

The sp ectra shown in Figure 1 are highly idealized in that they take account only of

absorption by the homogeneous HI gas b etween z and z . In reality, the blo cks of transmitted

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ux shown in Figure 1 will be suppressed due to absorption by the residual HI islands in the

clump ed IGM which pro duce the Ly forest after reionization. In order to simulate the e ect

of the dense Ly forest (or \Ly jungle"), we created mo ck catalogs of absorption lines with

statistical prop erties constrained by observational data at z < 5. Press & Rybicki (1993) have

We consider detection by the High Resolution Camera and the Low Energy Transmission Grating, based on the

prop osal planning to olkit at http://asc.harvard.edu/cgi-bin/prop to olkit.cgi.

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analyzed in detail the statistics of Ly absorb ers observed between redshifts 1:5

derived a convenient form for the mean number n(N ;b;z)dN dbdz of clouds with HI column

H H

densitybetween N and N + dN , Doppler velo city parameter b etween b and b + db, and redshift

H H H

between z and z + dz ,

14 2 1

n(N ;b;z)=2:63 10 (1 + z ) p(b) cm km s; (1)

14 2

10 cm

with =2:46, =1:43, and

" #

(b b )

p(b) / exp (b>0) (2)

1 1

with p(b)db = 1, and the b est{ t values b = 32 km s , b = 23 km s . We used

a Monte Carlo approach to generate a catalog of absorb ers along the line of sight to the

source, with redshifts, column densities, and b{parameters in the ranges 0 z z ;

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12 2 20 2

ndz dN db. The probability cm N 10 cm ; and b 0, for 1 i N = 2 10

H H;i i

abs

distribution of these parameters was chosen according to the ab ove equations. Although these

equation are based on data from redshifts 1:5 < z < 4:3, in the absence of additional data at

higher z , we extend their validity to all redshifts b elow z . A more rigorous extrap olation

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of this equation to high redshift would b e to use three-dimensional numerical simulations of the

high{redshift IGM (e.g., Hernquist et al. 1996). However, even such a calculation would b e highly

uncertain due to the unknown evolution of the ux and sp ectrum of the UV background at z>5.

In computing the observed ux F from the source at a wavelength we include absorption

obs

by the rst nine Lyman series lines from each of the N (z ) absorb ers along the line of sight,

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abs

Y Y

U (x ;a )

i;n i;n i;n

F ( )=F e : (3)

obs

n2[1;9] i2[1;N ]

abs

Here F is the continuum ux that would have b een observed in the absence of Ly absorb ers;

2 th th

= (e =m c)N f =b is the integrated optical depth for the n Lyman line of the i

i;n e H;i n n i

absorb er; and and f are the rest wavelength and oscillator strength of this line. The pro le of

n n

each line is given by the normalized Voigt function U (x; a), where x (c=b )[ =(1 + z ) ]= ;

i;n i i n n

obs

a =4b ; and is the natural decay rate of the n Lyman line (see Press & Rybicki

i;n n n i n

1993 for more details).

Figure 2 shows ve examples of source sp ectra pro cessed through the mo ckLy jungle. As in

Figure 1, we assume sudden reionization at z =7 but include the damping wings of the GP

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troughs. The several thousand absorb ers along a typical line of sight yield a considerable mean

optical depth, 4:5. Although the underlying continuum ux is not visible at anywavelength,

the gure reveals a series of narrow features of transmitted ux { remnants of the pro cessing by

the underlying Ly jungle { to whichwe refer hereafter as \transmission features". The sp ectra

contain many such features with central ux values that rise infrequently up to a signi cant

{6 {

fraction (up to 50%) of the original continuum ux. These features could be detected by an

instrument with a suciently high sensitivity and sp ectral resolution.

As an example, we show in Figure 3 a blow{up of the sp ectrum around the Ly and

GP troughs of a source with a redshift z = 7:08 . The sp ectrum indeed contains numerous

transmission features; these features are typically a few A wide, have a central intensityofa few

p ercent of the underlying continuum, and are separated by 10A. With a sensitivity reaching 1%

of the continuum, the edges of the Ly GP trough b etween 8201 and 8283 A could b e identi ed to

a 10 A accuracy. A similar precision applies to the Ly GP trough, although the damping wing

there suppresses the ux within 10 A of the edges by a factor of 3. The longest wavelength

at which ux is detected towards the blue edge of the Ly GP trough, at 8201 A, provides the

b est direct measurement of the reionization redshift. In practice, this metho d only yields a lower

limit to z , since the rst observed transmission feature could b e o set from the true blue edge

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of the GP trough. The uncertainty in the measurement of (1 + z ) would be equal to the

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typical separation b etween the transmission features. Figure 3 shows that at a sensitivity reaching

1% of the continuum, the separation would b e small ( 10A), leading to a fractional error of only

10=8200 0:1% in the measurement of z . Note that this accuracy is similar to the level

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allowed by p eculiar velo cities of a few hundred km/s, which could move either observed edge of

the GP trough by 10A.

It is apparent from Figure 3 that the ab ove pro cedure applies only as long as the typical

separation between the transmission features is much smaller than the width of the GP trough,

i.e. for (1 + z ) 1:01 (1 + z ). The b ottom three panels in Figure 2 also show that the

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transmission features gradually disapp ear as the GP troughs of the Ly and Ly resonances

approachoverlap at (1 + z )=(1 + z )= = =32=27. Hence, suitable sources must lie in the

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< <

somewhat more restricted redshift range, 1:01 (1 + z )=(1 + z ) 1:17. Finally,we note that

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an extrap olation of equation (1) to even higher redshifts predicts that the mean optical depth of

the Ly clouds increases strongly with redshift. For example, using our mo ckLy cloud catalog,

we nd that at wavelengths just b elow (1 + z ), the mean optical depth increases from

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=4:5 for z =7 to =13:1 for z = 10. Similar numb ers are obtained by extrap olating

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the expressions for the mean optical depth from Madau (1995). This implies that detection of

the remnant transmission features is considerably more dicult at higher redshifts, since the

numb er density of lines ab ove a given sensitivity threshold drops as exp( ). In order to detect

transmission features separated by roughly 10A, as in Figure 3, the sp ectroscopic sensitivity

1 2 3 4 6

must reach the approximate fractions of 10 ; 10 ; 10 ; 10 , and 10 of the continuum ux

for z =6;7;8;9, and 10, resp ectively.

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3. Abundance of Suitable High Redshift Sources

The detection of a single bright source from the epoch, 1:01(1 + z ) < (1 + z ) <

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1:17(1 + z ), could in principle provide an unambiguous measurement of z . How likely

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{7 {

is it to nd such sources? The b est candidates are high{redshift quasars, since in analogy with

their z < 5 counterparts, they are exp ected to have a hard sp ectrum extending into the far UV.

Alternative sources are Gamma-Ray Burst (GRB) afterglows, sup ernovae, or primeval galaxies.

The advantage of GRB afterglows is that they are bright and have featureless p ower{law sp ectra;

however, their abundance at high redshifts might b e small. Sup ernovae and galaxies may b e more

abundant than either quasars or GRBs, but are likely to b e faint and p ossess soft sp ectra in the

relevant UV range.

As the abundance of quasars at z>5 is currently unknown, wemust resort to an extrap olation

of the observed luminosity function (LF) of quasars at z 5. Such an extrap olation has b een

carried out by HL98 using a simple mo del based on the Press{Schechter (1974) formalism. In the

mo del of HL98, the evolution of the quasar LF at faint luminosities and high redshifts is derived

from three assumptions: (i) the formation of dark{matter halos follows the Press{Schechter theory,

(ii) each dark halo forms a central black hole with the same eciency, and (iii) the light{curve

of all quasars, in Eddington units, is a universal function of time. As shown in HL98, these

assumptions provide an excellent t to the observed quasar LF at redshifts 2:6

exp onentially decaying lightcurve with a time{constant of 10 years. The mo del provides a

simple and natural extrap olation of the quasar LF to high redshifts and faint luminosities. At the

faint end of the LF, the numb er counts of quasars are exp ected to b e reduced b ecause of feedback

due to photoionization heating that prevents gas from reaching the central regions of shallow

p otential wells. To b e consistent with the lack of faint p oint{sources in the Hubble Deep Field, we

imp osed a lower limit of 75 km s for the circular velo cities of halos harb oring central black

holes (Haiman, Madau & Lo eb 1998).

Figure 4 shows the total number N (z; F ) of quasars brighter than the minimum ux F ,

0 0

lo cated within the redshift interval 1:01(1 + z ) < (1 + z ) < 1:17(1 + z ), in a 16 16 eld (16 times

the eld of view of NGST). How many suitable sources would NGST detect? For z =7, the

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average transmitted ux shortward of the Lyman and GP troughs is a fraction exp( ) 1%

3 0 0

of the continuum. Around z 7, we exp ect roughly a single 10 nJy source p er 16 16 eld,

based on Figure 4. Such a source has an average ux of 10 nJy blueward of (1 + z due to

absorption by the Ly jungle. According to the metho d depicted on Figure 3, a determination

of z to 1% accuracy would require sp ectroscopy with a resolution of R =100. Requiring a

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signal-to-noise of S/N=3, the necessary integration time for a 10 nJy source with NGST would b e

roughly one hour . This is a conservative estimate for the detection of ux, since it assumes that

the ux is uniformly distributed across the sp ectrum, while in reality it would be concentrated

in transmission features that cover narrowwavelength bins and yield a higher S/N ratio in these

bins. We therefore conclude that NGST will b e able to measure the reionization redshift to 1%

p ercent accuracy up to z =7. The accuracy would degrade considerably with redshift for

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This result was obtained using the NGST Exp osure Time Calculator, available at http://augusta.stsci.edu. We assumed a mirror diameter of 8m.

{8 {

z 7.

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0 0 3

The total number of sources per 16 16 eld, irresp ectiveof their redshifts, is 3 10 ,

600, and 90 for a minimum intrinsic ux of F =10, 100, and 1000 nJy, resp ectively. In the

most optimistic case, for which the reionization redshift is close to the p eak of the relevant curve

in Figure 4, up to 25% of all detected sources in each image would lie in the redshift range

1:01(1 + z ) < (1 + z ) < 1:17(1 + z ), and reveal the features depicted in Figure 2. However, since

only a small fraction of all baryons need to b e incorp orated in collapsed ob jects in order to ionize

the IGM, reionization is likely to o ccur b efore the redshift at which the source numb er-count

3 2

p eaks (z = 3:5; 4:5, or 6 at sensitivities of 10 ; 10 , or 10 nJy). Pre{selection of sources in

p eak

particular redshift bins could b e achieved photometrically by bracketing the asso ciated lo cation of

their Ly troughs with two narrow-band lters.

4. Conclusions

We have shown that the Gunn{Peterson e ect breaks into individual Lyman series troughs

in the sp ectra of sources lo cated in the redshift interval 1 < (1 + z )=(1 + z ) < 32=27.

s reion

Although the transmitted ux in between these troughs is heavily absorb ed by the Ly jungle

after reionization, the residual features it shows allow a determination of the reionization redshift,

z , for suciently bright sources. For a single source, a reionization redshift z 7 could

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b e determined to a precision of 1% with a sp ectroscopic sensitivityof 1% of the continuum

ux. A simple mo del for the abundance of high{redshift quasars predicts that a single source p er

0 0

16 16 eld could allow this detection at the 10 nJy sp ectroscopic sensitivityof NGST.Itmay

also be feasible to prob e reionization with ground{based telescop es. Using the Keck telescop e,

Dey et al. (1998) have recently detected a source at z =5.34, and found no continuum emission

b elow the rest{frame Ly wavelength. The authors were able to infer a lower limit of =1:2 on

the optical depth of the Ly forest between 1050 and 1170 A to z =5.34, which falls just short

of the 1:3 < <1:9 implied by equation (1) for this redshift and wavelength range. Therefore,

a somewhat more sensitive sp ectrum of this ob ject could p otentially constrain reionization at

z<5:34.

The signal-to-noise ratio in the determination of z might b e improved by co{adding the

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sp ectra of several sources. In the absence of Ly jungle absorption, the cumulative sp ectrum

would approach the sawto oth template sp ectrum derived by Haiman, Rees, & Lo eb (1998, Fig. 1)

and would b e isotropic across the sky. An alternative signature of reionization should app ear at

the soft X-ray region of the sp ectrum (E 0:1 keV), where the continuum optical depth to H

and He ionization drops b elow unity. AXAF could detect sucha signature in the sp ectra of only

exceptionally bright ob jects.

In order to enable a measurement of z at redshifts as low as 6, it is essential that the

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wavelength coverage of NGST would extend down to 7 =0:7m. Detection of the transmitted

{9 {

ux features requires progressively higher sensitivities as z increases b ecause of the likely

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increase in the optical depth of the Ly jungle with redshift. The nominal integration time

of ab out one hour for a 10 nJy sensitivity (with R =100 and S/N=3) would be sucient to

determine z up to a redshift of 7 with a precision of 1%. Following the extrap olation

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of equation (1) to higher redshifts, the required sensitivity needs to be one or two orders of

magnitude higher if z 8 or 9. Note, however, that if z 10, then it will be more

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easily measurable through the damping of the CMB anisotropies on small angular scales (HL98).

Near the planned sp ectroscopic sensitivityof NGST, most sources are exp ected to have redshifts

lower than z . However, suitable high-redshift sources could b e pre-selected photometrically in

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analogy with the UV drop out technique (Steidel et al 1996), by searching for the exp ected drop in

the ux at the blue edge ( [1 + z ]) of the Ly GP trough.

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This work was supp orted in part by the NASA ATP grants NAG5-3085, NAG5-7039, and the

Harvard Milton fund. We thank George Rybicki for advice on the statistics of the Ly clouds,

and Peter Sto ckman for useful information ab out NGST.

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{10{

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{11{

Fig. 1.| Sp ectra of ve sources lo cated beyond the reionization redshift (here taken to be

z = 7), when all contaminating e ects, such as p eculiar velo cities, the ionization of the IGM in

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the vicinity of the source, or absorption by the Ly forest, are ignored.

{12{

Fig. 2.| Sp ectra of the ve sources in Figure 1, when the absorption due to the p ost-reionization

Ly forest is taken into account.

{13{

Fig. 3.| Blow{up of the sp ectrum of a source at z = 7:08, assuming sudden reionization at a

redshift z = 7. The solid curves show the sp ectrum without absorption by the high{redshift

reion

Ly forest, and the dashed lines show the sp ectrum when the damping wings are also ignored.

{14{

Fig. 4.| Predicted numb er of quasars within the redshift interval 1:01(1 + z ) < (1 + z ) < 1:17(1 + z ),

0 0 0 0

with a minimum intrinsic ux F , in a 16 16 eld (sixteen 4 4 NGST elds of view). The

observed quasar luminosity function was extrap olated to high redshifts using the mo del in HL98.