Astro-Ph/9509093

RADIATIVE TRANSFER IN A CLUMPY UNIVERSE

I I THE ULTRAVIOLET EXTRAGALACTIC BACKGROUND

Francesco Haardt and Piero Madau

Space Telescope Science Institute San Martin Drive Baltimore MD USA

Department of Astronomy Astrophysics Institute of Theoretical Physics

University of Goteborg Chalmers University of Technology Goteborg Sweden

ISASSISSA via Beirut Trieste Italy

ABSTRACT

The integrated ultraviolet ux arising from QSOs andor hot massive stars in metalpro ducing

young galaxies is likely resp onsible for maintaining the intergalactic diuse gas and the Ly forest

clouds in a highly ionized state The sp ectrum and intensity of such UV background have generally

b een obtained by mo deling the repro cessing due to intervening material as a pure photo electric

absorption pro cess However owing to the emission from radiative recombinations within the ab

sorbing clouds a photoionized clumpy medium could contribute substantially to the metagalactic

ux In other words QSO absorptionline systems are sources not just sinks of ionizing photons

We present a detailed calculation of the propagation of AGNlike ionizing radiation through

the intergalactic space We mo del the ionization state of absorbing clouds and show that the

universe will b e more opaque ab ove Ryd than previously estimated Singly ionized helium

in Ly forest clouds and Lymanlimit systems is found to b e very ecient in repro cessing soft

Xray heliumionizing photons into ultraviolet hydrogenionizing ones We demonstrate that

a signicant fraction of the absorb ed primary photons emitted eg by quasar sources will

b e reradiated by the photoionized gas through Ly line emission twophoton continuum and

recombination continuum radiation

In the light of new data and recent studies we also reassess the contribution of the QSOs

observed in optical surveys to the UV extragalactic background and nd that the sto chastic

repro cessing of quasar Lyman continuum radiation by hydrogen and helium along the line of

sight will signicantly aect the amplitude sp ectral shap e and uctuations prop erties of the

metagalactic ux In a scenario in which QSOs are the primary source of ionizing photons in the

universe the integrated H I Ly emission at z from photoionized Ly clouds and Lyman

limit systems is found to b e at a level of less than of current observational limits on the farUV

extragalactic radiation ux We show that J increases from ergs cm s Hz sr

at the present ep o ch to ergs cm s Hz sr at z The attenuated direct

quasar emission plus recombination radiation from intergalactic gas app ears to provide enough

hydrogenionizing photons to satisfy the proximity eect at large redshift The He II H I ratio

in the diuse intergalactic medium and the Ly clouds increases from at z to at

z to decrease again b elow for z The sp ectrum of the ionizing background at high

redshift is shown to have a hump at energies b elow eV due to redshiftsmeared He II Ly line

and twophoton continuum emission We prop ose that observations of lowionization sp ecies such

as O II in metalline absorption systems may b e able to test the presence of such a prominent

feature in the UV background sp ectrum We also note that if the metagalactic ux is dominated

by QSOs the suggested steep decline of their ionizing emissivity b eyond z should pro duce

an increase in the observed rate of incidence of Ly forest clouds at these redshifts relative to an

extrap olation from the intermediatez regime as observed by Williger et al

Subject headings cosmology observations diuse radiation intergalactic medium quasars absorption lines

INTRODUCTION

The existence of a uniformly distributed intergalactic medium IGM which contains the

bulk of the baryonic matter of the universe in most mo dels of structure formation is predicted as

a pro duct of primordial nucleosynthesis The hydrogen comp onent of this IGM must have b een

highly ionized by z as the ux decrement observed on the blue side of the Ly emission

line of neutral hydrogen in the sp ectra of high redshift QSOs app ears entirely consistent with the

blanketing by discrete absorption lines along the line of sight Steidel Sargent Giallongo

et al It is widely b elieved but see eg Sciama that the integrated ultraviolet ux

arising from QSOs andor hot massive stars in metalpro ducing young galaxies is resp onsible

for maintaining the intergalactic diuse gas and the Ly forest clouds in a highly ionized state

Such UV background may also b e resp onsible for the ionization of the metalrich QSO absorption

systems Steidel Vogel Reimers and of the hydrogen clouds lo cated in the galactic

halo Fransson Chevalier Ferrara Field and for pro ducing the sharp edges of

H I disks observed in nearby spiral galaxies Bo chkarev Sunyaev Maloney Corb elli

Salp eter Dove Shull Photoionization by UV radiation may also inhibit the

collapse of smallmass galaxies Dekel Rees Efstathiou

The Hubble Space Telescope Faint Ob ject Camera FOC detection of redshifted He II A

absorption in the sp ectrum of the z quasar Q Jakobsen et al has recently

provided new constraints on the thermal and ionization state of the IGM and on the sp ectrum

of the UV metagalactic ux at early ep o chs The high ratio of He II to H I which is necessary to

account for the observed absorption trough requires a soft radiation eld at Ryd compared to

Ryd Madau Meiksin Giroux Fardal Shull Although the mean sp ectrum of the

individual sources which dominate the metagalactic ux might not b e very steep the cosmological

ltering through material along the line of sight is known to signicantly soften the background

intensity Absorption by intervening matter actually makes the universe at high redshift optically

thick to Lyman continuum LyC photons enough neutral hydrogen and singly ionized helium is

contained in the intergalactic clumps of highly ionized gas which form the Ly forest and in the

metalline absorption systems asso ciated with the halo regions of bright galaxies to signicantly

attenuate the LyC ux from all but the nearby sources Bechtold et al MiraldaEscude

Ostriker Mller Jakobsen Madau Meiksin Madau Zuo

Phinney Madau

This is the second pap er in a series aimed at a detailed numerical study of the absorption

and repro cessing of UV photons in a clumpy photoionized universe In Paper I Madau

we have assessed the eects of the sto chastic attenuation pro duced by QSO absorption systems

along the line of sight on the broadband colors of galaxies at cosmological distances It is the

purp ose of this pap er to fo cus on the eects of intervening discrete absorb ers on the propagation

of ionizing diuse radiation The primary motivation of this study is the realization that the

integrated UV background will actually b e the sum of the direct radiation from discrete sources

and the emission from radiative recombinations within the absorbing clouds and the intercloud

diuse IGM Since the intercloud medium is optically thin to LyC photons its contribution to the

photoionizing radiation eld will b e negligible We show in this pap er that this will not b e true

however for the cloudy comp onent as a signicant fraction of the absorb ed primary photons will

b e reradiated by the photoionized gas through Ly line emission twophoton continuum and

recombination continuum radiation The plan is as follows In x we review the basic theory

of cosmological radiative transfer in a clumpy universe In x we mo del the physical state of

absorbing clouds as the knowledge of their ionization structure is critical to understanding the

propagation of ionizing photons through intergalactic space In x we determine the contribution

of recombination radiation from Ly forest clouds and Lymanlimit systems to the metagalactic

ux In x we numerically compute the sp ectrum of the background radiation eld as a function

of redshift assuming that the quasars detected in optical surveys are the primary source of LyC

photons in the universe We derive expressions for the hydrogen and helium ionization rates

and discuss the implications of our results for the GunnPeterson test the proximity eect the

He II Ly cosmic opacity the uctuations of the metagalactic ionizing ux at high redshift and

the prop erties of the Ly forest clouds and metalline absorption systems We briey summarize

our conclusions in x In App endix A we provide some tting formulae to the recombination

rate co ecients while in App endix B we present useful analytical approximations to the eective

cosmic opacity and the recombination emissivity Finally in App endix C we discuss a numerical

algorithm for a fast iterative solution to the equation of radiative transfer Readers who are

interested in the main results and not in the technical details of the mo del may wish to pro ceed

directly to x at this p oint

BASIC THEORY

Cosmological Radiative Transfer

The radiative transfer equation in cosmology describ es the evolution in time of the sp ecic

intensity J in units of ergs cm s Hz sr of a diuse radiation eld eg Peebles

a a c

J J cJ

t a a

where a is the cosmological scale parameter c the sp eed of the light the continuum absorption

co ecient p er unit length along the line of sight and is the prop er spaceaveraged volume

emissivity Integrating equation and averaging over all lines of sight yields the mean sp ecic

intensity of the radiation background at the observed frequency as seen by an observer at

redshift z

d z

z z

ef f o o

dz z e J z

o o

dz z

where z z

o o

c d

z q z

dz H

is the line element in a Friedmann cosmology H h km s Mp c the Hubble constant

and q the deceleration parameter

Intergalactic Absorption

The eective optical depth due to discrete absorption systems is dened as

ef f

lnhe i ef f

where he i is the average transmission over all lines of sight For Poissondistributed clouds we

have Paresce McKee Bowyer

Z Z

1 z

dN dz z z e

HI ef f o o

N z

where N N z is the redshift and column density distribution of absorb ers along the line of

sight The continuum optical depth through an individual cloud is assuming a pure hydrogen

helium gas

0 0 0 0

N N N

HI HI HeI HeI HeI I HeI I

0 0

where z z and and are the hydrogen and helium photoioniza

o o HI HeI HeI I

tion crosssections When b ecomes equal to the mean optical depth In the opp osite

ef f

limit the obscuration is picket fencetype and the eective optical depth b ecomes equal to the

mean number of optically thick systems along the line of sight

Two classes of absorb ers are known to dominate the cosmic LyC opacity with the Ly forest

clouds b eing the most numerous These have neutral column densities ranging from to

maybe cm close to primordial metal abundances and evolve rapidly b etween z

Murdo ch et al The distribution of the number of clouds as a function of H I column

roughly follows a single p owerlaw dN dN N with Tytler et al a Tytler

The redshift evolution of the rarer Lymanlimit systems log N which are

optically thick to radiation with energy greater than Ryd is much weaker over the range

z StorrieLombardi et al Sargent Steidel Boksenberg Ab out of

the Lymanlimit absorb ers are asso ciated with heavyelement lines

To facilitate a comparison with previous estimates of the UV background MiraldaEscude

Ostriker Madau MiraldaEscude Ostriker Meiksin Madau

Giroux Shapiro we assume in the following a constant value of over decades

in N For the redshift and column density distribution of intervening absorb ers we take

z N cm N N

N z

z N cm N

where N and for z With the ab ove normalization there are

dN dz z Ly forest clouds with rest equivalent width W A corresp onding

to N cm for an average Doppler width of km s as measured at high redshift

by Press Rybicki At z the number of Ly forest line is times larger than

exp ected from a simple extrap olation of the high redshift evolution Bahcall et al Morris

et al For z we therefore take and normalize imp osing continuity at z

This gives lines p er unit redshift with W A at the present ep o ch consistent with

the ndings of Bahcall et al At highz the mo del adopted will provide ab out the same

photo electric opacity as in mo del A of MiraldaEscude Ostriker and in the medium

attenuation mo del MA of Meiksin Madau It is fair to p oint out that deviation from

a single p owerlaw in column density could b e signicant In particular there is very limited

information on Ly forest absorb ers with N cm These high column density

clouds will dominate the Ly forest contribution to the eective photo electric optical depth

making its value rather uncertain Meiksin Madau have suggested that the published

data may actually indicate an underdensity of Ly with columns N cm Giallongo et

al Petitjean et al and Kulkarni et al have also rep orted evidence for a

break in the N p owerlaw at log N This decit could result in a signicant reduction

HI HI

of the forest continuum opacity and therefore in an increased background ionizing ux We will

discuss this p ossibility in more details in x

In the following we will also neglect the photo electric opacity asso ciated with a uniformly

distributed IGM This is consistent with the lack of a H I GunnPeterson absorption trough in the

sp ectra of QSOs at large redshift eg Giallongo et al Note however that if the recent

Hubble Space Telescope observation of a He II Ly trough in the sp ectrum of quasar Q

Jakobsen et al were to require a GunnPeterson optical depth the He II LyC opacity

of a diuse IGM comp onent would b e signicant Madau Meiksin

THE IONIZATION STATE OF QUASAR ABSORPTION SYSTEMS

A selfconsistent calculation of the eective optical depth in equation requires a de

tailed understanding of the ionization state of intervening material In particular the amount of

He I and He II which is present along the line of sight must b e inferred by mo deling the phys

ical conditions in the absorbing clouds themselves This will b e done in this section We will

assume the gas to b e in ionization equilibrium with the background UV radiation Deviation

from equilibrium will b e small of order the ratio of the ionization timescale to the Hubble time

z h where the background intensity is measured at the t t J

ion H

hydrogen Lyman edge in units of ergs cm s Hz sr

In principle the temp erature T of the absorbing gas should also b e computed selfconsistently

by balancing photoionization heating with freeb ound and freefree radiative losses collisional

excitation losses and Compton co oling losses from scattering o the microwave background The

temp erature fully ionized gas may reach dep ends however on the p o orly known cloud density For

cm collisional excitation of neutral hydrogen is the dominant co oling mechanism n

and the cloud temp erature increases with decreasing density to drop again at lower densities when

cm the typical Compton co oling starts to dominate Meiksin Moreover when n

density of a spherical Ly cloud with neutral hydrogen column cm and diameter kp c

in equilibrium with a radiation eld of intensity J the co oling timescale is longer than

the age of the universe at the redshift of interest and the gas will retain a memory of the initial

conditions The contraction or expansion of the gas toward hydrostatic equilibrium will further

aect its thermal prop erties On the other hand we can estimate the temp erature of the absorbing

gas from the measurements of Ly line proles in high resolution high signaltonoise sp ectra

For simplicity we shall assume here a xed temp erature of T K This is the value

derived from mo deling the broader Ly absorption lines as blends of clouds each with thermal

width k T m km s and a velocity disp ersion of km s Hu et al We

B H

will also assume that intergalactic material acts only as a lter of external background photons

emitted from quasars andor starforming galaxies ie there are no lo cal discrete sources of

UV radiation within individual clouds Although the photoionization equilibrium of a H and He

gas is standard textb o ok topic we are applying it in such an unusually wide range of parameters

ab out decades in N and nearly decades in J that it is worth stating the basic equations

HI and approximations used

Clouds Optically Thin To LyC Radiation

If we dene Y N N Y N N and Y N N the steady state

HI HI H HeI HeI He HeI I HeI I He

ionization equilibrium equations can b e written as

Y Y I

HI HI HI

Y Y I

HeI I HeI HeI

Y Y Y I

HeI HeI I HeI I HeI I

where

n T

e HI

Here

HI HI

is the photoionization rate p er hydrogen atom the Case A recombination rate co ecient to

all levels of hydrogen n the electron number density and J the background radiation intensity

Analogous expressions are valid for I and I Collisional ionizations have b een neglected we

HeI HeI I

will discuss in x the validity of this approximation The radiative recombination co ecients

for hydrogenic ions are taken from Arnaud Rothenug while those for neutral helium

are taken from Black The H I and He II photoionization crosssections are adopted from

Osterbro ck For the photoionization crosssection of neutral helium we used the following

t to within a few p ercent up to keV of the results of Reilman Manson

HeI

E E

for E where E is the photon energy in units of eV

Notice that while He III recombines for J n hydrogen is mostly ionized for

n Thus in the case of a QSOdominated background the typical conditions J

of the Ly clouds assure that most of the gas is completely ionized In this case we can write

HI HI thin HeI I

where

n I I I N

He HI HI HeI HeI I

thin

N n I I I

HI H HeI HeI I HeI I

thin

assuming a helium to hydrogen cosmic abundance ratio equal to

The solution of the ionization equilibrium given ab ove neglects any kind of radiative transfer

within the individual clouds and has b een extensively used in previous investigations Miralda

Escude Ostriker Madau Giroux Shapiro These authors

have argued that equations and might describ e reasonably well the overall transmission

prop erties of the universe even when optically thick clouds are present The reason is that for

AGNlike or softer sp ectra the ratio J J is much greater than unity this implies

thin

that clouds which are ab out to b ecome optically thick in the He II LyC are still optically thin

in the H I LyC To b e more sp ecic let us denote with N Ryd the H I column at which

He II selfshielding sets in Clouds with N N Ryd have optical depth of unity at Ryd

HI HI

or equivalently an He II column N Ryd Ryd cm Similarly

HeI I

selfshielding at Ryd sets in ab ove N Ryd Ryd cm While our

estimate of the singly ionized helium to neutral hydrogen ratio from equation is then quite

accurate for all values of N less than N Ryd it is clearly inadequate at larger H I columns

HI HI

In this regime the absorption of He II LyC photons within the clouds must b e taken into account

in calculating the exp ected ionization structure It turns out however that the contribution of

clouds with N N Ryd to the eective optical depth of the universe at Ryd is more or

HI HI

less indep endent of their actual He II column This is b ecause the exact value of for greater

than a few is irrelevant in equation as most of the photons are removed anyway For a column

density distribution dN dN N like the one given in equation most of the eective

opacity at frequency actually comes from absorb ers with

We have found that although the optically thin formula correctly estimates the cosmic

transmission at or just ab ove the He II Lyman edge it breaks down when A The

problem is that due to the wavelength dep endence of LyC absorption absorb ers which are just

optically thick for these p enetrating photons A are very optically thick at

Ryd In these clouds the ratio N N is generally much higher than the value estimated

HeI I HI

from equation since He III almost completely recombines see b elow The trasmittance of

photons ab ove Ryd actually drops to zero for clouds with N N Ryd The net eect is

HI HI

that the Universe wil l be more opaque above Ryd than previously estimated In the next section

we will provide a more accurate alb eit still approximate radiative transfer solution for the actual

ionization state of individual optically thick absorb ers

Clouds Optically Thick to LyC Radiation

We shall consider a pure HHe semiinnite slab The ionization equilibrium equation for

the neutral hydrogen density at depth R within the slab is

Z Z

1 1

d d p T n n n e

HI abs HI e HI I HI

h h

L L

where h Ryd

dr n n n

HI HI HeI HeI HeI I HeI I

and the term p is the fraction of recombination continuum radiation with emissivity which

abs r

is absorb ed within the slab Analogous expressions can b e written for the helium ions Since the

recombination emissivity is strongly p eaked at threshold we can approximate the last term in

equation as

p Ryd n n d p

abs e HI I abs

where is the recombination co ecient to the ground level of hydrogen see App endix A For

simplicity and b ecause of the steep dep endence of the photoionization crosssection with energy we have neglected lo cal helium recombination radiation as a source of hydrogenionizing photons

Note however that helium recombination photons will b e more eective in ionizing hydrogen as

they escap e into the intergalactic space and are redshifted by the cosmological expansion cf x

We shall take

Ryd

p Ryd

abs

Ryd

Equation is strictly valid only in regions of constant ion and electron density It is

p ossible to show that for the conditions typically encountered the pro duct n n is indeed

e HI I

fairly constant even throughout absorb ers which are very optically thick log N to

hydrogen LyC radiation This is not true for helium however as He III recombines faster than

hydrogen and the radiation intensity at the He II edge is in general smaller than the intensity at

the H I ionization edge The He III number density in clouds which are optically thick at Ryd

is constant up to the He II photosphere where n RydR then drops sharply by

HeI I HeI I

more than an order of magnitude as He III starts to recombine Since most of the reemission and

absorption of photons ab ove Ryd o ccurs at the He II photosphere and h Ryd

HeI I

the absorb ed fraction of He II recombination radiation can b e written as

p Ryd

abs

where

dr n r Ryd min

HeI I HeI I

Therefore while only a fraction Ryd of H I LyC photons will escap e from clouds which

are very optically thick at Ryd at least of the He II LyC photons pro duced in individual

systems will always b e able to leak out into the IGM

We can now solve for the n n and n number densities as a function of R We obtain

HI HeI HeI I

n n

HI e HI

e n d

HI e HI

where p Ryd Again similar expressions can b e written for the n n

HI HI abs HeI He

and n n number ratios Finally the H I He I and He II column densities can b e derived

HeI I He

by integrating through the slab

Simple Approximations

An iterative solution to the radiative transfer equation which included a detailed com

putation of the ionization structure of individual absorb ers would b e very time consuming In

this section we develop a simple approximation to the exact form of the function He II H I

which is capable of repro ducing the full absorption prop erties of intergalactic material

Assuming a spherical geometry for the clouds would change eqs and allowing

slightly more photons to escap e for a given optical depth For p indep endent of

abs

geometry When the dierence b etween a slab and a sphere can b e signicant but in this

case p anyway and its exact value is irrelevant in the denition of abs

The asimptotic limit for low N is readily obtained in the optically thin regime see eq

The selfshielding of He II LyC radiation b ecomes imp ortant as N approaches the value

N Ryd N Ryd

HI HI

thin

At ab out twice this value He III recombines and the He II column rises sharply while hydrogen is

still mostly ionized The He II to H I column density ratio quickly reaches its maximum value

n n

HI e HI He

max

n n

H e HI

where the factor e takes into account the partial selfshielding of neutral hydrogen

is the photoionization rate in the limit of an optically thin cloud n

HI HI e

and we have assumed a negligible fraction of neutral helium It is straightforward to write down

a more general expression including the He I comp onent The contribution of He I to the overall

opacity of the universe is fully taken into account in our numerical calculations This is found to

b e negligible except at the very highest redshift z where the quasar emissivity drops and

helium starts to recombine see x b elow Finally at even higher H I columns N several

cm b oth H II and He II recombine The He II to H I ratio b ecomes a decreasing function

of H I and nally reaches the asymptotic limit of a completely neutral gas

thick

We have found that the exact form of N can b e well approximated by a steplike function

as shown in Figure for dierent values of the background intensity an assumed temp erature of

T K and a hydrogen gas density of n cm a larger n would decrease

H H

the value of thereby decreasing the cosmological eective opacity ab ove eV The drop

max

cm A at large hydrogen columns is well mo deled by assuming N for N

HI HI

similar approximation has b een used for the neutral helium comp onent Note that in order to

take into account the fact that b oth faces of the slab are actually illuminated by the metagalactic

ux we have asso ciated the value of at a given R to a cloud with column density equal to

N R Figure shows again as a function of H I column the absorption probability through

an individual cloud exp for various ionizing photon energies We compare the exact

value of this probability function with those obtained from the steplike approximation and

the optically thin const limit used in previous investigations When integrated

thin

over the actual column density distribution the steplike approximation gives typical errors of

a few p ercent with a maximum value for photon energies eV However at such

short wavelengths the eective optical depth of the universe is and the p ercental error in

ef f

computing the sp ecic background intensity J e is a factor smaller

ef f

Since the integration over N in equation can b e done analytically over ranges of con

stant and for N the steplike approximation for the ionization structure of individual

absorb ers along the line of sight reduces signicantly the computational time This will allow

a fast computation of the contribution of recombination radiation to the sp ecic intensity see

App endix B Dierent p ossibilities for the nature of the ionizing sources and uncertainties in the

column and redshift distribution of intervening absorb ers can then b e quickly explored

Importance of Col lisional Eects

In the relevant range of densities for the Ly clouds and the Lymanlimit systems n

cm collisional ionizations are always negligible for the helium comp onent b ecause

of the large ionization p otentials For hydrogen collisional ionization can b e imp ortant when the

photoionization rate is low ie for low background intensities or in the core of optically thick

clouds A related issue concerns the imp ortance of collisionally excited line emission notably

H I Ly relative to recombination radiation Since collisional pro cesses are strong functions

of the gas temp erature it is imp ortant to check that they are indeed negligible in the relevant

regime We have therefore solved the equation of thermal equilibrium for a gas slab immersed in

a background radiation eld In Figure upp er panel we show for three dierent background

intensities the average temp erature of the cloud as a function of H I column density For illus

trative purp oses and to show the dep endence on the assumed gas density the total hydrogen

density is taken to b e cm for the Ly forest clouds N cm and

cm for the thicker Lymanlimit systems Heating is provided by photoionization of hy

drogen and helium while recombinations and collisional excitation of neutral hydrogen dominate

the co oling term

Figure lower panel also shows the fractional p opulation of the n level of atomic

hydrogen due to recombinations of photoionized H II ions collisional excitations from the ground

state and recombinations of collisionally ionized H II ions for clouds of dierent H I columns The

last contribution is never imp ortant assuring that collisional ionizations can b e neglected in the

computation of the ionization structure of absorbing clouds This is also seen in Figure where

the dotted lines depict the derived He II to H I ratio including collisional eects Deviations from

the values computed in x by assuming a purely photoionized isothermal slab are indeed small

It is fair to note however that a fraction of H I Ly and two photon decay emissions

could still b e due to radiative deexcitations of collisionally excited atoms This contribution has

not b een included in our numerical calculations of the metagalactic ux

RECOMBINATION RADIATION FROM QUASAR ABSORPTION SYSTEMS

The attenuation due to the accumulated H I and He II LyC absorption by Ly forest clouds

and Lymanlimit systems causes a large reduction of the background ionizing ux However a

signicant fraction of the absorb ed photons is reradiated by the photoionized gas in the ultraviolet

band In this section we will show that diuse radiation from intergalactic material will in fact

dominate the cosmic ionizing emissivity at characteristic frequencies Candidates for the source

of the metagalactic ux includes AGNs see x and starforming galaxies but the precise nature

of the background is not imp ortant in this context

The dominant emission from a highly photoionized dustfree gas which contains by number

of hydrogen of helium and traces of metals at a temp erature of K is due to

radiative recombinations and collisional excitations of the H I and He II Ly lines at and

A resp ectively As only Lyman series lines of He II ions can signicantly aect the ionization

state of the universe and since in the considered range of densities collisionally excited He II line

emission is always negligible we have taken into account only radiation arising from radiative

recombination pro cesses Under the typical physical conditions encountered the hydrogen and

helium ions in the absorbing medium are in their ground state as recombinations to excited levels

are followed by radiative decays to the ground level Among direct recombinations and radiative

decays only few pro cesses are imp ortant as sources of farultraviolet photons In the following

we analyze them in turn

a He II processes Direct captures of free electrons to the n L levels of He II are an ob

vious source of ionizing photons As the resulting continuum radiation is strongly p eaked at

frequency Z n direct captures to the ground level will pro duce a signicant amount of

th L

He II ionizing photons while captures to the L level will radiate a Balmer continuum just ab ove

Within clouds which are optically thick to resonant scattering in the lines of the Lyman series

all helium recombinations eventually p opulate the S and P levels and are converted into two

photon continuum and Ly A photons In the absence of metals and dust the Ly photons

will diuse into the wings and nally escap e Most He II recombination radiation will b e emitted

from clouds with N N Ryd cm as these are the dominant absorb ers of

HI HI

photons ab ove Ryd and will escap e into the intergalactic space without appreciable destruction

by lo cal H I absorption

b H I processes Although only freeb ound captures to the ground state of hydrogen are able

to generate photons ab ove Ryd we have also computed the contribution of H I Ly and two

photon continuum to the nearultraviolet background As in the case of He II pro cesses we have

taken into account only radiation arising from radiative recombinations As discussed in x

these account for at least of the total hydrogen Ly and twophoton continuum emission

c Emissivity from Radiative Recombinations To summarize our calculations will include the

emission from Ly forest clouds and Lymanlimit systems due to H I and He II Ly recombination

radiation twophoton continuum and freeb ound captures to the ground and for He II only to

the L levels We have ignored He I recombination radiation b ecause of the smallness of the

N N and N N ratios encountered in typical situations Note that this will b e a

HeI HeI I HeI HI

p o or approximation at the very highest redshift z where the abundance of neutral helium

increases as the space density of observed quasars drops

In general the sp ecic recombination emissivity asso ciated with a given atomic transition

can b e expressed as

z h f B z

where

Z Z

1 1

0 ef f

J z N

0 0

p w d B z dN

em abs HI

N z h

This formula simply states that the rate of recombination photons which escap e into the inter

galactic space is prop ortional to the number of photons absorb ed p er second at any given redshift

by the relevant atom or ion times the fraction of recombinations which lead to the radiative

ef f ef f

transition under consideration the ratio where is the eective recombination co ef

cient Osterbro ck times the fraction p of the emitted photons which are able to escap e

from an individual cloud The fraction of incident photons which are absorb ed by a given ion X

having optical depth can b e written as

0 0

w d e e

abs X

The last equality is correct as long as the He II to H I and He I to H I ratios are constant through

the slab and it is easily generalized if these ratios vary in a steplike manner instead In analogy

with equation and the fraction of He II LyC photons which can escap e from a cloud is

exp

N N Ryd

HI HI

em L

exp

N N Ryd

HI HI

Note that for energies eV we have that Only hydrogen and ab ove eV

HeI I

neutral helium will absorb He II Balmer continuum twophoton continuum and Ly photons

as well as H I LyC The function f d in equation represents the normalized probability

p er recombination that a photon is emitted in the interval d We stress that the

recombination emissivity from intervening material is largely indep endent on the p o orly known

sizes and gas densities of the absorb ers and dep ends only weakly on the temp erature of the

emitting media

d Recombination Continuum The rate of direct recombinations to the n L level can b e com

puted using the Milne relation Osterbro ck This together with equation for hydrogen

like ions yields

n h

h k T

f e

HI th

n L

c m k T Z

where all symbols have their usual meaning or have b een dened in the text Direct captures

to the L level of He II result in a radiation continuum with sp ecic volume emissivity equal

to N N N N of the emissivity arising from freeb ound captures to the

HeI I I HI I He H

ground state of H I

e Ly Line Radiation Inserting equation into equation and taking f

where is the Ly frequency and x is the usual delta function the sp ecic intensity asso ciated

with Ly line radiation can b e written as

z h

z z

ef f o o

dz B z e J z

o o

z z

ef f o o em

B z z e

em o

where z denotes the redshift of the Ly line emitters z z The eective

em em o o

recombination co ecient to the P level has b een assumed to b e indep endent of column density

since resonant absorption of Ly photons p opulates the P level which subsequently decays via

H and twophoton emission The p opulation of the P level arising from downward cascading

of n levels following the resonant absorption of higher order Lyman lines can b e neglected

see Pengelly and App endix A

f TwoPhoton Continuum The S level is p opulated by direct recombinations and by down

ward cascades following recombinations to higher levels The function g h f for the

twophoton continuum decay of neutral hydrogen is tabulated in Osterbro ck The emis

sivity due to the twophoton continuum decay of the S level of He II can b e computed using

the relation

g g

HeI I HI

The eective recombination co ecient to the S level strongly dep ends on the Ly line center

ef f

opacity Ly As this increases from to increases by a factor However for

clouds with which are the ma jor contributors to the recombination emissivity Ly

We have therefore assumed that the p opulation of the S is well describ ed by Case B

recombination for all values of N see App endix A for details

NUMERICAL RESULTS

The formalism we have developed so far including the eects of the repro cessing of UV

photons by a clumpy intergalactic medium can b e applied to compute the metagalactic ux

arising from any discrete source of photoionizing radiation the most plausible candidates b eing

AGNs and young starforming galaxies The last contribution is the most dicult to assess and

also the most intriguing as a determination of the UV background intensity andor sp ectrum

at high redshift might constrain the history of cosmic metal pro duction and galaxy formation

Bechtold et al MiraldaEscude Ostriker Songaila Cowie Lilly Madau

Shull The intensity and sp ectrum of the ultraviolet background arising from massive stars

in metalpro ducing galaxies will b e the sub ject of a companion pap er Madau Haardt

Below we will fo cus our attention on quasar sources

a Quasar Emissivity as a Function of Redshift According to recent surveys see eg the one

by Boyle Shanks Peterson with ab out ultravioletexcess quasars a pure luminosity

evolution mo del in which QSOs statistically conserve their number since z describ es well

the global prop erties of the quasar p opulation at low redshift Beyond z the comoving space

density of quasars app ears to stay constant up to a redshift of see eg Ko o Kron

Boyle Jones Shanks The decline in the quasar counts at z has b een the sub ject

of a longstanding debate and it is still controversial It has b een argued by Boyle and

Irwin et al that the space density of bright M quasars at z is similar

to that at z On the other hand Warren Hewett Osmer nd strong evidence

for p ositive evolution of the quasar luminosity function LF b eyond z According to these

authors the evolution ceases at z with a marked decline by a factor in space density

at larger redshift as rst suggested by Osmer A decline in the LF is also seen at the

prob ed by the Schmidt et al grism survey We remark that low luminosities M

these estimates are quite uncertain b ecause of corrections for incompleteness and the adopted

continuum emission sp ectrum and b ecause of the p ossible bias introduced by dust obscuration

arising from intervening systems Ostriker Heisler Wright Fall Pei

We shall estimate the integrated volume emissivity from QSOs following Pei who has

recently derived an analytical mo del which ts well the empirical LF estimated by Hartwick

Shade and Warren et al The b estt to the QSO LF is the standard double

p owerlaw

1 2

L L

L z

L z L z L z

Hartwick Shade have compiled ma jor optical surveys with more than

quasars covering mo derate redshifts z Most recently Warren et al have

combined their own and four other surveys to form a sample with contains ab out quasars

covering the range of high redshift z

The entire LF shifts along the luminosity axis as the p osition of the break L evolves with redshift

L z L z expz z z

where a p owerlaw sp ectral distribution for the typical quasar UV sp ectrum has b een assumed

f and the dep endence on the sp ectral index is explicitly shown According to Pei

this Gaussian form can t reasonably well the observational data in the entire range

z the evolution of QSOs reaches a maximum at z and declines at higher redshits

In a cosmology with h and q the LF tting parameters values are

z and log Gp c the Bmagnitude at the break is

M At the present ep o ch this LF is in go o d agreement with estimates of the Seyfert

LF by Cheng et al The prop er volume emissivity can b e written as

z z expz z z

Q Q B B

where is the extrap olated z emissivity at the reference frequency c A

Q B B

L LdL ergs Gp c s Hz

Q B

min

The LF of Seyfert galaxies matches remarkably well that of optically selected QSOs at M

and do es not show clear evidence of leveling o down to M Cheng et al

corresp onding to L L For the given shap e of the LF a value of L times

min min

smaller would increase the emissivity by only

b Quasar Spectral Energy Distribution One of the biggest uncertainties in these calculations

has always b een the detailed shap e of the UV continuum sp ectrum of quasars Recently however

the results of several sp ectroscopic surveys have signicantly advanced our knowledge of the QSO

emission prop erties In particular a very high signaltonoise comp osite sp ectrum of the rest

frame ultraviolet and optical region of ab out high luminosity intermediate redshift quasars

part of the Large Bright Quasar Survey has b een constructed by Francis et al Force

tting a p owerlaw to the constituent sp ectra yields a median sp ectral index of in the

range A In the UV longward of the Ly emission line the survey of Sargent Steidel

Boksenberg yields a softer slop e see also OBrien Gondhalekar

Wilson Finally the Tytler et al b Hubble Space Telescope FOC snapshot survey

QSOs at z has provided for the rst time statistical information on the intrinsic ionizing

photon distribution of quasar After accounting for intervening absorption Tytler et al nd an

even softer slop e in the wavelength range A

We shall therefore adopt the following mo del for the typical quasar sp ectral energy distri

bution

where the dierent slop es have b een continuosly matched In the farUV this mo del is similar to the medium QSO sp ectrum used in Bechtold et al and Mo del QS of MiraldaEscude

Ostriker its extrap olation to keV gives in agreement with the value for

QSOs measured by the Einstein Observatory Zamorani et al The soft keV Xray

sp ectral index is consistent with ROSAT observations of QSOs eg Laor et al but is

signicantly steep er than suggested by earlier Einstein and EXOSAT data Wilkes Elvis

Comastri et al Note that we have ignored luminosity and redshift dep endent eects in

QSO UVsoft Xray emission sp ectra OBrien et al Bechtold et al and that the

adopted Xray sp ectral slop e is to o steep to t the diuse Xray background b elow keV see

eg Madau Ghisellini Fabian and references therein Also no attempt has b een made

to include the soft Xray excess emission b elow keV which has b een detected in many AGNs

Turner Pounds and is well mo deled by the tail of a thermal sp ectrum with k T

eV Comastri et al It has b een suggested see Sciama that the presence of this

thermal farUV bump might help to account for the large abundances of N V and O VI observed

in some Lymanlimit systems

In Figure we plot the prop er volume emissivity at the H I He I and He II Lyman edges

due to QSOs as a function of redshift Note that the K correction term in equation has

b een matched to take into account the varying sp ectral index of equation In the redshift

range z Az matches to within the volume emissivity adopted in Madau

from the Boyle quasar LF At z the former is ab out larger than

the latter then falls like a gaussian b eyond z in contrast to the constant comoving emissivity

scenario Boyle Madau

c Spectrum of the Ionizing Background The formal solution of the radiative transfer equation

is not an explicit form of the sp ecic background intensity as its righthanded term implicitly

contains J in the emissivity term J and in the eective optical depth J Phys

Q r ef f

ically this simply means that the metagalactic ux dep ends on the ionization state of intervening

clouds which is in turn determined by the background eld itself In order to solve for J an iter

ative scheme must b e implemented see App endix C Figure shows the background radiation

eld pro duced by the observed QSOs in a q cosmology as a function of redshift from the

present ep o ch to z The sp ectrum from to A results from the numerical integration

of equation and is selfconsistently ltered through a clumpy IGM For comparison we have

also plotted the same sp ectrum in the limit of a p erfectly transparent universe and

ef f

a purely absorbing intervening medium As already discussed by a number of authors Bechtold

et al MiraldaEscude Ostriker Madau Meiksin Madau

Zuo Phinney the absorption by hydrogen and helium in intervening material pro duces

a very strong eect in the sp ectrum of the ultraviolet metagalactic ux This will b e generally

characterized by two breaks at the H I and He II ionization edges the amplitudes of which gener

ally increase with redshift The background intensity ab ove Ryd is in particular a nonlinear

function of the number of photons emitted by QSOs at these frequencies a relative small de

crease in this number causes a large increase in the size of the He II break The imp ortance of the

repro cessing of ionizing photons by intergalactic material is clearly seen in Figure While red

shifted He II Ly and twophoton continuum emission dominate the metagalactic ux from

to Ryd direct recombinations to the ground level of hydrogen and singly ionized helium provide

a substantial number of LyC ionizing photons close to the ionization thresholds Because of the

larger cosmic opacity at early ep o chs the amplitude of the jump in the background intensity at

A and A due to H I and He II Ly emission increases with redshift from z to z

to decrease again at z as the QSO emissivity drops and the background ux b ecomes dom

inated by more lo cal less attenuated sources At low redshift Ly line recombination radiation

forms an extended hump in the background sp ectrum due to the integrated contribution of QSO

absorb ers along the line of sight The diuse Ly ux b ecomes more p eaked at early ep o chs

again b ecause of the rapid decrease in the quasar ionizing emissivity ab ove z Also note how

at z helium starts to recombine this pro duces a small absorption feature in the sp ectrum

of the metagalactic ux at A

d Photoionization Rates The net eect of recombination emission from QSO absorb ers on

the ionization state of the universe is b est depicted in Figure where the total photoionization

rates and are plotted as a function of redshift and compared to the case of a

HI HeI HeI I

purely absorbing IGM Relative to the latter our mo del calculations including riemission

pro duce a value of ab out times higher nearly indep endent of redshift Typically less

than of the IGM diuse contribution comes from optically thick Lymanlimit systems The

eect of recombination radiation makes times larger at z and times larger at

HeI I

z How do these rates compare with observational constraints Diuse H surface brightness

observations of the HaynesGiovanelli intergalactic cloud by Vogel et al have recently

yielded an upp er limit to the lo cal metagalactic photoionization rate of s The total

QSOIGM contribution at z from Figure is ab out eight times lower s

Because of the larger QSO emissivity adopted here and the inclusion of recombination radiation

from intergalactic material this value is ab out two times higher than the one obtained by Madau

The amount of diuse ionizing radiation predicted by our mo del at the present ep o ch

is consistent with the value derived by Kulkarni Fall by applying the proximityeect

technique towards QSOs at hz i Observations at cm of the fairly abrupt truncation in

the H I distribution at the edge of nearby spiral galaxies have also b een used to infer values of the

metagalactic photoionzing ux This technique is somewhat mo deldep endent and yields rates

in the range s Maloney Corb elli Salp eter Dove Shull

again consistent with our mo del calculations

At high redshift the proximity eect which is the measured decrease in the number of Ly

absorbing clouds induced by the UV radiation eld of a QSO in its neighborho o d provides an

estimate of the intensity of the metagalactic ux at the hydrogen Lyman edge Determinations

of J in recent years include the following log J at z Bechtold

b etween and at z Williger et al log J at z

Ba jtlik Duncan Ostriker Lu Wolfe Turnshek and log J at

z for a velocity oset of km s b etween the emission lines in the broad line

region and the QSO restframe see Esp ey If J the corresp onding photoionization

rate equals J s Our QSOdominated background mo del generates

s at z and a value three times lower at z We conclude that within the

uncertainties the observed QSOs appear able to provide the number of ionizing photons required

by the proximity eect at z

A Gaussian t A z expz z S yields for the H I photoionization rate

plotted in Figure A sec B z and S This t can

b e applied over the range z with a maximum error lower than A similar tting

formula to accuracy in the same redshift range gives for the He II rate A sec

B z and S c

e Integrated H I Ly Emission at z from Quasar Absorption Systems We now address

the longstanding question of whether redshifted A H I Ly emission from intergalactic gas

might b e detected in the diuse farUV background in the range A The intensity

of the ionizing diuse ux from quasar sources implies that the redshiftsmeared background

at z due to H I Ly recombination radiation from photoionized Ly clouds and Lyman

limit systems ab out phot cm s A sr at A is at a level of less than ve p ercent of

current observational limits see Bowyer for a review Therefore in a universe photoionized

by QSOs redshifted Ly recombination emission from intergalactic material can b e ruled out as

a signicant source of farUV radiation

f Intensity Fluctuations of the Ionizing Background The attenuation by QSO absorption

line systems reduces signicantly the total number of primary sources involved in the pro duction

of the metagalactic ux The qualitative b ehaviour can b e readily obtained by expanding the

eective optical depth in redshift around z From equation B we obtain

A z z z z

ef f

at the hydrogen Lyman edge where the two terms on the righthand side represent the con

tribution of the Ly clouds and Lymanlimit systems to the eective opacity At z

A for z in a low q universe this corresp onds to a prop er absorp

ef f

tion length of h Mp c The ionizing radiation eld is thus largely lo cal at Ryd as

in the attenuation volume the QSO LF eq predicts only ob jects with

L L z

As argued by Zuo and Fardal Shull this fact might have an interesting

consequence namely intergalactic absorption should greatly enhance the intensity and sp ectrum

uctuations of the ultraviolet background at high redshift The imp ortance of this eect re

sides in the p ossibility that the study of the inuence of a uctuating metagalactic ux up on

Ly absorption lines eg the pro duction of clearings and voids in the forest along the line of

sight could shed some light ab out the nature of the main contributors of ionizing background

photons Kovner Rees Here we want to stress that as recombination radiation from

the numerous relative to QSOs Ly clouds and Lymanlimit systems contributes of the

total photoionization rate at z the UV background will b e much smo other in space than

previously considered In particular the twopoint correlation function induced in the Ly forest

by intensity uctuations will b e reduced by a factor of ab out Fardal Shull

g H I GunnPeterson Test In the presence of uniform material of density nz along the path

to a distant ob ject any resonance line with wavelength will pro duce a GunnPeterson

absorption trough with optical depth z e m cH z f nz where z is the redshift

GP e

at which the observed radiation passes through the resonance H z is the Hubble constant

f is the oscillator strength of the transition and all other symbols have their usual meaning

The H I optical depth is related to the photoionization rate through the condition of ionization

equilibrium

h T h z q z

where T is the temp erature of the ionized diuse intercloud medium its mass density param

eter and is the ionization rate in units of s The strongest limit on the amount

of diuse intergalactic neutral hydrogen at z is provided by a direct estimate of the quasar

Q ux in regions of the sp ectrum where lines are absent Giallongo Cristiani Trevese

The derived upp er b ound is Inserting this limit into equation with

T z q and yields h Nucleosynthesis constraints on

HI D

the cosmological baryon density require h Walker et al and would b e consis

tent with the limit on ab ove if less than of the baryons were in un uniformly distributed

medium the rest having collapsed into galaxies and discrete absorption systems Two p ossible

problems must b e noted here

If the diuse IGM is photoionized by quasars sources only the GunnPeterson test b ecomes

more and more dicult to satisfy at earlier ep o chs b oth b ecause of the strong dep endence of

with redshift and of the rapid drop in the QSO emissivity b eyond z As depicted in Figure

the background ionization rate due to QSOs falls by more than a factor of from z to

z while the cosmological term in equation increases by Therefore we would exp ect

the GunnPeterson optical depth to increase over times However an analysis of the sp ectrum

of the QSO by Giallongo et al yields at z

In the gravitational instability scenario for the formation of cosmic structures the as

sumption of a uniform intercloud medium has no theoretical justication As recently argued

by Reisenegger MiraldaEscude a photoionized IGM must b e inhomogeneous on scales

larger than the Jeans length and the GunnPeterson opacity should uctuate Moreover as the

lling factor of underdense regions or voids is large the median should b e signicantly lower

than the value exp ected for a uniform medium with Reisenegger MiraldaEscude

D B

h He II GunnPeterson Test The recent HST observations of quasars Q at z

Jakobsen et al and PKS at z Tytler et al b and the ASTRO

HUT sp ectrum of quasar HS at z Davidsen et al show the presence

of absorption troughs at the redshifted wavelength of He II A It is still unclear whether

line blanketing from discrete Ly forest clouds alone can pro duce the observed ux reduction

or whether a signicant contribution from absorption in a smo othly distributed IGM is needed

instead see eg Songaila Hu Cowie In the latter case the He II GunnPeterson

test could p otentially provide stringent constraints on the amplitude and sp ectral shap e of the

UV ionizing background Meiksin Madau MiraldaEscude Madau Meiksin

Giroux et al The He II and H I optical depths can b e related as

HeI I

thin

In Figure we plot as a function of redshift the He II H I ratio for an optically thin gas in

ionization equilibrium with our mo del ultraviolet background The predicted value increases

from at z to at z to decrease again b elow at z This is b ecause

at low redshifts the universe is nearly transparent while at z the decline in the quasar

counts makes the metagalactic ux dominated by more lo cal unattenuated sources Note how

recombination radiation from intergalactic material tends to decrease the exp ected value of

thin

for z

A background dominated by quasar sources could then pro duce a He II GunnPeterson optical

HeI I

depth at z and still b e consistent with the lack within the uncertainties of any GP

detectable We conclude that the He II A absorption decrement observed by Jakobsen

et al Tytler et al b and Davidsen et al should b e partly due to uniformly

distributed He II unless most of the baryons have b een removed from the IGM p ossibly into the

Ly forest

i He II Ly Clouds With the launch of HUT on ASTRO it has b ecome p ossible to detect

and identify He II Ly lines from Ly forest clouds Davidsen et al These could provide

together with the corresp onding H I Ly lines constraints on the sp ectrum of the metagalactic

ux A curve of growth analysis would enable us to estimate the parameter and thus to

thin

test the QSOdominated background scenario Note that b ecause of the relatively soft diuse

radiation eld pro duced by QSOs He II lines asso ciated with H I lines which are still in the linear

part of the curve of growth are exp ected to b e heavily saturated even more so if massive stars in

starforming galaxies provide a signicant contribution to the background ux

j He II Ly Line Blanketing At wavelengths shortward of the H I and He II Ly lines the

quasars continuum intensity is attenuated by the combined blanketing eect of many absorption

lines arising from intervening discrete systems As mentioned ab ove the relative strength of

He II versus H I continuum and line opacity dep ends on the intensity of the metagalactic ux at

Ryd compared to Ryd The recent detection of He II Ly absorption in the sp ectra of three

highz quasars can thus b e used as a diagnostic to ol of the ambient physical conditions at early

ep o chs The eective H I lineblanketing optical depth due to Poissondistributed absorb ers is

given by

max

N z

W dW z

ef f

W z

min

Paresce McKee Bowyer where N W z is the observed rest equivalent width dis

tribution The He II eective optical depth may b e obtained from equation using a curve of

growth analysis and a distribution of Doppler parameters b for H I and He II From the numerical

study of Madau Meiksin we derive for thermally broadened clouds b const km

with W W A N cm

min HI

HeI I

ef f thin

a t to accuracy over the range As our mo del background generates

thin

corresp onding to a softness parameter S J J at z

thin L thin

we conclude that a He II Ly line blanketing opacity greater than unity is to b e exp ected in

a universe photoionized by QSOs MiraldaEscude Madau Meiksin Giroux et al

Note that as the blanketing opacity is dominated by those lines which lie at the transition

HeI I

is in fact sensitive to the b etween the linear and the at part of the curve of growth

ef f

undetermined H I distribution at very low H I equivalent widths and increases if the hydrogen

and helium absorption lines have the same width turbulent broadening instead Madau

Meiksin Cowie et al

k The Redshift Evolution of the Ly Clouds As mentioned in x the number of Ly forest

lines seen by the HST at z is larger than predicted by extrap olating from the highz regime

Bahcall et al Morris et al It has b een suggested by Ikeuchi Turner that

this excess might b e related to the sharp drop in the ionizing photon ux exp ected for z in

a QSOdominated UV background We p oint out that a similar eect should b e observable at

z As shown in Figure the photoionization rate from QSOs is estimated to decrease

by a factor of b etween z and z If there is no comp ensating change in the evolution

of cloud prop erties this drop should pro duce an increase in the neutral hydrogen column and

therefore in the number of Ly clouds observed p er unit redshift A strong increase in the rate

of incidence of Ly clouds at large redshift has b een claimed by Williger et al who nd

dN dz z in the range z

l Photoionization Models for MetalLine Absorption Systems It has b een long recognized that

it is p ossible to mo del the ionization structure of the heavyelement QSO absorption systems and

discriminate b etween dierent background sp ectral shap es by lo oking at the line strengths of

various elements Chaee et al Bergeron Stasinska Steidel Sargent Mea

surements of the column densities of H I and several ionized sp ecies of C N and O in three

optically thin systems by Vogel Reimers have b een used in conjuction with photoion

ization mo dels to rule out starforming galaxies as the main source of the UV background The

dominance of highionization sp ecies can b e b est explained by an AGNtype sp ectral energy distri

bution with softness S However when combined with the presence of strong He I resonance

lines Reimers Vogel these observations app ear incompatible with photoionization equi

librium mo dels Giroux Sutherland Shull Using Si II Si IV and C IV lines Songaila

et al have recently estimated S to b e in the range b etween and at z

Here we only want to p oint out the inadequacy of photoionization mo dels which assume

a background p owerlaw ionizing sp ectrum As clearly shown in Figure the repro cessing of

LyC photons by intergalactic material introduces bumps wiggles and breaks at characteristic

wavelengths in the sp ectrum of the metagalactic ux the presence of which must b e taken into

account when mo deling metal systems The integrated background due to He II Ly line emission

at eV is clearly going to aect the abundance of eg O II ions We nd that the O II C III

ratio is particularly sensitive to the sp ectrum of the metagalactic ux at eV compared to

eV and hence to He II Ly recombination radiation see Fig The absorption line O II

together with C III has b een recently identied by Vogel Reimers in the sp ectrum

of the quasar HS

m A Case with q For z optical surveys are complete to a suciently faint

magnitude level to detect the QSOs that contribute the bulk of the ionizing background and

the computed metagalactic ux do es not dep end on the assumed cosmology However at larger

z this will no longer b e true as more and more quasars fall b elow the survey limit It is then

necessary to correct for the missing QSOs the selection function one adopts dep ends on the value

of q In the attempt to bracket the uncertainties on J z we have run a q background

mo del using the quasar LF tting parameters given in Pei for this cosmology In a at

universe the usual Gaussian t A z expz z S go o d to over the relevant

redshift range yields for the H I photoionization rate A sec B z

and S Similarly the parameters for the He II rate are A sec B

z and S Relative to the q case see fo otnote the at universe mo del

provides ab out less hydrogen and heliumionizing photons ab ove z

n A Case with Low Intergalactic Absorption As already mentioned in x a steep ening in the

N p owerlaw distribution of the Ly clouds at high columns suggested by several observations HI

may result in a smaller eective cosmic opacity and thus in an increased ionizing metagalactic

ux Meiksin Madau In order to quantify this eect we have run a q background

mo del using the same column density distribution of intervening absorb ers given in equation

but assuming no forest clouds b etween and cm The Gaussian t to the new

photoionization rates yields A sec B z and S for H I

and A sec B z and S for He II Relative to the

standard q case see fo otnote the low attenuation mo del provides ab out

more hydrogenionizing photons at z However the eect on the He II ionizing ux is

much larger as the lack of Ly forest clouds ab ove cm signicantly decreases the cosmic

opacity ab ove eV thereby increasing by ab out a factor of Such a mo del would b e

HeI I

characterized by a smaller He II over H I ratio and may therefore have diculties in accounting

for a signicant absorption trough at A Jakobsen et al

SUMMARY

In this pap er we have shown that b eside the attenuated direct radiation emitted from quasars

andor starforming galaxies the ionizing metagalactic ux will also have a signicant diuse

comp onent due to recombinations within the clumpy intergalactic gas In a photoionized universe

the following pro cesses will contribute to the diuse hydrogenionizing background eld from

Ly forest clouds and Lymanlimit systems

Recombinations to the ground state of H I and He II

He II Ly emission P S at eV

He II twophoton S S continuum emission

He II Balmer continuum emission at eV

In Case A a fraction of the excitedstate recombinations will p opulate the P state while

the remainder end up in the S state In the presence of a p owerlaw emissivity at a level

currently envisaged from QSOs the He II present in QSO absorptionline systems will eciently

degrade soft Xray Heionizing photons into ultraviolet Hionizing photons The addition of

He I recombination radiation would b e an improvement of this work although this should only

change our results at the very highest z redshift considered in this pap er We have mo deled

in detail the ionization state of intervening clouds and the propagation of ultraviolet radiation

through intergalactic space and shown that the universe is more opaque ab ove Ryd than previ

ously estimated We have also reassessed the contribution of the QSOs observed in optical surveys

to the UV extragalactic background and found that the attenuated direct quasar emission plus

the recombination radiation from the intergalactic gas can provide enough hydrogenionizing pho

tons to satisfy the proximity eect at large redshift The repro cessing of LyC background photons

by the intergalactic medium has b een shown to signicantly aect the intensity sp ectrum and

uctuations prop erties of the metagalactic ux

The recent discovery by Cowie et al and Tytler et al b of metals in the

Ly clouds has shown that the IGM at high redshift is contaminated by the pro duct of stars In

the context of our results these measurements raise two imp ortant issues which will b e discussed

in detail in a companion pap er Madau Haardt

As Ly clouds have large lling factors and contain a signicant fraction of the baryons in the universe they might trace the bulk of star formation o ccurring in galaxies at high redshift

Madau Shull have shown that the background intensity of photons at Ryd that ac

companies the pro duction of metals in the Ly clouds may b e signicant comparable with the

estimated contribution from QSOs unless a large fraction of the UV radiation emitted from stars

cannot escap e into the IGM or if most of the metals observed at z were pro duced at much

earlier ep o chs If this is true the signature of a stellar sp ectrum should app ear in several places

notably the He II GunnPeterson eect and the distribution of metal ionization states of the Ly

forest and Lymanlimit absorb ers

The new data could also imply the presence of a widespread distribution of dust in the

IGM Even a small amount of dust in the Ly forest and Lymanlimit systems might provide a

signicant source of absorption of ionizing radiation in the universe Further studies of this eect

would b e an improvement of the present work

We thank A Meiksin J MiraldaEscudeJ Ostriker Y Pei D Tytler and D Weinberg for

useful discussions and N Panagia for clarifying various issues concerning the physics of radiative

transfer This research was partially supp orted by the Directors Discretionary Research Fund at

STScI FH also acknowledges nancial supp ort by the Italian MURST and by the Swedish NFR Council

APPENDIX A

RECOMBINATION RATE COEFFICIENTS

In this App endix we provide some useful tting formulae to the hydrogen recombination rate

co ecients in units of cm s needed for our computations The recombination co ecient

n L

to the ground level of hydrogen can b e written as

T T

ln T

T T

This expression ts the results of Burgess within for T We have also used

the following tting formulae within for T to the Case B results of Pengelly

ln T

T T

ef f

ln T

T T

and

ln T

T T

ef f

ln T

T T

APPENDIX B

RECOMBINATION EMISSIVITY

The integration over the H I column density distribution of QSO absorptionline systems

app earing in the recombination emissivity term eq can b e p erformed analitically over

ranges of constant N N and for N using approximated formulae for the

HeI I HI HI

absorption and escap e probabilities Taking

B e

in the formulae for p w and the integral

em abs

0 0

K p N w N B dN

em HI abs HI HI

N z N

HI HI

and the integral over the column density distribution which app ears in the expression for the

cosmic eective optical depth eq can b e solved analytically The computations are simple

but lengthy Though the right hand side of eq B do es not have the right limit for large optical

depths it is a b etter approximation than for with an error for which is

lower than The typical error of the analytical approximations presented in this App endix

is of order a few p ercent with maximum values

a Eective Optical Depth The approximation given in eq B can b e used to calculate the

integral over the column density distribution which app ears in eq When or when L

and the integration is over ranges of costant ie for N N cm

L HI

we can write

ef f

N z arctan N r B

where the constant N and the exp onent are sp ecied according to eq We have dened

r with N When and the integration is over ranges of

HI L

N ie for N N we have

HI HI

ef f

p p

B r N z arctan N

dz r

where N Here r with taking into account only

max HeI I

the opacity due to H I and He I

b H I Recombination Continuum In computing the emissivity due to H I LyC radiation we

0 0

rst note that the contribution of photons with to the integral over app earing in eq

is negligible and that the emissivity at is small compared to the emissivity due

to He II LyC radiation at the same frequencies Thus we can evaluate eq B for and

to obtain

0 0

K N z r r arctan B N r

HI HI i

B i

for where N r Ryd r Ryd

HI B HeI I HeI I B

r r and

R r r r r r r

R r r r r r r B

R r r r r r r

It is easy to obtain a similar formula when In this case the second order multiplicity

of the ro ot leads to a dierent decomp osition of the integrand into integrable elementary

partial fractions We nd

0 0 0

r K N z

p p

R N R R

i HI

arctan arctan N r N r

p p

HI i HI

r r N r r r

i HI

where now

R r r r r

c H I Ly and TwoPhoton Continuum The integral in eq B can b e ulteriorly simplied

when p eg in the case of H I Ly and twophoton emission We obtain

0 0

r arctan K N z B N r

HI HI i

B i

where

R r r r r

The formulae B B and B ab ove are strictly valid for any integration range only when

h eV At higher photon energies they are only correct as long as N N Ryd as

M HI

clouds with larger columns are characterized by a larger He I to H I ratio The correct form of

w N for these thicker clouds is

abs HI

B w const e

abs

The integral over column in eq B can then b e split into two distinct terms and solved

d He II Recombination Continuum The evaluation of the emissivity due to He II recombination

continuum can b e simplied noting that the absorption of He II ionizing photons o ccurs at the

He II photosphere We also note that photons ab ove eV are eectively absorb ed only by

He II The integral in eq B for N N Ryd can then b e written as

HI HI

ef f

0 0

B p K

where p is given by eq The result for N N Ryd is analogous to eq B with

em HI HI

replaced by and evaluated at Ryd in r and r

HI HeI I

e He II Ly and TwoPhoton Continuum The arguments given ab ove also imply that in

the case of He II Ly and twophoton emission p The integral in eq B for N

em HI

N Ryd can then b e written as

ef f

0 0

K B

This b ecomes analogous to eq B for N N Ryd again with replaced by and

HI HI HI HeI I

evaluated at Ryd in r and r

APPENDIX C

NUMERICAL INTEGRATION OF THE EQUATION OF RADIATIVE TRANSFER

The key problem to address for an iterative solution of the radiative transfer equation is how

to achieve a fast numerical estimate of the eective optical depth in each iteration This

ef f

is a threedimensional function since at any observed frequency it dep ends on the observer o

and emission redshifts z and z Computing time can b e optimized noting that in the explicit

o em

form of eq these three variables app ear in the combination z z

ef f o o

A logarithmic redshift grid in the variable x z is therefore designed so that the ratio

R x x is constant for any j J We also set up a frequency grid longward of the H I and

j j

He II Lyman edges dened by

Z R i I C

i L

We make sure that the Ly frequency coincides with one of the sampling p oints in this grid by

prop erly adjusting the value of R ie by setting R where m is an integer A third

frequency grid provides coverage of the frequency range ab ove eV The next step consists of

computing the two sets of integrals which are needed to evaluate as well as d dz The

ef f ef f

rst of them

e C U i j dN

N z

where

N x x x x x C

ij HI HI i j HeI I i

is computed for i I and j i A second set of integrals

Li j dN e C

N z

where

N x x x x x C

ij HI HI i j HeI I i

is evaluated for i I and j J Note that U j L j and Li j longward of

the H I Lyman limit We can now calculate the eective optical depth z z T i j k

ef f o o em

j k over the frequencyredshiftredshift space Using the fact that the redshift distribution

of the clouds can b e expressed as a p owerlaw eq we nd the following recursive relation

T j k T j k R U k j k U k j k d k

T i j j R Li j Li j d i C

T i j k T i j j T i j k

where

C d x

Note that T i j j and T i j k for k i j longward of the H I Lyman limit

A computer co de named CUBA from Cosmic Ultraviolet BAckground has b een designed

based on the scheme sketched ab ove For each of the three frequency ranges CUBA computes

a number of integrals less that I J It is worth to p oint out that one should b e careful in

estimating the cloud emissivity as describ ed in App endix B at the photoionization threshold

frequencies Indeed the opacity for photons at observed frequency is zero for z

j o

z z while the volume emissivity is nonzero for z z The sp ectra shown

j o j o

in Figure have b een computed by CUBA over timefrequency grid p oints in a single

run Convergence part in was reached after iterations Each iteration to ok ab out

seconds of CPU on a Digital VAX Alpha

REFERENCES

Arnaud M Rothenug R AAS

Bahcall J N et al ApJS

Bahcall J N Jannuzi B T Schneider D P Hartig G F Bohlin R Junkkarinen V

ApJ L

Ba jtlik S Duncan R C Ostriker J P ApJ

Bechtold J ApJS

Bechtold J Weymann R J Lin Z Malkan M ApJ

Bechtold J Elvis M Fiore F Kuhn O Cutri R M McDowell J C Rieke M Siemigi

nowska A Wilkes B J AJ

Bergeron J Stasinska G AA

Black J H MNRAS

Bo chkarev N G Sunyaev R A Soviet Astron

Bowyer S ARAA

Boyle B J Ann NY Acad Sci

Boyle B J Shanks T Peterson B A MNRAS

Boyle B J Jones L R Shanks T MNRAS

Burgess A MmRAS

Chaee F H Foltz C B Bechtold J Weymann R J ApJ

Cheng FZ Danese L De Zotti G Franceschini A MNRAS

Comastri A Setti G Zamorani G Elvis M Giommi P Wilkes B J McDowell J C

ApJ

Corb elli E Salp eter E E ApJ

Cowie L L Songaila A Kim TS Hu E M AJ

Davidsen A et al preprint

Dekel A Rees M J Nature

Dove J B Shull J M ApJ

Efstathiou G MNRAS P

Esp ey B R ApJ L

Fall S M Pei Y C ApJ

Fardal M A Shull J M ApJ

Ferrara A Field G B ApJ

Francis P J Hewett P C Foltz C B Chaee F H Weymann R J Morris S L

ApJ

Fransson C Chevalier R ApJ

Giallongo E Cristiani S Fontana A Trevese D ApJ

Giallongo E Cristiani S Trevese D ApJ L

Giallongo E DOdorico S Fontana A McMahon R G Savaglio S Cristiani S Molaro

P Trevese D ApJ L

Giroux M L Fardal M Shull J M ApJ in press

Giroux M L Shapiro P R ApJS in press

Giroux M L Sutherland R S Shull J M ApJ L

Gunn J E Peterson B A ApJ

Hartwick F D A Schade D ARAA

Hu E M Kim TS Cowie L L Songaila A Rauch M AJ in press

Ikeuchi S Turner E L ApJ L

Irwin M McMahon R G Hazard C in ASP Conf Ser The Space Distribution

of Quasars ed D Crampton San Francisco ASP p

Jakobsen P Boksenberg A Deharveng J M Greeneld P Jedrzejewski R Paresce F

Nature

Ko o D C Kron R G ApJ

Kovner I Rees M J ApJ

Kulkarni V P Fall S M ApJ L

Kulkarni V P Huang K Green R F Bechtold J Welty D E York D G

submitted to MNRAS

Laor A Fiore F Elvis M Wilkes B J McDowell J C ApJ

Lu L Wolfe A M Turnshek D A ApJ

Madau P ApJ L

ApJ L

ApJ

Madau P Ghisellini G Fabian A C MNRAS L

Madau P Haardt F in preparation

Madau P Meiksin A ApJ L

Madau P Shull J M ApJ in press

Maloney P ApJ

Meiksin A ApJ

Meiksin A Madau P ApJ

MiraldaEscudeJ MNRAS

MiraldaEscudeJ Ostriker J P ApJ

ApJ

MiraldaEscudeJ Rees M J MNRAS

Mller P Jakobsen P AA

Morris S L Weymann R J Savage B D Gilliland R L ApJ L

Murdo ch H S Hunstead R W Pettini M Blades J C ApJ

OBrien P T Gondhalekar P M Wilson R MNRAS

Osmer P S ApJ

Osterbro ck D E Astrophysics of Gaseous Nebulae and Active Galactic Nuclei Mill Valley

University Science Bo oks

Ostriker J P Heisler J ApJ

Paresce F McKee C Bowyer S ApJ

Peebles P J E Principles of Physical Cosmology Princeton Princeton University Press

Pei Y C ApJ

Pengelly R M MNRAS

Petitjean P Webb J K Rauch M Carswell R F Lanzetta K MNRAS

Press W H Rybicki G B ApJ

Reilman R F Manson S T ApJS

Reimers D Vogel S AA L

Reisenegger A MiraldaEscudeJ ApJ

Sargent W L W Steidel C C Boksenberg A ApJS

Schmidt M Schneider D P Gunn J E in ASP Conf Ser The Space Distribution

of Quasars ed D Crampton San Francisco ASP p

Sciama D W Mo dern Cosmology and the Dark Matter Problem Cambridge Cambridge

University Press

Sciama D W ApJ L

Songaila A Cowie L L Lilly S J ApJ

Songaila A Hu E M Cowie L L Nature

Steidel C C ApJS

Steidel C C Sargent W L W ApJ

Steidel C C Sargent W L W ApJ L

StorrieLombardi L J McMahon R G Irwin M J Hazard C ApJ L

Turner T J Pounds K A MNRAS

Tytler D ApJ

Tytler D et al a in preparation

Tytler D Fan XM Burles S Cottrell L David C Kirkman D Zuo L b in QSO

Absorption Lines Pro c ESO Workshop ed J Bergeron G Meylan J Wampler

Heidelb erg Springer

Vogel S Reimers D AA L

Vogel S Reimers D AA in press

Vogel S N Weymann R Rauch M Hamilton T ApJ

Walker T P Steigman G Schramm D N Olive K A Kang H ApJ

Warren S J Hewett P C Osmer P S ApJ

Wilkes B J Elvis M ApJ

Williger G M Baldwin J A Carswell R F Co oke A J Hazard C Irwin M J McMahon

R G StorrieLombardi L J ApJ

Wright E L ApJ

Zamorani G et al ApJ

Zuo L MNRAS

Zuo L Phinney E S ApJ

Figure Captions

Figure Solid curves The He II H I ratio as a function of H I column density through a

slab illuminated on b oth sides The assumed total hydrogen gas density and temp erature are

cm and K resp ectively The three curves refer from top to b ottom to a meta

galactic ux at the Lyman edge of intensity and ergs cm s Hz sr

The sp ectral index is taken to b e Dashed curves Our steplike approximation see text

for details Dotted curves same ratio obtained by selfconsistently solving the thermal structure

of the clouds

Figure Solid curves Absorption probability e through an individual cloud as a

function of neutral hydrogen column for four dierent ionizing photon energies and

eV Dashed curves Same with our steplike approximation to the to the probability Dotted

curves Same assuming a constant He II H I value as derived in the optically thin limit All

curves are relative to the J ergs cm s Hz sr background mo del adopted

for Figure

Figure Upper panel Average temp erature of a cloud as a function of neutral hydrogen column

for the three background mo dels adopted for Figure solid line dotted line

and dashed line ergs cm s Hz sr The gas total hydrogen density is taken to

b e cm for N cm and cm for thicker systems Lower

panel Fractional p opulation density of the n H I level due to recombinations of photoionized

ions upp er curves collisional excitations of neutral atoms middle curves and recombinations

of collisionally ionized ions lower curves as a function of the neutral hydrogen column

Figure The QSO prop er volume emissivity at from top to b ottom the H I He I and

He II ionization edges as a function of redshift See text for details on the assumed QSO lu

minosity function and sp ectral energy distribution

Figure a The ionizing background from to A solid lines at ep o chs z and

computed in a q cosmology taking into account the absorption and repro cessing of

QSO radiation by discrete absorption systems The sp ectrum is compared to that arising from

a p erfectly transparent universe dotted lines and a purely absorbing intervening

ef f

medium dashed lines

Figure b Same as Figure a but for z and

Figure c Same as Figure a but for z and

Figure Upper panel Photoionization rates for H I solid line He I dashed line and He II dot

dashed line derived from our mo del background as a function of redshift Lower panel Ratios

b etween these rates and the photoionization rates computed in the limit of a purely absorbing

intervening medium We also plot again relative to the same quantity in the limit of a purely

absorbing medium the ratio b etween the O II and C III photoionization rates As the O II and

C III ionization p otentials are and eV resp ectively this quantity will b e particularly sen

sitive to He II Ly line and twophoton continuum recombination radiation from intergalactic

absorb ers

Figure Solid curve The He II H I ratio as a function of redshift for an optically thin gas in

ionization equilibrium with the ultraviolet background shown in Fig Dashed curve Same in

the limit of a purely absorbing medium