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 o redshift z o Z 1 d z o z z ef f o o dz z e J z o o dz z z o where z z