Mon. Not. R. Astron. Soc. 340, 473–484 (2003) The nature of the ionizing background at z ≈ 2.5–5 Aaron Sokasian, Tom Abel and Lars Hernquist Department of Astronomy, Harvard University, Cambridge, MA 02138, USA Accepted 2002 November 22. Received 2002 October 7; in original form 2002 June 25 ABSTRACT Using radiative transfer calculations and cosmological simulations of structure formation, we study constraints that can be placed on the nature of the cosmic ultraviolet (UV) background in the redshift interval 2.5 z 5. Our approach makes use of observational estimates of the opacities of hydrogen and singly ionized helium in the intergalactic medium during this epoch. In particular, we model the reionization of He II by sources of hard ultraviolet radiation, i.e. quasars, and infer values for our parametrization of this population from observational estimates of the opacity of the He II Lyman-α forest. Next, we estimate the photoionization rate of H I from these sources and find that their contribution to the ionizing background is insufficient to account for the measured opacity of the H I Lyman-α forest at a redshift z ∼ 3. This motivates us to include a soft, stellar component to the ionizing background to boost the hydrogen photoionization rate, but which has a negligible impact on the He II opacity. In order to simultaneously match observational estimates of the H I and He II opacities, we find that galaxies and quasars must contribute approximately equally to the ionizing back- ground in H I at z 3. Moreover, our analysis requires the stellar component to rise for z > 3 to compensate for the declining contribution from bright quasars at higher redshift. This inference is consistent with some observational and theoretical estimates of the evolution of the cosmic star formation rate. The increasing dominance of the stellar component towards high redshift leads to a progressive softening of the UV background, as suggested by observations of metal line absorption. In the absence of additional sources of ionizing radiation, such as mini-quasars or weak active galactic nuclei, our results, extrapolated to z > 5, suggest that hydrogen reionization at z ∼ 6 mostly probably occurred through the action of stellar radiation. Key words: radiative transfer – intergalactic medium – quasars: general – diffuse radiation. 1 INTRODUCTION Determining the relative contributions of different sources to the cosmic ultraviolet background is essential for understanding the evolution of the intergalactic medium (IGM). In particular, this metagalactic radiation field is believed to have reionized hydrogen at z ∼ 6 (e.g. Becker et al. 2001) and helium slightly later, although the epoch of helium reionization has yet to be determined observa- tionally (for a discussion, see e.g. Sokasian, Abel & Hernquist 2002, SAH hereafter). Evidence from measured temperature changes, op- tical depth variations, and evolution in the relative abundances of metal line absorbers strongly suggests that most intergalactic he- lium became fully ionized at redshifts close to ∼3.2 (e.g. Jakobsen et al. 1994; Davidsen, Kriss & Zheng 1996; Reimers et al. 1997; Songaila 1998; Ricotti, Gnedin & Shull 2000; Kriss et al. 2001; Bernardi et al. 2002; Theuns et al. 2002a,b and references therein). E-mail: [email protected] (AS); [email protected] (TA); lars@cfa. harvard.edu (LH) An important probe of the physical state of the intergalactic medium is provided by bright objects at great distances, such as quasars. For example, it is now believed that absorption by dif- fuse, cosmologically distributed gas is responsible for the hydrogen Lyman-α forest (e.g. Cen et al. 1994; Zhang, Anninos & Norman 1995; Hernquist et al. 1996). Similarly, Lyα absorption by He II along a line of sight to a distant quasar probes gas in the intervening IGM at even lower overdensities (Croft et al. 1997), characteristic of much of the baryonic matter in the Universe (e.g. Croft et al. 2001; Dav´ e et al. 2001). At a given redshift, the number and strengths of these spectral features is sensitive to the local density of absorbing atoms, which in turn depends on the gas density, cosmological pa- rameters and the intensity of the ionizing background. In fact, much of the interpretation of spectroscopic observations of high-redshift quasars relies strongly on this simple picture of the Lyman-α forest. Specifically, given a model for the formation of large-scale struc- ture, the number of lines detected in the Lyman-α forest as a function of redshift directly constrains the evolution and spectral properties of the radiation field. In a recent study, Kim, Cristiani & D’Odorico (2001) showed that the number of lines per unit redshift, d N /dz , C 2003 RAS Downloaded from https://academic.oup.com/mnras/article/340/2/473/1000718 by guest on 16 September 2020
Transcript
Mon. Not. R. Astron. Soc. 340, 473–484 (2003)
The nature of the ionizing background at z ≈ 2.5–5
Aaron Sokasian,� Tom Abel� and Lars Hernquist�Department of Astronomy, Harvard University, Cambridge, MA 02138, USA
Accepted 2002 November 22. Received 2002 October 7; in original form 2002 June 25
ABSTRACTUsing radiative transfer calculations and cosmological simulations of structure formation, westudy constraints that can be placed on the nature of the cosmic ultraviolet (UV) backgroundin the redshift interval 2.5 � z � 5. Our approach makes use of observational estimates ofthe opacities of hydrogen and singly ionized helium in the intergalactic medium during thisepoch. In particular, we model the reionization of He II by sources of hard ultraviolet radiation,i.e. quasars, and infer values for our parametrization of this population from observationalestimates of the opacity of the He II Lyman-α forest. Next, we estimate the photoionizationrate of H I from these sources and find that their contribution to the ionizing background isinsufficient to account for the measured opacity of the H I Lyman-α forest at a redshift z ∼ 3.This motivates us to include a soft, stellar component to the ionizing background to boost thehydrogen photoionization rate, but which has a negligible impact on the He II opacity.
In order to simultaneously match observational estimates of the H I and He II opacities, wefind that galaxies and quasars must contribute approximately equally to the ionizing back-ground in H I at z � 3. Moreover, our analysis requires the stellar component to rise forz > 3 to compensate for the declining contribution from bright quasars at higher redshift. Thisinference is consistent with some observational and theoretical estimates of the evolution of thecosmic star formation rate. The increasing dominance of the stellar component towards highredshift leads to a progressive softening of the UV background, as suggested by observationsof metal line absorption. In the absence of additional sources of ionizing radiation, such asmini-quasars or weak active galactic nuclei, our results, extrapolated to z > 5, suggest thathydrogen reionization at z ∼ 6 mostly probably occurred through the action of stellar radiation.
Key words: radiative transfer – intergalactic medium – quasars: general – diffuse radiation.
1 I N T RO D U C T I O N
Determining the relative contributions of different sources to thecosmic ultraviolet background is essential for understanding theevolution of the intergalactic medium (IGM). In particular, thismetagalactic radiation field is believed to have reionized hydrogenat z ∼ 6 (e.g. Becker et al. 2001) and helium slightly later, althoughthe epoch of helium reionization has yet to be determined observa-tionally (for a discussion, see e.g. Sokasian, Abel & Hernquist 2002,SAH hereafter). Evidence from measured temperature changes, op-tical depth variations, and evolution in the relative abundances ofmetal line absorbers strongly suggests that most intergalactic he-lium became fully ionized at redshifts close to ∼3.2 (e.g. Jakobsenet al. 1994; Davidsen, Kriss & Zheng 1996; Reimers et al. 1997;Songaila 1998; Ricotti, Gnedin & Shull 2000; Kriss et al. 2001;Bernardi et al. 2002; Theuns et al. 2002a,b and references therein).
An important probe of the physical state of the intergalacticmedium is provided by bright objects at great distances, such asquasars. For example, it is now believed that absorption by dif-fuse, cosmologically distributed gas is responsible for the hydrogenLyman-α forest (e.g. Cen et al. 1994; Zhang, Anninos & Norman1995; Hernquist et al. 1996). Similarly, Lyα absorption by He II
along a line of sight to a distant quasar probes gas in the interveningIGM at even lower overdensities (Croft et al. 1997), characteristic ofmuch of the baryonic matter in the Universe (e.g. Croft et al. 2001;Dave et al. 2001). At a given redshift, the number and strengths ofthese spectral features is sensitive to the local density of absorbingatoms, which in turn depends on the gas density, cosmological pa-rameters and the intensity of the ionizing background. In fact, muchof the interpretation of spectroscopic observations of high-redshiftquasars relies strongly on this simple picture of the Lyman-α forest.
Specifically, given a model for the formation of large-scale struc-ture, the number of lines detected in the Lyman-α forest as a functionof redshift directly constrains the evolution and spectral propertiesof the radiation field. In a recent study, Kim, Cristiani & D’Odorico(2001) showed that the number of lines per unit redshift, dN/dz,
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474 A. Sokasian, T. Abel and L. Hernquist
with column densities in the interval N H I = 1013.64−16 decreases con-tinuously from z ∼ 4 to 1.5 according to dN/dz ∝ (1 + z)2.19±0.27.Combined with the results of Weymann et al. (1998), who find amuch flatter distribution for dN/dz ∝ (1 + z)0.16±0.16 at z < 1, itappears that the line number density of the Lyα forest is well de-scribed by a double power law with a break at z ∼ 1. These resultssuggest that the evolution of the forest above z >1.5 is governedmainly by Hubble expansion and that there is little change in theionizing background until the break occurring at z ∼ 1.
The location of the observed break, however, is inconsistent withtheoretical predictions derived from numerical simulations. In par-ticular, studies of the Lyman-α forest carried out by Dave et al.(1999) and Machacek et al. (2000) predict a break in the doublepower law occurring near z ∼ 1.8. While these simulations haveprovided a successful general description of the evolution of theLyman-α forest, their apparent inability to match the location ofthe break indicates that the underlying assumptions regarding theform of the ultraviolet (UV) background may be incomplete. Morespecifically, these simulations assume a quasar- (quasi-stellar object,QSO-) type source population mainly responsible for producing theradiation field. Since the emissivity of quasars is known to fall offsteeply below ∼2, so would their contribution to the UV back-ground, thereby producing a break in dN/dz around this redshift.One way to reconcile the inconsistency between the simulations andobservations is to appeal to other types of sources to maintain theintensity of the UV background at a relatively high level until z ∼ 1.
Recently, Bianchi, Cristiani & Kim (2001) have explored the pos-sibility that galaxies might provide this additional contribution tothe radiation field. In particular, they derived the H I ionizing back-ground resulting from the integrated contribution of quasars andgalaxies, taking into account the opacity of the intervening IGM.The quasar emissivity was derived from fits to an empirical lumi-nosity function, while a stellar population synthesis model and acosmic star formation history from UV observations were used toestimate the galaxy emissivity. They found that the break at z ∼ 1implied by the Kim et al. (2001) analysis can be understood if thecontribution from galaxies is comparable to or larger than that ofquasars. This is consistent with other determinations of the galacticcomponent of the background (Giallongo, Fontana & Madau 1997;Devriendt et al. 1998; Shull et al. 1999; Steidel, Pettini & Adelberger2001). A significant contribution to the radiation field from galax-ies would imply a considerable softening of its spectrum comparedwith previous models that included only quasars as the dominantsource of the ionizing metagalactic flux.
In this paper, we shift the focus to higher redshifts to see whetherincluding an additional component from galaxies together with arealistic quasar model is capable of producing the required ioniz-ing intensity to match observational estimates in the redshift range2.5 < z < 5. Our method involves combining numerical and em-pirical results on the reionization of singly ionized helium (He II)by quasars as a tool for estimating the additional contribution fromgalaxies to the background that would be necessary to simultane-ously match results derived from the H I Lyα forest. In particular, weselect a quasar model based on the study conducted in our earlierpaper (SAH), where we applied a numerical method to study the3D reionization of He II by quasars. The adopted model is then usedto calculate the contribution to the H I background from quasarsonly. We can then estimate the required contribution from galaxiesto match the observed H I flux decrements measured by Rauch et al.(1997) in the redshift range 2.5 < z < 5. Consequently, this ap-proach allows us to make estimates of the amplitude and evolutionof this component.
This paper is organized as follows. In Sections 2–4 we describeour approach to calculating the emissivities of quasars, galaxies andrecombination radiation from the IGM, respectively. The procedurefor determining the ionizing background for hydrogen given theseemissivities is presented in Section 5. Results of our analysis arediscussed in Section 6 and conclusions are given in Section 7.
2 M E T H O D
In this section we describe our motivation for adopting a specificQSO model for the purpose of deriving the associated contribution tothe H I ionizing background. This component may be estimated froma QSO luminosity function (LF). However, this requires making anumber of assumptions concerning the emission from the sourcesand how easily this radiation can escape into the IGM. Instead, wewill constrain the quasar component of the ionizing background byappealing to numerical modelling of He II reionization along withobservational estimates of the evolution of the He II opacity.
To this end, we compile a list of quasar-type sources that wereselectively extracted from a cosmological simulation according to aQSO LF and a set of characteristic source parameters. This approachprovides us with a source list that is directly applicable as input fora cosmological radiative transfer simulation designed to examinethe He II reionization process (as in SAH). The advantage of suchan approach is that it provides us with a way of choosing the mostsuccessful model for our analysis based on a comparative studybetween the numerical and empirical results for the He II opacitiesmeasured in quasar spectra.
The numerical scheme used to calculate the 3D reionizationof He II by quasars is described in Sokasian, Abel & Hernquist(2001). In SAH, we used this approach to explore the parameterspace associated with the characteristics of the sources and stud-ied how they influenced global properties of the reionization pro-cess. Comparisons with observational results were made possibleby extracting synthetic spectra from the simulations. There our aimwas twofold: to develop an understanding of the sensitivity of thereionization process to source properties and to examine the pre-dictions of the different models in the light of recent observationalresults.
The cosmological simulation we used in SAH was based on asmoothed particle hydrodynamics (SPH) treatment, computed usingthe parallel TREESPH code GADGET developed by Springel, Yoshida& White (2001a). The particular cosmology we examine is a �-colddark matter (�CDM) model with b = 0.04, DM = 0.26, � =0.70, and h = 0.67 (see, e.g., Springel, White & Hernquist 2001b).The simulation uses 2243 SPH particles and 2243 dark matter par-ticles in a 67.0 Mpc h−1 comoving periodic box, resulting in massresolutions of 2.970 × 108 and 1.970 × 109 M� h−1 in the gas anddark matter components, respectively. The gas can cool radiativelyto high overdensity (e.g. Katz, Weinberg & Hernquist 1996) and isphotoionized by a diffuse radiation field that is assumed to be ofthe form advocated by (Haardt & Madau 1996, see also, Dave et al.1999). When sources are included in our treatment of helium reion-ization, the ionization state of the helium is recalculated, ignoringthe diffuse background that was included in the hydrodynamicalsimulation (see Sokasian et al. 2001 for details).
2.1 The QSO model
In SAH, QSO models were differentiated from one another basedon their respective values for the free parameters associated withthe source selection algorithm. The full details of our scheme are
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The nature of the ionizing background 475
described in Sections 2 and 3 of SAH. The basic procedure involvesidentifying dense clumps of gas in the cosmological simulationsthat represent plausible quasar sites, and adopting a prescription forselecting a subset of these objects as actual sources according to anempirical quasar luminosity function. In our analysis, we choose thedouble power-law form of the quasar luminosity function presentedby Boyle, Shanks & Peterson (1988) using the open-universe fittingformulae from Pei (1995) for the B band (4400-A rest wavelength)LF of observed quasars, with a rescaling of luminosities and vol-ume elements for our �CDM cosmology. Our selection algorithmrequires us to adopt an evolving mass-to-light ratio, ξ (z), whichscales with z as the break luminosity Lz inherent in the LF.
Once a source with mass, M, has been selected, it is assigned a B-band luminosity, LB = M/ξ (z) (in erg s−1). Along with an assumedspectral form, this luminosity is then used to compute the amountof ionizing flux that will be generated while the source is active. Forall sources, we assume a piecewise power-law form for the spectralenergy distribution (SED),
L(ν) ∝
ν−0.3 (2500 < λ < 4400 A);
ν−0.8 (1050 < λ < 2500 A);
ν−αQSO (λ < 1050 A),
(1)
where a choice of αQSO = 1.8 corresponds to the SED proposedby Madau, Haardt & Rees (1999) based on the rest-frame opticaland UV spectra of Francis et al. (1991) and Sargent, Steidel &Boksenberg (1989) and the extreme ultraviolet (EUV) spectra ofradio-quiet quasars (Zheng et al. 1998).
The entire selection process, including the assigning of intensities,introduces five free parameters associated with source characteris-tics. They are: (i) a universal source lifetime, T life; (ii) a minimummass, Mmin; (iii) a minimum luminosity at z = 0, Lmin,0; (iv) anangle specifying the beaming of the bi-polar radiation, β; and (v) atail-end spectral index, αQSO, in the regime λ < 1050 A. In SAH,we computed and analysed six models with different sets of valuesfor the free parameters. Below, we discuss the parameter choices formodels 1 and 5, which represent our fiducial andbest-fitting models,respectively. Table 1 lists the corresponding parameter choices.
In model 1, our fiducial case, we adopted a widely quoted valuefor Lmin,0 based on the results of Cheng et al. (1985), who showthat the LF of Seyfert galaxies (which is well correlated with that ofoptically selected quasars at MB = −23) exhibits some evidence oflevelling off by MB �−18.5 or Lmin � 3.91 × 109 L B,� at z = 0. Thetail-end spectral index parameter for this model was chosen to beα = 1.8, making the SED in this model identical to that advocated byMadau et al. (1999). In model 5, we examined the effect of reducingthe ionizing emissivity from the sources. This was accomplishedby increasing Lmin,0 by a factor of 6 and by steepening the tail-endspectral index to α = 1.9. In both models, the sources are assumed toradiate their flux isotropically (β = π) and to have a minimum masscut-off of Mmin = 1.80 × 1010 M�, which produces good agreementwith the B-band emissivity predicted by the LF and that provides arealistic mass function given the level of resolution of the simulationat this mass limit (see SAH for further details). The value of the mass
Table 1. Quasar source parameters.
Quasar T life Lmin,0 Mmin β αQSO
model (107 yr) (109 L B,�) (1010 M�) (rad)
1 2.0 3.91 1.8 π 1.85 2.0 23.5 1.8 π 1.9
cut-off is also consistent with the assumption that the sources aregalaxy-type objects acting as quasar hosts. It is important to pointout that in both models, a large fraction of the predicted luminosityat z >2 arises from quasars that have not yet been observed. Witha fit to the LF, which goes as φ(L) ∝ L−1.83 at the faint end, theemissivity,
∫φ(L , z)L dL (in erg s−1 Hz−1 cm−3), converges only
as L0.17, and it becomes apparent that a large portion of the totalemissivity will arise from this regime. In particular, Madau et al.(1999) used an LF very similar to that adopted here and calculatedthat approximately 90 per cent of the ionizing emissivity at z = 4 isproduced by quasars that have not been actually observed and areassumed to be present based on extrapolation from lower redshifts.
Fig. 1 shows the redshift evolution of the effective mean opti-cal depth for He II absorption derived from both models. The meanoptical depth is defined as τHei i ≡ − loge〈T 〉, where T is the trans-mittance extracted from the synthetic spectra from each model. Theaverage is performed over 500 lines of sight within 35 wavelengthbins of width � λ = 6.57 A in the observed frame. Hatched re-gions represent the optical depth derived from the simulations at the90 per cent confidence level with the dashed lines indicating meanvalues. For comparison, we also plot the opacities measured at dif-ferent redshifts in the spectra of Q 0302-003 (Heap et al. 2000), PKS1935-692 (Anderson et al. 1999, reported values come from Smetteet al. 2002 who performed an optimal reduction of the whole dataset) and HE 2347–4342 (Smette et al. 2002). It is important to pointout here that there is a variance among the smoothing lengths asso-ciated with the data points, indicated by the horizontal lines passingthrough each point. Given the fixed smoothing length assumed inthe opacity predictions, the presented comparison is not meant tolead to conclusions regarding the observed scatter, rather it is meantto provide a rough gauge as to how well a particular quasar modelis able to match the observed opacities that have been smoothedover comparable lengths. Having stated this point, it is clear fromthis figure that model 5 provides a much better match to the obser-vational results. This model also predicts full He II reionization byz � 3.4, a result consistent with the recent analysis conducted byTheuns et al. (2002b) who show clear evidence for a sudden de-crease in the effective optical depth in H I at the same redshift owingto the temperature increase associated with He II reionization. In theanalysis presented in this paper, we will adopt model 5 as our mostpromising quasar model, based on its predictions for the evolutionof the He II opacity. In Section 7, however, we summarize the relateddegeneracy associated with successful quasar models and discussthe resulting implications in the context of our study.
Given our QSO model, the emergent emissivity at each redshiftis calculated by summing up the B-band emissivity (in erg s−1 Hz−1
cm−3) contributions from each source and then using the universalSED to derive the following expression for λ < 1050 A:
εQSO(ν, z) � 0.423εQSO(νB, z)
(ν
ν1050
)−1.9
, (2)
where the numerical pre-factor accounts for the spectral mappingfrom the blue frequency, νB , to the frequency evaluated at λ =1050 A, ν1050. In the following section, we describe our prescriptionfor adding a component from galaxies and define an expression forits emissivity.
3 G A L A X I E S
Galaxies will represent the second class of sources that we allowto contribute to the H I ionizing background. We assign a spectralprofile of the form f (ν)∝ ν−αgal for λ < 912 A to these sources.
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476 A. Sokasian, T. Abel and L. Hernquist
2.8 3 3.2 3.4 3.6
0.01
0.1
1
10
Redshift
2.8 3 3.2 3.4 3.6
0.01
0.1
1
10
Redshift
Figure 1. Redshift evolution of the effective mean optical depth of He II absorption in models 1 and 5 from SAH. Hatched regions represent the optical depthderived from the simulations at the 90 per cent confidence level with the dashed lines indicating mean values. Observational results from quasars HE 2347-4342,PKS 1935-692 and Q 0302-003 are plotted for comparison. We adopt model 5 for our analysis in this paper.
In this paper we assume αgal = 5, which is widely regarded as arealistic value based on spectral studies of stellar atmospheres. Themuch steeper spectral slope relative to quasars means that galax-ies produce an insignificant number of He II ionizing photons forany reasonable luminosity model. This result justifies our approachof relying on an He II reionization simulation that contains onlyquasars. We emphasize that our conclusions are insensitive to thevalue adopted for αgal as long as galaxies contribute negligibly toHe II reionization.
The next step is to adopt a functional form describing the red-shift evolution of the emissivity of this component. Here we makethe assumption that the emissivity responsible for the ionizing UVbackground from this component is directly proportional to the in-herent star formation rate (SFR) within the galaxies. This is a fairpremise since the SFR is a direct tracer of the young OB stars thatare the dominant producers of H I ionizing photons in galaxies. Thisassumption allows us to utilize empirical measurements of the SFRat various redshifts as a basis for modelling the redshift evolutionof the emissivity within the redshift range in question. In the future,it will also be interesting to contrast this with an analysis of directtheoretical predictions of the SFR (e.g. Nagamine, Cen & Ostriker2000; Springel & Hernquist 2002b). For our present purposes it isconvenient to parametrize the comoving emergent emissivity fromgalaxies using the following expression:
εgal,c(ν, z) = εgal,c(νHI, 3) f (z)
(ν
νHI
)−αgal
, (3)
where εgal,c (νH I, 3) represents the comoving emissivity from galax-ies at the hydrogen ionization frequency νH I at z = 3 and f (z)is a dimensionless redshift-dependent function that is normalizedto unity at z = 3. The function f (z) can then serve to charac-terize the evolution of a particular galactic model while the valueof εgal,c (νH I, 3) provides an overall normalization.
In Fig. 2, we present extinction-corrected data points for the co-moving SFR in a flat � cosmology with parameters (m , �) =(0.37, 0.63) and h = 0.7, as provided by Nagamine et al. (2000).While not identical to the cosmology we employ, that of Nagamineet al. is very similar to ours and their summary of the observationsis thus adequate for our present purposes. As is apparent, the sparseand loosely constrained observations beyond a redshift z ∼ 2 hardlywarrant any attempt to fit the data as a means to derive f (z). Rather,we chose the simple form f (z) = 10m(z−3) and consider two valuesfor the slope, m, which represent the subject of recent debates as towhether the SFR continues to slightly rise or fall off beyond z ∼ 3(see, e.g., Madau et al. 1996; Steidel et al. 1999). These models areindicated by the bold short-dashed and long-dashed lines in Fig. 2,which we refer to as our galactic model 1 (M1: m = −0.260) andgalactic model 2 (M2: m = 0.135), respectively. Our choices for the
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The nature of the ionizing background 477
0.01
0.1
1
0 1 2 3 4 5
0.01
0.1
1
10
Madau et al.(1996)/Madau(1997) Pascarelle et al.(1998) Steidel et al.(1999) Treyer et al.(1998)
Connolly et al.(1997) Cowie et al.(1999) Lilly et al.(1996) Sawicki et al.(1997)
Figure 2. Extinction-corrected data points for the comoving SFR in a flat � cosmology with parameters (m , �) = (0.37, 0.63) and h = 0.7 as summarizedby Nagamine et al. (2000). Sources for the raw data are listed above according to their corresponding points. The bold short-dashed and long-dashed linesrepresent models 1 (M1) and 2 (M2) for our comoving redshift evolution factor f (z) (right axis), respectively. Note that f (z) is normalized to unity at z = 3for both models, in accord with our parametrization of the comoving galactic emissivity: εgal,c(ν,z) = εgal,c(νH I,3) f (z) (ν/νH I)−αgal .
slopes in these two cases are somewhat arbitrary, but they roughlybracket the observations and will, therefore, enable us to gauge theimpact of a rising or falling SFR at z > 3 in the context of the analysisconducted in this paper. In both of these models, we set εgal,c (νH I,3) = 3.6 × 10−49 erg s−1 Hz−1 cm−3, which is roughly 9 per centsmaller than the corresponding quasar contribution. We discuss themotivation behind this choice in Section 6 where we present resultsfor the photoionization rates.
4 R E C O M B I NAT I O N R A D I AT I O NF RO M T H E I G M
Recombination radiation from the ionized IGM can also provide asignificant contribution to the ionizing background. In particular,Haardt & Madau (1996) have shown that this component can pro-vide a fair fraction of the ionizing photons at redshifts near z ∼ 3.For helium, only recombinations to the ground level of He II are ableto contribute to the diffuse He II ionizing background. The heliumreionization simulation used in this paper includes an approximatetreatment to account for this component, which is directly incor-porated into the radiative transfer calculations (see Section 3.1.3 ofSokasian et al. 2001).
For hydrogen, the following processes contribute to the diffuseionizing background: (i) recombinations to the ground state of H I;(ii) He II Lyα emission (22P−→ 12S) at 40.8 eV; (iii) HeIII two-photon (22S −→12S) continuum emission; and (iv) He II Balmercontinuum emission at �13.6 eV. We ignore the contribution of He I
and He II recombination to the hydrogen-ionizing background. In thecase of the former, this is motivated by the relative smallness of thenHeI/nHeII and nHeI/nH I ratios encountered in typical intergalacticgas that has been photoionized by galaxies and quasars. For the
latter, the exclusion is motivated by the fact that the relative cross-section for absorption of photons with energies �54.4 eV is muchlarger for He II than H I. Coupled with the fact that the typical ratiofor nHe III/nH I encountered in the photoionized IGM is large, wefind that within the context of our analysis it is safe to make theapproximation that all the photons released from recombinations tothe ground state of He II are absorbed by nearby He II ions beforethey have a chance to ionize H I atoms.
For the purposes of this paper, we find that it is sufficient to useglobal number densities representative of the IGM to approximatethe corresponding emissivity from the relevant processes. In orderto properly account for the inhomogeneity of the IGM, we computeglobal volume-averaged clumping factors from the radiative transfergrid at each redshift, Cf (z), which we then incorporate into therelevant expressions. We discuss the details associated with thesecalculations in the following sections.
4.1 Radiative recombinations
Given the electron number density, ne, and the ion number densityni, the emissivity from direct recombinations to the n2 L level forhydrogen-like atoms with atomic number Z and ionization thresholdfrequency ν th from a photoionized gas that is in local thermodynamicequilibrium at temperature, T , can be computed using the Milnerelation (Osterbrock 1989), which yields
ε f b(ν) = 4π
c2
(h2
2πmekT
)3/2
× neni2n3
Z 3hν3σHI(ν/νth)e−h(ν−νth)/kT , (4)
where σ H I(ν/ν th) is the frequency-dependent hydrogen photoion-ization cross-section, h andk are the Planck and Boltzmann
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478 A. Sokasian, T. Abel and L. Hernquist
constants, respectively, me is the electron mass andc is the speedof light. Following the reasoning in Sokasian et al. (2001) we artifi-cially set all temperatures for the ionized gas to T = 2.0 × 104 K as acorrection to the SPH temperatures, which exclude the extra heatingintroduced by radiative transfer effects (see Abel & Haehnelt 1999).As a further approximation, we set σ H I(ν/ν th) = σ HI,o(ν/ν th)−3
where σ H I,o = 6.30 × 10−18 cm2 is the photoionization cross-sectionat the Lyman limit for H I (Osterbrock 1989).
To compute realistic values for the recombination emissivity,we require information regarding the clumping statistics associatedwith the IGM. In the context of our calculation, this will reduce toa global volume-averaged clumping factor for each redshift, Cf (z),which we can then use as a multiplicative prefactor in the above ex-pression. In order to obtain reliable values for the clumping factor ofthe IGM from our radiative transfer grid, it is necessary to discountcells harbouring collapsed objects with cold gas that are not part ofthe IGM, but which can significantly alter the clumping statistics.We achieve this by considering only cells below a specific overden-sity cut-off. The choice for the cut-off is somewhat arbitrary sincethe distinction between the IGM and collapsed objects is blurred.In this paper, we employ scatter plots showing the density versustemperature for the SPH particles (see, e.g., Dave et al. 1999 orSpringel & Hernquist 2002a) to estimate this cut-off. In particular,these plots show a bifurcation between the reservoir of underdensecool gas (i.e. the IGM) and shock-heated gas of moderate density orcold high-density gas in collapsed objects, which occurs somewherebetween an overdensity of 10–50, independent of redshift. In ouranalysis, we adopt a median value of 30 for our overdensity cut-offat all redshifts. This value results in an exclusion of only 0.14 percent of the volume and a global volume-averaged clumping factorof 3.88 at z = 3. Adopting an overdensity cut-off of 10 (50) wouldlead to a −32 per cent (+27 per cent) change in the clumping factorat the same redshift. Although only 0.14 per cent of the volume isexcluded at z = 3 with the adopted value for the cut-off, the cor-responding mass harboured in these excluded cells corresponds toroughly 11.5 per cent of the total mass in the simulation volume.For consistency, we exclude the corresponding collapsed mass ateach redshift when deriving ne and ni.
We note that our estimates for the clumping factor are consider-ably smaller than those of (as summarized by their fig. 16 Springel& Hernquist (2002b, as summarized by their fig. 16), because herewe exclude high-density regions from our estimate of Cf (z). This isappropriate because in this paper we are interested in the volume-averaged properties of the IGM at a redshift when the Universewas essentially optically thin to hydrogen-ionizing photons, whileSpringel & Hernquist (2002b) were concerned with the situationleading to hydrogen reionization when most of these photons wouldhave been absorbed in the vicinity of the sources that produced them.In any event, as indicated above, a modest increase in the overdensitythreshold would have a similarly modest impact on the clumpingfactor and the inferred emissivity from radiative recombination.
For simplicity, the latter densities are approximated by assumingcomplete ionization (ni/ntot = 1) within the photoionized regions.This approximation is certainly justified in comparison to other un-certainties present in our analysis. The relevant densities are thusgiven by
ne(z) = 2nHe,tot IHe III + nH,tot IH II(z) (5)
nH I(z) = nH,tot IH II(z) (6)
nHe III(z) = nHe,tot IHe III(z), (7)
where ni,tot represents the total number density of species i averagedover the entire simulation box (excluding the collapsed mass as de-fined above) and I i(z) is the fraction of the volume that has becomeionized in species i by redshift z. In the case of He III, I He III(z) isextracted directly from the helium simulation results. For H II, weapproximate I H II(z) as the ratio of the cumulative number of H I ion-izing photons that were released by quasars and galaxies by redshiftz to the total number of hydrogen atoms present in the IGM (whichagain excludes the collapsed-mass fraction). Obviously, we restrictthe maximum value of I H II(z) to unity. It is also important to pointout that we limit contributions to the H I ionizing pool only to pho-tons with frequencies in the range νH I < ν < νHe II under the earlierpremise that photons with frequencies ν > νHe II are immediatelyabsorbed in the IGM by the He II ions.
4.2 Ly α emission
Recombinations into He II which end up populating the 22P levelare converted to Lyα 304-A photons that are capable of ionizingH I. These photons resonantly scatter, and therefore diffuse onlyslowly away from their point of origin before they are absorbed. Asa result, the immediate fate of a He II Lyα photon mainly dependsupon the competition between H I continuum absorption and thelocal opacity at the He II Lyα frequency να (the effect of dust ondestroying Lyα radiation is negligible Haardt & Madau 1996). Forthe purposes of our analysis, it is sufficient to assume that all Lyα
photons eventually contribute to the H I ionizing background eitherby scattering enough times to encounter an H I atom in the cloudof origin or eventually redshifting below the line frequency andescaping into the IGM. Which process comes first depends on thevelocity gradient versus the absorption coefficient of H I at the He II
Lyα frequency. In either case, assuming all the energy is releasedexactly at the line frequency, the emissivity associated with Lyα lineradiation can be written as
εLyα(ν) = hνδ(ν − να)n22P A22P,12S, (8)
where A22P,12S is the transition probability for 22P −→12S transi-tions in He II and n22P is the number density of He II ions in the22P state. In our case, the transition probability cancels out in theabove expression since we derive n22P by assuming the equilibriumcondition,
0.75αBnenHe III = n22P A22P,12S, (9)
where the use of the Case B recombination coefficient, αB, implicitlyassumes that all n >2 recombinations will eventually cascade downand populate the n = 2 level. For this paper, we use the fitting formulaprovided by Hui & Gnedin (1997) and arrive at αB = 9.089 × 10−13
cm3s−1 for T = 2.0 × 104 K. The factor of 0.75 represents thefraction of recombinations to the excited states that will eventuallypopulate the 22P state based on the degeneracy of available statesin the P level (the remainder end up in the 22S state). This assumesthat the rate of transitions between the S and P states is small, whichis valid at the typical densities associated with the IGM.
4.3 Two-photon continuum
The radiative decay 22S −→ 12S in He II is almost entirely causedby two-photon emission and is also capable of contributing to thediffuse H I ionizing background. The emissivity for this process canbe expressed as
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The nature of the ionizing background 479
where A22S,12S(ν/να) is the frequency-dependent transition proba-bility, which again cancels out via the assumption of the equilibriumcondition,
0.25αBnenHeIIh = n22S A22S,12S, (11)
adopted under the premise mentioned in the preceding section.
5 C O M P U T I N G T H E I O N I Z I N G BAC K G RO U N D
Given the emissivities of each component, we can proceed to the cal-culation of the resulting ionizing background intensity and the corre-sponding photoionization rate. The cosmological radiative transferequation for diffuse radiation can be expressed as (see, e.g., Peebles1993),(
∂
∂t− ν
a
a
∂
∂ν
)J = −3
a
aJ − cκ J + c
4πε, (12)
where a is the scalefactor, κ is the continuum absorption coefficientper unit length along the line of sight and ε is the proper space-averaged volume emissivity, which in our case can be expressed asthe sum ε(ν, z) = εQSO (ν, z) + εgal(ν, z) + εIGM(ν, z) where εIGM(ν,z) = ε fb(ν, z) + εLyα(ν, z) + ε2ph(ν, z). The mean specific intensityof the background, J, at the observed frequency νo, as seen by anobserver at redshift zo is then,
J (νo, zo) = 1
4π
∫ ∞
zo
dl
dz
(1 + zo)3
(1 + z)3ε(ν, z)e−τeff dz, (13)
where ν = νo(1 + z)/(1 + zo) and dl/dz is the proper line elementin our �CDM cosmology,
dl
dz= c
Ho(1 + z)[0.3(1 + z)3 + 0.7]−1/2, (14)
where c is the speed of light and H o is the present-day Hubbleparameter. The remaining exponential term accounts for absorptionoccurring through dz owing to discrete absorption systems, whichis parametrized by a mean optical depth τ eff which, for a Poisson-distribution of clouds, can be expressed as
τeff(νo, zo, z) =∫ z
zo
dz′∫ ∞
0
∂2 Ncol
∂Ncol,HI∂z′ (1 − e−τ )dNcol,HI (15)
(Paresce, McKee & Bowyer 1980), where ∂2 N col/∂N col,H I ∂z′ is theredshift and column density (N col) distribution of absorbers along aline of sight and τ is the Lyman continuum optical depth through anindividual cloud. The usual form for the redshift and column densitydistribution of absorber lines is given as
∂2 Ncol
∂Ncol,H I∂z= Ao N−3/2
col,H I(1 + z)γ (16)
with Ao and γ acting as fitting parameters. For our analysis here, wechoose to fit the above function exactly as in Madau et al. (1999),where a single redshift exponent, γ = 2, is assumed for the entirerange in column densities with a normalization value of Ao = 4.0 ×107. At z = 3, the adopted values produce roughly the same numberof Lyman limit systems and lines above N col,H I = 1013.77 cm−2 asobserved by Stengler-Larrea et al. (1995) and estimated by Kimet al. (1997), respectively. With a single power law describing thedistribution of absorbers along a line of sight, the effective opticaldepth can now be expressed as an analytic function of redshift andfrequency (i.e. equation 6 in Madau et al. 1999),
τeff(νo, zo, z) = 4
3√
πσH I,o No(νo/νH I)−3/2(1 + zo)3/2
× [(1 + z)3/2 − (1 + zo)3/2
]. (17)
It is important to note that the expression above for the mean opacitydoes not explicitly include the contribution of helium to the atten-uation. While the opacity caused by He I ionizations at 504 A isnegligible in the case of a background composed in part by hardsources such as quasars (Haardt & Madau 1996), He II absorptionmay still contribute a measurable level of opacity for the populationof photons with frequencies ν > νHe II (produced almost exclusivelyby quasars). However, as we shall show below, any additional atten-uation owing to helium absorption has a very small effect on the H I
photoionization rate and does not affect the results of this analysis;we therefore omit this component.
Given the background intensity J (ν, z), the global photoioniza-tion rate can then be calculated according to
�H I(zs) =∫ ∞
νH I
4πJ (ν, z)
hνσH I,o(ν/νH I)
−3 dν, (18)
where we have an adopted a frequency dependence of (ν/νH I)−3 forthe photoionization cross-section. Here we note that for the quasarmodel employed in this paper, an integration up to only νHe II wouldhave decreased the photoionization rate by roughly 0.2 per cent at z= 3.0. This thus represents the maximum decrement any additionalattenuation from helium absorption may cause and is small enoughfor us to continue with its omission.
6 R E S U LT S A N D D I S C U S S I O N
In Fig. 3, we plot the resulting background intensities at λ =912 A for three cases: (i) quasars alone, (ii) quasars combined withan M1 galactic component and (iii) quasars combined with an M2galactic component. In both galactic models, we set εgal,c(νH I, 3) =3.4 × 10−49erg s−1 Hz−1 cm−3, which is roughly equal to thecorresponding contribution from the quasars at the same redshift.The associated recombination component from the ionized IGM isalso included in all three cases. The values plotted for the quasarcontribution reflect an average over 20 unique realizations associ-ated with the quasar section algorithm. The shaded region refers tothe Lyman limit background estimated from the proximity effect(Giallongo et al. 1996; Cooke, Espey & Carswell 1997; Scott et al.2000). Here we see that all three cases produce total intensities thatappear to be consistent with measurements, although it is obviousthat observational uncertainties are quite large. Nevertheless, it isarguable that the larger intensities associated with the inclusion ofthe galactic component M2 appear to offer the best agreement withthe measurements at z � 3.8.
To make comparisons with observed measurements of the H I fluxdecrement, we first compute mean photoionization rates at each red-shift using equation (18), which we then apply uniformly on to thedensity field. After computing new H I ionization fractions every-where, we extract synthetic spectra in the range 2.8 � z � 4.3 (seeSection 4.5 of SAH for the details regarding extraction of syntheticspectra). Flux decrement results are then computed over smoothinglengths corresponding to roughly 100 A in the observed frame. Itis important to point out that in computing the line profiles we usea minimum gas temperature of 2.0 × 104 K as a correction to theSPH temperatures that exclude the extra heating introduced by ra-diative transfer effects (see Abel & Haehnelt 1999). In Fig. 4 weplot the resulting evolution in the H I flux decrement as a functionof redshift averaged over 200 lines of sight in each of the threecases. The dotted line in each plot represents the mean values, whilethe hatched regions represent the range of values corresponding tothe 90 per cent confidence level from the 200 realizations. The two
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480 A. Sokasian, T. Abel and L. Hernquist
a
b
Redshift
c
Figure 3. Background intensity at λ = 912 A resulting from (a) quasarsonly, (b) quasars and galactic model M1 and (c) quasars and galactic modelM2. Shown are the separate contributions from quasars (dotted), galaxies(dashed), and the ionized IGM (dashed-dotted). The shaded region refers tothe Lyman limit background estimated from the proximity effect (Giallongoet al. 1996; Cooke et al. 1997; Scott et al. 2000).
data points are measurements of the H I flux decrement over the indi-cated redshift ranges (horizontal lines) given by Rauch et al. (1997),who measured the H I Lyα forest absorption from the interveninggas in seven high-resolution QSO spectra obtained with the Kecktelescope. The values of these data points are independent of cos-mology and are therefore directly comparable to our results. Here wecan clearly see that quasars alone, although successful in matchingz � 3 measurements, fail to produce the observed rates in the range3.5 < z < 4.5 by a large factor. The inclusion of the M1 galac-tic component, the contribution of which tapers off with redshift,does not appear to do any better. Only by including an M2 galacticcomponent do we obtain a reasonable match to the observations.
These conclusions have potential implications for our understand-ing of recent observations indicating that hydrogen in the Universewas reionized by redshift z ∼ 6 (e.g. Becker et al. 2001). In par-
0
0.2
0.4
0.6
0.8
1 a
0
0.2
0.4
0.6
0.8
1 b
2.5 3 3.5 4 4.5
0
0.2
0.4
0.6
0.8
1
Redshift
c
Figure 4. Hydrogen flux decrement extracted from synthetic spectra as afunction of redshift resulting from (a) quasars only, (b) quasars and galacticmodel M1 and (c) quasars and galactic model M2. The dotted line in eachplot represents the mean values, while the hatched regions represent therange of values corresponding to the 90 per cent confidence level from 200lines of sight (see the text for further details). The two data points representmeasurements of the decrement over the indicated redshift ranges (horizontallines) obtained by Rauch et al. (1997) and are independent of cosmology.
ticular, from Fig. 3(c), we see that the background intensity at thehydrogen Lyman limit predicted by our model becomes increas-ingly dominated by stars for z > 4. This suggests that unless thereare other sources of ionizing radiation present in the real Universethat have been neglected in our analysis, such as mini-quasars orweak active galactic nuclei, hydrogen reionization at z ∼ 6 musthave been driven mainly by stellar radiation.
The fact that our choice for εgal,c(νH I, 3) results in a reasonablematch to the decrement measurements in the latter case is not coinci-dental as it was specifically chosen for this purpose. To investigatewhether this value is reasonable in the context of correspondingmeasurements of the emissivity of galaxies at longer wavelengths
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The nature of the ionizing background 481
2 3 4 5
Redshift
Model M2
Figure 5. Comoving emissivity at λ = 1500 A from our galactic model M2 as a function of redshift based on the two values of the observed flux ratio fromSteidel et al. (2001) (dotted line) and Giallongo et al. (2002) (solid line). Also plotted are the relevant observations of the UV emissivity at λ = 1500 A fromSteidel et al. (1999), Pascarelle et al. (1998), Madau et al. (1996) and Madau et al. (1998) adjusted for a flat � cosmology: (m , �) = (0.37, 0.63) and h =0.7 (extinction-corrected data obtained from Nagamine et al. 2000).
(λ � 1500 A), we will need to first adopt a realistic ratio between theflux densities at 1500 and 900 A, f [1500]/ f [900]. After analysing acomposite spectrum of 29 Lyman break galaxies (LBGs) at z ∼ 3.4,Steidel et al. (2001) derived an observed ratio of f [1500]/ f [900]� 17.7. However, it should be emphasized that the LBGs com-prising their composite spectrum were drawn from the bluest quar-tile of intrinsic far-UV colours and may be exhibiting larger thanaverage 900-A continuum emission. In fact, more recently, Gial-longo et al. (2002) examined the spectra of two galaxies at z = 2.96and 3.32, which exhibited little or no flux at λ = 900 A and werenot included in the latter subsample. They derived a lower limit off [1500]/ f [900] > 71 which is roughly four times the value derivedby Steidel et al. (2001).
In Fig. 5 we plot the resulting comoving emissivity at λ = 1500 Afrom our galactic model M2 as a function of redshift based on thetwo values of the observed flux ratio from Steidel et al. (2001) andGiallongo et al. (2002). Also plotted are the relevant observationsof the UV emissivity at λ = 1500 A from Steidel et al. (1999),Pascarelle, Lanzetta & Fernandez-Soto (1998), Madau et al. (1996)and Madau, Pozzetti & Dickinson (1998) adjusted for a flat �CDMcosmology similar to ours. With the exception of the Madau et al.data point at z = 4, it appears as if the adopted galactic model M2offers good agreement with the observations if the typical value forf [1500]/ f [900] lies somewhere between the values advocated bySteidel et al. (2001) and Giallongo et al. (2002). This behaviouris consistent with the recent theoretical predictions of Springel &Hernquist (2002b), who find that the SFR in high-resolution simu-
lations, which include hydrodynamics and a multiphase model forstar-forming gas (Springel & Hernquist 2002c) rises from z = 0 outto z ≈ 5.4 before declining at even higher redshifts.1
Our value of εgal,c(νH I, 3) also appears to be consistent with therecent suggestion that LBGs emit a comparable number of ionizingphotons to QSOs at z ∼ 3 (Steidel et al. 2001), although we remindthe reader that the adopted QSO model (model 5 from SAH) in thispaper has less emission than the ‘standard’ QSO model (model 1from SAH), as is required in order to match the He II opacity mea-surements (see Table 1, Fig. 1). More specifically, in the case thatcombines the adopted QSO model and galactic model M2 we findJ gal(νH I)/J QSO(νH I) � 0.77 at z � 3, whereas the same galacticcomponent combined with the standard QSO model would produceJ gal(νH I)/J QSO (νH I) � 0.47 at the same redshift. It is interestingto point out that the standard QSO model not only proves to be un-successful in matching the helium opacity measurements but wouldalso correspond to an unsuccessful model in the context of the hy-drogen flux decrement measurements by Rauch et al. (1997). Inparticular, without any additional contribution from a galactic com-ponent, the resulting decrement from the standard QSO model would
1 We note that the analysis performed by Springel & Hernquist (2002b)ignored metal cooling, which in principle, could boost the star formationrate at late times relative to earlier ones. A preliminary analysis of this effectby Hernquist & Springel (2002) suggests that the consequences of metalcooling in this context will be modest and will shift the peak in the cosmicstar formation rate to only slightly lower redshifts, z ≈ 5.
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482 A. Sokasian, T. Abel and L. Hernquist
severely underpredict the 2.5 < z < 3.5 measurement. Furthermore,any attempt to include a reasonable contribution from a galacticcomponent, such as in model M2, would inevitably exacerbate thisdisagreement. It therefore appears as if the standard QSO modelas defined by the parameters in Table 1 for model 1 in conjunctionwith the Pei (1995) B-band fit to the luminosity function presentedby Boyle et al. (1988) overpredicts the ionizing emissivity in bothhydrogen and helium at z � 3. This conclusion is consistent withthe preliminary analysis of the density of faint QSOs carried out bySteidel et al. (1999) in which their LBG survey indicated that thestandard extrapolated QSO luminosity function may slightly over-predict the QSO contribution to J (νH I) at z ∼ 3.
If we are to accept the form and fit to the QSO luminosity func-tion, then the incompatibility between the standard QSO model andobservations suggests that either the extrapolation to the faint endor the adopted SED or a combination of both is misrepresented.The extrapolation to faint galaxies is parametrized by the minimumluminosity allowed for the quasars, Lmin. The widely adopted pro-cedure for estimating Lmin is based on the idea that present-daySeyfert galaxies are counterparts to high-redshift quasars and thatthe faintest luminosities associated with Type I Seyferts should berepresentative of the minimum luminosities of quasars once a lumi-nosity evolution model has been factored in. A logical choice forthe evolution model, which we subsequently adopted in this paper,is based on the observed evolution of the break luminosity in theLF of quasars. However, as the failure of the standard model sug-gests, adopting the faintest values for Lmin,0 from Seyfert galaxiesappears to produce too many faint QSOs and is partly responsiblefor the apparent overproduction of ionizing photons in both H I andHe II. The implication then could be that the minimum luminosityevolves separately from the apparent evolution in the break lumi-nosity. A possible motivation for such a scenario could be providedby theories of hierarchical structure formation that are more effi-cient in inhibiting the formation of the smallest supermassive blackholes and/or the accretion rate on to them. Delving into the theoryrelated to such speculations is beyond the scope of this paper; in-stead we refer the reader the work of Haiman & Menou (2000) andKauffmann & Haehnelt (2000), which provide a good review of thesubject.
With respect to the form for the SED, it is important to point outthat the EUV spectral indices observed in quasar spectra exhibit asignificant amount of scatter (see, e.g., Zheng et al. 1998; Telferet al. 2002), which makes it difficult to define a universal indexrepresentative of all quasars. This dispersion is apparent in Fig. 6where we show the combined distribution of EUV indices for radio-quiet and radio-loud QSOs from Telfer et al. (2002) (data kindlyprovided by G. Kriss). The indices in this distribution are definedby f (ν) ∝ ν−α between 500 and 1200 A, which is comparable to ourdefinition for αQSO. It is clear from this plot and the correspondingstatistics that it is difficult to represent this quantity by a singlevalue appropriate for all quasars. Within this context, our choice ofαQSO = 1.9 seems entirely plausible. We must note, however, thatthe situation would be much more convoluted if there existed somecorrelation between the spectral index and the intrinsic luminosityof the source, as suggested by the strong luminosity evolution in theX-ray and optical wavebands of quasars (see, e.g., Boyle et al. 1994).Recent investigations into this matter (Brinkmann, Yuan & Siebert1997; Yuan, Siebert & Brinkmann 1998) have revealed that theobserved α-luminosity correlation can be attributed to the dispersionin the observational data points and is thus not an underlying physicalproperty of the sources.
0 2 4
0
20
40
60
1.74
1.80
0.40 2.40
Mean
Median
90%Confid.
Figure 6. Quasar EUV spectral index distribution compiled from the datain Telfer et al. (2002). The distribution includes results for subsamples ofradio-quiet and radio-loud QSOs (see the text). The indices are defined asf (ν) ∝ ν−α between 500 and 1200 A. The mean, median, and rms deviation(σ ) of the distribution are indicated.
6.1 Other QSO models
We have shown that a QSO model with a larger value for the mini-mum luminosity at z = 0 and a slightly steeper tail-end slope than thestandard model, can simultaneously provide a fair match to the ob-served helium opacity and hydrogen flux decrement measurementswhen one includes a realistic soft contribution from galaxies. It isimportant to point out, however, that the specific examples chosenin this paper represent a degenerate class of models that can alsobe combined to produce similar results. More specifically, in thecase of quasars, the parameters Lmin,0 and αQSO can both be ad-justed to deliver the required ionizing emissivity in helium whilechanging the resulting ionizing emissivity in hydrogen. This wouldtherefore create a large set of different galactic models that wouldalso be fairly successful at reproducing the observations. In Fig. 7,we demonstrate this degeneracy by plotting the absolute value of thedifference between the logarithms of the computed hydrogen pho-toionization rate (�H I) and the required hydrogen photoionizationrate that would match the decrement measurements at z = 3 (�HI,m =8.71 × 10−13 s−1) and z = 4 (�HI,m = 5.68 × 10−13 s−1) measuredby Rauch et al. (1997) as a function of quasar parameters Lmin,0
and αQSO at redshifts 3 and 4. The labelled contours in each panelshow the percentage difference from the corresponding measuredvalue. To tie in the correlation with the helium observations, we alsoplot in each panel the curve (dashed line) in the Lmin,0–αQSO planethat produces the same number of He II ionizing photons as quasarmodel 5 from SAH. The success of the latter model in matchingthe He II opacity measurements and the strong correlation betweenthe number of ionizing photons released and the resulting opacities,effectively restricts us to consider models only in the vicinity of thiscurve. The plots make it apparent that a pure quasar model based onthe adopted LF, while capable of producing agreement at z = 3, fails
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The nature of the ionizing background 483
Figure 7. Grey-scale plots showing the absolute value of the difference between the logarithms of the computed hydrogen photoionization rate, �H I, andthe required hydrogen photoionization rate, �HI,m , which would match the decrement measurement by Rauch et al. (1997) as a function of quasar parametersLmin,0 and αQSO at redshifts 3 and 4. The top panels show the results for the case with only quasars, while the bottom panels show the results for quasars withM2 galaxies included. The labelled contours in each panel show the percentage difference from the corresponding required value. Also plotted in each panel isthe curve (dashed line) in the Lmin,0–αQSO plane that would produce the same number of He II ionizing photons as quasar model 5 from SAH.
by a large factor at z = 4 for any reasonable range in Lmin,0 and αQSO.On the other hand, as the bottom panels indicate, a quasar modelthat is supplemented with an additional soft component, which inthis case is galactic model M2, is able to significantly reconcilethis failure. It is important to point out to the reader that Fig. 7 isbased on relatively sparse data in both H I and He II (seven and fourquasar spectra, respectively) and that more observations, especiallyat high redshift, are necessary to place definitive constraints on themodels.
7 C O N C L U S I O N
In this paper, we have utilized observations in both H I and He II toestimate the contributions to the UV background from quasars andgalaxies. The fact that only quasars are capable of producing radia-tion hard enough to ionize He II has allowed us to select a particularquasar model based solely on the He II opacity measurements, inde-pendent of the galactic model. Including measurements of the fluxdecrement in H I between 2.5 � z � 4.5 then enables us to study
predictions based on two hotly debated models for the galactic con-tribution.
We find that a quasar model with less emission than the widelyquoted ‘standard’ model in conjunction with a galactic model witha slightly rising SFR that contributes a comparable amount of H I
ionizing radiation at z � 3, is necessary to achieve good agreementwith all relevant observations. Such a composite model makes itmuch easier to understand how the intergalactic medium can remainhighly ionized at redshifts z > 4 where the contribution from brightquasars falls off significantly. The particular choice for the galacticcomponent in the above model is further bolstered by the fact thatthe galactic model appears to match observations for the emissivityof LBGs between 2.5 � z � 4.5 as it appears that the adoptedgalactic model M2 offers good agreement with the observations ifthe typical value for f [1500]/ f [900] lies somewhere between thevalues measured by Steidel et al. (2001) and Giallongo et al. (2002).Moreover, the rise in the SFR beyond z ∼ 3 is in accord with someobservations and theoretical predictions (for a discussion, see e.g.Springel & Hernquist 2002b).
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484 A. Sokasian, T. Abel and L. Hernquist
We have also shown that there exists a degenerate class of quasarmodels that are equally successful at matching the He II observa-tions while producing a large dispersion in their H I contributions.However, the particular QSO model adopted in this paper has theinteresting property of being characterized by plausible values forLmin and αs, while naturally requiring an additional galactic com-ponent that seems to be consistent with observations of both itsamplitude and shape.
While the scenario presented in this paper appears promising, wemust emphasize that it is based on relatively sparse data. Futureobservations gathered with the Sloan Digital Sky Survey (SDSS)will allow us to reduce the uncertainties associated with quasarmodels at high redshifts. Coupled with future measurements of theproximity effect and the evolution of the intensity ratio of metallines, it should soon be possible to place even tighter constraintson the relative contributions from quasars and galaxies to the UVbackground at z ∼ 2.5–5.
AC K N OW L E D G M E N T S
We thank Kentaro Nagamine for providing us with data related to theSFRs of LBGs in a convenient and useful form and providing usefulcomments regarding the nature of galactic sources. We also thankVolker Springel for comments on the manuscript, Martin Elvis forinformative discussions concerning the specifics of quasar SEDs inthe context of our analysis, Kurt Adelberger for useful discussionsconcerning the UV emissivity of LBGs, and George Rybicki fordiscussions related to radiative processes. AS thanks Daniel Harveyfor many constructive discussions related to this study. This workwas supported in part by NSF grants ACI96-19019, AST-9803137and PHY 9507695.
R E F E R E N C E S
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