The Spectral Slope and Escape Fraction of Bright Quasars at z∼3.8 : the Contribution to the Cosmic UV Background
Stefano Cristiani, Luisa Maria Serrano, Fabio Fontanot, Rajesh R. Koothrappali, Eros Vanzella, Pierluigi Monaco
aa r X i v : . [ a s t r o - ph . C O ] J u l Mon. Not. R. Astron. Soc. , 000–000 (0000) Printed 21 July 2016 (MN L A TEX style file v2.2)
The Spectral Slope and Escape Fraction of Bright Quasars at z ∼ . : the Contribution to the Cosmic UV Background Stefano Cristiani , , Luisa Maria Serrano , , Fabio Fontanot , Rajesh R. Koothrappali ,Eros Vanzella , Pierluigi Monaco INAF-Osservatorio Astronomico di Trieste, Via Tiepolo 11, I-34143 Trieste, Italy INFN-National Institute for Nuclear Physics, via Valerio 2, I-34127 Trieste, Italy Dipartimento di Fisica, Sezione di Astronomia, University of Trieste, via G.B. Tiepolo 11, I-34143, Trieste, Italy INAF-Osservatorio Astronomico di Bologna, via Ranzani 1, I-40127, Bologna, Italyemail: [email protected]
Accepted ... Received Apr 1, 2016
ABSTRACT
We use a sample of 1669 QSOs ( r < . , . < z < . ) from the BOSS survey tostudy the intrinsic shape of their continuum and the Lyman continuum photon escape frac-tion (f esc , q ), estimated as the ratio between the observed flux and the expected intrinsic flux(corrected for the intergalactic medium absorption) in the wavelength range 865-885 ˚A rest-frame. Modelling the intrinsic QSO continuum shape with a power-law, F λ ∝ λ − γ , we find amedian γ = 1 . (with a dispersion of . , no dependence on the redshift and a mild intrinsicluminosity dependence) and a mean f esc , q = 0 . (independent of the QSO luminosity and/orredshift). The f esc , q distribution shows a peak around zero and a long tail of higher values,with a resulting dispersion of . . If we assume for the QSO continuum a double power-lawshape (also compatible with the data) with a break located at λ br = 1000 ˚A and a softening ∆ γ = 0 . at wavelengths shorter than λ br , the mean f esc , q rises to = 0 . .Combining our γ and f esc , q estimates with the observed evolution of the AGN luminosityfunction (LF) we compute the AGN contribution to the UV ionizing background (UVB) as afunction of redshift. AGN brighter than one tenth of the characteristic luminosity of the LF areable to produce most of it up z ∼ , if the present sample is representative of their properties.At higher redshifts a contribution of the galaxy population is required. Assuming an escapefraction of Lyman continuum photons from galaxies between . and . , independent ofthe galaxy luminosity and/or redshift, a remarkably good fit to the observational UVB data upto z ∼ is obtained. At lower redshift the extrapolation of our empirical estimate agrees wellwith recent UVB observations, dispelling the so-called Photon Underproduction Crisis. Key words: cosmology: observation - early Universe - quasars: general - galaxies: active -galaxies: evolution
After more than thirty-five years (Sargent et al. 1980) the issueof the sources driving the reionization of the hydrogen in theUniverse and keeping it ionized afterward does not appear to besettled. It is commonplace that galaxies should be able to pro-duce the bulk of the UV emissivity at high redshift (see, for ex-ample, Robertson et al. 2015), but the AGN population is alsoproposed as a relevant or dominant contributor (Giallongo et al.2015, Madau & Haardt 2015, see also Fontanot et al. 2012 andHaardt & Salvaterra 2015, for different views).A direct measurement of the 1-4 Ryd photons escaping thevarious types of sources is unpractical at z > ∼ . , due to the re-duced mean free path of these photons in the intergalactic medium(IGM). At lower redshift direct observations of galaxies, after ac- counting for the statistical contamination of interlopers, have ingeneral provided upper limits in the fraction of ionizing photons,produced by young stars, that are able to escape to the IGM (f esc , g ,see Vanzella et al. 2012). These limits tend to be significantly lowerthan the ∼ required at z ≃ to re-ionize the Universe withgalaxies only (Bouwens et al. 2011; Haardt & Madau 2012), and anincreasing f esc , g with decreasing luminosity (possibly with a steepfaint-end of the LF) has been invoked to circumvent this shortcom-ing (Fontanot et al. 2014). The corresponding f esc , q for QSOs istypically assumed to be about .In this paper we aim to obtain a precise measurement ofthe QSO contribution to the cosmic UV background in the range . < z < . , where the QSO LF is well determined and the IGMtransmission not too low. Our strategy is first to estimate the intrin- c (cid:13) Cristiani et al.
Figure 1.
Redshift distribution of the QSOs in the present sample shownin bins of ∆ z = 0 . . z corr on the x-axis indicates the redshift estimatedaccording to the procedure described in Sect. 2 sic QSO continuum shape up to 4 Ryd (Sect. 3), then we comparethe fitted SED with the observed flux (corrected for the effect of theIGM absorption with the model of Inoue et al. (2014)), and finallywe compute the fraction of UV photons below the Lyman Limit es-caping to the IGM (f esc , q , Sect. 4). We take advantage of the largesamples of QSOs that can be extracted from the Sloan Digital SkySurvey (SDSS) to investigate possible correlations with the lumi-nosity and redshift. Finally, we combine this information with theknowledge of the QSO LF to synthesize the global production ofionizing photons from QSOs at various redshifts and compare itwith measurements of the UVB obtained from observations of theIGM (Sect. 5). In this way it is possible to assess how much roomis left/needed for the contribution of galaxies at the various cosmicepochs and where preferably to look for it. The Baryon Oscillation Spectroscopic Survey (BOSS,Dawson et al. (2013)) provides a large database of quasarspectra. The quasar target selection used in BOSS is summarizedin Ross et al. (2012), and combines various targeting methodsdescribed in Y`eche et al. (2010); Kirkpatrick et al. (2011), andBovy et al. (2011).We have extracted from the eleventh Data Release (DR11) thequasars in the redshift range . < z . with magnitudesbrighter than r = 20 . . The lower limit in the redshift intervalis due to a known selection effet in the BOSS survey outlined byProchaska et al. (2009): the QSOs found in the range < z < . are selected with a bias against having ( u − g ) < . , which trans-lates into a tendency to select sightlines with strong Lyman limit ab-sorption. On the other hand the analysis by Prochaska et al. (2009)shows that beyond z em = 3 . very few QSOs are predicted tohave such a blue ( u − g ) < . color, removing the possibilityof a bias. We are therefore confident that the sample used can beconsidered statistically complete and representative of the bright( M V < ∼ − . ) QSO population. In particular, for the discussionto follow, we note that BAL objects are included in the presentsample. The upper limit in the redshift range of the present sample, z = 4 . , is due to the requirement to have the observed spectrareaching the rest-frame wavelength of ˚A in order to have a Table 1.
Regions used for the continuum fittingRegion start endrest-frame wavelength( ˚A)1 1990 20202 1690 17003 1440 14654 1322 13295 1284 1291 sufficiently extended domain to estimate the intrinsic QSO contin-uum shape.The spectral energy distribution (SED) of each quasar hasbeen adjusted using a linear multiplicative slope (in magnitude) inorder to match the g , r , i , z magnitudes from the SDSS photometriccatalog and then corrected for galactic extinction according to themaps of Schlafly & Finkbeiner (2011) and the average Milky Wayextinction curve of Cardelli et al. (1989).All the spectra have been visually inspected and their systemicredshifts calculated. We have adopted the offsets of − km/sand +177 km/s, respectively assigned to the CIV 1549 and SiIV1398 lines (Tytler & Fan 1992) to derive the systemic redshift. Asmall fraction ( < ∼ ) of spectra showing problems in terms ofthe observed S/N ratio have been excluded from the subsequentanalysis. The resulting sample consists of 1669 objects and the as-sociated redshift distribution is shown in Fig. 1. The number ofQSOs declines from about 300 per ∆ z = 0 . bin in the interval . < z < . to about 100 at z ≃ , following the general trendof the BOSS Survey. The distribution of the recomputed redshiftsshows a small systematic difference with respect to the SDSS data, < ∆ z > = < z corr − z SDSS > = − . , with a dispersion of . . In order to estimate the QSO production of UV ionizing photonsit is necessary to model their intrinsic spectral shape. Customarilythis is achieved by fitting a power-law, F λ ∝ λ − γ , in the regionredward of the Lyman- α emission, selecting windows free of emis-sion lines and extrapolating it in the region blueward of the Lyman- α (e.g. Fig. 2). Previous works by Zheng et al. (1997); Telfer et al.(2002); Shull et al. (2012); Stevans et al. (2014) at relatively lowredshift ( z < ∼ . ), where the IGM absorption is minimized, haveidentified a break in the spectral distribution with a softening of theslope at wavelengths shorter than λ br ∼ ˚A.In the following we have chosen to fit the continuum spectrumof each quasar both with a single and with a broken power-law. Inboth cases five windows, listed in Tab. 1, have been used for thefit as emission-line-free regions. In the case of the broken power-law fit we have imposed a flattening in the spectral slope bluewardof ˚A of ∆ γ = 0 . with respect to the power-law at longerwavelengths, as reported by Stevans et al. (2014). Pixels affectedby absorption lines have been iteratively rejected on the basis ofa three sigma k-clipping. We have checked that the results are notsensitive to the particular choice of the windows.As a check of the goodness of the assumptions, we havestacked all the spectra after dividing them by the continuum slopeand by the expected mean transmission of the IGM according to c (cid:13) , 000–000 SOs contribution to the UVB Figure 2.
Two illustrative cases for the estimate of the continuum power-law and the escape fraction. The upper panels show a QSO of redshift 3.815 witha f esc , q ∼ , the lower panels a QSO of redshift 3.726 with a f esc , q ∼ . Left column : the two spectra are plotted in black. Note that the region bluewardof the Lyman- α has been divided by the average transmission of the IGM estimated (see Sect. 4) according to Inoue et al. (2014) in order to show where theaverage continuum should be located. The green line shows the uncertainty of the flux. The red line shows the fitted power-law continuum. Right column : thetwo observed spectra are plotted in black, the expected position of the power-law continuum multiplied by the average IGM transmission is in red and theuncertainty of the observed flux in green. The cyan portion of the spectrum is the region where the escape fraction of the UV photons produced by the QSOhas been estimated. the computation by Inoue et al. (2014). For the IGM transmissionwe have used the numerical tables kindly provided by the authors,which are slightly more accurate than the analytical approximation,especially in the region between the Lyman- β and the Lyman limit.The result is shown in Fig. 3. The continuum normalized averageflux, corrected by the IGM absorption, in a true-continuum windowof the Lyman- α forest ( < λ < , see Shull et al. 2012and Stevans et al. 2014) turns out to be . ± . (see Fig. 3).It is also remarkable to see the correspondence between the emis-sion bumps observed in the Lyman forest by us and by Shull et al.(2012) and Stevans et al. (2014), in particular around ˚A (FeIII) and ˚A(NII, He II).We have then analyzed the ensemble properties of the quasarsin our sample. The median (mean) spectral index of the populationfor the single power-law case (and for the region with λ > ˚Afor the broken power-law) is γ = 1 . ( . ), with a dispersionof . , computed as half of the difference between the 84.13 and15.87 percentiles (Fig. 5). A KS test on the two samples above and below redshift z = 3 . does not show any significant difference inthe two distributions (see also Fig. 4 and 5). We have checked thatselecting QSOs with . < z < . (and r < . ) we wouldobtain a value of γ significantly lower than the one we measure inthe range . < z . , confirming the above mentioned biasfound by Prochaska et al. (2009). The dependence of the spectralindex on the SDSS r magnitude has also been analyzed by split-ting the sample in two halves: r . and r > . . Thecorresponding median spectral indices turn out to be γ = 1 . and γ = 1 . , respectively, with fainter objects generally characterizedby “redder” spectral indices. A KS test rejects with a high signifi-cance the hypothesis that the two subsamples have the same distri-bution function. We interpret this effect as a property of the SEDsof the QSOs analyzed, rather than a bias introduced by the fittingprocedure, since a corresponding difference is present in the mea-sured colors of the QSOs: the average ( r − i ) is . for objectsbrighter than r = 19 . and . for the fainter ones.The median (mean) value of the spectral index for the full sam- c (cid:13) , 000–000 Cristiani et al.
Figure 3.
Stacked spectrum of the 1669 BOSS QSOs, after dividing eachQSO spectrum by the average IGM transmission and by the estimated in-dividual power-law continuum. Upper panel: − ˚A rest-framewavelength range. Lower panel: − ˚A wavelength range. In thelower panel the lower black line corresponds to a single power-law contin-uum, while the upper blue line to the broken power-law fitting (see text).The region − ˚A restframe, where the escape fraction has beenmeasured (see Sect. 4), is shown in red. Figure 4.
Normalized probability distributions of the spectral index γ forQSOs in the redshift interval . < z . (blue dashed line) and .
Distribution of the spectral indices of the continuum power-lawof the QSO spectra as a function of the redshift. The median values in theintervals . < z . , . < z . , are shown as continuous redsegments. or with the broken power-law, convolved with the average trans-mission of the IGM at the given redshift (Inoue et al. 2014). Theinterval − ˚A has been chosen since its is expected to be a“true continuum” window (see Fig.6 in Shull et al. 2012 and Fig.5in Stevans et al. 2014). Besides, it represents a convenient compro-mise: on the one hand at wavelengths close to the Lyman edge themeasurement can be affected by errors in the determination of theemission redshift of the QSO, on the other hand the IGM transmis-sion is progressively decreasing at shorter and shorter wavelengthswith a consequent increase of the measurement uncertainty. Theresulting value of the f esc , q has been checked to be largely inde-pendent of the specific choice of the limits of the interval.The estimated f esc , q is an effective escape fraction, i.e. is ex-pected to include the escape fraction of the UV photons from theQSO host galaxy and all the extra absorption due to clustered neu-tral hydrogen in the vicinity of the QSO that is not accounted forin the model of Inoue et al. (2014) which applies to the average,intervening IGM.The average escape fraction in the redshift interval . < z < . , measured on the ensemble of 1669 objects of our sample turnsout to be f esc , q = 0 . and f esc , q = 0 . in the case of the single andbroken power-law respectively. As shown in Fig. 6 and 7, a ratherlarge dispersion is observed, . , computed as half of the differencebetween the . and . percentiles, in a kind of bimodal dis-tribution with a narrower peak around the value zero and a largerdispersion around the value . In each object f esc , q is computed bycomparing the observed flux shortward of the Lyman edge and theexpected flux on the basis of an average correction for the IGMabsorption. It is not surprising therefore that for some objects ourmeasured f esc , q turns out to be larger than one - besides the mea-surement errors - due to lines of sight with an actual transmissionlarger than the average estimate from the Inoue et al. (2014) com-putation.Fig. 6 shows the escape fraction measured in the QSO spec-tra as a function of the redshift. In the intervals . < z . and . < z . the result is similar: f esc , q = 0 . andf esc , q = 0 . , respectively for the single power-law, f esc , q = 0 . and f esc , q = 0 . , respectively, for the broken power-law.Splitting the sample in two halves, brighter and fainter than r = 19 . does not show any significant difference in the meanf esc , q and a KS test cannot reject the hypothesis that the parent c (cid:13) , 000–000 SOs contribution to the UVB Figure 6.
Escape fraction measured in the QSO spectra as a function of theredshift. The mean values in the intervals . < z . and . < z . are shown as continuous red segments, with the dispersion estimated ashalf of the difference between the 84.15 and 15.87 percentiles. Figure 7.
Normalized probability distributions of the escape fraction f esc , q for QSOs in the redshift interval . < z . . The black continuousline shows the full sample. The red dashed line corresponds to objects with r . , while the blue dashed line refers to objects with r > . . population is the same for the two groups, both in the case of asingle and of a broken power-law.No significant correlation of f esc , q is therefore found as afunction neither of the redshift (see Fig. 6), nor of the magnitude(Fig. 7).We have also checked that no dependence of f esc , q is presentas a function of the spectral index γ : dividing sample in two halves,the average f esc , q of QSOs with γ > . is . , while f esc , q = 0 . for QSOs with γ < . , for the single power-law, . and . for the broken power-law. We use the results of the previous section to estimate the QSO con-tribution to the observed photon volume emissivity (Fig. 8, upperpanel) and photoionization rate (lower panel), adopting the sameformalism as in Fontanot et al. (2014).We consider functional forms for the AGN LF Φ( L, z ) as afunction of luminosity and redshift and we use them to compute the rate of emitted ionizing photons per unit comoving volume as afunction of the redshift: ˙ N ion ( z ) = Z ν up ν H ρ ν h p ν dν (1) ρ ν = Z ∞ L min f esc ( L, z ) Φ(
L, z ) L ν ( L ) dL (2)where ν H is the frequency corresponding to ˚A and ν up = 4 ν H (i.e. we consider that more energetic photons will be mainly ab-sorbed by He II atoms), while ρ ν is the monochromatic comovingluminosity density brighter than L min . The redshift evolution of thecorresponding photoionization rate Γ is computed solving the fol-lowing equations (see e.g. Haardt & Madau (2012) and referencestherein): Γ( z ) = 4 π Z ν up ν H J ( ν, z ) h p ν σ HI ( ν ) dν (3)where σ HI ( ν ) is the absorbing cross-section for neutral hydrogenand J ( ν, z ) is the background intensity: J ( ν, z ) = c/ π Z ∞ z ǫ ν ( z ) e − τ e (1 + z ) (1 + z ) | dtdz | dz (4)where ν = ν z z , ǫ ν ( z ) represents the proper volume emissiv-ity (equivalent to ρ ν in the comoving frame) and τ e ( ν, z, z ) theeffective opacity between z and z : τ e ( ν, z, z ) = Z z z dz Z ∞ dN HI f ( N HI , z )(1 − e − τ c ( ν ) ) (5)where τ c is the continuum optical depth through an individual ab-sorber at frequency ν = ν (1+ z )(1+ z ) and f ( N HI , z ) is the bivari-ate distribution of absorbers. For the latter quantity, we considerdifferent functional forms available in the literature, namely thoseproposed by Haardt & Madau (2012), Becker & Bolton (2013) andInoue et al. (2014). In the following, we adopt Becker & Bolton(2013) as a reference, because we want to compare our predictionsfor the photon volume emissivity and photoionization rate in partic-ular with their dataset, which covers a redshift range encompassingour sample. We consider two different estimates for the AGN-LF,namely the luminosity function at 145 nm (see Fig. 9) defined in theframework of the Hopkins et al. (2007) bolometric LF and the HardX-ray LF from Fiore et al. (2012). We use the resulting space den-sities in Eq. 2 and 4, we then integrate Eq.1 and 3 using the medianspectral index from Sect. 3 and using the corresponding L as anormalization. In Fig. 8, the solid line represents predictions corre-sponding to the Hopkins et al. (2007) 145 nm LF at z < (andits extrapolation at higher redshifts), while dashed line refers tothe Fiore et al. (2012) LF ( z > . ), assuming a single power-lawSED. We adopt as L min one tenth of the characteristic luminosityof the LF (i.e. L min = 0 . L ⋆ ). Cowie et al. (2009) have shown, infact, that most of the ionizing flux is produced by broad-line QSOsstraddling the break luminosity. Although our formulation allowsfor a luminosity and redshift dependent escape fraction, we assumea fixed f esc , q = 0 . , consistently with the results in Sect.4.In Fig. 8, we use hatched and grey areas to highlight the ef-fect of two of the main uncertainties involved in the estimate ofthe photon volume emissivity and photoionization rate. In partic-ular, the hatched orange area represents the variation correspond-ing to different functional forms for the column density distribution(Haardt & Madau 2012; Becker & Bolton 2013; Inoue et al. 2014),while the grey area refers to the difference between the single and c (cid:13) , 000–000 Cristiani et al.
Figure 8.
Upper panel : predicted photon volume emissivity. Observed datafrom Wyithe & Bolton (2011) (asterisks) and Becker & Bolton (2013) (di-amonds).
Lower Panel : predicted hydrogen photoionization rate. Observa-tions from Becker & Bolton (2013, diamonds), Calverley et al. (2011, pen-tagons), Shull et al. (2015, stars) and Gaikwad et al. (2016, empty circles).In both panels, solid and dashed lines (in blue) represent the predictionscorresponding to the AGN-LF from Hopkins et al. (2007) and Fiore et al.(2012), respectively, integrated up to . L ⋆ assuming a single power-lawquasar SED. The grey area extends down to the double power-law results,to show the deriving systematic uncertainty, while the hatched orange arearepresents the uncertainty relative to the shape of the assumed column den-sity distribution (see text). The short thick segments (in green) in the red-shift range . < z < , show the contribution of QSOs brighter than M UV ∼ − . roughly corresponding to the absolute magnitude limitin the present sample, assuming the Hopkins et al. (2007) bolometric LF.The dot-dashed red lines show the total UV background and photoioniza-tion rate adding to the blue solid line a contribution of the galaxy populationestimated assuming an f esc , g = 5 . (see text for more details). the broken power-law assumption for the AGN spectral shape. Tothe zeroth order, adopting a single power-law with a 0.75 f esc , q ora broken power-law with a 0.82 f esc , q is degenerate from the pointof view of the UV background: the assumption of the SED type iscompensated by the resulting f esc , q and the same flux is predictedat the Lyman Limit. The difference between the two predictionsarises from the extrapolation of the flux up to 4 Ryd with differentslopes.Our estimates are then compared with a collectionof observational results for the photon volume emissivity(Wyithe & Bolton 2011; Becker & Bolton 2013) and pho-toionization rate (Calverley et al. 2011; Adams et al. 2011;Becker & Bolton 2013; Shull et al. 2015; Gaikwad et al. 2016). Itis worth stressing that our estimates do not exactly correspond tothe predictions of the Haardt & Madau (2012) model. The maindifference lies in the assumption by Haardt & Madau (2012) ofa QSO emissivity based on the Hopkins et al. (2007) LF with acontribution of relatively bright ( M B < − ) QSOs only. Here,we are considering objects down to . L ⋆ , which implies a fainter(and variable with redshift) limiting magnitude. Figure 9.
QSO Luminosity function at 1450 ˚A. Solid blue lines refer tothe analytical fits from Hopkins et al. (2007) and are compared to observa-tional estimates from Wolf et al. (2003, stars) , Richards et al. (2006, opensquares), Fontanot et al. (2007, filled circles) and Siana et al. (2008, opendiamonds).
Our predictions are consistent with a number of observationalconstraints, and in particular with the data at < z < ∼ fromBecker & Bolton (2013): this suggests both that sources brighterthan . L ⋆ account for the observed ionizing photons and, con-versely, that objects fainter than . L ⋆ should provide a negligiblecontribution to the ionizing photon budget. It will be therefore ofinterest to test with future observations the f esc , q for low-luminosityQSOs to check whether smaller values with respect to the presentsample are measured. There is already an indication from the obser-vations of Cowie et al. (2009) that this is indeed the case. The thickgreen segments in Fig. 8 spanning the redshift range of the presentsample represent the integration of the Hopkins et al. (2007) LF upto M UV ∼ − . , roughly corresponding to the absolute magni-tude limit in our QSO sample, in the range . < z < ∼ . . Theylie ∼ . dex below the solid lines, highlighting that the QSOs inthe present sample account for less than one sixth of the full back-ground and, again, observations of fainter objects would be advis-able in order to avoid extrapolations. The prediction obtained withthe luminosity function by Fiore et al. (2012) highlights the effectof the uncertainties in the LF estimate and the need for a betterdetermination of this distribution at high-z.We confirm that the QSO cannot dominate the ionizing pho-tons production at z > : in fact none of our predictions repro-duces the observational data, typically underestimating them, thushighlighting the need for additional ionizing sources at these red-shifts (e.g. galaxies, dot-dashed red lines in Fig. 8). The contri-bution from galaxies has been computed from the LF of LymanBreak Galaxies (Bouwens et al. 2011) using eq. 1-5, assuming theredshift-depedent spectral emissivity as in Haardt & Madau (2012),the column density distribution as in Becker & Bolton (2013) anda constant value for the f esc , g (i.e. independent of either the lumi-nosity or the redshift). The corresponding LFs have been integrated c (cid:13) , 000–000 SOs contribution to the UVB up to a limiting redshift-dependent faint magnitude computed as inFontanot et al. (2014, their Fig. 3).If we limit the analysis to the photon volume emissivity shownin the upper panel of Fig. 8 and fix the contribution of the QSO pop-ulation to the above determined bona fide amount (shown by theblue solid line), then in the case of a single power-law quasar SEDthe best fit to the observational data (with a χ = 2 . for six pointsand one free parameter) turns out to be f esc , g = 6 . +6 . − . % , with theconfidence interval estimated for ∆ χ = 1 . If we apply the sameanalysis to the photoionization rate (lower panel of Fig. 8) we ob-tain a best fit f esc , g = 5 . +3 . − . % , with a χ = 9 . for nine pointsand one free parameter). In the case of a double power-law quasarSED the best fit to the upper panel (with a χ = 2 . for six pointsand one free parameter) turns out to be f esc , g = 7 . +6 . − . % , andfor the lower panel we obtain a best fit f esc , g = 6 . +2 . − . % , with a χ = 8 . . It is interesting to note that all these values are fully com-patible with the limits obtained by various authors with direct mea-surements of the f esc , g (e.g. Vanzella et al. (2012); Bouwens et al.(2015); Reddy et al. (2016)).Finally, at z < our estimates agree with the most recent de-terminations for the HI photoionization rate by Shull et al. (2015)and Gaikwad et al. (2016), based on HST-COS data (Danforth et al.2016). Both groups find values of the photionization rate sig-nificantly smaller than the results presented in Kollmeier et al.(2014), giving origin to the so-called Photon Underproduction Cri-sis (PUC). Our computation shows that relatively bright QSOs atlow redshift (i.e. brighter than . L ⋆ ) may account for the totalphoton budget required by observations. A similar result has beenobtained by Khaire & Srianand (2015). In this paper, we use a sample of 1669 QSOs with r . inthe redshift range . < z < . , taken from the BOSS sample,to estimate the contribution of type I QSOs to the UV background.Each spectrum in the sample has been recalibrated to match the ob-served SDSS photometry, and the corresponding systemic redshifthas been recomputed, taking into account the velocity shifts asso-ciated with the SiIV and
CIV emission lines. For each QSO, wefit the intrinsic continuum spectrum, by means of five windows rel-atively free of emission lines, both with a single, F λ ∝ λ − γ , andwith a broken power-law with a break located at λ br = 1000 ˚Arest-frame.In order to constrain the Lyman continuum photon escapefraction, f esc , q in our sample, we consider the spectral range − ˚A rest frame, close to the Lyman limit. We computef esc , q as the ratio between observed flux in this interval and theflux expected on the basis of the intrinsic quasar continuum and theaverage attenuation due to the IGM.Using our reference sample, we estimate a median γ = 1 . ,with a dispersion of . in its distribution, and a mean f esc , q =0 . in the case of the single power-law fit and = 0 . for thebroken power-law.We do not find any evidence for a redshift dependence of bothquantities. γ shows a small dependence on the r -mag, which islikely due to an intrinsic effect, with the fainter sources having flat-ter continua ( γ = 1 . for QSOs brighter than r = 19 . and γ = 1 . for r > . ). The statistical distribution of f esc , q ischaracterized by a kind of bimodality: this shape suggest an in-terpretation of f esc , q as a probabilistic distribution, rather than amean value, with ∼ − of the object characterized by a negligible escape fraction and the rest with roughly clear lines ofsight. For comparison the percentage of BAL quasars in the BOSSsurvey has been estimated to be around − (Pˆaris et al.2014; Allen et al. 2011). No dependence of f esc , q with luminosityis present in our sample.We have combined the observed evolution of the AGN/QSO-LF with our measurement of the escape fraction to compute the ex-pected rate of emitting ionizing photons per unit comoving volume ˙ N ion and photoionization rate Γ , as a function of redshift. We showthat, given our mean values for f esc , q , L > . L ⋆ ( z ) sources areable to provide enough photons to reproduce the reionization his-tory in the redshift interval < z < ∼ , while we confirm that at z > ∼ additional sources of ionizing photons are required. How-ever, the details on the reionization history are affected by the un-certainties in the QSO luminosity function evolution as estimatedin the optical and X-ray bands.Overall, our results imply that, at < z < , the contributionto the ionizing background of AGNs fainter than the LF charac-teristic luminosity, . L ⋆ , should be negligible. Since our samplecovers only magnitudes brighter than M UV ∼ − . , we alsoforecast that fainter QSOs (but still brighter than . L ⋆ ) shouldbe characterized by an f esc , q as large as those found in this work,in order for the QSO population to account for the whole photonbudget at the redshift of interest.Our predictions are perfectly compatible with the low redshiftestimate of Shull et al. (2015); Gaikwad et al. (2016), suggestingthat QSOs brighter than . L ⋆ may account for the total photonbudget at low redshift.At z > a contribution to the UV background from the galaxypopulation is needed. A good fit from z = 2 to z = 6 of the data isobtained assuming an escape fraction f esc , g between . and . (depending on the assumptions on the quasar SED and the com-parison with the ionizing background or photoioniziation rate mea-surements), independent of the galaxy luminosity and/or redshift,added to the present determination of the QSO contribution.On the basis of the present approach, future area of progress,besides the obvious direct determination of f esc , g ( L, z ) , are linkedto a better knowledge of the QSO luminosity function, the f esc , q for fainter quasars (at least down to . L ⋆ ) and its possible de-pendence on the redshift, the intensity of the UVB, which in turnrequires improved simulations of the IGM. ACKNOWLEDGMENTS
We are grateful to A.Inoue, S. Cooper, E. Giallongo, F.Haardt, L.Hofstadter, J.Japelj, I. Pˆaris and H. Wolowitz, for providing un-published material and enlightening discussions. We acknowledgefinancial support from the grants PRIN INAF 2010 “From the dawnof galaxy formation” and PRIN MIUR 2012 “The IntergalacticMedium as a probe of the growth of cosmic structures”. Fundingfor SDSS-III has been provided by the Alfred P. Sloan Founda-tion, the Participating Institutions, the National Science Founda-tion, and the U.S. Department of Energy Office of Science. TheSDSS-III web site is . SDSS-III ismanaged by the Astrophysical Research Consortium for the Partici-pating Institutions of the SDSS-III Collaboration including the Uni-versity of Arizona, the Brazilian Participation Group, BrookhavenNational Laboratory, University of Cambridge, Carnegie MellonUniversity, University of Florida, the French Participation Group,the German Participation Group, Harvard University, the Institutode Astrofisica de Canarias, the Michigan State/Notre Dame/JINA c (cid:13) , 000–000 Cristiani et al.
Participation Group, Johns Hopkins University, Lawrence BerkeleyNational Laboratory, Max Planck Institute for Astrophysics, MaxPlanck Institute for Extraterrestrial Physics, New Mexico StateUniversity, New York University, Ohio State University, Pennsyl-vania State University, University of Portsmouth, Princeton Uni-versity, the Spanish Participation Group, University of Tokyo, Uni-versity of Utah, Vanderbilt University, University of Virginia, Uni-versity of Washington, and Yale University.
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