Photon underproduction crisis: Are QSOs sufficient to resolve it?
aa r X i v : . [ a s t r o - ph . C O ] A p r Mon. Not. R. Astron. Soc. , 1– ?? (2015) Printed 13 October 2018 (MN L A TEX style file v2.2)
Photon Underproduction Crisis: Are QSOs sufficient toresolve it?
Vikram Khaire ⋆ and Raghunathan Srianand † IUCAA, Post Bag 4, Pune, India - 411007
ABSTRACT
We investigate the recent claim of ‘photon underproduction crisis’ by Kollmeier etal. (2014) which suggests that the known sources of ultra-violet (UV) radiation maynot be sufficient to generate the inferred H i photoionization rate (Γ HI ) in the lowredshift inter-galactic medium. Using the updated QSO emissivities from the recentstudies and our cosmological radiative transfer code developed to estimate the UVbackground, we show that the QSO contributions to Γ HI is higher by a factor ∼ HI by Kollmeier et al. (2014). Interestingly, we find that the contribution from QSOsalone can explain the recently inferred Γ HI by Shull et al. (2015) which used the sameobservational data but different simulation. Therefore, we conclude that the crisis isnot as severe as it was perceived before and there seems no need to look for alternateexplanations such as low luminosity hidden QSOs or decaying dark matter particles. Key words:
Quasars, galaxies, intergalactic medium, diffuse radiation.
Recently, Kollmeier et al. (2014, hereafter K14), used a cos-mological hydrodynamic simulation together with the lat-est measurements of the H i column density distribution, f ( N HI ), by Danforth et al. (2014) in the low- z intergalac-tic medium (IGM) and reported a H i photoionization rate(Γ HI ) at z = 0. This is 5 times higher than the one (refer toas Γ HMHI ) obtained from the theoretical estimates of cosmicultraviolet background (UVB) by Haardt & Madau (2012,hereafter HM12). This apparent discrepancy has led to theclaim of a ‘photon underproduction crisis’ suggesting thatthe origin of more than 80% of H i ionizing photons is un-known and perhaps generated from non-standard sources.For a given sight-line in a cosmological simulation, theinferred f ( N HI ) depends on the assumed Γ HI , the distribu-tion of gas temperature and the clumping factor of the regionproducing the Ly- α absorption. The latter two quantities de-pend not only on the assumed initial power spectrum butalso on various feedback processes that inject energy and mo-mentum into the IGM from star forming galaxies. Therefore,the Γ HI estimates using the f ( N HI ) will depend on how re-alistic the various feedbacks used in the simulation are. K14have used the smooth particle hydrodynamics code gadget2.0 (Springel 2005) that includes feedback from galaxies in ⋆ E-mail: [email protected] † E-mail: [email protected] the form of momentum driven winds (Oppenheimer & Dav´e2008). However, Dav´e et al. (2010) suggested that these feed-backs produce negligible effect on f ( N HI ) for N HI < cm − .Recently, Shull et al. (2015) have independently esti-mated Γ HI , using the same observed data but simulated spec-tra obtained using the grid based Eulerian N-body hydrody-namics code enzo (Bryan et al. 2014). They found a smallerΓ HI than K14 but it is still a factor 2 higher than Γ HMHI . Theyattributed the decrease in the derived Γ HI as compared toK14 to the differences in the implementations of feedbackprocesses in the simulations used. While Shull et al. (2015)reduced the apparent tension, it still requires an appreciablecontribution to the UVB from galaxies when one uses thepreviously estimated QSO emissivity.In this study, we revisit the UVB calculations at z ∼ HI inferredby Shull et al. (2015) and to get the Γ HI inferred by K14, weneed only 4% of the ionizing photons to escape from galaxies(and not 15% as suggested by K14) . Throughout this paperwe use a cosmology with Ω Λ = 0 .
7, Ω m = 0 . H = 70km s − Mpc − . c (cid:13) Khaire and Srianand
Following the standard procedure(Miralda-Escude & Ostriker 1990; Shapiro et al. 1994;Haardt & Madau 1996; Fardal et al. 1998; Shull et al.1999), the average specific intensity, J ν (in units of ergcm -2 s -1 Hz -1 sr -1 ), of the UVB at a frequency ν andredshift z is given by, J ν ( z ) = 14 π Z ∞ z dz dldz (1 + z ) ǫ ν ( z ) e − τ eff ( ν ,z ,z ) . (1)Here, dldz is the Friedmann-Lemaˆıtre-Robertson-Walker lineelement, ǫ ν ( z ) is the comoving specific emissivity of thesources and τ eff is an average effective optical depth encoun-tered by photons of frequency ν at a redshift z which wereemitted from a redshift z > z with a frequency ν > ν . Thefrequency ν and ν are related by ν = ν (1 + z ) / (1 + z ).Assuming that the IGM clouds of neutral hydrogen columndensity, N HI , are Poisson-distributed along the line of sight, τ eff can be written as (see Paresce et al. 1980), τ eff ( ν , z , z ) = Z zz dz ′ Z ∞ dN HI f ( N HI , z )(1 − e − τ ν ′ ) . (2)Here, f ( N HI , z ) is the number of H i clouds per unit red-shift and column density interval having column density N HI . The continuum optical depth τ ν ′ is given by τ ν ′ = N HI σ HI ( ν ′ ) + N HeI σ HeI ( ν ′ ) + N HeII σ HeII ( ν ′ ) , where, N i and σ i are the column density and photoionization cross-section,respectively, for species i and ν ′ = ν (1 + z ′ ) / (1 + z ).We use the same f ( N HI , z ) used by HM12 and neglectthe contribution of He i to τ ν because of its negligible abun-dance at z <
6. We calculate τ eff following the prescriptiongiven in HM12. In the following section we provide the up-dated source emissivity. We calculate the UVB assuming only QSOs and galaxies aresources of the UV radiation. Therefore, ǫ ν ( z ) = ǫ Qν ( z )+ ǫ Gν ( z )where ǫ Qν ( z ) and ǫ Gν ( z ) are the comoving specific emissivityfrom QSOs and galaxies, respectively. The ǫ Qν ( z ), in units of erg s − Hz − Mpc − , using the ob-served QSO luminosity function (QLF) at a frequency ν isgiven by ǫ Qν ( z ) = Z ∞ L minν L ν ( z ) φ ( L ν , z ) dL ν , (3)where, φ ( L ν , z ) is the QLF at z given in terms of specificluminosity L ν by φ ( L ν ) = ( φ ∗ L /L ∗ ) [ ( L ν /L ∗ ) − γ + ( L ν /L ∗ ) − γ ] − , (4)and using the absolute AB magnitudes, M, by φ ( M ) = φ ∗ M [10 . γ +1)( M − M ∗ ) + 10 . γ +1)( M − M ∗ ) ] − , (5)where φ ∗ M = 0 . φ ∗ L . We use L minν = 0 . L ∗ to calculatethe ǫ Qν . Note that, for most of the QLFs at z < . γ > − . ǫ Qν is insensitive to the values of L minν < . L ∗ . For example, the maximum difference in the ǫ Qν calculated for L minν = 0and 0 . L ∗ is less than 5% for γ > − . γ = − . left panel ), we plot the L ν φ ( L ν ) estimatesagainst g -band magnitudes from various studies at two dif-ferent z . The area under each curve is proportional tothe respective emissivity at g -band ( ǫ Qg ). It is clear fromthe Fig.1 that, as compared to old QLF measurements ofBoyle et al. (2000) and Croom et al. (2004), using the newmeasurements of Croom et al. (2009, hereafter C09) andPalanque-Delabrouille et al. (2013, hereafter PD13) will givea larger ǫ Qg . This is indeed the case, as demonstrated in the right panel of Fig.1 where we plot the ǫ Qg for these QLFmeasurements. We have also plotted the ǫ Qg converted fromthe ǫ Q ( z ) given at the H i Lyman limit (i.e at 912˚A) byHM12 using the relation log( ǫ Qg ) = log( ǫ Q )+0 .
487 which isconsistent with the spectral energy distribution (SED) usedby HM12. This ǫ Qg is consistent with Boyle et al. (2000) andCroom et al. (2004) which is smaller by factor ∼ λ band ) at which the QLFis reported, respectively. For 0 . < z < .
5, in each redshiftbin we fit the observed QLF with the form given in Eq. 5using an idl mpfit routine by fixing the values of γ and γ to those reported in the respective references (our fitsare also presented in Fig 1). We use our best fit φ ∗ M and M ∗ to obtain ǫ λ band ( z ) (see Table 1). At other redshifts,we take the best fit QLF parameters given in the respectivereferences and calculate the ǫ Qλ band ( z ). In Fig 1 ( right panel ),we show that the ǫ Qg ( z ) at z < ǫ Qλ band ( z ) into ǫ Q ( z ) using the brokenpower law QSO SED L ν ∝ ν − α , which we adopt for ourUVB calculations. In the soft X-ray regime above energy0.5 keV ( λ . α = 0 . α = 1 . . < λ and α = 0 . < λ λ > α = 0 . z < .
5, the SEDs used toperform continuum K -corrections in the original references(L ν ∝ ν − α ′ ; α ′ is given in the last column of Table 1) aredifferent from our adopted SED at λ > ǫ Qλ rest ( z ) at λ rest = λ band / (1 + z ) using α ′ from the corresponding refer-ence and then use our adopted SED to convert ǫ Qλ rest ( z ) in to ǫ Q ( z ). This is not needed for z > K -corrections.The errors on the ǫ Q ( z ) given in the Table 1 are the maxi-mum and minimum difference we get using the errors in γ and γ given in original references except at z = 0 .
15. Inthis case the error on ǫ Q is the difference we get in ǫ Q ifwe use L minν = 0 . ǫ Q ( z ) measurements as a function of z are plot- Stevans et al. (2014) found α = 1 . ± .
15 using QSO com-posite spectrum down to about 500˚A. We extrapolate it upto λ ∼ λ < HI . c (cid:13) , 1– ?? ow- z ionizing background L ν φ ( L ν ) x M p c - -30 -28 -26 -24 -22 -20M z = 1.25 -30 -28 -26 -24 -22 -20M020406080100120 L ν φ ( L ν ) x M p c - z = 1.63 Croom et al. 2009PD13 l og ( ε g Q ) e r g s - H z - M p c - This work HM12
Boyle et al. 2000Croom et al. 2004Richards et al. 2005Bongiorno et al. 2007Croom et al. 2009PD13This work (fit to PD13)
Figure 1.
The L ν φ ( L ν ) is plotted against M at g-band for two redshifts using various QLF reported in the literature. The area undereach curve is proportional to the ǫ Qg ( left panel ). The ǫ Qg obtained for these QLFs, our ǫ Qg from the fit to the PD13 and C09 QLF (cyanpoints; see table 1 for details) and the ǫ Qg ( z ) inferred from ǫ Q ( z ) of HM12 are also plotted ( right panel ). Here, the best fit PLE modelsof Boyle et al. (2000), Croom et al. (2004), with 2SLAQ data of Richards et al. (2005), C09 and PD13 and the luminosity dependentdensity evolution model of Bongiorno et al. (2007) are used. ted in Fig. 2. We fit these points using a functional formsimilar to that of HM12 and obtain the following best fit, ǫ Q ( z ) = 10 . (1 + z ) . exp( − . z )exp(2 . z ) + 25 . . (6)For comparison, in Fig.2, we show this best fit ǫ Q ( z ) alongwith the ǫ Q ( z ) used by HM12. For z < .
5, our ǫ Q ( z ) ishigher than that of HM12 and the maximum difference offactor 2.1 occurs at z ∼ .
5. The peak in ǫ Q ( z ) also changesfrom z = 2 . z = 1 .
95. In Fig. 2, we also showthe ǫ Q ( z ) obtained using the PLE models of C09 and PD13and the luminosity evolution and density evolution (LEDE)model of Ross et al. (2013). These are consistent with ourfit in Eq.6. Note that the PLE models of C09 and PD13give identical values of ǫ Qg ( z ) (see right panel of Fig.1) butdiffer slightly in the ǫ Q ( z ) since they use different SED forcontinuum K -correction (see Table 1). In Khaire & Srianand (2014, hereafter KS14), by match-ing the observed galaxy emissivity from multi-band, multi-epoch galaxy luminosity functions, we have determined self-consistent combinations of the star formation rate density(SFRD) and dust attenuation magnitude in the FUV band( A FUV ) for five well known extinction curves. It has been found that the SFRD( z ) and A FUV ( z ) estimated using theaverage extinction curve of the Large Magellanic Cloud Su-pershell (LMC2) is consistent with various observations.Here, as our fiducial model, we use the ǫ Gν ( z ) computedfrom the SFRD( z ) and A FUV ( z ) obtained in KS14 for theLMC2 extinction curve (see tables 2 and 4 in KS14). OurSFRD at z < . ∼ z , and becomes less than 10% at z ∼ f esc , of the generated H i ionizing photons( λ < λ < ii ionizing photons ( λ z -range of ourinterest. We approximate the galaxy emissivity at λ < ǫ Gν ∝ ν − . . The exponent is fixed to repro-duce the Γ HI obtained from the model spectrum itself. Notethat the exponent and the total H i ionizing photons gen-erated inside the galaxy depends on the metallicity, initialmass function (IMF), stellar rotation rates and adopted evo-lutionary tracks (see Topping & Shull 2015). In our galaxymodels obtained from starburst99 (Leitherer et al. 1999),we use the Salpeter IMF with 0 . z ) and A FUV ( z ) arising from the assumed metallicityand IMF. c (cid:13) , 1– ?? Khaire and Srianand l og ( ε Q ) e r g s - H z - M p c - This workHM12Croom et al. 2009 (PLE)Ross et al. 2013 (LEDE)PD13 (PLE)
Figure 2.
The best fit comoving ǫ Q ( z ) used in this paper ( blue curve ) along with the ǫ Q ( z ) used by HM12. The green circles are the ǫ Q given in Table 1. The blue curve is simply a fit to these points. The ǫ Q ( z ) obtained using the PLE model of C09 ( dot dash curve )and PD13 ( dotted curve ) and the LEDE model of Ross et al. (2013, orange curve) is shown. In addition to this, we have also included some of thediffuse emission from the IGM clouds. We model the He ii Ly- α and He ii Balmer continuum recombination emissionfollowing the prescription given in HM12 and the Lyman con-tinuum emission due to recombination of H i and He ii usingthe approximations given in Faucher-Gigu`ere et al. (2009).We do not include the contributions to UVB from He i re-combinations and the two photon continuum. These contri-butions are negligible, and if included, can increase Γ HI bya maximum of 10% (Faucher-Gigu`ere et al. 2009). We alsodo not include the resonance absorption of He ii which has anegligible effect on Γ HI , especially at low- z (see HM12). Here, we focus on the H i photoionization rate, Γ HI , obtainedusing our UVB model. This is defined asΓ HI = Z ∞ ν HI dν πJ ν hν σ HI ( ν ) , (7)where ν HI corresponds to λ = 912˚A. In Fig. 3, we summa-rize various available Γ HI measurements as a function of z .In particular, denoting Γ HI , = Γ HI × s − , the pointsof interest for the present study are Γ HI , ∼ . z = 0 . HI , ( z ) = 0 . z ) . at z < . HI ( z ) determinedby HM12 ( long dashed curve ) and the result of our code ob-tained using the ǫ Qν ( z ), SED and f esc used by HM12 ( dottedcurve ). Both match with each other within ∼
5% accuracy.The minor differences noticed can be attributed to the dif-ferent metallicities used and contributions of some of thediffuse emission processes ignored in our model. Having val-idated our code, we use the updated QSO emissivity ǫ Q ( z ) (see Eq. 6) and the ǫ Gν ( z ) mentioned above (in Section 3.2)to calculate the UVB (and hence Γ HI ) for different values of f esc .When we use only the QSOs as the source of the UVB(by taking f esc = 0) and use our updated ǫ Qν ( z ), we get theΓ HI at z < . , as defined in Shull et al.(2015) is to be 5030 cm − s − for our UVB at z = 0 as com-pared to 5700 cm − s − obtained by Shull et al. (2015). How-ever, because of the statistical uncertainties in the observed f ( N HI ), the Γ HI and Φ predicted by Shull et al. (2015) canbe even higher. Our Γ HI , values are 0.41, 0.94, 1.9 and 3.3at z = 0, 0.2, 0.4 and 0.6, respectively. These are ∼ HMHI values. Now, instead ofusing our ǫ Qν ( z ) fitting form, if we take the best fit PLEmodels given in C09 and PD13 (see Fig 2) for z < .
2, andestimate the UVB by assuming ǫ Q ( z ) = 0 at z > .
2, we getthe Γ HI , at z = 0 to be 0.48 and 0.39, respectively. It showsthat, irrespective of our QLF fits and the fitting form, theupdated QSO emissivity will lead to Γ HI ∼ . . × Γ HMHI .Therefore, we conclude that the Γ HI inferred by Shull et al.(2014) and Shull et al. (2015) can be explained by the QSOsalone without requiring any significant contribution from thegalaxies (i.e with f esc = 0). This is consistent with many low- z upper limits on average f esc measured in samples of galax-ies (Siana et al. 2007; Cowie et al. 2009; Siana et al. 2010;Bridge et al. 2010; Leitet et al. 2013). Therefore, there is noreal photon underproduction crisis when we consider the Γ HI measurements of Shull et al. (2015) .In our UVB calculations with f esc = 0, we use a differentQSO SED and an updated ǫ Qν ( z ) as compared to HM12.However, since the Γ HI ∝ (3 + α ) − , changing α from 1.57(HM12) to 1.4 at λ < HI by only 4%.The main difference in Γ HI between our UVB and that ofHM12 arises because of the updated ǫ Qν ( z ). It is importantto realize that even though the ǫ Q used by us matches with ǫ Q of HM12 at z = 0, the local UVB is contributed more c (cid:13) , 1– ?? ow- z ionizing background Γ H I ( i n - s - ) HM12This work f esc = 0This work f esc = 0.04
Becker+2013 Faucher-Giguere+2008 Bolton+2007 Kollmeier+2014
Shull+2014
Adams+2011 Shull+2015
Figure 3.
The Γ HI vs z obtained for our UVB with f esc = 0 ( solid curve ) and with f esc = 4% ( dot-dash curve ) along with the Γ HI fromHM12 ( dash curve ) is plotted. The dotted curve shows the Γ HI when we obtain the UVB using our code with the ǫ Q ( z ), SED and f esc taken from HM12. The Γ HI measurements at high- z by Faucher-Gigu`ere et al. (2008) ( squares ), by Bolton & Haehnelt (2007) ( circles )and by Becker & Bolton (2013) ( triangles ) are shown. At low- z , the lower limit Γ HI by Adams et al. (2011) using non-detection of H α from UGC 7321 ( arrow ; for more details on the validity of it see sec. 3.2 of Shull et al. 2014), the Γ HI which is found consistent with thecosmic metal abundances by Shull et al. (2014) ( diamond ) and the inferred Γ HI of Kollmeier et al. (2014) ( star ) and Shull et al. (2015)( green curve with diamonds ) are also plotted. by ionizing photons coming from high- z , up to z ∼
2, wherethe mean free path for H i ionizing photons is very large and ǫ Q ( z ) peaks.Next we explore the f esc requirements in order to repro-duce the Γ HI inferred by Kollmeier et al. (2014). For sim-plicity we run models keeping f esc constant over the full z range. We find f esc = 4% is needed to get the Γ HI , = 1 . z = 0 . f esc needed in ourcalculations is much less than the f esc = 15% required in theHM12 UVB model. Apart from 2 times higher QSO emissiv-ity, it is partly because of our ∼ z SFRDas compared to HM12. Note that, the value of f esc ∼ . z = 0 . z observations. In passing,we note that for our models with different combinations ofSFRD and A FUV explored for different extinction curves inKS14, we require f esc values similar to or less than what wehave obtained here for our fiducial model.In order to compare with observations, we use a relativeescape fraction, f esc , rel , defined as f esc , rel = f esc × . A FUV .To match the Γ HI of K14, the model of HM12 that assumes A FUV = 1 at z <
2, will require f esc , rel = 38% while we needonly f esc , rel = 15% for our fiducial LMC2 model at z = 0(where we determined A FUV = 1 . f esc , rel = 15% isabout a factor ∼ z upper limits on f esc , rel given in various studies of galaxy samples as men-tioned above. However the f esc observed in individual galax-ies (Borthakur et al. 2014) and many theoretical estimates(e.g. Kimm & Cen 2014; Roy et al. 2014) are consistent withit. Therefore, we conclude that with the updated QSO andgalaxy emissivities presented here, even if we wish to gener-ate Γ HI inferred by K14, the required f esc of ionizing photonsfrom star forming galaxies is not abnormally high enough towarrant an alternate non-standard source of the UVB. Interestingly, our updated QSO emissivity alonecan reproduce the Γ HI measurements at high z (Bolton & Haehnelt 2007; Becker & Bolton 2013) up to z ∼ .
7. However, f esc = 4% gives a Γ HI ( z ) which marginallyoverestimates the Γ HI measurements at 2 < z < z Γ HI , at z > z , using the observations ofH i and He ii Ly- α forest, it will be possible to constraintsthe f esc from galaxies (see, Khaire & Srianand 2013). Weplan to do this in the near future. The recent claim of a ‘photon underproduction crisis’(Kollmeier et al. 2014) requires the low- z Γ HI to be 5 timeshigher than the one obtained by the UVB model of HM12. Asimilar investigation performed by Shull et al. (2015) findsa lower Γ HI which is still 2 times higher than that of HM12.Here, we present an updated H i ionizing QSO emissivityby using recent QLF measurements. It turns out that thisemissivity is a factor of 1.5 to 2 times higher than what isused by HM12 at 0 . < z < .
5. We estimate the UVB usingthis emissivity with the help of a radiative transfer code de-veloped by us. We show that QSOs alone can give a factor2 required by Shull et al. (2015). Using our updated SFRDwhich is ∼ z , to get theΓ HI predicted by Kollmeier et al. (2014) we require only 4%of the ionizing photons generated by galaxies to escape intothe IGM. Therefore, there is no need to look for additionalsources of ionizing photons such as hidden QSOs or decayingdark matter particles. c (cid:13) , 1– ?? Khaire and Srianand
Table 1.
Details of observed QLF used to get ǫ Q in our study.Reference λ band z log φ ∗ M ∗ γ γ log ǫ Qλ band log ǫ Q α ′ (1) (2) (3) (4) (5) (6) (7) (8) (9) (10)Schulze et al. (2009) 4450˚A 0.15 -4.81 -19.46 -2.0 -2.82 24.30 23.83 ± .
20 0.5 ⋆ Croom et al. (2009) 4686˚A 0.54 -5.98 -24.10 -1.4 ± . ± . ± .
05 0.3PD13 † ± . ± . ± .
05 0.51.25 -5.81 -25.65 25.38 24.90 ± . ± . ± . +0 . − . -3.5 +0 . − . +0 . − . +0 . − . +0 . − . +0 . − . +0 . − . +0 . − . +0 . − . +0 . − . +0 . − . Glikman et al. (2011) 1450˚A 4.0 -5.89 -24.10 -1.6 +0 . − . -3.3 ± . +0 . − . NA ‡ Masters et al. (2012) 1450˚A 4.25 -7.12 -25.64 -1.72 ± .
28 -2.6 ± .
63 24.32 24.13 +0 . − . NAMcGreer et al. (2013) 1450˚A 5.0 -8.47 -27.21 -2.03 +0 . − . -4.0 23.78 23.60 +0 . − . NAKashikawa et al. (2015) 1450˚A 6.0 -8.92 -26.91 -1.92 +0 . − . -2.81 23.13 22.94 ± .
15 NAColumn (4) gives φ ∗ in units Mpc − mag − , column (5) gives M ∗ in AB magnitudes and column (8) and (9) gives ǫ Qν in units erg s − Hz − Mpc − . The λ band at 1450˚A, 4450˚A, 4686˚A and 7480˚A corresponds to FUV, B, g and i band, respectively. ⋆ We assume α ′ = 0 . k -correction of Schulze et al. (2009). † PD13 stands for Palanque-Delabrouille et al. (2013). ‡ NA indicates that the K -correction is not applied. ACKNOWLEDGMENTS
We thank M. Shull, D. Weinberg, F. Haardt, A. Paranjape, T.R. Choudhury and H. Padmanabhan for useful comments on themanuscript. VK acknowledges support from CSIR.
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