Astronomy & Astrophysics manuscript no. (will be inserted by hand later) The Parkes quarter-Jansky flat-spectrum sample 3. Space density and evolution of QSOs 5 0 J.V. Wall1,⋆, C.A. Jackson2,⋆⋆, P.A. Shaver3, I.M. Hook1, and K.I. Kellermann4 0 2 1 Department of Astrophysics, Universityof Oxford, DenysWilkinson Building, Keble Road, Oxford OX13RH, n UK a 2 ResearchSchoolofAstronomy&Astrophysics,TheAustralianNationalUniversity,MountStromloObservatory, J Canberra, ACT 2611, Australia 7 3 European Southern Observatory,Karl-Schwarzschild-Strasse 2, 85748 Garching bei Mu¨nchen, Germany 1 4 National Radio Astronomy Observatory,520 Edgemont Road, Charlottesville, VA 22903-2475, USA 2 v 2 2005 Jan 10 2 1 Abstract.WeanalyzetheParkesquarter-Janskyflat-spectrumsampleofQSOsintermsofspacedensity,including 8 theredshiftdistribution,theradioluminosity function,andtheevidenceforaredshiftcutoff.Withregard tothe 0 luminosity function, we note thestrong evolution in space density from the present day to epochs corresponding 4 to redshifts ∼ 1. We draw attention to a selection effect due to spread in spectral shape that may have misled 0 other investigators to consider the apparent similarities in shape of luminosity functions in different redshift / h shells as evidencefor luminosity evolution. To examine the evolution at redshifts beyond 3, we develop a model- p independent method based on the Vmax test using each object to predict expectation densities beyond z = 3. - Withthisweshowthatadiminutioninspacedensityatz >3ispresentatasignificancelevel>4σ.Weidentify o aseverebiasinsuchdeterminationsfrom usingflux-densitymeasurementsatepochssignificantly laterthanthat r t of thefindingsurvey.The form of thediminution is estimated, and is shown to be verysimilar to that found for s a QSOs selected in X-ray and optical wavebands. The diminution is also compared with the current estimates of : star-formation evolution,with less conclusiveresults. Insummary wesuggest that thereionization epoch is little v influenced by powerful flat-spectrum QSOs,and that dust obscuration does not play a major role in our view of i X theQSO population selected at radio, optical or X-ray wavelengths. r a Key words.catalogs —radiocontinuum:galaxies —galaxies: active—galaxies: evolution—quasars:general— BL Lac objects: general — cosmology: observations 1. Introduction dence for a redshift cutoff provided by the sample, and the form of this cutoff. This is the last in a series of three papers describing the Paper 1 described how the identification programme results ofa programto searchfor high-redshiftradio-loud for 878 flat-spectrum radio sources selected from the QSOsandtostudytheevolutionoftheflat-spectrumQSO Parkes catalogues yielded a near-complete set of optical population. counterparts. Indeed for the sub-sample at declinations Paper 1 (Jackson et al. 2002) set out the sample, dis- ◦ above 40 withflux densities above cataloguecomplete- cussing selection, identification and reconfirmation pro- − ness limits, only one source remains unidentified. Of the grammes to determine the optical counterparts to the ra- 379QSOsinthissub-sample,355havemeasuredredshifts, dio sources. Paper 2 (Hook et al. 2003) presented new obtainedfromearlierobservationsandtheextensivespec- spectroscopic observations and redshift determinations. troscopy programme described in Paper 2. This relative This paper considers the radio-loud QSO space distribu- completeness is idealfor studies ofspace density,asit be- tion, the epoch-dependent luminosity function, the evi- comes possible to map the entire “quasar epoch” with a single homogeneous sample, having no optical magnitude Sendoffprintrequeststo:J.V.Wall,e-mail:[email protected] ⋆ now at Department of Physics and Astronomy, University limitandfreeofobscurationeffects.Infactasub-sampleof of British Columbia, Vancouver,B.C. V6T 1Z1, Canada objects from an earlier analysis was used by Shaver et al. ⋆⋆ now at Australia Telescope National Facility, CSIRO, PO (1996) to study the evolution of QSO space density at Box 76, Epping, NSW 1710, Australia high redshifts. The study showed that the space density 2 J.V. Wall et al.: The Parkes quarter-Janskyflat-spectrum sample of high-luminosity radio QSOs decreased significantly at pernovae. Assuming no obscuration, current results from redshifts beyond 3. Preliminary data were also used by the SCP (Supernova Cosmology Project) collaboration Jackson & Wall (1999) in considering a dual-population (Knop et al. 2003) and the Hi-z team (Tonry et al. 2003) scheme of space densities for unified models of QSOs and favour an Ωm = 0.3, ΩΛ = 0.7 universe. Two further radio galaxies. related issues make delineation of the QSO epoch very Generalfeaturesoftheluminosityfunctionanditsred- important: galaxy formation, and the reionization of the shift dependence have long been established for QSOs Universe. selected at optical and radio wavelengths (e.g. Longair 1966; Schmidt 1968; Fanti et al. 1973). Powerful evolu- tion is required, similar in magnitude for selection at 1.1. Galaxy formation either waveband; the space density of the more lumi- nous QSOs at redshifts of 1 to 2 is at least 102 that ThedramaticcosmicevolutionofradiogalaxiesandQSOs at the present epoch. It has been hotly debated as to stood as a curiosity on its own for over 30 years since the whether the form of this change is luminosity evolution birth of the idea (Ryle 1955), clouded as it was in the (e.g. Boyle et al. 1988) or luminosity-dependent density source-count controversy (Scheuer 1990). It is relatively evolution(e.g. Dunlop & Peacock1990). It does notmat- recentlythatcorrespondingevolutionhasbeendelineated ter: physical models are not available that require either forthestar-formationrate(Lilly et al.1996;Madau et al. form, although it is clear that luminosity evolution re- 1996) and for galaxy evolution, particularly blue galaxies sults inlifetimes ofnon-physicallength(Haehnelt & Rees (Ellis 1999). The correlation between star-formation rate 1993, andreferencestherein).Thespacedensityofradio- and AGN space density (Wall 1998) strongly suggested selectedQSOs,constitutingsome10percentofallQSOs, a physical connection (Boyle & Terlevich 1998). Before generally appears to parallel that of optically-selected the emergence of the Lilly-Madau plot of star-formation QSOs (e.g. Schmidt et al. 1991; Stern et al. 2000). history, it was recognized that the model of hierarchi- There are many reports of a redshift cutoff in the lit- cal galaxy development in a Cold Dark Matter (CDM) erature: paper after paper speaks of ‘the quasar epoch’, Universewouldresultina‘quasarepoch’(Haehnelt1993; ‘a strongly-evolving population peaking at a redshift of Haehnelt & Rees 1993). The issue of ‘quasar epoch’ and about 2’, or ‘the quasar redshift cutoff’ without spe- ‘redshift cutoff’ has therefore assumed particular impor- cific reference. For optically-selected QSOs, several clas- tance in consideration of galaxy formation in low-density sic studies demonstrated that such a cutoff does exist CDM universes. The very existence of any high-redshift (Schmidt et al. 1991; Warren et al. 1994; Kennefick et al. QSOs sets constraints on the epoch of formation of the 1995). The Sloan Digital Sky Survey (SDSS) has now first galaxies. Haehnelt (1993) showed how the then-new foundQSOsouttoredshiftsbeyond6,andanalysesofthe COBE normalization (Smoot et al. 1992) together with space density (Fan et al. 2001a,c,b) provide the strongest the QSO luminosity function at high redshifts as mea- evidence to date of the drop in space density beyond sured by Boyle et al. (1991), provided substantial infor- z = 3. X-ray surveys now appear to show that the X-ray mationontheinitialfluctuationspectrumandthematter QSO population exhibits a decline at high redshifts sim- mix. He found that the z = 4 luminosity function ex- ilar to that found for optically-selected QSOs (Hasinger cluded an initial-spectrum index of n 0.75 or a Hot ≤ 2003; Barger et al. 2003; Silverman et al. 2004). But do Dark Matter fraction 25 per cent. Relevant to the cur- ≥ all these observations indicate a real diminution or – at rent view of the low-matter-density CDM Universe, he least at optical wavelengths – could it be due to a dust found that Ω 0.75. Haehnelt & Rees (1993) devel- Λ ≤ screen (Heisler & Ostriker 1988; Fall & Pei 1993)? It is oped a model for the evolution of the QSO population here that radio-selected samples such as the present one based on the existence of 100 generations and link- ∼ can provide a powerful check: if a significant diminution ing the QSO phenomenon with the hierarchical build-up is seen in the radio luminosity function, it cannot be the of structure in the Universe. The evolution of host ob- result ofdust obscuration.Dunlop & Peacock(1990) pre- jects is mirrored in the evolution of the mass of newly sented some evidence for just such a cutoff of the ra- formed black holes; only a moderate efficiency for forma- dio luminosity function (RLF) for flat-spectrum (QSO- tion of an average black hole is necessary to model the dominated) populations; and an earlier analysis of a sub- luminosity function. The model suggested that nearly all sample from the present work (Shaver et al. 1996) added galaxies are likely to have passed through a QSO phase. confirmation. More recently Vigotti et al. (2003) defined Kauffmann & Haehnelt (2000) produced a more sophis- a complete sample of13radioQSOsatz 4,fromwhich ticated model by incorporating a simple scheme for the ∼ they concluded that the space density of radio QSOs is growth of supermassive black holes into the CDM semi- a factor of 1.9 0.7 smaller than that of similar QSOs analytic models that chart the formation and evolution ± at z 2. However, Jarvis & Rawlings (2000) questioned of galaxies. In addition to reproducing the observed re- ∼ these radio-QSO results, focussing on the possible effects lation between bulge luminosity and black-hole mass in of spectral curvature. nearbygalaxies(Magorrianet al.1998),the modelisable A possible dust screen has serious implications for to mimic the enormous increase in the QSO population the interpretation of the Hubble diagram for SN Ia su- from redshift 0 to 2, a feature that the Haehnelt-Rees J.V. Wall et al.: The Parkes quarter-Janskyflat-spectrum sample 3 model was able to describe only qualitatively. Their con- possibletodetectthisreionizationepochdirectlyasastep clusion: “Our results strongly suggest that the evolution in the background radiation at radio frequencies between of supermassive black holes, quasars and starburst galax- 70 and 240 MHz (redshifted 21-cmHI) or in the infrared, ies is inextricably linked to the hierarchical build-up of 0.7to2.6µm,fromHrecombination(Shaver et al.1999). galaxies.” It may be possible with results from the Planck mission to identify features in the CMB that identify what the predominant mechanisms are; and it may be possible to 1.2. Reionization detect the UV sources responsible for the ionizing flux The paradigm of hierarchical structure growth in a at z 10 20 with the James Webb Space Telescope ∼ − CDM universe has long suggested that after the re- (Haiman & Holder 2003). combination epoch at z 1500, the reionization of QSOs have long been prime candidates for this ∼ the Universe took place at redshifts between 6 and 20 reionization. However the apparent decline in space (e.g. Gnedin & Ostriker 1997). This reionization is pre- density (from the evidence summarized above and by dicted to be patchy and gradual (Miralda-Escud´e et al. Madau et al. 1999), is inconsistent with this interpreta- 2000), although some models indicate that it should hap- tion. Madau(2000) showedthat in the face ofthis appar- pen quite rapidly (e.g. Cen & McDonald 2002; Fan et al. ent diminution, UV luminosity functions of Lyman-break 2002). Two major observational advances support the galaxies (LBG) provide 4 times the estimated QSO con- ‘patchy and gradual’ scenario. Firstly, SDSS discovery of tribution at z = 3. It is now commonly accepted that QSOs at redshifts of 6 or more (Fan et al. 2000, 2001a; suchobjects(ortheir progenitorcomponents)takeonthe Becker et al. 2001) has given a glimpse of what may mantle.Theformationofshort-livedmassivestarsinsuch be the end of the epoch of reionization: the first com- galaxies provides the UV photons (Haehnelt et al. 2001), plete Gunn & Peterson (1965) trough has been observed although QSOs may supply a significant fraction of the in the z = 6.29 QSO SDSS 1030+0524 (Becker et al. UV background at lower redshifts. 2001;Pentericci et al.2002)andasecondhasbeenseenin Becausethe cooling time is long,the low-density IGM z =6.43QSOSDSS J1148+5251(Fan et al.2003).There retains some memory of when and how it was ionized. is disagreement as to whether this marks the true end Several investigators have found a peak in temperature of reionization (Songaila & Cowie 2002); but the sugges- of the IGM at z 3 (Schaye et al. 2000; Theuns et al. ∼ tion is that it may be essentially complete by z 6 7. 2002) close to the peak of the ‘quasar epoch’. Moreover, ∼ − Secondly, the detection of polarized anisotropies with the observations of several QSOs at the wavelength of HeII WilkinsonMicrowaveAnisotropyProbe(WMAP) has re- Lyα near z =3 suggestdelayedreionization of He I, with sulted in a measurement of the optical depth τ 0.17 the process not yet complete by z =3 (Kriss et al. 2001). ∼ toThompsonscattering(Bennett et al.2003;Kogut et al. The implication is that the QSO ionizing photons coinci- 2003),implyingareionizationredshiftof17 5.TheCMB dentwiththepeakinactivitybothreionizeHeIanddump ± issensitivetotheonsetofionization,whileGunn-Peterson entropy into the IGM to raise its temperature. troughs are sensitive to the late stages, the cleanup of In all of these aspects, it is clear that conclusions on remaining HI atoms. Resolving the large uncertainties ionizing flux from QSOs are dependent on poorly de- in these redshifts could yet result in a rapid reioniza- termined high-power regions of luminosity functions, on tion scenario. Nevertheless several recent papers (see e.g. apparent cutoffs observed primarily in optically-selected Haiman & Holder2003)addressthecomplexandinteract- samples, and then only for the most luminous QSOs. ingsuiteofphysicalmechanismsthatmaybe atplaydur- It is a primary purpose of this paper to determine the ing an extended ‘patchy and gradual’ reionization epoch radio luminosity function using the near-complete data 6<z <17. of the present sample, and to examine the evidence for In either a fast or a gradual scenario, identifying the a redshift cutoff. Before this, we discuss the populations source of this reionization as well as epoch is of vital im- involved in the flat-spectrum sample by examining the portance for such interconnected reasons as: N(z)relation( 2).SubsequenttotheRLFdetermination § in 3, we consider the issue of a redshift cutoff ( 4), and § § – The role of reionization in allowing protogalactic ob- the form of this cutoff. In 5 we construct an overall § jects to cool into stars, picture of epoch dependence of space density for radio- – The small-scale temperature fluctuations in the CMB loud QSOs. We compare this with the parallel results for and how these are influenced by patchiness in the QSOsselectedatopticalandX-raywavelengths,andwith reionization, and thebehaviourofstar-formationratewithepoch.Thefinal – The epoch of the first generation of stars, or galaxies, section ( 6) summarizes results from this paper and our § or collapsed black-hole systems. preceding two papers. It is most likely that the reionization is via photoion- 2. The redshift distribution ization by UV radiation from stars or QSOs, rather than collisional ionizationine.g.blastwavesfromtheexplosive For a sample of objects complete to some flux-density deaths of Population III stars (Madau 2000). It may be limit,theredshiftdistribution,N(z),givespreliminaryin- 4 J.V. Wall et al.: The Parkes quarter-Janskyflat-spectrum sample formationontheepochoftheobjects,andallowsthemost directcomparisonwithothersamples.Theredshiftdistri- bution gives direct information on neither the luminosity functionnoritsepochdependence;howeveritprovideses- sential data for use with other data such as source counts to enable the constructionofepoch-dependent luminosity functions. There have been many versions of this. Most are a variant on either the V method (Schmidt 1968) max or the technique of defining the luminosity distribution (Wall et al. 1980; Wall 1983), obtained when a complete N(z) is available at one flux-density level at least. Such modelling processes now make use of statisti- cal techniques to incorporate data sets of varying com- pletenessatmanyfrequenciesandflux-densitylevels.The sample described here represents only one such data set, more complete than most. Dunlop & Peacock (1990) car- ried out the most extensive such modelling. They took as a starting point two populations, ‘flat-spectrum’ and ‘steep-spectrum’ radio sources,now broadlyconsideredin thelightofunifiedmodelsasbeamed radiosources(radio- loud QSOs and BLLac objects) and their unbeamed pro- genitors,orhosts(FRIandFRIIradiogalaxies).Allthese objects are deemed to be powered by accretion-disk / ro- tating black-hole systems from which a pair of opposing relativistic jets feed double radio lobes. The single axis is collimated during the feeding process by rotation of Fig.1. The spectral index distribution for the compila- the black-hole system. The beamed objects, QSOs and tion of sources from Parkes surveys known as PKSCat90. BLLacs, beamed because of relativistic ejections of com- The sub-sample selected has S2.7GHz 0.25 Jy, in re- ponents alongaxesalignedwiththe line-of-sight,havera- ≥ gionssurveyedtoalimitingfluxdensityof0.25Jyorless. dio structures dominated by relativistically-boosted core The hatched area shows the sources identified as QSOs emission. This core emission shows the effects of syn- or BLLac objects. These beamed objects dominate the chrotron self-absorption and therefore has a flat or in- ‘flat-spectrum’ region of the diagram. verted radio spectrum. The radio emission from powerful radio AGN whose axes are not aligned with the line-of- Table 1. Sample 1: an all-source sample selected from sightis dominated by their steep-spectrumlobe emission, the sourcelist ofPaper1 inordertoestimate the redshift on the large scales of 10’s of Kpc up to 100’s of Mpc. ◦ The dichotomy between beamed and unbeamed objects distribut◦ion: S2.7GHz ≥ 0.25 Jy, Slim ≤ 0.25 Jy, 2.5 ≥ δ 40 . as evidencedby their integratedradiospectra is shownin ≥− Fig. 1. Ident No Redshift Redshift Total The widely-used Dunlop-Peacock models of the lumi- QSO 20 308 328 nosity functions may be simply tested againstthe present BL 34 9 43 databymeansoftheN(z)distributionsthattheypredict. G 57 27 84 We constructed a redshift distribution from the sam- Obsc 2 0 2 ple of Paper 1 as follows. We selected all sources with e 1 0 1 S2.7GHz 0.25 Jy in regions for which the 2.7-GHz flux- Totals 114 344 458 ≥ density limit was 0.25 Jy or less, and at declinations ◦ ◦ 2.5 δ 40 .We referto this asSample1 andthe to- ≥ ≥− talareaitcovers(Fig.1ofPaper1)is2.676sr.Thesource composition,identificationandredshiftdataforthis sam- unmeasured redshifts of the 34 BLLac objects were as- ple are shown in Table 1. Choice of the declination limit sumed to have the same distribution as those measured. comes from both identification and radio-spectral com- Such an approximation is inappropriate for the galaxies, pleteness; see 3. however. A crude Hubble diagram was plotted for the 27 § The entries in the identification column, Table 1, re- galaxieswithredshiftsandasimplepolynomialwasfitted fer to (QSO)s, (BL)Lac objects, (G)alaxies, (Obsc)ured to make rough estimates of the redshifts for the remain- fields, and (e) not identified for reasons discussed in ing 57 galaxies based on their B magnitudes. Finally the Paper1.Asreasonableapproximations,the20QSOswith- 3 Obsc ande sourceswereassumedto havethe same red- out measured redshifts were assumed to have the same shift distribution as the total sample; the N(z) obtained redshift distribution as those with redshifts; likewise the byaddingthe QSO,BLLacandgalaxyredshiftswassim- J.V. Wall et al.: The Parkes quarter-Janskyflat-spectrum sample 5 ply scaled by (344+111+3)/(344+111) to obtain the Inviewofuncertaintiesinspectralindexandofequat- final N(z) of Fig. 2. ing the flat-spectrum population of Dunlop & Peacock withcompactradiosources,theoverallagreementisgood. The form of the decline in N(z) to higher redshifts is im- pressively described by the Dunlop-Peacock models. Two models stand out in Fig. 2. One model with a space- density cutoff at z = 5 predicts a redshift distribution greatlyatvariancewithobservations,showingadominant spikeinthedistributionatredshiftsjustbelowthiscutoff. It has been left out of the averaging process. The pure- luminosity-evolution model, shown as the dashed line, is distinctinhavingaquickerriseandflattermaximumthan the others. These two features provide a better represen- tation of the data in the range 0 < z < 1.5 than do the other models. The good fit of the Dunlop-Peacock models to the to- tal N(z) distribution for flat-spectrum objects does not imply a good description of the N(z) for beamed ob- jects (hatched area, Fig. 2) alone. The Dunlop-Peacock models clearly rely on the presence of low-luminosity flat-spectrum galaxies for the quality of overall fit; the ‘flat-spectrum’ models describe the beamed objects alone rather poorly. Models considering populations in terms of beamed and host object were developed by Jackson and Wall Fig.2. The redshift distribution (histogram) for the (Wall & Jackson 1997; Jackson & Wall 1999). The N(z) sourcesofSample1(Table1).Thehatchedareashowsthe predictions from these models are shown in Fig. 2. redshift distribution for beamed objects alone, the QSOs Agreementisreasonable;normalizationiscorrect,andthe + BLLac objects, while the clear region represents the formsofthecurvesaresimilar.Thisagreementisexpected galaxies.The6dottedlinesshowtheappropriately-scaled on the basis of the fit of the model to the 5-GHz source distributions predicted by the flat-spectrum (α 0.5) count and the incorporation of a redshift cutoff in the ≥ − components of the Dunlop-Peacock (1990) luminosity- modelevolution.Themodelsover-predictobjectsatz >2, function models,withthe dashedline distinguishing their due primarily to a lack of constraint on the evolution of pure-luminosity-evolutionmodel.Thesolidlinerepresents low-luminosity sources. theaverageof6ofthemodels,omittingthemodelshowing the very steep rise to z = 5. The symbol + line systems 3. The Radio Luminosity Function (RLF) show the predictions from the dual-population models of Jackson & Wall (1999), red representing all beamed ob- Completenessofidentificationsenablestheradioluminos- jects (QSOs + BLLacs), blue for QSOs only. ity function to be constructed in a straightforward way, using the 1/Vobs approach (Schmidt 1968; Felten 1976; Avni & Bahcall1980). The contributionofeachobjectto Dunlop & Peacock derived luminosity functions for spacedensityiscalculatedasthe reciprocalofthe observ- their two-population model, flat-spectrum and steep- able volume, the volume defined by the redshift range(s) spectrum radio sources,representing the luminosity func- inwhichtheobjectcanbeseen.Becausethesampleisop- tionsaspolynomialsoverthesurface(ρ,P ,z),andob- ticallycomplete,onlyradiodata(apartfromtheredshifts) radio taining coefficients by best-fitting to multi-frequency sur- are relevant in defining this range. vey data including source counts and redshifts. Different An appropriate sub-sample for this calculation is that models resulted from different starting points and fac- referred to as Sample 2 in Table 2. Selected from the torizations of the epoch-dependent luminosity function. catalogue of Paper 1, it includes all the QSO identifica- Their division between flat-spectrum and steep-spectrum tions with flux densities above survey limits and within ◦ ◦ sub-populations took spectral index α = 0.5 as the the declination range +2.5 to 40 . Defining Vobs re- − − dividing criterion. The predictions of redshift distribu- quires knowledge of the radio spectrum both above and tions from the flat-spectrum portions of Dunlop-Peacock below the survey frequency. Above 2.7 GHz, there are luminosity functions are shown in Fig. 2. In order to the 5.0-GHz data of the Parkes catalogues for all sources scale these to our spectral-selectioncriterion,we usedthe in the 2.7-GHz surveys, flux densities at 8.4 GHz for spectral-index histogram of Fig. 1; the ratio of objects many of these sources (Wright et al. 1990), and about 40 with α 0.4 (our selection criterion, Paper 1) to those 8.87-GHz flux densities for some of the brighter sources ≥ − with α 0.5 is 1060/1275= 0.831. (Shimmins & Wall 1973). Below 2.7 GHz, flux densities ≥− 6 J.V. Wall et al.: The Parkes quarter-Janskyflat-spectrum sample exist for most members of Sample 2 at 365 MHz from These data are displayed in Fig. 3. First impressions the Texas survey (Douglas et al. 1996), and at 1.4 GHz arethatthecurvesslidesideways,suggestingsimplelumi- from the NRAO VLA sky survey (Condon et al. 1998). nosityevolution,asdeducedfromsimilarbehaviourinred- The Texas survey covers the sky at declinations down shift shells for optical luminosity functions (Boyle et al. ◦ ◦ to 35.5 and the NVSS down to 40 . As a compro- 1988). However, the transition from the lowest redshift − − mise between sample size and spectral completeness, the range (z <0.5) to the next redshift range (0.5<z <1.0) sub-sample chosen for definition of the RLF, Sample 2 of is not described by a lateral shift. It is possible that the Table 2, was therefore taken to have a southern declina- lower bin is contaminated by unbeamed objects such as ◦ tion limit of 40 . Most of the area surveyed at 2.7 GHz Seyfert galaxies and elliptical-galaxy cores; such objects − in this range has a completeness limit of S2.7GHz = 0.25 may have entirely different central engines and different Jy,but someregionshavelimits of0.10,0.20and0.60Jy; luminosity functions asaresult.The dataofFig.3 shown see Fig. 1 of Paper 1. in integral form (Fig. 4) suggest that the RLF changes in formrightoutto the 1<z <2shell,anditis improbable that contamination by unbeamed objects persists beyond Table 2. QSO samples for RLF and redshift-cutoff anal- z > 0.5. A closer investigation by both morphology and yses. spectrum is needed to determine if removal of unbeamed objects could ‘save’ luminosity evolution. However, it is Sub-sample Sample 2† Sample 3‡ probably beyondsaving.For example,from QSOsdiscov- eredintheSDSSsurvey,Fan et al.(2001c)notedthatthe with measured z UKSTID 342 242 high-power end of the QSO luminosity function appears with measured z CCD ID 13 10 flatter than that at lower redshifts. total QSOswith measured z 355 252 The impression of luminosity evolution may be mis- leadinginanycase.Spectralspreadlimitstheupperpower no measured zUKSTID 17 11 boundofcompletenessfor the RLFineachredshiftband. no measured zCCD ID 6 4 Atthemaximumredshiftoftheband,radiosourcesofthe total QSOswith no measured z 23 15 steepest spectra fall below the survey flux-density limit first; the power limit is determined simply from noID (no measured z) 1 1 1 1 Totals QSOs+ non-ID 379 379 268 268 Plim =Slim D2 (1+z)(1−αmax) × × †S2.7GHz≥Slim, +2.5◦ >δ>−40◦, area 3.569 sr. where D is the ‘luminosity distance’, and αmax is the ‡Slim=0.25, S2.7GHz≥Slim, area 2.278 sr. minimum (low-frequency) spectral index, i.e. that effec- tive index corresponding to the source with ‘steepest’ ra- dio spectrum in the particular redshift range. At lower The steps to defining V consist of (1) determining obs powers within the bin, the RLF will be incomplete for P2.7 GHz, the luminosity of the radio source at 2.7 GHz such objects, but will remain complete for objects of flat- (restframe),and(2)‘moving’thesourcewithitsspectrum ter spectra. (The limit is well defined for our sample; we defined by the measured flux densities, from 0 < z < ∞ selectedobjectsofα 0.4,i.e.thespectrallimitwasim- todetermine inwhichredshiftrange(s)itisobservable.It ≥− posedonthe‘steep’side,withofcoursenolimitastohow is observable at a given redshift if (a) its flux density ex- ‘flat’ or ‘inverted’ the spectra might be.) This limit may ceedsthesurveylimitS2.7 =0.25Jyand(b)itsredshifted cause RLFs of similar slopes to appear to have a knee at spectrum over the observer’s range 2.7 to 5.0 GHz has a similar space densities, mimicking luminosity evolution. spectralindex 0.4.Weinterpolatedbetweenmeasured ≥− In previous discussions of space densities it is not clear spectralpointsinthelogSν -logν plane.Despitetherela- that this limit plus spectral spread have been considered; tively sparse sampling in this plane, combined luminosity several such studies appear to ascribe a single canonical and spectral effects of ‘moving’ the source are complex, spectrum to every QSO. sometimes resulting in a source having two regions of ob- One regrettable result of this power limit is that trac- servable volume defined by four redshifts. (These effects ing the space densities in the higher-redshift rangesdown arediscussedfurtherinthefollowingsection.)Incalculat- to low powers is not possible. Composite RLFs (galax- ing the RLF, the contribution of each source is then ies plus QSOs) extending over many decades show rel- i i X1/(Vmax−Vmin) atively few QSOs at low redshifts, where the RLFs are i dominated by low-luminosity (mostly star-forming) radio whereiisusuallyunitybutissometimestwo.Throughout galaxies (Sadler et al. 2002). The RLFs of QSOs at high the analyses we have used the geometry H =70 km s−1 redshifts must therefore flatten and drop drastically to- 0 Mpc−1, Ω =1.0, Ω =0.3, Ω =0.7. wards the lower powers. The dual-population models of tot m Λ Following these precepts, the radio luminosity func- Jackson & Wall(1999)demonstratesuchbehaviour.From tions calculated for rest-frame powers at 2.7 GHz for 5 the present data, the limit-lines show that the only con- redshift ranges are given in Table 3. clusionto be drawnis that the RLFs may reduce in slope J.V. Wall et al.: The Parkes quarter-Janskyflat-spectrum sample 7 Table 3. The radio luminosity function ρ, in units of log(Mpc−3) per ∆z = 0.5 per ∆(logP) = 0.4, as derived from Sample 2, Table 2. N is the number observed per bin and z the mean redshift of the sources in the bin. Power 0<z<0.5 0.5<z<1.0 1.0<z <2.0 2.0<z <3.0 3.0<z<5.0 log(P/ WHz−1sr−1) logρ N z¯ logρ N z¯ logρ N z¯ logρ N z¯ logρ N z¯ 24.8 −9.02 4 0.33 −10.22 1 0.58 — 0 — — 0 — — 0 — 25.2 −8.60 15 0.36 −9.13 6 0.62 — 0 — — 0 — — 0 — 25.6 −9.54 2 0.32 −8.91 29 0.73 −10.40 5 1.11 −11.43 1 2.12 — 0 — 26.0 −10.27 1 0.36 −9.26 19 0.77 −9.57 45 1.32 — 0 — — 0 — 26.4 −11.11 1 0.16 −9.85 15 0.78 −9.33 91 1.47 −10.34 19 2.24 −12.13 1 3.45 26.8 — 0 — −10.35 5 0.77 −10.05 29 1.69 −10.05 34 2.48 −11.02 12 3.47 27.2 — 0 — — 0 — −11.00 6 1.50 −10.98 8 2.33 −11.82 2 3.45 27.6 — 0 — — 0 — — 0 — −12.19 1 2.56 −12.32 1 3.57 Fig.3. The radio luminosity function (H =70 km s−1 Mpc−1, Ω =1.0, Ω =0.3, Ω =0.7) for the QSOs of the 0 tot m Λ Parkes0.25-Jyflat-spectrumsample.TheRLFwascomputedinredshiftranges0 0.5(red),0.5 1.0(green),1.0 2.0 − − − (blue), 2.0 3.0 (orange) and 3.0 5.0 (light blue). Vertical bars show the limits of completeness in power for each − − redshiftrange,asdescribedinthetext.Errorbarsare1/√N withN fromTable3.Skyareaandredshift-measurement completeness have been considered in order to plot true space densities per ∆z =0.5, ∆(logP)=0.4. towards the lower powers. In 5 we show how a differ- each power range decline, although statistical uncertain- § ent approach can yield some information throughout the ties are substantial. Fig. 3 also indicates such a decline; range of redshifts occupied by the present sample. thesedatathereforesuggestaredshiftcutoff,atsomelevel AthirdpresentationoftheRLFdataisgiveninFig.5, of significance. in which space densities are plotted as a function of red- shift for 5 ranges of intrinsic power. The initial dramatic increase in space density with redshift is evident, with 4. The Redshift Cutoff densities in the redshift range 1.0 2.0 some two orders − of magnitude above those for objects at redshifts < 0.5. Our preliminary analysis (Shaver et al. 1996) indicated a Small numbers at the highest redshifts (see Table 3) and decrease in radio-QSOspace density beyond z =3. Using thecompletenesslimitsatthelowerredshiftsconstrainthe a well-defined sub-sample from the present study, Shaver redshift range observable for each luminosity. In particu- etal.consideredthespacedensityofQSOswithP2.7GHz laritisnotpossibletojudgewhetherthemaximumspace 1.1 1027 W Hz−1 sr−1. On the basis of uniform spac≥e × density is a function of radioluminosity. The curves over- density, the 25 such radio QSOs seen at z 4 indicate ≤ lap adequately to show self-consistency, and to demon- that 15 similar objects would be expected in the range strate the increase in space density from small redshifts 5 z 7. None was found. From Poisson statistics, the ≤ ≤ to z 1.5. Beyond this redshift, the space densities for difference is significant at the 99.9% level. ∼ 8 J.V. Wall et al.: The Parkes quarter-Janskyflat-spectrum sample Fig.4. The integral radio luminosity function for the Fig.5.Spacedensitiesasafunctionofredshiftfor5power QSOs of the Parkes 0.25-Jy flat-spectrum sample, com- puted in the five redshift ranges of Fig. 3: 0 0.5 (red), ranges,logP2.7 =25.8−26.2,26.2−26.6,26.6−27.0,27.0− − 27.4, and 27.4 27.8, denoted by decreasing line weight. 0.5 1.0 (green), 1.0 2.0 (blue), 2.0 3.0 (orange) and − − − − Abscissa values are the mean redshifts in each element of 3.0 5.0(lightblue).Verticallinesagainindicatelimitsof com−pletenessforeachredshiftrange,duetospectral-index (∆P2.7,∆z).Foreachofthe twolowestpowerranges,the final point with error bar represents incomplete data, as spread.Theuppercurveisthetotalintegratedluminosity thesepointsfallatpowersbelowthespectralcutoffsshown function, complete for all powers only at the very highest inFig.3.Upperlimits,representedbythesingledots,were luminosities. obtained by extrapolating the RLF to this power from higher powers. The actual values therefore lie somewhere along the two dashed lines. 4.1. The Power-Volume plane; using the whole sample This preliminary study drew attention to a possible Fig.7(left)showssourcesofSample3(Table2)inaplotof difficulty inthe analysisdue tothe curvednatureofsome radio luminosity vs. co-movingvolume.We need this new of the radio spectra. Jarvis & Rawlings (2000) examined sample for such a plot. Recall that Sample 1 (Table 1) thisinsomedetail,pointingouttheapparentlycurvedna- included all sources, not just QSOs, while Sample 2 ture ofmanyofthe radiospectrainvolved,andindicating (Table 2), although confined to QSOs, was drawn from howsuchaneffect,asteepeningtothehighfrequenciesin regions of the survey with different completeness limits. particular, might reduce or remove the significance of an In order for a plot of luminosity vs. z (or equivalently, apparent redshift cutoff. Their model-dependent analysis co-moving volume) to be interpreted, the sample must used only the highest-power objects and indicated that haveasinglesurveylimit.Sample3isthereforecomposed the apparent cutoff on the basis of such objects might of all QSOs from our data table of Paper 1 with survey have a significance level as low as that corresponding to 2σ.Theysuggestedthatestablishingtherealityofthecut- completeness limit at exactly S2.7 GHz = 0.25◦Jy (Fig. 1, Paper1),andagainatdeclinationsabove 40 forreasons offforsuchobjectstoahighlevelofsignificancemightbe − ofradio-spectralcompleteness.Fig.7showslinesofsurvey difficult even with all-sky samples. However,Fig. 6 shows completeness corresponding to 0.25 Jy for three different that there is no clear majority of sources with spectra radio spectral indices. steepening to the higher frequencies. Moreover, we show Theplotwithco-movingvolumeontheabscissarather belowthat the spectraldata inthe literaturearemislead- than redshift gives direct indication of space density. ing interms of the proportionofsourcesshowingspectral There is an apparent diminution in the density of points steepening to the higher frequencies. at redshifts above 2.5. The question is whether this is ∼ Subsequently we have considered alternative methods real and significant. In what follows we test the null hy- to study space density and redshift distribution, methods pothesis that the space density of QSOs at high redshifts to utilize the entire sample which can demonstrate sim- remains constant and equal to that at 1<z <3. ple attributes of the space-distribution without recourse Redshift information is not complete for Sample 3; in to modelling the luminosity function or its epoch depen- order to make comparison with prediction we must esti- dence. mate the number of possible objects at z > 3. Table 2 J.V. Wall et al.: The Parkes quarter-Janskyflat-spectrum sample 9 Fig.7. The Luminosity - Volume plane for the 252 QSOs with measuredredshifts, in survey areas with completeness limitS2.7GHz =0.25Jy(Sample3,Table2).Verticalgridlinesindicateredshifts,asmarkedalongthetopborder.The curved lines indicate survey completeness limits at 0.25 Jy for three spectral indices. Left: the sources plotted with symbolstoindicatedifferentspectralindicesα2.7 :soliddotsfor 0.4<α< 0.2;opencirclesfor 0.2<α<+0.2, 5.0GHz − − − crosses for +0.2 < α < +0.6, and stars for the extreme spectral inversions α > +0.6. Rest-frame luminosities (P2.7) for this plot were calculated assuming a power-law spectrum given by this index. Note that the dots lie above the α = 0.2 limit line; the open circles above the +0.2 line; the crosses above the +0.6 line; and the stars scatter to − below the +0.6 line. Right: The effects of considering spectral data at frequencies below the Parkes survey frequency (2.7 GHz). The values of P2.7 are substantially changed. Crosses indicate the original positions as in the left panel, while dots show the positions revised with improved estimates due to incorporationof lower-frequency data. presentsthe summary.The keyelementis the sub-sample 0225-065) escaped the CCD identification programme by of 16 objects in the sample of 268 for which redshifts are beingde-identifiedlateronthe basisofanimprovedradio not available. position. Had it been included we can be confident that an identification would have been obtained, as it was in The redshift distribution for QSOs is known to be a each of the 87 cases we tried. For these 5 objects, then, function of both apparentmagnitude andflux density,al- we use the CCD-identified QSOs with redshifts, totalling beit with huge scatter and only a gentle dependence in 10 in the sample, for which two redshifts exceeded 3. We each case. Thus in order to estimate redshift proportions thus anticipate 2/10 5 = 1.0 of the 5 objects will have for the objects without suchdata, we treatedthe identifi- × z >3.Thenumberofobjectsinthesamplewithmeasured cationsmadeonUKSTplatesandthosefromthe(deeper) z >3 is 10.Thus the number with which to compare pre- CCD observations separately. dictions for z > 3 is 10(observed)+1.4(estimated)= 11.4. Consider the 11 QSOs without redshifts and identi- The principal point is that redshift incompleteness does fied from UKST plates. Of the 242 objects identified on not impede our analysis. UKST plates and with measured redshifts, 8 have z > 3. There is no bias in the redshift measurements or lack of; Asimple analysismaybe carriedthroughonthe basis and thus we expect 8/242 11 = 0.36 of the 11 objects of Fig. 7. If we consider QSOs in specific narrow bins of × to have z > 3. The remaining 5 objects may be treated luminosityandsurveylimitimposedbyspectralindexand equally;the singleunidentifiedsourceinthe sample(PKS surveyfluxlimitS ,thensuchhorizontalstripesinFig.7 lim 10 J.V. Wall et al.: The Parkes quarter-Janskyflat-spectrum sample issue is not so important, because most sources detected inthemhavepower-lawspectracharacterizedbyanindex close to 0.75. In corresponding P z or P V planes, − − − most sources from low-frequency surveys cluster closely along or just to the left of the single limit line given by this spectral index.) The analysis of Shaver et al. (1996) attempted to cir- cumventthe difficulties bystickingtopowerssohighthat the observational cutoff, the survey completeness limit, did not come in to play. In doing so, the available sub- samplebecomessmallandthestatisticaluncertaintiesare inevitably larger. These difficulties suggest the following refinement. 4.2. Source-by-source analysis: the ‘Single-Source Survey’ Fig.6. The radio spectra of all sources in Sample 2, There is no need to stick to a single survey-limit line in Table 2, in their rest frame. Data are at observing fre- the P V plane. Each source can be considered alone, quencies of 0.365, 1.4, 2.7, 5.0, 8.40 and 8.87 GHz, and − conceptually the result of a survey which found it as a flux densities are normalizedby S , the interpolated rest- 0 single source. For each such ‘single-source survey’,a limit framefluxdensity at2.7GHz.The redlinesrepresentthe line maybe drawninthe planepeculiar to that object and brightest sources, those with S2.7GHz 2.0 Jy. ≥ incorporating all its radio-spectral information. The pre- diction of this object for sources at redshifts above 3 may then be added to the predictions from all ‘single-source intersectingthe curvedsurvey-cutofflinesprovideanarea surveys’ to derive a prediction total. In effect this is us- in the figure in which QSOs can be seen by the survey. ing the V method to predict the number of objects in On the null hypothesis, no redshift diminution, if we now max volumes at higher redshift on the hypothesis that space split this area into a region with z <3 and a region with density is uniform; it is doing so using the spectral prop- z >3, we can use the surface density of QSOs in the low- erties of each source individually. redshift area to form an expectation value for the higher redshift area. We chose the prediction region to be 1 < Afurtheradvantageinsuchaprocessisthatthereisno z <3 to coincide roughly with the plateau of the ‘quasar longeraneedtosticktoasampledefinedbyasingleflux- epoch’,andweselectedthehigh-redshiftregiontorunout densitylimit.Toimprovestatisticalweight,allzonesofthe to z = 8, the approximate limit to which we could hope surveycanbeused,nomatterwhattheflux-densitylimit, to see QSOs givenour survey limits and the knownrange providedofcoursethatthe valueofthe 2.7-GHzfluxden- of luminosity and spectral index. sity is greater than or equal to the completeness limit for This process described above can be refined by reduc- the area in which it was detected. (Sources for which this ing the stripes of radio power to zero width; each source is notthe caseweremarkedin the data-tableofPaper1.) thenbecomesapredictor,providedofcoursethatthesur- Each source in this analysis contributes a predicted num- veylimitallowsittobeseenbeyondaredshiftof3.Table4 berofsourcesgivenbytheratioofitsaccessibleco-moving presentsresultsofthisanalysisunderthesub-heading‘sin- volumeintheredshiftrange3<z <8tothatintherange gle survey cutoff’. The immediate result is the apparent 1 < z < 3. The sum of all such predicted sources, based one:apredictionofsignificantlymoreQSOsatz >3than on all sources observed in the redshift range 1 < z < 3, the 11.4 ‘seen’. gives us the total number of 3 < z < 8 sources expected The results reveala fundamental flaw of this analysis, in the survey for a constant comoving space density. namely what limit line to adopt, corresponding to which A sample appropriate to this analysis is Sample 2 of spectral index. It is apparent from Fig. 7 that adopting Table 2, giving a total of 379 radio QSOs, 355 with mea- α = 0.2 is extreme; but even confining the analysis suredredshifts.Fromananalysisanalogoustothatcarried − to narrow bands of spectral index does not define where outforSample3,weestimatethatcompleteidentification within that band the survey cutoff or completeness line andredshiftdatawouldadd1.8sourcestothe16members should be placed. The analysis at this point appears to of this sample observed to have z >3. confirmwhatthe eyeseesinFig.7,butshowsthattaking Asabasicanalysisofthis type,whenindividuallimits the figure at face value is dangerous. Moreover here we areappliedasdescribed,usingthe α5.0 spectralindex 2.7GHz haveusedthe2.7 5.0GHzspectralindex,characterizing appropriateto eachsource,apredictionof51.5sourcesin − each spectrum as a single power law; spectral curvature the redshiftrange3<z <8isobtained(Table4),c.f.the or indeed any complexity of radio spectrum has not been 17.8sources‘observed’.Howevera particularlyimportant considered.(Forlow-frequencysurveys,thespectral-index feature of the approachis that it enables incorporationof