The XXL Survey: XXXVI. Evolution and black hole feedback of high-excitation and low-excitation radio galaxies in XXL-S
Andrew Butler, Minh Huynh, Anna Kapinska, Ivan Delvecchio, Vernesa Smolcic, Lucio Chiappetti, Elias Koulouridis, Marguerite Pierre
AAstronomy & Astrophysics manuscript no. XXL-XXXVI-BH-FeedBack-20190429 © ESO 2019April 30, 2019
The XXL Survey
XXXVI. Evolution and black hole feedback of high-excitation andlow-excitation radio galaxies in XXL-S
Andrew Butler (cid:63) , Minh Huynh , , Anna Kapi´nska , , Ivan Delvecchio , Vernesa Smolˇci´c , Lucio Chiappetti ,Elias Koulouridis , , and Marguerite Pierre International Centre for Radio Astronomy Research (ICRAR), University of Western Australia, 35 Stirling Hwy,Crawley WA 6009, Australia CSIRO Astronomy and Space Science, 26 Dick Perry Ave, Kensington WA 6151, Australia National Radio Astronomy Observatory, 1003 Lopezville Rd, Socorro NM 87801, USA Physics Department, University of Zagreb, Bijeniˇcka cesta 32, 10002 Zagreb, Croatia INAF, IASF Milano, via Corti 12, 20133 Milano, Italy Institute for Astronomy & Astrophysics, Space Applications & Remote Sensing, National Observatory of Athens,GR-15236 Palaia Penteli, Greece AIM, CEA, CNRS, Universit´e Paris-Saclay, Universit´e Paris Diderot, Sorbonne Paris Cit´e, F-91191 Gif-sur-Yvette,FranceReceived date / Accepted date
ABSTRACT
The evolution of the comoving kinetic luminosity densities ( Ω kin ) of the radio loud high-excitation radio galaxies (RLHERGs) and the low-excitation radio galaxies (LERGs) in the ultimate XMM extragalactic survey south (XXL-S)field is presented. The wide area and deep radio and optical data of XXL-S have allowed the construction of the radioluminosity functions (RLFs) of the RL HERGs and LERGs across a wide range in radio luminosity out to high redshift( z = . ). The LERG RLFs display weak evolution: Φ ( z ) ∝ (1+ z ) . ± . in the pure density evolution (PDE) case and Φ ( z ) ∝ (1+ z ) . ± . in the pure luminosity evolution (PLE) case. The RL HERG RLFs demonstrate stronger evolutionthan the LERGs: Φ ( z ) ∝ (1+ z ) . ± . for PDE and Φ ( z ) ∝ (1+ z ) . ± . for PLE. Using a scaling relation to convert the1.4 GHz radio luminosities into kinetic luminosities, the evolution of Ω kin was calculated for the RL HERGs and LERGsand compared to the predictions from various simulations. The prediction for the evolution of radio mode feedback inthe Semi-Analytic Galaxy Evolution (SAGE) model is consistent with the Ω kin evolution for all XXL-S RL AGN (all RLHERGs and LERGs), indicating that the kinetic luminosities of RL AGN may be able to balance the radiative coolingof the hot phase of the IGM. Simulations that predict the Ω kin evolution of LERG equivalent populations show similarslopes to the XXL-S LERG evolution, suggesting that observations of LERGs are well described by models of SMBHsthat slowly accrete hot gas. On the other hand, models of RL HERG equivalent populations differ in their predictions.While LERGs dominate the kinetic luminosity output of RL AGN at all redshifts, the evolution of the RL HERGs inXXL-S is weaker compared to what other studies have found. This implies that radio mode feedback from RL HERGsis more prominent at lower redshifts than was previously thought. Key words. galaxies: general – galaxies: evolution – galaxies: active – galaxies: statistics – galaxies: luminosity function– radio continuum: galaxies
1. Introduction
Understanding how massive galaxies evolve is an importanttopic in modern astrophysics. Massive galaxies make up alarge fraction of the total baryonic matter in the universe,and therefore their evolution reflects how the universe asa whole has evolved. It is now commonly understood thatnearly all massive galaxies have supermassive black holes(SMBHs) at their centres (e.g. Kormendy & Ho 2013). Fur-thermore, the properties of SMBHs are related to the prop-erties of their host galaxies. For example, the masses ofSMBHs are correlated with the stellar velocity dispersions(e.g. Magorrian et al. 1998; Gebhardt et al. 2000; Graham (cid:63)
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Article number, page 1 of 27 a r X i v : . [ a s t r o - ph . GA ] A p r &A proofs: manuscript no. XXL-XXXVI-BH-FeedBack-20190429 lar medium, which would otherwise collapse to form stars(B¨ohringer et al. 1993; Binney & Tabor 1995; Forman et al.2005; Best et al. 2006; McNamara & Nulsen 2007; Cattaneoet al. 2009; Fabian 2012). Consequently, AGN can affect thestellar and gas content of their host galaxies, fundamentallyaltering their properties.AGN feedback is often thought of as existing in twoforms: ‘quasar’ mode and ‘radio’ mode (Croton et al. 2006).The quasar mode involves radiatively efficient accretionand feedback in the form of radiative winds, whereas theradio mode involves radiatively inefficient accretion andfeedback in the form of radio jets that carry kinetic en-ergy (Best & Heckman 2012 and references therein). Radiomode feedback has been identified as the most likely mecha-nism behind the heating of the interstellar medium becausegalaxy formation models that include this extra AGN com-ponent are able to more accurately reproduce many ob-served galaxy properties for z ≤ . (particularly at thehigh-mass end), including the optical luminosity function,colours, stellar ages, and morphologies (e.g. Bower et al.2006; Croton et al. 2006, 2016). Therefore, AGN feedback,and in particular radio mode feedback, is a crucial compo-nent to galaxy evolution models and fundamental to overallgalaxy evolution. This is likely due to the fact that most ofthe energy from the radio jets is deposited locally in thesystems that generate them, increasing the feedback effi-ciency compared to quasar mode feedback (B¨ohringer et al.1993; Carilli, Perley & Harris 1994; McNamara et al. 2000;Fabian et al. 2006).Radio mode feedback has been found to manifest in twodifferent AGN populations – high-excitation radio galax-ies (HERGs) and low-excitation radio galaxies (LERGs).HERGs and LERGs are characterised by different hostgalaxy properties. HERGs exhibit either strong [O iii ] emis-sion (e.g. Best & Heckman 2012; Hardcastle et al. 2013),high X-ray luminosity ( L X > erg s − , e.g. Xue et al.2011; Juneau et al. 2011), or redder mid-infrared colours(e.g. Jarrett et al. 2011; Mateos et al. 2012) than normalgalaxies. They also tend to have higher radio luminosi-ties (e.g. Best & Heckman 2012; Heckman & Best 2014),are hosted by less massive bluer galaxies (e.g. Tasse et al.2008; Janssen et al. 2012; Best & Heckman 2012; Hard-castle et al. 2013; Miraghaei & Best 2017; Ching et al.2017b), and fit into the unified AGN model as summarisedby Urry & Padovani (1995). The dominant form of feed-back in HERGs is the quasar mode, but a small fraction ofHERGs are radio loud, and therefore they exhibit some ra-dio mode feedback. This is manifested in some HERGs hav-ing red colours that are consistent with passively-evolvinggalaxies (e.g. Ching et al. 2017b; Butler et al. 2018b, here-after XXL Paper XXXI). On the other hand, LERGs showweak or no [O iii ] emission (e.g. Hine & Longair 1979; Lainget al. 1994; Jackson & Rawlings 1997) and little to no ev-idence of accretion-related X-ray or MIR emission typicalof a conventional AGN (e.g. Hardcastle et al. 2006, 2009;Mingo et al. 2014; G¨urkan et al. 2014; Ching et al. 2017b),and therefore do not fit into the unified AGN model. Theyalso have lower radio luminosities and are hosted by moremassive redder galaxies (e.g. Janssen et al. 2012; Best &Heckman 2012; Heckman & Best 2014; Miraghaei & Best2017; Ching et al. 2017b). LERGs are identified as AGNonly at radio wavelengths (Hickox et al. 2009), and thusonly exhibit radio mode feedback. It has been hypothesisedthat HERG and LERG differences are driven by a split in their Eddington-scaled accretion rates (e.g. Best et al.2005a; Hardcastle 2018a). LERGs tend to accrete the hotX-ray emitting phase of the intergalactic medium at a rateless than ∼ z (cid:46) ,HERGs evolve strongly and LERGs exhibit volume densi-ties that are consistent with weak or no evolution. On theother hand, Williams et al. (2018) constructed HERG andLERG RLFs using 150 MHz LOFAR observations of the ∼ Bo¨otes field, and found that the HERG RLFswere consistent with no evolution and the LERG RLFs ex-hibit negative evolution from z = . to z = . This demon-strates that separating between LERGs and HERGs is im-portant not only because the two populations have differenthost galaxies, but because they make different contribu-tions to radio mode feedback at different times and at dif-ferent observing frequencies. These different contributions Article number, page 2 of 27utler et al.: The XXL Survey XXXVI: Evolution and black hole feedback of HERGs and LERGs in XXL-S can be linked to the environments of HERGs and LERGsand the different origins of their fuelling gas (e.g. Chinget al. 2017a), which in turn can be used to constrain theAGN jet launching mechanism and its dependence on ac-cretion mode, which are poorly understood (e.g. Romeroet al. 2017 and references therein).The radio data in the 1.4 GHz studies probed no deeperthan S . ∼ mJy (over very large areas of (cid:38)
800 deg ),and so the RLFs are not well-constrained at the low-luminosity end ( L . (cid:46) W Hz − ) for intermediateto high redshifts ( z > . ). In addition, the local HERGand star-forming galaxy (SFG) RLFs from these papers dis-agree with each other for L . (cid:46) W Hz − , indicatingthat these two populations can be difficult to discriminateat low radio luminosities. More clarity on this discrepancyrequires a deep radio survey over a relatively wide areacombined with excellent multi-wavelength data in order tocapture the largest possible range of radio luminosities outto z ∼ . In light of this, the 25 deg ultimate XMM ex-tragalactic survey (Pierre et al. 2016; XXL Paper I) southfield (hereafter XXL-S) was observed with the AustraliaTelescope Compact Array (ATCA) at 2.1 GHz, achieving amedian rms sensitivity of σ ≈ µ Jy beam − and a resolu-tion of ∼
5” (Butler et al. 2018a, hereafter XXL Paper XVIII;Smolˇci´c et al. 2016, hereafter XXL Paper XI). Due to thesize and depth of XXL-S, rare luminous objects not foundin other fields have been captured and a large populationof low-luminosity AGN have been detected simultaneously.The large area and depth of the radio observations of XXL-S, combined with the excellent multi-wavelength coverage,enables the construction of the RL HERG and LERG RLFsin multiple redshift bins. It also enables the bright and faintend of the RLF to be probed over a large redshift range,which has been difficult thus far due to small sky coverage(e.g. Smolˇci´c et al. 2009, 2017b) or shallow radio obser-vations of previous surveys (Best & Heckman 2012; Bestet al. 2014; Pracy et al. 2016). This new capability allowsfor a new measurement of the cosmic evolution of the radiomode feedback of RL HERGs and LERGs out to high red-shift ( z ∼
1) that includes a more complete sampling of theradio luminosity distribution of the two populations.The purpose of this paper is to measure the evolutionof the kinetic luminosity densities of the RL HERGs andLERGs in XXL-S and compare the results to the litera-ture, particularly simulations of radio mode feedback. Sec-tion 2 summarises the data used, while Section 3 describesthe construction of the RLFs and the comparison to otherRLFs in the literature. The measurement of the evolutionof the RL HERG and LERG RLFs is discussed in Section4. Section 5 details the calculations involved in measuringthe RL HERG and LERG kinetic luminosity densities andcompares the results to the literature. Section 6 draws theconclusions. Throughout this paper, the following cosmol-ogy is adopted: H = . km s − Mpc − , Ω m = . and Ω Λ = . (Hinshaw et al. 2013). The following notationfor radio spectral index ( α R ) is used: S ν ∝ ν α R .
2. Data
The ATCA 2.1 GHz radio observations of XXL-S reacheda median rms of σ ≈ µ Jy beam − and a resolution of ∼ (cid:48)(cid:48) over 25 deg . The number of radio sources extracted Table 1.
Results of classification of XXL-S radio sources fromXXL Paper XXXI. Unclassified AGN potentially include LERGsand RL HERGs, while unclassified sources potentially includeLERGs, RQ HERGs, and SFGs.
Source type Number Fraction of final sampleLERGs 1729 36.3%RL HERGs 1159 24.4%RQ HERGs 296 6.2%SFGs 558 11.7%Unclassified AGN 910 19.1%Unclassified sources 106 2.2%above 5 σ is 6287. More details of the observations, datareduction and source statistics can be found in XXL PaperXVIII and XXL Paper XI. Out of the 6287 radio sources in the XXL-S catalogue, 4758were cross-matched to reliable optical counterparts in theXXL-S multi-wavelength catalogue (Fotopoulou et al. 2016;XXL Paper VI) via the likelihood ratio method (Ciliegiet al. 2018; XXL Paper XXVI). For a discussion of how ex-tended radio sources (for which maximum likelihood meth-ods tend to fail) were treated, see Sections 3.6 and 3.7 inXXL Paper XVIII. XXL Paper XXXI describes the clas-sification of the 4758 optically-matched radio sources asLERGs, radio loud (RL) HERGs, radio quiet (RQ) HERGs,and star-forming galaxies (SFGs), but some sources (includ-ing radio AGN) are unclassified because of a lack of dataavailable for those sources. In this context, RL HERGs aredefined as high-excitation sources with radio emission orig-inating from an AGN, and RQ HERGs are defined as high-excitation sources with radio emission that likely originatesfrom star formation, although there could be some con-tribution from radio AGN in these sources. The definitionof ‘radio galaxy’ one adopts (whether a galaxy with radioemission from an AGN or a galaxy with detectable radioemission arising from either AGN or star formation) has nobearing on the results of this paper, as RQ HERGs were re-moved from the RL AGN sample (comprised of RL HERGsand LERGs). Once the HERGs were identified, the LERGswere separated from the SFGs on the basis of optical spec-tra, colours, and radio AGN indicators, particularly theirradio excesses (the ratio of 1.4 GHz radio luminosity toSFR derived by magphys ). See Section 3.7 of XXL PaperXXXI for an overview of the decision tree used to classifythe XXL-S radio sources. Table 1 summarises the numberof sources classified into each source type. Tables 2 and 3display the list of columns in the catalogue containing theoptically-matched XXL-S radio sources and the full suite oftheir radio and associated multi-wavelength data (see XXLPaper XXXI). The catalogue is available as a queryabledatabase table XXL ATCA 16 class via the XXL MasterCatalogue browser . A copy will also be deposited at theCentre de Donn´es astronomiques de Strasbourg (CDS) . http://cosmosdb.iasf-milano.inaf.it/XXL http://cdsweb.u-strasbg.fr Article number, page 3 of 27 &A proofs: manuscript no. XXL-XXXVI-BH-FeedBack-20190429 Table 2.
Columns 1-38 in the catalogue containing the optically-matched XXL-S radio sources and the full suite of their radioand associated multi-wavelength data (see XXL Paper XXXI). The table is available online (see text for details). The cataloguehelp file explains each quantity and their possible values.
Quantity Description UnitsIAU name IAU-registered radio source numeric identifier –ID XXL-S radio source catalogue identification number –RAdeg Right ascension (J2000) degDEdeg Declination (J2000) degredshift Final redshift of radio source –zspec flag Spectroscopic redshift flag –classification Final source classification –agn radio L flag Radio AGN (luminosity) flag –agn radio morph flag Radio AGN (morphology) flag –agn radio alpha flag Radio AGN (spectral index) flag –agn radio excess flag Radio AGN (radio excess) flag –agn xray L flag X-ray AGN (luminosity) flag –agn xray HR flag X-ray AGN (hardness ratio) flag –agn sed flag SED AGN flag –agn IRAC1 IRAC2 flag MIR AGN (IRAC1+IRAC2) flag –agn W1 W2 flag MIR AGN (W1+W2) flag –agn W1 W2 W3 flag MIR AGN (W1+W2+W3) flag –agn W1 W2 W3 W4 flag MIR AGN (W1+W2+W3+W4) flag –agn bpt flag BPT AGN flag –agn OIII flag [O iii ] AGN flag –agn spec temp flag AGN spectral template flag –Sp 1400MHz 1.4 GHz peak flux density mJy beam − S 1400MHz 1.4 GHz integrated flux density mJySNR 1400MHz 1.4 GHz S / N –alpha R Radio spectral index –alpha R err Radio spectral index error –L R 1800MHz 1.8 GHz radio luminosity W Hz − L R 1400MHz 1.4 GHz radio luminosity W Hz − alpha X X-ray spectral index –gamma X X-ray photon index –Xray HR X-ray hardness ratio –L X 2 10 keV 2-10 keV X-ray luminosity erg s − W1WISEmag WISE W apparent magnitude magW2WISEmag WISE W apparent magnitude magW3WISEmag WISE W apparent magnitude magW4WISEmag WISE W apparent magnitude magIRAC1mag I RAC (3.6 µ m) apparent magnitude magIRAC2mag I RAC (4.5 µ m) apparent magnitude mag
3. Radio luminosity functions
The RLFs were constructed using the / V max method(Schmidt 1968), which is summarised here. The maximumdistance out to which each source can be detected before itfalls below the detection limit of the ATCA XXL-S radiosurvey was calculated according to d max = d src (cid:115) ( S / N ) src ( S / N ) det , (1)where d src is the comoving distance of the source at its red-shift, ( S / N ) src is the source’s S / N at 1.8 GHz (the effectivedetection frequency) and ( S / N ) det = is the 1.8 GHz detec-tion limit. The corresponding maximum volume V max thatthe source can occupy was calculated via V max = Ω frac π ( d − d ) (2) where Ω frac ≈ . × − is the fraction of the whole skythat XXL-S covers and d min is the comoving distance cor-responding to the lower redshift limit of the redshift binthe source is contained in. It is common practice to alsoaccount for the limiting optical magnitude in determining V max , but including the optical V max in the calculation re-sulted in almost no difference to the RLFs, especially afterthe M i < − optical cut was made to measure the evolutionof the RL HERGs and LERGs (see Section 4.1). Therefore,only the radio V max was considered.For comparison with the literature, the rest-frame 1.4GHz monochromatic luminosity densities (hereafter lumi-nosities) of each source were calculated. This was done byconverting each 1.8 GHz flux density into a 1.4 GHz fluxdensity ( S . ) using the radio spectral index α R for eachsource (see Section 2.4.3 and Appendix A of XXL PaperXXXI for details). Then the 1.4 GHz luminosity of each Article number, page 4 of 27utler et al.: The XXL Survey XXXVI: Evolution and black hole feedback of HERGs and LERGs in XXL-S
Table 3.
Columns 39-83 in the catalogue containing the optically-matched XXL-S radio sources and the full suite of their radioand associated multi-wavelength data (see XXL Paper XXXI). The table is available online (see text for details). The cataloguehelp file explains each quantity and their possible values.
Quantity Description UnitsNUVGALEXMag NUV (GALEX) absolute magnitude maguSDSSMag u (SDSS) absolute magnitude maggBCSMag g (BCS) absolute magnitude maggDECamMag g (DECam) absolute magnitude magrDECamMag r (DECam) absolute magnitude magiBCSMag i (BCS) absolute magnitude magiDECamMag i (DECam) absolute magnitude magzDECamMag z (DECam) absolute magnitude magJVISTAMag J (VISTA) absolute magnitude magKVISTAMag K (VISTA) absolute magnitude magiDECammag i (DECam) apparent magnitude magzDECammag z (DECam) apparent magnitude magsfr magphys med Median magphys star formation rate M (cid:12) yr − stellar mass magphys stellar mass M (cid:12) zphot Photometric redshift –opt spectrum ID Optical spectrum ID –zspec Spectroscopic redshift –zspec qual flag Spectroscopic redshift quality flag –SNR cont Continuum S / N of optical spectrum –spectral template Best fit marz spectral template –OII lambda [O ii ] line wavelength ˚AOII rel flux [O ii ] line relative flux –OII SNR [O ii ] line S / N –OII EW [O ii ] line equivalent width m˚AOII EW err [O ii ] line equivalent width error m˚AHb lambda H β line wavelength ˚AHb rel flux H β line relative flux –Hb SNR H β line S / N –Hb EW H β line equivalent width m˚AHb EW err H β line equivalent width error m˚AOIII lambda [O iii ] line wavelength ˚AOIII rel flux [O iii ] line relative flux –OIII SNR [O iii ] line S / N –OIII EW [O iii ] line equivalent width m˚AOIII EW err [O iii ] line equivalent width error m˚AHa lambda H α line wavelength ˚AHa rel flux H α line relative flux –Ha SNR H α line S / N –Ha EW H α line equivalent width m˚AHa EW err H α line equivalent width error m˚ANII lambda [N ii ] line wavelength ˚ANII rel flux [N ii ] line relative flux –NII SNR [N ii ] line S / N –NII EW [N ii ] line equivalent width m˚ANII EW err [N ii ] line equivalent width error m˚Asource was computed with the following equation: L . = π d L S . ( + z ) −( + α R ) , (3)where d L is the luminosity distance in metres and z is thesource’s best redshift (spectroscopic if available, otherwisephotometric).Each radio source was placed in its corresponding red-shift bin, all four of which are listed in Table 4. An upperlimit of z = . was chosen for three reasons: 1) the majority of the positive evolution in RL AGN takes place between < z < . (e.g. see Smolˇci´c et al. 2017b, Ceraj et al.2018); 2) it allows a more direct comparison between theRLFs of Smolˇci´c et al. (2009) and Smolˇci´c et al. (2017b); 3)almost all ( ∼ z < . .In each redshift bin, every source was placed in its corre-sponding L . bin, which are . W Hz − (1 magnitude) Article number, page 5 of 27 &A proofs: manuscript no. XXL-XXXVI-BH-FeedBack-20190429
Table 4.
Redshift bins chosen for the XXL-S RLFs. See Section3.1 for justification of the z = . upper limit. Redshift Redshift Median Numberbin number range redshift of sources1 . < z < . . < z < . . < z < . . < z < . L . bin, Φ , is then: Φ = N (cid:213) i = f i V max , i , (4)where the sum is over all N galaxies in the L . bin and f i is the radio completeness correction factor. If source hada peak flux density S p < . mJy (the flux density regimeexhibiting less than ∼ f i was calculatedas the inverse of the completeness fraction at the source’sflux density, as shown in Figure 11 of XXL Paper XVIII.Otherwise, f i = . The uncertainty in Φ was calculatedaccording to d Φ = (cid:118)(cid:117)(cid:116) N (cid:213) i = (cid:18) f i V max , i (cid:19) . (5) < z < Using the classifications of the radio sources from XXL Pa-per XXXI, the RLFs were initially constructed for the fol-lowing source types: all radio sources, all RL AGN (LERGsplus RL HERGs), and SFGs (which includes RQ HERGsbecause the dominant source of radio emission is likely tobe star formation).Figure 1 shows the 1.4 GHz RLF for all radio sources,all RL AGN, and SFGs (including RQ HERGs) in the localuniverse (0 < z < ∼ < z < Φ between the definite RL Fig. 1. < z < Fig. 2. < z < HERG RLF and the RLF that results from combining thedefinite RL HERGs with all unclassified RL AGN. The redcircles represent the equivalent for LERGs. The upper er-ror bars represent the upper extrema of the error bars fromthe RL HERG and LERG plus all unclassified RL AGNRLFs, and the lower error bars represent the lower extremaof the error bars from the definite RL HERG and LERGRLFs. The blue and red circles, with their correspondingerror bars, have been chosen as the data points that rep-resents the final RL HERG and LERG RLFs, respectively.These data are shown in Table 5.
Article number, page 6 of 27utler et al.: The XXL Survey XXXVI: Evolution and black hole feedback of HERGs and LERGs in XXL-S
Table 5.
RLF data for all XXL-S sources, SFGs (including RQ HERGs), all RL AGN, RL HERGs, and LERGs in the localuniverse (0 < z < L . ) represents the median value for each 1.4 GHz radio luminosity bin (which are 0.4 dex, or 1mag, wide), N is the number of sources in each log( L . ) bin for the given population, and log( Φ ) is the median volume densityper log( L . ) bin for the given population. N corresponds to the median number of sources between the definite RL HERGand LERG RLFs and the RLFs that include the definite RL HERGs and LERGs plus all unclassified RL AGN added to eachpopulation. For RL HERGs and LERGs, if N is not a whole number in a given log( L . ) bin, it indicates that there is an oddnumber of unclassified RL AGN in that log( L . ) bin. All sources SFGs RL AGN RL HERGs (median) LERGs (median)log( L . ) N log( Φ ) N log( Φ ) N log( Φ ) N log( Φ ) N log( Φ )(W Hz − ) (mag − Mpc − ) (mag − Mpc − ) (mag − Mpc − ) (mag − Mpc − ) (mag − Mpc − )21.8 66.0 -3.24 + . − . + . − . + . − . + . − . + . − . + . − . + . − . + . − . + . − . + . − . + . − . + . − . + . − . + . − . + . − . + . − . + . − . + . − . + . − . + . − . + . − . + . − . + . − . + . − . + . − . + . − . + . − . + . − . + . − . + . − . + . − . + . −∞ + . − . + . − . + . − . + . − . + . − . + . − . + . − . + . − . + . − . + . − . + . − . + . −∞ + . −∞ + . −∞ Fig. 3. < z < < z < Figures 3, 4, and 5 show the XXL-S 1.4 GHz RLFs in red-shift bins 0.3 < z < < z < < z < The XXL-S RLFs for RL AGN and SFGs are similar tothose of Pracy et al. (2016) (hereafter Pracy16) and Best& Heckman (2012), although the XXL-S volume densitiesare higher (by a factor of ∼ < log[ L . (W Hz − ) ] < Fig. 4. < z < were classified and to the deeper XXL-S radio and opticaldata (see Section 3.4.2 for an explanation). The RLFs fromPracy16 are consistent with the RLFs from Mauch & Sadler(2007), which are known to be in good agreement with pre-viously constructed RLFs (e.g. Sadler et al. 2002). There-fore, the RLFs for RL AGN and SFGs in XXL-S broadlyagree with previously constructed RLFs for the local uni-verse, but are different in a way that reflects the uniqueXXL-S data and radio source classification scheme. The XXL-S LERG RLFs are consistent with (within 1 σ of) the LERG RLFs from Pracy16 and Best & Heckman(2012), but the HERG RLF from Pracy16 shows lower vol-ume densities than the XXL-S RL HERG RLF, and theone from Best & Heckman (2012) is lower still. This is dueto two things: the classification method used to distinguish Article number, page 7 of 27 &A proofs: manuscript no. XXL-XXXVI-BH-FeedBack-20190429
Table 6.
RLF data for all RL AGN, RL HERGs, and LERGs in XXL-S for 0.3 < z < RL AGN RL HERGs (median) LERGs (median)log( L . ) N log( Φ ) N log( Φ ) N log( Φ )(W Hz − ) (mag − Mpc − ) (mag − Mpc − ) (mag − Mpc − )23.4 252.0 -4.64 + . − . + . − . + . − . + . − . + . − . + . − . + . − . + . − . + . − . + . − . + . − . + . − . + . − . + . − . + . − . + . − . + . − . + . − . + . − . + . − . + . − . Table 7.
RLF data for all RL AGN, RL HERGs, and LERGs in XXL-S for 0.6 < z < RL AGN RL HERGs (median) LERGs (median)log( L . ) N log( Φ ) N log( Φ ) N log( Φ )(W Hz − ) (mag − Mpc − ) (mag − Mpc − ) (mag − Mpc − )23.8 197.0 -5.06 + . − . + . − . + . − . + . − . + . − . + . − . + . − . + . − . + . − . + . − . + . − . + . − . + . − . + . − . + . − . + . − . + . − . + . − . + . − . + . − . + . − . + . − . + . −∞ + . −∞ Table 8.
RLF data for all RL AGN, RL HERGs, and LERGs in XXL-S for 0.9 < z < RL AGN RL HERGs (median) LERGs (median)log( L . ) N log( Φ ) N log( Φ ) N log( Φ )(W Hz − ) (mag − Mpc − ) (mag − Mpc − ) (mag − Mpc − )24.2 178.0 -5.44 + . − . + . − . + . − . + . − . + . − . + . − . + . − . + . − . + . − . + . − . + . − . + . − . + . − . + . − . + . − . + . − . + . − . + . − . + . − . + . − . + . − . + . − . + . − . + . − . RL HERGs from RQ HERGs and SFGs and the optical andradio depths probed by each sample.The RLFs constructed by Pracy16 use the sample of ra-dio galaxies in the LARGESS survey classified by Chinget al. (2017b), who primarily employed optical spectro-scopic diagnostics to determine the origin of the radio emis-sion in each source. For example, all radio sources at z < . that had L . ≤ W Hz − and that were located inthe star-forming galaxy region of the BPT diagram (belowthe Kauffmann et al. 2003 line) were classified as SFGs. Inaddition, all sources in the AGN region of the BPT diagram(above the Kewley et al. 2001 line) were considered radio-loud AGN, unless their radio luminosity placed them within3 σ of the one-to-one relation between the SFR inferred by L . and the SFR inferred by the H α line luminosity, asfound in Hopkins et al. (2003). In the latter case, they wereconsidered radio-quiet AGN (i.e. AGN existing in galaxiesin which the origin of the radio emission is predominantlystar formation). All other sources were considered radio-loud AGN and separated into LERGs and HERGs on thebasis of their EW([OIII]). The XXL-S radio sources were classified differently: all XXL-S HERGs were identified be-fore any other sources (no matter where they lied in theBPT diagram), whereas the SFGs in the LARGESS sam-ple were identified first and assumed to all lie in the star-forming galaxy region of the BPT diagram. However, Figure15 of XXL Paper XXXI shows that some XXL-S galaxiesin this region have EW([OIII]) > z > . . These are two verydifferent ways of classifying radio sources and evidently leadto different RLFs, especially for RL HERGs.The effect that different classification techniques haveon the final classification results is also reflected in the dif- Article number, page 8 of 27utler et al.: The XXL Survey XXXVI: Evolution and black hole feedback of HERGs and LERGs in XXL-S
Fig. 5. < z < ferences between the HERG and SFG RLFs from Pracy16and Best & Heckman (2012). Best & Heckman (2012) weremore strict in identifying HERGs than Pracy16 because theauthors had access to more spectroscopic diagnostics. Themain difference between the two classification methods isthat Best & Heckman (2012) employed a method compar-ing the strength of the 4000 break ( D ) to the ratioof radio luminosity to stellar mass ( L rad / M ∗ ) . Pracy16 didnot employ this method because, as they point out, Her-bert et al. (2010) showed that a sample of high luminos-ity HERGs clearly exhibiting radio emission from an AGNhave a range of D values that are spread among boththe AGN and SFG regions of the D vs L rad / M ∗ plot.In addition, Figure 9 in Best et al. (2005b) demonstratesthat some sources identified as AGN in the BPT diagramfall in the SFG region of this technique. Therefore, some ofthe sources that Best & Heckman (2012) classified as SFGsPracy16 would have classified as HERGs, which caused thevolume densities of the Pracy16 HERGs to increase rela-tive to the Best & Heckman (2012) HERGs. This is evidentfrom Figure 2. At the same time, the volume densities ofthe Best & Heckman (2012) SFGs are increased relative tothe Pracy16 SFG RLF. This is reflected in Figure 1, whichshows the Best & Heckman (2012) SFG RLF slightly offsetabove the Pracy16 SFG RLF.In addition, XXL-S probed deeper in the optical than ei-ther of these two other samples, and so more optical sourceswere available to be cross-matched to the radio sources.The sample of Pracy16 probed down to i -band magnitude m i < . , whereas XXL-S probed down to m i = . (XXLPaper VI; Desai et al. 2012, 2015; XXL Paper XXXI). Thedifference this made can be seen in the fainter absolute mag-nitudes present in the XXL-S RL HERG population. Figure6 in Pracy16 shows that, in their local redshift bin, virtu-ally no HERGs with L . > W Hz − are fainter than M i ≈ − , but ∼
44% (45/102) of the XXL-S RL HERGs The central wavelength of the i -band (DECam) is 784 nm(Flaugher et al. 2015). with L . > W Hz − in the local redshift bin have M i > − . Clearly, the deeper optical data available forXXL-S detected faint RL HERGs at z < . missed byother surveys, which contributed to an increase in the vol-ume densities of the RL HERGs compared to the Pracy16and Best & Heckman (2012) samples.Furthermore, Pracy16 applied a radio flux density cutof S . > m i < . to their local RLFs. In order to properly com-pare the XXL-S sample to the Pracy16 sample, these cutsshould be applied to the XXL-S data. However, applyingthe S . > S . ∼ L . values were calculated usingthe flux densities of the effective frequency ( ∼ α = − . spectral index to all sources to calculate the 1.4 GHz lumi-nosities. Accordingly, applying a 1.4 GHz flux density cutto a 1.8 GHz sample effectively redistributes the L . values of the sources, changing the shape of the 1.4 GHzRLF. Therefore, for the purposes of comparing the Pracy16sample and the XXL-S sample as fairly as possible, a cutof S . > m i < . cut.The RLFs were then reconstructed using the 1.8 GHz lumi-nosities. The resulting 1.8 GHz RL HERG and LERG RLFsare shown in Figure 6. This time, the RL HERG RLF forXXL-S is consistent with that of Pracy16 within 1-2 σ at allluminosities, albeit lower for L . (cid:46) W Hz − . Theremaining differences are probably due to the classificationmethods and differences in the L . values. It is likelythat more low luminosity RL HERGs would have been ableto be identified if more XXL-S sources had a spectrum avail-able. The m i < . cut simultaneously lowered the XXL-SLERG RLF for L . (cid:46) W Hz − , but this flatten-ing at low luminosities is also evident in the LERG RLFfrom Best & Heckman (2012), which was constructed us-ing a relatively bright sample of optical counterparts (with r -band magnitudes between . ≤ m r ≤ . ). The dif-ferences between XXL-S RL HERG and LERG RLFs andthose from Pracy16 and Best & Heckman (2012) for the lo-cal universe ( < z < . ) can be confidently attributed todifferences in the optical and radio depth probed by eachsample and to the classification criteria used to identify RLHERGs and LERGs. < z < The RLFs for radio AGN in the COSMOS field fromSmolˇci´c et al. (2009) and Smolˇci´c et al. (2017b) are shownin Figures 3-5 as the black dashed lines and black dashdot lines, respectively. The XXL-S and COSMOS RL AGNRLFs are consistent (within σ , where σ is the uncertainty The central wavelength of the r -band (DECam) is 642 nm(Flaugher et al. 2015). Article number, page 9 of 27 &A proofs: manuscript no. XXL-XXXVI-BH-FeedBack-20190429 Fig. 6.
RL HERG and LERG RLFs for XXL-S in < z < . forthe sub-sample that corresponds to the cut that Pracy16 appliedto their local HERG and LERG RLFs ( m i < . and S . > σ ) with the HERG RLF fromPracy16 at all radio luminosities sampled in XXL-S. in the COSMOS RLFs) at all radio luminosities plotted inall redshift bins, except for redshift bin 3 ( . < z < . ).The XXL-S RL AGN RLF in this bin has a lower normal-isation (at a > σ level) than the Smolˇci´c et al. (2017b)COSMOS RLF for L . < W Hz − . However, thisis probably due to the fact that the COSMOS RLF wasbinned between . < z < . , so the median redshift inthat bin is higher than for XXL-S. The offset is likely dueto evolution of the sources, and therefore does not consti-tute a major discrepancy.Overall, the XXL-S RLFs for all RL AGN are ingood agreement with (within 3 σ of) the COSMOS RLFs(Smolˇci´c et al. 2009, 2017b) for all radio AGN in red-shift bins 2-4 ( . < z < . ). The similarity between thethree RLFs is probably due to the fact that both fieldsprobed similar limiting magnitudes in the i -band (COS-MOS probed m i ≤ and XXL-S probed m i ≤ . ). De-spite the similarities, the high redshift ( . < z < . ) XXL-S results are more significant than the high redshift resultsfor COSMOS because XXL-S probed a larger volume. Theremaining differences between the COSMOS and XXL-SRLFs are likely due to cosmic variance in the survey areas,different median redshifts, and the different radio depths(the VLA-COSMOS 1.4 GHz Large/Deep Projects reachedan rms noise of ∼ ∼ µ Jy beam − , respectively, andthe VLA-COSMOS 3 GHz Large Project reached ∼ µ Jybeam − ). < z < In order to ensure near 100% optical and radio completenessfor the analysis of HERG and LERG evolution, Pracy16constructed the RLFs using a sub-sample of sources with M i < − and S . > M i < − and S . > < z < . ) for XXL-Sbecause it left virtually no sources available for the con-struction of the local RLFs. However, this cut was able tobe made for the higher redshift bins.Figure 7 shows the RLFs in XXL-S for redshift bin 2( . < z < . ) for the sub-sample of RL HERGs andLERGs with M i < − and S . > . < z < . ). Despite small differences in theredshift ranges of the samples, the XXL-S RL HERG andLERG RLFs for sources with M i < − and S . > . < z < . are consistent with (within 1 σ of) theHERG and LERG RLFs from Pracy16 for . < z < . .Figure 8 shows the RLFs in XXL-S for redshift bin 3( . < z < . ) for the sub-sample of RL HERGs andLERGs with M i < − and S . > . < z < . ) and from Best et al. (2014) fortheir second redshift bin ( . < z < ). Best et al. (2014)used eight different samples to construct their final sample,but given that 90% of their radio sources have S . > M i < − and S . > . < z < . are consistent with (within ∼ σ of) theHERG and LERG RLFs from Pracy16 for . < z < . and from Best et al. (2014) for . < z < .The fact that the XXL-S LERG and (particularly) RLHERG RLFs are consistent with that of Pracy16 and Bestet al. (2014) when the samples are matched in optical mag-nitude depth and radio flux density as closely as possiblevalidates the construction of the RLFs made using the fullXXL-S sample. It is also strong evidence that RL HERGsat all radio luminosities exist in galaxies with a wide rangeof optical luminosities, some of which are missed in shallowsurveys. Raising the optical magnitude limit of the XXL-Ssources to M i < − and increasing the radio flux den-sity limit to S . > z > . ( L . > W Hz − ).
4. Evolution of RL HERGs and LERGs
It is possible that a number of the radio sources withoutoptical counterparts exist at z < . (the maximum redshiftout to which the RLFs in this paper are constructed). Ifthis is the case, the RLFs would be missing galaxies thatshould be included, which would affect the measurement ofthe evolution of the RL HERGs and LERGs.In order to assess the optical counterpart completenessof the optically-matched radio sources in XXL-S, the z -band source counts for these sources was constructed for The central wavelength of the z -band (DECam) is λ = 926nm (Flaugher et al. 2015).Article number, page 10 of 27utler et al.: The XXL Survey XXXVI: Evolution and black hole feedback of HERGs and LERGs in XXL-S Fig. 7. M i < − and S . > . < z < . ). There areonly four log( L . ) bins for the XXL-S data because of the M i and S . cuts. For comparison, the RLFs for HERGs andLERGs from Pracy16 for . < z < . are shown as the blueand red dashed lines, respectively. Fig. 8. M i < − and S . > . < z < . ). The RLFsfor HERGs and LERGs from Pracy16 for . < z < . areshown as the blue and red long-dashed lines, respectively. TheHERG and LERG RLFs from Best et al. (2014) for . < z < . are shown as the blue and red short-dashed lines, respectively. < z < z -band source countsfor the ∼ COSMOS field (Schinnerer et al. 2007),which has ∼ i + AB < (see Laigle et al. 2016). The COSMOS z -bandsource counts were constructed by selecting a sample ofoptically-matched COSMOS radio sources with S . ≥ µ Jy ( S / N ≥ z -band source counts, defined as thenumber of z -band sources per 0.5 magnitude bin per squaredegree, for XXL-S and COSMOS. The XXL-S source counts Fig. 9. z -band (AB) source counts from COSMOS and XXL-Sfor sources with S . > µ Jy and at z < . in both surveys.The y-axis is the number of sources per 0.5 magnitude per squaredegree and the x-axis is z -band apparent magnitude (AB) in binsof 0.5 magnitude. The error bars for each bin are calculated as σ = √ N srcs − deg − . The COSMOS source counts arewithin 3 σ of the XXL-S source counts for each magnitude bin,but for < m z < . the COSMOS counts are systematicallyhigher the XXL-S counts, indicating that XXL-S potentially hasless than ∼ m z > . are within 3 σ of the COSMOS source counts at all m z val-ues, but for m z > the COSMOS counts are systematicallyhigher than the XXL-S counts (excluding the m z > . bins with large uncertainties). Since the COSMOS field ismissing virtually none of the optical counterparts for theradio sources corresponding to the XXL-S field ( S . > µ Jy), this may indicate that the optical counterpartcompleteness for XXL-S radio sources with m z > is lessthan ∼ z = . . Figure 10 shows M i as a function of redshift for XXL-S RL HERGs and LERGs.In the highest redshift bin ( . < z < . ), the faintestLERG has M i ≈ − . Therefore, in order to probe the sameoptical luminosity distribution for both the LERGs and RLHERGs and to minimise Malmquist bias, a cut of M i < − was chosen. A brighter optical cut would leave too fewsources in the local redshift bin to construct an RLF ofsufficient precision. For the remainder of this paper, the sample that is usedfor analysis is the subset of XXL-S RL HERGs and LERGsthat have M i < − (unless otherwise specified). Figure 11shows the local RLF for RL HERGs and LERGs when the M i < − cut has been applied, and Figures 12, 13, and 14show the RLFs for RL HERGs and LERGs with M i < − in redshift bins 2, 3, and 4, respectively. Tables 9-12 showthe RLF data for all RL AGN, RL HERGs and LERGswith M i < − in redshift bins 1-4, respectively. The RLF Article number, page 11 of 27 &A proofs: manuscript no. XXL-XXXVI-BH-FeedBack-20190429
Fig. 10. M i as a function of redshift for all XXL-S radio sources.At the high redshift end, the faintest LERG reaches down to M i ≈ − , as shown by the dashed black line. Therefore, onlysources with M i < − are included in analysis of the RL HERGand LERG evolution. Fig. 11.
Local (0 < z < M i < − . The best fit function for the RL HERGs isthe solid blue line and the best fit function for the LERGsis the solid red line. The fits exclude the data points withlog[ L . (W Hz − )] < m i < . (including all sources) and M i < − are shown. data in these tables are used to measure the evolution of theXXL-S RL HERGs and LERGs and their kinetic luminositydensities. The RLF of a radio source population can be parametrisedusing the following double power law as the functional form
Fig. 12. M i < − in 0.3 < z < Fig. 13. M i < − in 0.6 < z < (Dunlop & Peacock 1990; Mauch & Sadler 2007): Φ ( L ) = Φ ∗ ( L ∗ / L ) α + ( L ∗ / L ) β , (6)where Φ ∗ is the RLF normalisation, L ∗ is the luminosity atwhich Φ ( L ) starts decreasing more rapidly (the ‘knee’ in theRLF), α is the slope at low luminosities (i.e. luminositieslower than L ∗ ), and β is the slope at high luminosities (i.e.luminosities higher than L ∗ ). Other functional forms havebeen used in previous work (e.g. Saunders et al. 1990; Sadleret al. 2002; Smolˇci´c et al. 2009), but many recent authors(e.g. Best et al. 2014; Heckman & Best 2014; Smolˇci´c et al.2017b; Pracy16) have used Equation 6. In order to be ableto compare the results of this work to theirs more directly,Equation 6 is used to model the XXL-S RLFs. Article number, page 12 of 27utler et al.: The XXL Survey XXXVI: Evolution and black hole feedback of HERGs and LERGs in XXL-S
Fig. 14. M i < − in 0.9 < z < Similar to the HERG RLF in Pracy16, the XXL-S RLHERGs in the local redshift bin have very few objects athigh radio luminosities ( L . > W Hz − ). This re-sults in a poor constraint on the slope of the RL HERG RLFbeyond these luminosities, which means that the β parame-ter can approach - ∞ with minimal impact on the χ statisticof the fit. Pracy16 approached this by setting an upper limiton the parameter of β < . However, since the local XXL-SRL HERG RLF does not probe luminosities as high as thatof Pracy16 because of the smaller area of XXL-S, merelysetting an upper limit for β for the local XXL-S RL HERGRLF resulted in a good fit for the local RL HERG RLF and,simultaneously, an unrealistically sharp decrease in the vol-ume density of RL HERGs in redshift bin 4 ( . < z < . )at L . = W Hz − . Therefore, in order to avoid thisdramatic cut off at high luminosities while still minimising χ for the local RL HERG RLF, a value of β = − . waschosen. Values of β significantly below this (even orders ofmagnitude) do not alter the final results for the comovingkinetic luminosity densities for RL HERGs (see Section 5).In fact, the best fit values that Pracy16 found for β whilemodelling the evolution of their HERG RLFs are β = − . for pure density evolution and β = − . for pure luminos-ity evolution, which further justifies the choice of β = − . .Ceraj et al. (2018) also chose β = − . to fit their localHLAGN (HERG equivalent) RLFs in the COSMOS field.The Pracy16 local HERG RLF parameters and theiruncertainties (log[ Φ ∗ ] = − . + . − . , log[ L ∗ ] = . + . − . , α = − . + . − . ) with β = − . + . − . were used as constraintsin the fit to the local XXL-S RL HERG RLF (includingall optical luminosities) using the lmfit python module(Newville et al. 2016). Once the M i < − cut was made,however, the parameters from Pracy16 no longer provideda good fit to the data because the normalisation and slopewere now different. In addition, there are fewer sources inthe M i < − local RLF, making its best fit slope ( α )more uncertain. The volume densities start turning overfor log[ L . (W Hz − )] = 22.6, so data points below this luminosity were discarded. Furthermore, only one sourceexists in the log[ L . (W Hz − )] = 23.8 bin, which steep-ens the best fit value for α to − . . This steeper α did notproduce a good fit for the higher redshift RL HERG RLFs.Therefore, in order to use the local RL HERG RLF to de-scribe the evolution of the RL HERGs while still minimising χ , the local RL HERG RLF with the M i < − cut wasrefit in the following way. The values for L ∗ and α were de-termined by fitting the RL HERG RLFs in all four redshiftbins simultaneously (keeping only β fixed at − . ) for twoscenarios: pure density and pure luminosity evolution (seeSection 4.5). The average values for log( L ∗ ) and α betweenthe pure density and pure luminosity fits (26.78 and − . ,respectively) were used as the values for the local RL HERGRLF fit. The best fit normalisation for the local RLF wasthen found by repeating the fitting process, allowing Φ ∗ tobe a free parameter and keeping α fixed at − . , L ∗ fixedat log( L ∗ ) = 26.78, and β fixed at − . . The final resultsfor the best fit parameters for the local RL HERG RLF areshown in Table 13, and the corresponding best fit functionfor the M i < − local RLF is shown as the solid blue linein Figure 11. The slope of the fit ( α = − . ) is steeper thanthe slope of the fit for the local HERG RLF with M i < − from Pracy16 ( α = − . ), which is the result expected fora fainter optical cut. However, the slope is very close to theaverage between the latter slope ( α = − . ) and the slopeof the local Pracy16 HERG RLF with the m i < . cut( α = − . ; i.e. their HERG RLF including all sources), asevidenced in Figure 11. This indicates that the method offitting the local XXL-S RL HERG RLF generates a suffi-ciently accurate model for evolution measurement purposes,given the different classification methods, optical selections,and survey areas of XXL-S and the Pracy16 sample. How-ever, see Appendix B for a description of the effect thatrebinning has on the local XXL-S RL HERG RLF.A similar procedure was needed for the LERGs becausethe knee in the local LERG RLF from Pracy16 occurs at aluminosity (log[ L ∗ ] = 25.21) that is too low to accuratelymodel the XXL-S LERG RLFs at all redshifts (even if alloptical luminosities are included). In other words, the vol-ume density in the local LERG RLF from Pracy16 decreasestoo rapidly for log[ L ∗ ] > Φ ∗ ] = − . + . − . , log[ L ∗ ]= . + . − . , α = − . + . − . , β = − . + . − . ) were initiallyused as constraints in the fit to the local XXL-S LERG RLF(for all optical luminosities) using the lmfit python mod-ule. The best fit parameters found by lmfit were then usedas the initial (free) parameter values to simultaneously fitthe LERG RLFs at all redshifts for pure density and pureluminosity evolution (see Section 4.5). The average valuefor each parameter ( Φ ∗ , L ∗ , α , β ) between the pure den-sity and pure luminosity fits were used as the values for theparameters describing the local LERG RLF fit (includingall optical luminosities). Like the RL HERG RLFs, the pa-rameters for the LERG RLF from Pracy16 did not providea good fit to the XXL-S LERG RLF with the M i < − cut. Therefore, the M i < − local LERG RLF was refit byallowing Φ ∗ and α to be free parameters, keeping L ∗ fixedat log( L ∗ ) = 25.91 and β fixed at − . (the same values Article number, page 13 of 27 &A proofs: manuscript no. XXL-XXXVI-BH-FeedBack-20190429 used for the local LERG RLF that included all optical lu-minosities). For consistency with the RL HERGs, the datapoints below log[ L . (W Hz − )] = 22.6 were discarded.The final results for the best fit parameters for the localLERG RLF are shown in Table 13, and the correspondingbest fit function for the M i < − local RLF is shown as thesolid red line in Figure 11. The slope of the fit ( α = − . ),like the RL HERG RLF slope, is steeper than the slope ofthe fit for the local Pracy16 LERG RLF with M i < − ( α = − . ), but is similar to the local Pracy16 LERG RLFwith m i < . ( α = − . ). This result is consistent withthe fact that the majority of LERGs are optically brightgalaxies: the M i < − cut selects only the brightest ofLERGs and the M i < − selects more, but only a smallfraction in the local redshift bin are missed by the lattercut. Therefore, this suggests that the fit to the local XXL-SLERG RLF can be used to accurately model the evolutionof the LERGs. The evolution of a radio source population is usually ex-pressed via changes only in volume density (pure densityevolution, ‘PDE’) or changes only in luminosity (pure lu-minosity evolution, ‘PLE’). PDE results in a change in theRLF normalisation ( Φ ∗ ) as a function of redshift as Φ ∗ ( z ) = Φ ∗ ( + z ) K D , (7)where Φ ∗ is the local RLF normalisation and K D is a param-eter that defines how rapidly the volume density changes.On the other hand, PLE results in a change in the luminos-ity knee ( L ∗ ) as a function of redshift as L ∗ ( z ) = L ∗ ( + z ) K L , (8)where L ∗ is the luminosity knee for the local RLF and K L isa parameter that defines how rapidly the sources evolve inluminosity. Inserting Equation 7 into Equation 6 gives forPDE: Φ ( L , z ) = Φ ∗ ( + z ) K D ( L ∗ / L ) α + ( L ∗ / L ) β . (9)Inserting Equation 8 into Equation 6 yields for PLE: Φ ( L , z ) = Φ ∗ ( L ∗ ( + z ) K L / L ) α + ( L ∗ ( + z ) K L / L ) β . (10)Using Equations 9 and 10, and fixing the local RLF pa-rameters for each population to be the M i < − valueslisted in Table 13, the RLFs for RL HERGs and LERGswith M i < − across all redshift bins (Tables 9-12) werefit using the default χ -minimisation method of the lmfit python module. For the RL HERGs, this procedure gavebest fit parameters and 1 σ uncertainties of K D = 1.812 ± K L = 3.186 ± K D = 0.671 ± K L = 0.839 ± Fig. 15. M i < − for each redshift bin. See Table 14 for the best fitparameters. Fig. 16. M i < − for each redshift bin. See Table 14 for the best fit parameters. The comoving luminosity density ( Ω . ) of a given radiosource population represents its total radio luminosity perunit comoving volume as a function of time. At a givenredshift between < z < . , Ω . was calculated for RLHERGs and LERGs for both PDE (Equation 9) and PLE(Equation 10) by evaluating Ω . ( z ) = ∫ L . × Φ ( L . , z ) d ( log [ L . ]) (11)over the full range of radio luminosities probed at all red-shifts (22.4 < d log[ L . (W Hz − )] < Ω . for RL HERGs, LERGs, andall RL AGN in XXL-S. The shaded regions represent theuncertainties in the K D and K L parameters for PDE andPLE, respectively, for each population. Article number, page 14 of 27utler et al.: The XXL Survey XXXVI: Evolution and black hole feedback of HERGs and LERGs in XXL-S
Fig. 17.
Evolution of the 1.4 GHz comoving luminosity den-sity ( Ω . ) for RL HERGs (blue lines), LERGs (red lines),and all RL AGN (black lines) in XXL-S, integrated fromlog[ L . (W Hz − )] = 22.4 to 27.2 (the full range of lumi-nosities probed in the RLFs) at each redshift for best fit PDE(solid lines) and PLE (dashed lines) models. The red and ma-genta shaded areas represent the uncertainties for the LERGPDE and PLE fits, the blue and cyan shaded areas representthe uncertainties for the RL HERG PDE and PLE fits, and theblack and grey shaded areas represent the uncertainties for theRL AGN PDE and PLE fits, respectively. The light green linesrepresent Ω . for the low luminosity ( L . < × WHz − ) radio AGN in COSMOS from Smolˇci´c et al. (2009). The Ω . values for the XXL-S LERGs (red lines inFigure 17) are very similar to Ω . for the low luminos-ity radio AGN ( L . < × W Hz − ) in the COS-MOS field studied by Smolˇci´c et al. (2009), shown as thelight green lines. This is a reflection of the fact that LERGsdominate the RL AGN population at low luminosities.
5. Cosmic evolution of RL HERG and LERG kineticluminosity densities
As SMBHs accrete matter from infalling gas, energy is re-leased that can be transformed into radiation via an accre-tion disc or converted into kinetic form via jets of relativisticparticles, which can reach up to hundreds of kpc beyond thehost galaxy and are detectable in the radio (McNamara &Nulsen 2012). In the latter scenario (radio mode feedback),the jet structures are able to do mechanical work on thesurrounding environment, which can heat the ISM or IGM,and therefore prevent cooling flows from adding stellar massto the host galaxy (e.g. Fabian 2012).Some observations of nearby resolved radio galaxies in-dicate that they create cavities in the surrounding hot X-ray emitting ICM via the mechanical work done by theirradio lobes (e.g. B¨ohringer et al. 1993). These studies haveenabled the derivation of various scaling relations between L . and kinetic luminosity, L kin (e.g. Merloni & Heinz2007; Bˆırzan et al. 2008; Cavagnolo et al. 2010; O’Sullivanet al. 2011; Daly et al. 2012; Godfrey & Shabala 2016). However, there are large uncertainties associated with eachrelation, including the one that is arguably the most so-phisticated (Willott et al. 1999). The very large ( ∼ L kin (e.g. deviation from theconditions of minimum energy, uncertainty in the energyof non-radiating particles, and the composition of the jet).One parameter, f W , represents all these uncertainties andhas a range of 1-20, with different values corresponding todifferent RL AGN populations. A value of f W = 15 pro-duces kinetic luminosities close to those calculated via ob-servations of X-ray cavities (surface brightness depressions)in galaxy clusters induced by FRI radio jets and lobes (e.g.Bˆırzan et al. 2004, 2008; Merloni & Heinz 2007; Cavagnoloet al. 2010; O’Sullivan et al. 2011), and f W = 4 produces L kin values that closely agree with the results of Daly et al.(2012), who derived a relationship between radio luminosityand L kin for some of the most powerful FRII sources usingstrong shock physics.Recent simulations, which focus mostly on FRII sources,have produced varying results. English et al. (2016) usedrelativistic magnetohydrodynamics to model the dynamicalevolution of RL AGN with bipolar supersonic relativisticjets (i.e. FRII sources) in poor cluster environments andfound that that Willott et al. (1999) relation with f W = closely matches the results of their simulations of theevolution of L as a function of radio lobe length. Onthe other hand, Hardcastle (2018b) modelled the evolutionof the shock fronts around the lobes of FRII RL AGN andfound that the Willott et al. (1999) relation with f W = reproduces the L kin values for their simulated galaxiesexisting at z < . , but for all galaxies in their sample(which have z < ), high f W values (10-20) produced abetter fit. The difference is due to higher inverse Comptonlosses at higher redshift rather than intrinsic evolution ofthe scaling relation with redshift. These results illustratethe uncertainty regarding which f W parameter should beused to compare to observations.In addition, no observational study has yet developeddistinct scaling relations for low-power (FRI) and high-power (FRII) sources, despite theoretical expectations tothe contrary. One of the latest studies (Godfrey & Shabala2016), which incorporates theoretical considerations such asthe composition and age of the radio lobes, is inconclusiveabout whether FRI and FRII sources actually differ in theirscaling relations. They found a shallower slope for the cor-relation between radio luminosity and L kin for FRI sourcesthan other scaling relations have found, but no correlationfor FRII sources. However, their sample only extends outto z ≤ . , and therefore it is not clear how applicable thisnew result is to sources at higher redshift, where most of theXXL-S sources lie. In fact, Smolˇci´c et al. (2017b) demon-strated that for z (cid:38) . , the Godfrey & Shabala (2016)relation results in L kin values that are over an order of mag-nitude higher than those calculated by other scaling rela-tions, which further demonstrates the uncertainty in howbroadly it can be applied.In light of this uncertainty regarding which scaling rela-tion best applies to a given category of RL AGN, the rela-tion chosen for this paper should be the one that is most ap-propriate for the majority of RL AGN in XXL-S (LERGs).The Cavagnolo et al. (2010) relation is based on FRI galax-ies that exist in gas rich cluster environments, where LERGs Article number, page 15 of 27 &A proofs: manuscript no. XXL-XXXVI-BH-FeedBack-20190429
Fig. 18.
Distribution of L kin for RL HERGs and LERGs in XXL-S. L kin for each source was calculated according to the scalingrelation from Cavagnolo et al. (2010). are expected to exist. Although this relation has been shownto suffer from Malmquist bias (Godfrey & Shabala 2016),it is, within the uncertainties, consistent with the Willottet al. (1999) relation (for f W = ), which does not sufferfrom distance effects. Furthermore, the studies involving 1.4GHz radio data that have separated between LERGs andHERGs (Best & Heckman 2012; Best et al. 2014; Pracy16)used the Cavagnolo et al. (2010) relation. Moreover, thesimulations to which the XXL-S results are compared inSection 5.4 all exhibit kinetic luminosity densities that arerelatively high (for various reasons, one being the use ofthe Merloni & Heinz 2007 scaling relation, which produceshigher L kin values than Cavagnolo et al. 2010), implyingthat a positive scale factor would have to be applied tothe XXL-S data for the comparison to the simulations re-gardless. Considering all these factors, the Cavagnolo et al.(2010) relation is used for the primary results of this paper,although the Willott et al. (1999) relation is applied whererelevant. A comparison between the results obtained usingthese and other scaling relations is found in Appendix A.The relationship between X-ray cavity power inducedby the radio lobes ( P cav ) and 1.4 GHz radio power ( P . = ν L . ) found by Cavagnolo et al. (2010) is given by theirEquation 1. Converting that relation into units of W andreplacing the P cav symbol with L kin results in L kin ( L ) = ( W ) . [ log ( ν L )]− . , (12)where ν = . × Hz and the corresponding uncertaintyrange for a given L kin is given by: ∆ L kin ( L ) = ( W ) ( . ± . )[ log ( ν L )− ] + ( . ± . ) . (13)Figure 18 shows the distribution of L kin for RL HERGs andLERGs in XXL-S calculated according to Equation 12. The comoving kinetic luminosity density ( Ω kin ) of a givenradio source population represents its total kinetic lumi- Fig. 19.
Evolution of the comoving kinetic luminosity density( Ω kin ) for RL HERGs (blue lines), LERGs (red lines), and all RLAGN (black lines) in XXL-S using the Cavagnolo et al. (2010)scaling relation, integrated from log[ L . (W Hz − )] = 22.4to 27.2 (the full range of luminosities probed in the RLFs) ateach redshift for best fit PDE models. The PLE models do notdiffer significantly from the PDE models on this scale. The up-per and lower lines for each population represent the range ofuncertainties in the Cavagnolo et al. (2010) scaling relation. nosity per unit comoving volume throughout cosmic time.Thus, in order to constrain the evolution of radio modefeedback of the XXL-S RL HERGs and LERGs, Ω kin wascalculated for each population for both PDE (Equation 9)and PLE (Equation 10) at a given redshift value between < z < . by evaluating Ω kin ( z ) = ∫ L kin ( L . ) × Φ ( L . , z ) d ( log [ L . ]) (14)over the full range of radio luminosities probed at all red-shifts (22.4 < d log[ L . (W Hz − )] < Ω kin for RL HERGs andLERGs in XXL-S calculated according to Equation 14,where L kin and its uncertainty range are calculated usingEquations 12 and 13, respectively.The average value of the total Ω kin weakly increases fromlog[ Ω kin (W Mpc − )] ≈ ∼ < z < . .The average LERG Ω kin also shows weak positive evolution,ranging from log[ Ω kin (W Mpc − )] ≈ ∼ Ω kin evolves more strongly, start-ing at log[ Ω kin (W Mpc − )] ≈ z = and increasing to32.6 by z = . . In previous studies, higher luminosity radiosources have been found to evolve even more strongly (e.g.Dunlop & Peacock 1990; Willott et al. 2001; Best et al.2014; Pracy16). The difference between those results andthe XXL-S results for RL HERGs is a reflection of the in-creased optical and radio depths probed by XXL-S. The evolution of Ω kin for RL HERGs and LERGs in XXL-Scan be compared to the results from other samples. Fourof the main studies that have measured the Ω kin evolution Article number, page 16 of 27utler et al.: The XXL Survey XXXVI: Evolution and black hole feedback of HERGs and LERGs in XXL-S
Fig. 20.
Evolution of the kinetic luminosity density ( Ω kin ) for allRL AGN in XXL-S for PDE (solid black line) and PLE (dashedblack line) fits, integrated from log[ L . (W Hz − )] = 22.4 to27.2 (the full range of luminosities probed in the RLFs). Theblack and grey shaded areas represent the uncertainties for theRL AGN PDE and PLE fits, respectively. For comparison, Ω kin for the RL AGN from Smolˇci´c et al. (2009) and Smolˇci´c et al.(2017b) are displayed as the red shaded region and the blue line,respectively. The uncertainties in the Cavagnolo et al. (2010)scaling relation for the XXL-S data are shown as the black dashdot lines. The evolution of the RL AGN in XXL-S is broadlyconsistent with the evolution of the RL AGN in the samplesfrom Smolˇci´c et al. (2009) and Smolˇci´c et al. (2017b). for radio AGN are Smolˇci´c et al. (2009), Best et al. (2014),Pracy16, and Smolˇci´c et al. (2017b). The XXL-S Ω kin resultsare compared to each of these.Smolˇci´c et al. (2017b) extended the Smolˇci´c et al. (2009)sample out to z ∼ ∼ Ω kin at z = is log[ Ω kin (W Mpc − )] ≈ ∼ z = . for both PDE and PLE. This is below both theSmolˇci´c et al. (2009) and Smolˇci´c et al. (2017b) samples,but they are still within the uncertainties of the Cavagnoloet al. (2010) scaling relation for XXL-S. Therefore, for thesame L . - L kin scaling relation, the Ω kin evolution resultfor RL AGN in XXL-S is consistent with the Ω kin evolu-tion result for radio AGN in the Smolˇci´c et al. (2017b) andSmolˇci´c et al. (2009) samples.Best et al. (2014) measured Ω kin for jet-mode AGN(LERG equivalent) from . < z < . using a sample of211 RL AGN, which they constructed by combining data from eight different surveys. Their results (see their Fig-ure 8) are consistent with a model in which Ω kin rises by afactor of ∼ z = value) out to z ∼ ∼ Ω kin value by z ∼ Ω kin evolution seenin XXL-S, which steadily rises monotonically with redshift.However, the sample in Best et al. (2014) is more than 20times smaller than the XXL-S sample, and most of theirsample is much brighter in the radio (90% of their radiosources have S . > mJy). Therefore, the Best et al.(2014) sample is not able to probe the Ω kin evolution aswell as the XXL-S sample, which has allowed a more ac-curate Ω kin measurement due to the larger sample size andextension out to higher redshifts.Pracy16 measured Ω kin for LERGs and HERGs fora sample of ∼ S . > . mJy and M i < − out to z = . . TheirLERG Ω kin stays constant at log[ Ω kin (W Mpc − )] ≈ < z < . This is partially influenced by a redshiftdependent e -correction, which decreases the i -band mag-nitude of each source in order to account for the fading ofstellar populations with time. Without the e -correction, theLERGs evolve as K D = 0.81 + . − . , which is within 1 σ of theXXL-S LERG value ( K D = 0.671 ± Ω kin evolution is in good agreement with thatfound by Pracy16 if no e -correction is applied. However,when the e -correction is applied, the uncertainties in theCavagnolo et al. (2010) scaling relation for the LERGs inPracy16 range from 32.0 (cid:46) log[ Ω kin (W Mpc − )] (cid:46) Ω kin evolution (i.e. there is ∼ Ω kin evolution measured byPracy16, however, is fundamentally different to the XXL-SRL HERG Ω kin evolution. The HERGs from Pracy16 ex-hibit strong positive redshift evolution, contributing an av-erage log[ Ω kin (W Mpc − )] ≈ z = and increas-ing up to ∼ z = . The XXL-S RL HERGs, onthe other hand, evolve more weakly, exhibiting averagelog[ Ω kin (W Mpc − )] values of 32.0 at z =0 and ∼ z =1. The difference is, again, due to the increased opti-cal and radio depths probed by XXL-S. In other words,the Pracy16 sample simply measured the evolution allowedby the M i < − and S . > . mJy cuts. Neverthe-less, the range of Ω kin evolution of the Pracy16 HERGs(31.5 (cid:46) log[ Ω kin (W Mpc − )] (cid:46) Ω kin evolution of the XXL-S HERGs. The correspondence (or lack thereof) between observationsof galaxies and models of their formation and evolution isa powerful indication of how well the underlying physicsinvolved in the models is understood. A number of authorshave made various predictions for the cosmic evolution ofradio mode feedback. A selection of these is compared tothe Ω kin calculations of the XXL-S RL HERGs and LERGs.Croton et al. (2006) predicted that the black hole massaccretion rate density ( (cid:219) m BH ) associated with AGN exhibit-ing radio mode feedback would be relatively flat at log[ (cid:219) m BH (M (cid:12) yr − Mpc − )] ≈ − . out to z ∼ z ∼ (cid:219) m BH val-ues can be translated into Ω kin values via the mass-to-energy Article number, page 17 of 27 &A proofs: manuscript no. XXL-XXXVI-BH-FeedBack-20190429 conversion of L kin = η (cid:219) m BH c , where η = . is the canonicalefficiency of gravitational accretion (Frank et al. 1992) and c is the speed of light. The low redshift ( z < . ) (cid:219) m BH valuetranslates into log[ Ω kin (W Mpc − )] ≈ . . The Ω kin forall RL AGN in XXL-S weakly increases from log[ Ω kin (WMpc − )] ≈ ∼ < z < . , as seen in Fig-ure 20. Therefore, given the uncertainties in the Cavagnoloet al. (2010) scaling relation, the XXL-S Ω kin evolution forall RL AGN is in good agreement with the Croton et al.(2006) prediction for the evolution of radio mode feedbackfor < z < . . However, if another scaling relation is used,the agreement is poorer.Croton et al. (2016) updated the Croton et al. (2006)prediction with the addition of a ‘radio mode efficiency’parameter, κ R , for which the authors adopted a value of κ R = . . The motivation behind this modification isthat the Croton et al. (2006) model used an upper limitto the cooling rate of infalling gas by assuming that thecooling and heating are independent. However, in the realuniverse, AGN heating would have a lasting effect on thegas. Therefore, less AGN heating is required to offset thecooling flows. The Croton et al. (2016) model, called theSemi-Analytic Galaxy Evolution (SAGE) model, predictsthat the Ω kin from radio mode feedback for z < . islog[ Ω kin (W Mpc − )] ≈ . (approximately ten times lessthan the previous prediction). The XXL-S measurement ofthe Ω kin evolution of RL AGN, using the scaling relationfrom Cavagnolo et al. (2010), is inconsistent with this value,even considering the uncertainties. However, if the scalingrelation from Willott et al. (1999) with an uncertainty pa-rameter of f W = is used for the XXL-S Ω kin calculation,then the Ω kin for RL AGN in XXL-S is log[ Ω kin (W Mpc − )] ≈ z = and reaches ∼ z = . for PDE, asshown in Figure 21. This result is within ∼ Ω kin evolution for radio AGN in the Smolˇci´c et al.(2017b) sample is also most consistent with the predictionfrom Croton et al. (2016) if the Willott et al. (1999) scalingrelation with f W = is used (especially for z > ).More predictions of the evolution of radio mode feed-back have been made by Merloni & Heinz (2008), K¨ordinget al. (2008) and Mocz et al. (2013), who all separatelymodelled the Ω kin for their RL HERG and LERG equiva-lent populations. Figure 22 shows these predictions along-side the Ω kin measurements for RL HERGs and LERGs inXXL-S (using the Cavagnolo et al. 2010 scaling relation),the full uncertainty ranges of which are shown as the semi-transparent blue and red shaded regions, respectively. Mer-loni & Heinz (2008) called their LERG equivalent popula-tion ‘low kinetic mode’, or LK, and their RL HERG equiv-alent population ‘radio loud high kinetic mode’, or HK.Their scenario in which both flat- and steep-spectrum ra-dio sources are included in the simulations is consideredhere. K¨ording et al. (2008) labelled their LERG equivalentpopulation ‘low luminosity AGN’, or LLAGN. Their RLHERG equivalent population was obtained by combiningradio quiet (low radio-to-optical luminosity ratio) and radioloud quasars (‘RQQ’ and ‘RLQ’, respectively). Like Merloni& Heinz (2008), Mocz et al. (2013) designated their LERGand RL HERG equivalent populations as LK and HK. TheirHK prediction involves two scenarios: one in which the ra-dio AGN duty cycle (the fraction of HK sources with radio Fig. 21.
Evolution of Ω kin for all RL AGN in XXL-S (black line)using the scaling relation from Willott et al. (1999) with f W = ,integrated from log[ L . (W Hz − )] = 22.4 to 27.2 (the fullrange of luminosities probed in the RLFs). Only the PDE evo-lution is displayed for clarity (the PLE results are nearly indis-tinguishable from the PDE results on this scale). The predictionfrom Croton et al. (2016) over this redshift range (dashed redline) is within the uncertainties of the XXL-S RL AGN Ω kin cal-culated using the Willott et al. (1999) relation (defined by using f W =1 and f W =20, shown as the black dash-dot lines). jets switched on) is fixed at f = . and one in which f evolves with redshift.All three simulations mentioned previously make verysimilar predictions for the Ω kin evolution of the LERGequivalent populations: their slopes are consistent with theobserved weak evolution of the XXL-S LERGs, but theirnormalisations are systematically higher. This is due tothe simulations using different L . - L kin scaling relations,which results in different kinetic luminosity distributions.For example, Merloni & Heinz (2008) used the scaling rela-tion from Merloni & Heinz (2007), which generates Ω kin values that are higher than the Cavagnolo et al. (2010)scaling relation by ∼ L . ) integration range (see Figure A.2 in Smolˇci´cet al. 2017b). This is consistent with the offset seen in Fig-ure 22. Nevertheless, the consistency between the slope ofthe Ω kin evolution of the XXL-S LERGs and the predictionsfrom the simulations for their LERG equivalent populationsindicates that the current understanding of the physics ofthe evolution of slowly accreting SMBHs is well-matched toLERG observations.On the other hand, the Merloni & Heinz (2008) andK¨ording et al. (2008) predict that their HK and RQQ+RLQpopulations evolve strongly. As seen in Figure 22, thesepredictions agree with the evolution of the HERGs fromPracy16 and the XXL-S RL HERGs for z (cid:38) . , given theuncertainties in the Cavagnolo et al. (2010) scaling relation.The disagreement at lower redshifts reflects the assumptionin the simulations that the HERG population is dominatedby high luminosity sources that evolve strongly. The slopeof the HK predictions from Mocz et al. (2013) are moreconsistent with the slope of the XXL-S RL HERG evolu-tion for z (cid:46) . . Beyond this redshift, the Ω kin slope for the Article number, page 18 of 27utler et al.: The XXL Survey XXXVI: Evolution and black hole feedback of HERGs and LERGs in XXL-S
Fig. 22.
Comparison between the evolution of Ω kin for XXL-SLERGs and RL HERGs (red and blue shaded regions, respec-tively) and the prediction for LERG and RL HERG equivalentsources from Merloni & Heinz (2008), K¨ording et al. (2008),and Mocz et al. (2013). The hashed blue line is the scenariofor RL HERG equivalent sources from Mocz et al. (2013) whena varying radio AGN duty cycle ( f ) is utilised. The scalingrelation from Cavagnolo et al. (2010) was used to calculatethe XXL-S Ω kin values, and the RLFs were integrated fromlog[ L . (W Hz − )] = 22.4 to 27.2 (the full range of lumi-nosities probed in the RLFs). The thick cyan curve shows theevolution of Ω kin for the HERGs from Pracy16 (the values for z > have been linearly extrapolated). constant f scenario remains consistent with the XXL-S RLHERGs, but the Ω kin slope for the varying f scenario in-creases, becoming inconsistent with the XXL-S RL HERGsby z ≈ . . This may suggest that an evolving AGN dutycycle does not accurately reflect how RL HERGs accretethrough cosmic time. Regardless, the Mocz et al. (2013)prediction for the Ω kin evolution of their HK populationwith a constant AGN duty cycle is most closely alignedwith the evolution of the XXL-S RL HERGs out of all threesimulations, with only a slight ( ∼ It is possible that some RL HERGs were misclassified dueto the lack of far-infrared (FIR) photometric data, whichaids in constraining SED fits and the corresponding derivedSFRs (e.g. Delvecchio et al. 2014). In order to test this, acomparison between SED fitting results with and withoutFIR constraints for optically faint sources was performed.The COSMOS field has FIR
Herschel data available, andtherefore a sub-sample of the 3 GHz COSMOS radio sourceswith faint optical counterparts was constructed. In order tomatch the XXL-S radio sample as closely as possible, thefollowing cuts were applied to the COSMOS source cata-logue: m z > and S . > µ Jy (where S . wasconverted from the S value by using a spectral indexof α = − . ). These cuts resulted in a sub-sample of 411COSMOS sources, some of which have 3 σ Herschel detec-tions and some of which do not (upper limits to the FIR flux densities were used for the latter sources). The SED fit-ting was performed twice for each source: once with the FIRdata and once without it. For ∼
92% of the sources, the SEDclassification remained the same (AGN were still classifiedas AGN and SFGs were still classified as SFGs after theFIR data was removed). For the remaining ∼ ∼
8% of the RL HERGs would be reclassified as RQHERGs if FIR data became available for XXL-S. Even ifthis percentage of expected potential misclassifications wasreached, any change in classification would be spread outamong the different redshift and L . bins. Therefore,potential misclassifications of the RL HERGs are expectedto have minimal impact on the overall results of their evo-lution. In terms of the SFRs, there was a scatter of 0.3 dexbetween the SED fits with the FIR data and the fits with-out the FIR data, but no significant offset between the tworuns was found. Therefore, the radio excess parameter thatidentified low radio luminosity ( L . < . W Hz − )RL HERGs would not be strongly affected by the presenceof FIR Herschel data.In addition, the percentage of optically bright ( M i (cid:46) − . ) and optically faint ( M i (cid:38) − . ) XXL-S RL HERGsthat are X-ray AGN, SED AGN, and MIR AGN were com-pared. The percentages of optically bright RL HERGs thatare X-ray, SED, and MIR AGN (28.9%, 84.6%, and 19.6%,respectively) are similar (within 1 σ of the √ N / N Poisso-nian uncertainty) to the percentages of optically faint RLHERGs that are X-ray, SED, and MIR AGN (24.1%, 74.1%,and 11.2%, respectively). Very similar results were foundwhen comparing the RL HERGs with high radio luminosity( L . > . W Hz − ) and ones with low radio luminos-ity ( L . < . W Hz − ). This demonstrates that theclassification scheme applied to the XXL-S radio sources isrelatively insensitive to signal-to-noise ratio and photomet-ric data quality. The Pracy16 sample selected only the most radio lumi-nous, most massive galaxies, which is demonstrated inFigure 23. Clearly, making this selection excludes a largenumber of lower mass ( M ∗ (cid:46) . M (cid:12) ) and radio faint( L . (cid:46) . W Hz − ) galaxies, and even misses somesources with higher radio luminosity in the XXL-S sample.As described in Section 5.3, this results in a different mea-surement of the evolution of the RL HERG population. Thisimplies that the evolution measured for RL HERGs dependson the range of optical luminosities included by the sampleselection. This has more of an effect at lower redshift andfor higher radio luminosities, since fainter optical sourcesare more likely to exist at lower redshift and the majorityof the feedback power ( L kin ) in a given redshift bin comesfrom sources with luminosities that are close to the knee inthe RLF. For XXL-S RL HERGs with L . > . WHz − at z < . , those selected by Pracy16’s M i < − cutaccount for ∼
38% of the total L kin emitted by all RL HERGswith M i < − in that volume, whereas those that wereadded by the deeper XXL-S optical cut ( − < M i < − )account for ∼
49% of the total L kin from all RL HERGs with Article number, page 19 of 27 &A proofs: manuscript no. XXL-XXXVI-BH-FeedBack-20190429
Fig. 23.
Stellar mass vs 1.4 GHz radio luminosity for RLHERGs (blue dots) and LERGs (open red squares) at z < . with M i < − . The semi-transparent cyan squares and magentacircles show the RL HERGs and LERGs, respectively, that wouldhave been selected by the cuts that Pracy16 made ( M i < − and S . > . mJy). The latter galaxies are some of the mostmassive, most radio luminous in the XXL-S sample. M i < − in that volume (the remaining ∼
13% comes fromthe lower luminosity RL HERGs). The corresponding per-centages for XXL-S RL HERGs with L . > . WHz − at . < z < . are ∼
93% and ∼ − < M i < − increased the measurement of Ω kin forXXL-S RL HERGs at z < . by up to a factor of ∼ Ω kin values for . < z < . were virtually unaf-fected. This is reflected in the different Ω kin slopes betweenthe XXL-S RL HERGs and those from Pracy16 for z < . (see Figure 22). Overall, this results in lower PDE and PLEmeasurements for the evolution of RL HERGs and demon-strates the impact that deeper optical and radio data canhave on the calculation of radio mode feedback in RL AGNsamples. Furthermore, Figure 10 shows that a significantnumber of even fainter ( M i > − ) RL HERGs exist. Ifdeeper optical samples can be constructed in future surveys,the evolution of the RL HERG population may be found tobe weaker still. Deeper optical data would not affect LERGsas much because their hosts tend to be inherently brighterthan RL HERG hosts (only the most shallow flux limitedsurveys miss a substantial portion of the LERG popula-tion). All these results suggest that RL HERGs contributemore to radio mode feedback at low redshifts ( z (cid:46) . ) thanpreviously thought due to the inclusion of optically fainter( − < M i < − ) RL HERGs.
6. Summary and conclusions
Radio mode feedback is an important element in galaxyevolution because of its influence on a galaxy’s ability toform stars. Measuring the amount of radio mode feedbackthroughout cosmic history puts important constraints onthe amount of power available to prevent star formation,thus allowing an evaluation of its role in limiting the stellarmass of galaxies. The XXL-S field was observed at 2.1 GHz with ATCA for the purpose of measuring the evolution ofradio mode feedback of the RL HERGs and LERGs therein.The wide area ( ∼ ) and relatively deep radiodata ( σ ∼ µ Jy beam − ) of XXL-S allowed the constructionof the RLFs for both RL HERGs and LERGs across a widerange in radio luminosity out to z ∼ M i < − . The kinetic luminosity density ( Ω kin ) evolution of all RL AGN in XXL-S is consistent withother samples of RL AGN surveyed at similar optical andradio depths (e.g. Smolˇci´c et al. 2009, 2017b) within the un-certainties of the Cavagnolo et al. (2010) scaling relation.The LERGs contributed the majority of the total Ω kin ata given redshift and exhibited positive yet weak evolution( K D = . ± . and K L = . ± . ). This impliesthat LERGs account for most of the radio mode feedbackthroughout cosmic history and that accretion onto SMBHsin massive, passively evolving galaxies (which comprise thevast majority of the LERG population) has been steadilydecreasing since z ∼ K D = . ± . and K L = . ± . ). However, the latter result is weaker thanthe previously measured strong evolution in the HERG pop-ulation (e.g. Pracy16). This implies that radio mode feed-back from SMBHs existing in bluer, star-forming hosts ismore prominent in recent cosmic history than previouslythought. In turn, this suggests that radio mode feedback inRL HERGs, and not just LERGs, is important for under-standing the mechanism behind radio mode feedback andits ability to limit the mass of galaxies in the universe.The evolution results for RL HERG and LERGs inXXL-S were compared to the predictions of simulations ofradio mode feedback. The latest simulation (Croton et al.2016) predicts an approximately constant value (log[ Ω kin (W Hz − )] ≈ z ∼ Ω kin from all RLAGN in XXL-S is consistent with the prediction from Cro-ton et al. (2016) for < z < . . Other simulations(Merloni & Heinz 2008; K¨ording et al. 2008; Mocz et al.2013) expressed their predictions for radio mode feedbackwith separate contributions from LERG and RL HERGequivalent populations. All three simulations made simi-lar predictions for the LERG equivalent populations: theyhave similar slopes to but positive normalisation offsetsabove the XXL-S LERG measurement. This indicates thatmodels of slowly-accreting SMBHs undergoing advection-dominated accretion flows correspond closely to observa-tions of LERGs, with the difference in normalisation beingdue to the details of the conversion from radio luminos-ity to kinetic luminosity. The Ω kin predictions from Mer-loni & Heinz (2008) and K¨ording et al. (2008) for the RLHERG equivalent populations correspond more closely withthe HERG evolution from Pracy16, which evolved strongly.On the other hand, the Mocz et al. (2013) prediction forthe RL HERG equivalent population with a constant AGNduty cycle ( f = . ) had a similar slope to the XXL-S RLHERG evolution, but was slightly offset above it in normal-isation (by ∼ < z < . . This suggests that aconstant AGN duty cycle could be responsible for produc-ing a higher local abundance and relatively weak evolutionof SMBHs rapidly accreting cold gas, as found for the XXL- Article number, page 20 of 27utler et al.: The XXL Survey XXXVI: Evolution and black hole feedback of HERGs and LERGs in XXL-S
S RL HERGs. However, the mechanism that generates theconstant duty cycle is unknown.
Acknowledgements
AB acknowledges the University of Western Australia(UWA) for funding support from a University Postgrad-uate Award PhD scholarship and the International Centrefor Radio Astronomy Research (ICRAR) for additional sup-port. VS acknowledges funding from the European Union’sSeventh Framework programme under grant agreement333654 (CIG, ‘AGN feedback’), and VS and ID acknowl-edge funding under grant agreement 337595 (ERC StartingGrant, ‘CoSMass’). The Saclay group acknowledges long-term support from the Centre National d’Etudes Spatiales(CNES). All the authors thank the referee for his helpfulcomments that improved the clarity and quality of the pa-per. AB also thanks Elizabeth Mahoney, Tom Muxlow, andTim Heckman for additional comments. The Australia Tele-scope Compact Array is part of the Australia TelescopeNational Facility which is funded by the Australian Gov-ernment for operation as a National Facility managed byCSIRO. XXL is an international project based around anXMM Very Large Programme surveying two 25 deg ex-tragalactic fields at a depth of ∼ × − erg cm − s − inthe [0.5-2] keV band for point-like sources. The XXL web-site is http://irfu.cea.fr/xxl. Multi-band information andspectroscopic follow-up of the X-ray sources are obtainedthrough a number of survey programmes, summarised athttp://xxlmultiwave.pbworks.com/. References
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Article number, page 22 of 27utler et al.: The XXL Survey XXXVI: Evolution and black hole feedback of HERGs and LERGs in XXL-S
Table 9.
RLF data for all RL AGN, RL HERGs and LERGs in XXL-S with M i < − for < z < . . See the caption for Table5 for an explanation of the columns. RL AGN RL HERGs (median) LERGs (median)log( L . ) N log( Φ ) N log( Φ ) N log( Φ )(W Hz − ) (mag − Mpc − ) (mag − Mpc − ) (mag − Mpc − )21.8 1.0 -5.39 + . −∞ + . −∞ + . − . + . −∞ + . − . + . − . + . − . + . − . + . − . + . − . + . − . + . − . + . − . + . − . + . − . + . −∞ + . − . + . − . + . − . + . − . + . − . + . − . + . − . + . − . + . − . + . −∞ + . −∞ Table 10.
RLF data for all RL AGN, RL HERGs and LERGs in XXL-S with M i < − for . < z < . . See the caption forTable 5 for an explanation of the columns. RL AGN RL HERGs (median) LERGs (median)log( L . ) N log( Φ ) N log( Φ ) N log( Φ )(W Hz − ) (mag − Mpc − ) (mag − Mpc − ) (mag − Mpc − )23.4 192.0 -4.79 + . − . + . − . + . − . + . − . + . − . + . − . + . − . + . − . + . − . + . − . + . − . + . − . + . − . + . − . + . − . + . − . + . − . + . − . + . − . + . − . + . − . Table 11.
RLF data for all RL AGN, RL HERGs and LERGs in XXL-S with M i < − for . < z < . . See the caption forTable 5 for an explanation of the columns. RL AGN RL HERGs (median) LERGs (median)log( L . ) N log( Φ ) N log( Φ ) N log( Φ )(W Hz − ) (mag − Mpc − ) (mag − Mpc − ) (mag − Mpc − )23.8 168.0 -5.15 + . − . + . − . + . − . + . − . + . − . + . − . + . − . + . − . + . − . + . − . + . − . + . − . + . − . + . − . + . − . + . − . + . − . + . − . + . − . + . − . + . − . + . − . + . −∞ + . −∞ Table 12.
RLF data for all RL AGN, RL HERGs and LERGs in XXL-S with M i < − for . < z < . . See the caption forTable 5 for an explanation of the columns. RL AGN RL HERGs (median) LERGs (median)log( L . ) N log( Φ ) N log( Φ ) N log( Φ )(W Hz − ) (mag − Mpc − ) (mag − Mpc − ) (mag − Mpc − )24.2 175.0 -5.45 + . − . + . − . + . − . + . − . + . − . + . − . + . − . + . − . + . − . + . − . + . − . + . − . + . − . + . − . + . − . + . − . + . − . + . − . + . − . + . − . + . − . + . − . + . − . + . − . Article number, page 23 of 27 &A proofs: manuscript no. XXL-XXXVI-BH-FeedBack-20190429
Table 13.
Best-fitting double power law parameters for the local1.4 GHz XXL-S LERG and RL HERG RLFs.
LERGs RL HERGs LERGs RL HERGs(all) (all) ( M i < − ) ( M i < − )log( Φ ∗ ) − . − . − . − . log( L ∗ ) 25.910 27.212 25.910 26.776 α − . − . − . − . β − . − . − . − . Table 14.
Best-fitting PDE and PLE parameters ( K D and K L ,respectively) for the evolution of XXL-S RL HERG and LERGRLFs with M i < − . For comparison, the K D and K L parametersfor the HERG and LERG RLFs from Pracy16 are shown. XXL-S XXL-S Pracy16 Pracy16Parameter LERGs RL HERGs LERGs HERGs K D ± ± + . − . + . − . K L ± ± + . − . + . − . Article number, page 24 of 27utler et al.: The XXL Survey XXXVI: Evolution and black hole feedback of HERGs and LERGs in XXL-S
Appendix A: Comparison of kinetic luminosityscaling relations
A number of scaling relations between monochromatic ra-dio luminosity (e.g. L . ) and kinetic luminosity ( L kin )have been published in the literature (Willott et al. 1999;Merloni & Heinz 2007; Cavagnolo et al. 2010; O’Sullivanet al. 2011; Daly et al. 2012; Godfrey & Shabala 2016).All these log( L kin ) versus log( L . ) relations have similarslopes and intercepts (as demonstrated by Smolˇci´c et al.2017b in their Appendix A), but suffer from very large un-certainties due to the small sample sizes (tens of galax-ies) used to produce the relations. Furthermore, Shabala &Godfrey (2013) and Godfrey & Shabala (2016) have pointedout that these relations are distance dependent (i.e. are af-fected by Malmquist bias). This dependence arises from thenecessary range in distance required to probe a large rangeof radio and X-ray luminosity.More specifically, Shabala & Godfrey (2013) showedthat any derived relation between radio-luminosity and jetkinetic power depends sensitively on sample properties –in particular the size-luminosity correlation inherent in thesample. Their results indicate that accurate estimates ofthe integrated kinetic power output of AGNs can only beobtained if a measure of radio source ages, such as size orspectral index, is used in addition to their radio luminosi-ties. The sole use of radio luminosity as a proxy for jetpower underpredicts the jet powers for the largest sourcesand overpredicts the jet powers for the smallest sources.They conclude that adopting a simple scaling relation be-tween radio luminosity and jet power that does not includea measure of source size or age results in significant errorsin jet power estimates. Consequently, incorrect estimates ofAGN jet power will result in mismodelling of AGN feedbackprocesses. Accurate jet power measurements are requiredto test whether the AGN heating and gas cooling rates areindeed balanced. Accordingly, they determined a new ex-pression for jet power that accounts for the source size (seetheir Equation 8).In addition, Godfrey & Shabala (2016) found that in asample of FRI X-ray cavity systems, after accounting forthe mutual distance dependence, the jet power and radioluminosity are only weakly correlated, with slope β L ≈ ∼ Fig. A.1.
Distribution of kinetic luminosities of all RL AGNin XXL-S using different scaling relations. The relations fromGodfrey & Shabala (2013) for FRI and FRII sources are similarto the relation from Cavagnolo et al. (2010) (which is similarto Merloni & Heinz 2007 and O’Sullivan et al. 2011), but thisapparent agreement is due to the similar distance dependence ofjet-power measurement techniques used for FRI and FRII radiogalaxies in these samples. properties and how those properties correlate with distanceto each radio source. The reason that the results from God-frey & Shabala (2013) and Cavagnolo et al. (2010) (whichis similar to Merloni & Heinz 2007 and O’Sullivan et al.2011) are so similar is because the jet-power measurementtechniques used for FRI and FRII radio galaxies in thesesamples have similar distance dependences. For simplicity,the Shabala & Godfrey (2013) distribution was constructedby assuming each ATCA XXL-S radio source is unresolved,for which an upper limit to each source’s size was used (i.e.no larger than 5.39 (cid:48)(cid:48) , the major axis of the ATCA beam,across). The fact that this distribution not only producesa peak in the kinetic luminosity distribution that is overan order of magnitude less than the peak in the Cavagnoloet al. (2010) and Godfrey & Shabala (2013) distributions,but is broader as well (i.e. incorporates a wider range in ki-netic luminosity), illustrates the importance of taking intoaccount the source size when computing the kinetic lumi-nosity associated with radio jets. The Willott et al. (1999)relation takes into account distance effects, and this is re-flected in the fact that the peak of that distribution is veryclose to the peak in the Shabala & Godfrey (2013) distribu-tion. Finally, the Godfrey & Shabala (2016) relation clearlyproduced kinetic luminosities much higher than the otherrelations. This is probably due to the fact that it is based ona sample that extends to only z ≤ . and the slope of therelation is shallow ( ∼ z > . , the Godfrey & Shabala (2016) relation maynot be applicable to the full XXL-S sample. Regardless ofthe relative credibility of each scaling relation, Figure A.1demonstrates that there are very large differences in thekinetic luminosity distributions. Article number, page 25 of 27 &A proofs: manuscript no. XXL-XXXVI-BH-FeedBack-20190429
Table A.1.
Equations of the scaling relations discussed in Appendix A. All have been converted into the form in which amonochromatic radio luminosity is an input variable. In all cases, L kin has units of W and the monochromatic radio luminosities( L . , L ) have units of W Hz − . For the Willott et al. (1999) relation (see Heckman & Best 2014), a value of f W =4 waschosen. For the Cavagnolo et al. (2010) relation, ν = . × Hz. For the Shabala & Godfrey (2013) and Godfrey & Shabala (2013)relations, L was obtained by converting the S . values (the XXL-S flux densities measured at the effective frequency)into S assuming the spectral index assigned to each XXL-S radio source (see Appendix A in XXL Paper XXXI), g = 2 isthe normalisation factor, and D is the source size in kpc. For the Godfrey & Shabala (2016) relation, d L is the luminosity distancein Mpc. Reference EquationWillott et al. (1999) log( L kin ) = 0.86 · log( L . ) + 14.08 + 1.5 log( f W )Cavagnolo et al. (2010) L kin = ( W ) · . [ log ( ν L )]− . Shabala & Godfrey (2013) L kin = (10 W) · (cid:16) L W Hz − (cid:17) . · (1 + z ) · (cid:16) D kpc (cid:17) . Godfrey & Shabala (2013) (FRI) L kin = (5 · W) (cid:16) L W Hz − (cid:17) . Godfrey & Shabala (2013) (FRII) L kin = g (1.5 · W) (cid:16) L W Hz − (cid:17) . Godfrey & Shabala (2016) log( L kin ) = 36.56 + 0.27 log (cid:16) L W Hz − (cid:17) + 1.4 log (cid:16) d L
100 Mpc (cid:17) + 0.33
Expanding on this, Godfrey & Shabala (2016) foundthat the uncertainty regarding radio lobe dynamics in FRIand FRII sources provides some uncertainty in the pre-dicted scaling relations. Their theoretical modelling showedthat β L is expected to be significantly lower in samples ofFRI radio galaxies than it is for FRIIs, due to the differingdynamics for these two classes of radio source. For FRI X-ray cavity systems the model predicts β L (cid:38) β L (cid:38) Article number, page 26 of 27utler et al.: The XXL Survey XXXVI: Evolution and black hole feedback of HERGs and LERGs in XXL-S
Appendix B: Effect of rebinning the local RLHERG RLF
Rebinning the luminosity bins of the local RL HERG RLFpresented in Section 4.2 was investigated as a means of im-proving the model fit. This was done by shifting each lumi-nosity bin by 0.2 dex (half of the bin width). The result wasa smoother RLF with no gaps (i.e. no bins with 0 sources)in the range 22.6 < log[ L . (W Hz − )] < Φ ∗ ] = − . ), and Table B.1displays the RLF data.The evolution measured with the new local fit was K D = . ± . and K L = . ± . . These K D and K L values are very different to the original K D = 1.812 and K L = 3.186 values shown in Table 14, but the latter values arestill used in this paper for the following reasons:1. The K D = 0.838 and K L = 1.482 values ultimately re-sult in little difference to the evolution of Ω kin for theRL HERGs. The lower K D value caused the uncertaintyextrema of the RL HERG Ω kin curve derived using theCavagnolo et al. (2010) scaling relation (Equation 13) toincrease by ∼ ∼ z = and ∼ ∼ z = . (see Figure22). This increase is within the large uncertainty limitsof the Cavagnolo et al. (2010) scaling relation ( ∼ Fig. B.1.
Rebinned local XXL-S RL HERG RLF with M i < − (blue shaded region) and the corresponding fit (solid blue line).The original local RL HERG RLF with M i < − is shown asthe cyan circles and its fit is the dashed blue line. The rebin-ning caused an increase in the normalisation of the fit (log[ Φ ∗ ]= − . ). However, this did not significantly affect the mea-surement of the evolution of Ω kin for RL HERGs given the largeuncertainties in the Cavagnolo et al. (2010) scaling relation. Forcomparison, the Pracy16 HERG RLFs with m i < . (includingall sources) and M i < − are shown. Table B.1.
Data for the rebinned local XXL-S RL HERG RLFwith M i < − , shown in Figure B.1. See the caption for Table5 for an explanation of the columns. log( L . ) N log( Φ )(W Hz − ) (mag − Mpc − )22.4 4.5 -5.72 + . − . + . − . + . − . + . − . + . − . + . −∞ + . − .53