AGN and star formation across cosmic time
aa r X i v : . [ a s t r o - ph . GA ] F e b Mon. Not. R. Astron. Soc. , 1– ?? (2014) Printed 25 February 2021 (MN L A TEX style file v2.2)
AGN and star formation across cosmic time
M. Symeonidis, ⋆ and M. J. Page, Mullard Space Science Laboratory, University College London, Holmbury St. Mary, Dorking, Surrey RH5 6NT, UK
Accepted Received; in original form
ABSTRACT
We investigate the balance of power between stars and AGN across cosmic history,based on the comparison between the infrared (IR) galaxy luminosity function (LF)and the IR AGN LF. The former corresponds to emission from dust heated by starsand AGN, whereas the latter includes emission from AGN-heated dust only. We findthat at all redshifts (at least up to z ∼ L IR ). We partition the L IR − z parameter space into a star-formation and an AGN-dominated region, finding that the most luminous galaxies atall epochs lie in the AGN-dominated region. This sets a potential ‘limit’ to attainablestar formation rates, casting doubt on the abundance of ‘extreme starbursts’: if AGNdid not exist, L IR > L ⊙ galaxies would be significantly rarer than they currentlyare in our observable Universe. We also find that AGN affect the average dust temper-atures ( T dust ) of galaxies and hence the shape of the well-known L IR − T dust relation.We propose that the reason why local ULIRGs are hotter than their high redshiftcounterparts is because of a higher fraction of AGN-dominated galaxies amongst theformer group. In star-forming galaxies a significant fraction of the stel-lar UV and optical radiation is absorbed by dust and re-emitted in the infrared (IR). As a result infrared emissionis commonly used as a proxy for star-formation and thereexists a set of straight-forward, widely used calibrations forconverting total IR luminosity ( L IR , 8–1000 µ m) to the star-formation rate (SFR; e.g. Kennicutt 1998; et al. 2009). IR-luminous galaxies ( L IR > L ⊙ ) were discovered in largenumbers by the IRAS all sky survey in the 1980s (Soiferet al. 1984a; 1987a; 1987b; Sanders & Mirabel 1996). Itwas noted that these sources are rare in the local Universe(e.g. Kim & Sanders 1998) but much more numerous at ear-lier epochs (e.g. Takeuchi et al. 2005), being responsible forabout half the total light emitted from all galaxies integratedthrough cosmic time (e.g. Gispert et al. 2000; Lagache etal. 2005; Dole et al. 2006). Indeed the total star formationrate per unit volume (e.g. Hopkins & Beacom 2006; Madau& Dickinson 2014), at all epochs, is primarily made up ofgalaxies which are infrared-luminous (e.g. Takeuchi et al.2005).Apart from high star-formation rates, IR-luminousgalaxies are also characterised by an AGN incidence ratewhich increases as a function of L IR , with the vast majorityof the most luminous IR-galaxies at every epoch showingsome kind of AGN signature (e.g. Goto 2005; Kartaltepe etal. 2010; Yuan et al. 2010; Goto et al. 2011a). Indeed, lu- minous QSOs are seen to be strong far-IR/submm emitters(e.g. Willott et al. 2000; Priddey & McMahon 2001; Page etal. 2001; 2004; Priddey et al. 2007; Tsai et al. 2015; Podi-gachoski et al. 2015; 2016) and the plethora of extremelyinfrared-luminous sources recently discovered by the Wide-Field Infrared Survey Explorer (WISE; Wright et al. 2010)are thought to be primarily powered by AGN (e.g. Wu etal. 2012; Jones et al. 2014; Tsai et al. 2015; Fan et al. 2016;Glikman et al. 2018).The battle between stars and AGN in dust heating hasbeen a topic of much contention going back as early as the1990s (e.g. Gregorich et al. 1995; Genzel et al. 1998; Soiferet al. 2000; Klaas et al. 2001; Davies et al. 2002; Frances-chini et al. 2003) and subsequently had a revival with thelaunch of the Herschel Space Observatory (Pilbratt et al.2010), designed to target the 70-500 µ m wavelength rangein which most of the Universe’s obscured radiation emerges(e.g. Magnelli et al. 2010; Seymour et al. 2011; Rovilos et al.2012; Kirkpatrick et al. 2015; Rawlings et al. 2015; Khan-Ali et al. 2015; Masoura et al. 2018 and many more). Re-cently, Symeonidis et al. (2016; hereafter S16) and Syme-onidis (2017; hereafter S17) challenged the idea that far-IRemission is in all cases primarily powered by star-formation Herschel is an ESA space observatory with science instrumentsprovided by European-led Principal Investigator consortia andwith important participation from NASA. © M. Symeonidis and M. J. Page
Figure 1.
The IR LF ( φ IR ) from Gruppioni et al. (2013): black filled circles. The corresponding functional form and 1 σ uncertaintyare shown by the black dashed curve and shaded region. Shown with red squares is the IR AGN LF ( φ IR , AGN ), derived from the hardX-ray LF in Aird et al. (2015). The red dotted curve and shaded outline represents the functional form and 1 σ uncertainty. The 9 panelscorrespond to different redshift bins as indicated. The vertical blue line indicates the luminosity where the parametric forms of the twoLFs meet, L merge . The abscissa legend reads ‘log L IR or log L IR , AGN ’ because φ IR is a function of L IR , whereas φ IR , AGN is a functionof L IR , AGN . by showing that powerful AGN can dominate the entire in-frared spectral energy distribution (SED). The implicationsof this are that the correlation between infrared luminosityand SFR must break down at high luminosities, at whichpoint SFRs derived from infrared broadband photometrywould be significantly overestimated. In order to gain fur-ther insight into the balance of power between AGN andstars in the IR-luminous galaxy population, Symeonidis &Page (2018; hereafter SP18) and Symeonidis & Page (2019;hereafter SP19) compared the behaviour of the IR galaxyLF to the IR AGN LF at z ∼ − z ∼ L IR .In this paper, we merge the work of SP18 and SP19and subsequently develop it further with the following spe-cific aims in mind: (i) to understand the shape of the IRLF in the L IR ∼ − L ⊙ range, between z = 0 andz ∼ L − z space into AGN-dominatedand star-formation dominated regions, (iii) to examine thebreakdown in the SFR- L IR correlation and (iv) to quan- tify the effect of AGN in shaping the L IR - dust temper-ature ( T dust ) relation. Our paper is structured as follows:in sections 2 and 3 we describe our method and results.The discussion and conclusions are presented in sections 4and 5. Throughout, we adopt a concordance cosmology ofH =70 km s − Mpc − , Ω M =1-Ω Λ =0.3. We compare the galaxy LF and the AGN LF in the infrared(8–1000 µ m). This energy band is chosen for two main rea-sons: (i) the IR LF is more complete than the UV/opticalLFs at all redshifts as it includes galaxies which are heav-ily obscured in the UV/optical (ii) examining LFs in the8–1000 µ m spectral range, rather than focusing on a partic-ular monochromatic IR band, ensures that all IR-emittersare included irrespective of variations in their SEDs.As in SP18, for the IR galaxy LF ( φ IR ) we use the onepresented in Gruppioni et al. (2013; hereafter G13). φ IR isa function of L IR , which includes the total dust-reprocessed © , 1– ?? GN and star formation across cosmic time Figure 2.
The IR LF ( φ IR ) from Gruppioni et al. (2013): black filled circles. The corresponding functional form and 1 σ uncertaintyare shown by the black dashed curve and shaded region. Shown with red squares is the IR AGN LF ( φ IR , AGN ), derived from the hardX-ray LF in Aird et al. (2015). The red dotted curve and shaded outline represents the functional form and 1 σ uncertainty. The 9 panelscorrespond to different redshift bins as indicated. Included in this figure are also the IR space densities of AGN host galaxies as presentedin Gruppioni et al. (2013). The space densities and corresponding uncertainties of sources fitted with type-1 AGN SEDs are indicatedwith the blue shaded area, whereas the sources fitted with type-2 AGN SEDs are indicated with the purple shaded area. Where bothtype-1 and type-2 data are present, the number densities are added and the total is indicated by the open green diamonds. The abscissalegend reads ‘log L IR or log L IR , AGN ’ because φ IR is a function of L IR , whereas φ IR , AGN is a function of L IR , AGN . emission from stars and AGN. The uncertainties on φ IR fromG13 are a combination of Poisson errors and photometricredshift uncertainties derived through Monte Carlo simula-tions. The model fit to φ IR is the Saunders (1990) functionwhich behaves as a power-law for L < L ⋆ and as a Gaus-sian for L > L ⋆ (see G13 for more details). For the AGNLF we use the absorption-corrected hard X-ray (2-10 keV)AGN LF from Aird et al. (2015; hereafter A15). The er-rors on φ IR , AGN are Poisson. The A15 AGN LF is fit with adouble power-law model, whose parameters are themselvesfunctions of redshift evaluated at the centre of the relevantbin (see A15 for more details). Note that we examine the be-haviour of the luminosity functions up to z ∼ .
5, becauseas discussed in G13, there is a severe lack of spectroscopicredshifts amongst the population that makes up the IR LFat z > . φ IR , AGN ) as follows: first, hard X-ray luminosity is con-verted to optical luminosity at 5100˚ A ( νL ν, ), adopting the equation from Maiolino et al. (2007), who derived it fromthe α OX relation reported in Steffen et al. (2006) by convert-ing L in the Steffen et al. (2016) relation to L − using Γ = − .
7. To be consistent with the work of A15 whichassumes a Γ of -1.9, we modify the Maiolino et al. (2007)equation by adding the constant C:log [L − ] = 0 .
721 log [ ν L ν (5100˚A)] + 11 .
78 + C (1)where C = log(3 . − log(4 .
14) and 3.49 is the value of L − keV L keV for Γ = − . L − keV L keV for Γ = − .
7. A Γ = − . − . XMM-Newton (e.g. Mateo et al. 2005; 2010; Page et al.2006).Subsequently, to convert from νL ν, to infrared lumi-nosity in the 8–1000 µ m range ( L IR , AGN ) we use the intrin-sic AGN SED of S16, which represents the average optical-submm broadband emission from AGN. The L IR / νL ν, ratio for the S16 SED is 1.54. In section 3.9 we also in- © , 1– ?? M. Symeonidis and M. J. Page
Figure 3.
The luminosity density as a function of redshift: the to-tal infrared luminosity density ( ρ IR ; large black open circles), theinfrared luminosity density of AGN ( ρ IR , AGN ; red diamonds) andthe infrared luminosity density of star-formation ( ρ IR , SF ; smallblue filled circles). Table 1 lists the plotted data. vestigate effect of using other AGN SEDs with different L IR / νL ν, ratios.Note that in this work we assume (i) the geometric uni-fication of AGN, in which type-1 and type-2 AGN are in-trinsically the same objects viewed from different angles and(ii) that both type-1 and type-2 AGN infrared luminositiesscale in the same way with the accretion disc luminosity(e.g. Gandhi et al. 2009). Any differences in the shape ofthe intrinsic SED of type 2 and type 1 AGN are ‘washedout’, since we only make use of the integrated 8–1000 µ mluminosity (e.g. Polletta 2006, 2007; Tsai et al. 2015). φ IR , AGN is now a function of L IR , AGN , not X-ray lumi-nosity, where L IR , AGN is the intrinsic IR luminosity of theAGN, i.e. it does not include the contribution of dust heatedby starlight. Note that the A15 X-ray AGN LF does notinclude Compton-thick AGN. Therefore, following the pre-scription of A15, we scale the normalisation of the φ IR , AGN with their estimate of the Compton thick (CT) AGN frac-tion which is 34 per cent of the absorbed AGN population. Inthe A15 formulation the CT fraction is a constant fractionof the absorbed AGN population, but the absorbed AGNpopulation fraction is itself a function of redshift and lumi-nosity — so indirectly the CT fraction is also a function ofredshift and luminosity.At this stage, we take into account two forms of uncer-tainty in the conversion from the A15 X-ray LF to φ IR , AGN :one related to the conversion from X-ray to optical lu-minosity and the other to the conversion from optical toinfrared luminosity. For the former, we use the standarderror on the mean α OX computed using the data in ta-ble 5 of Steffen et al. (2006), averaged over all bins. Thiscorresponds to a 16.6 per cent (1 σ ) uncertainty on the L − / νL ν (5100˚ A ) ratio. For the conversion from op- tical to infrared, we make use of the full set of individ-ual intrinsic AGN SEDs used to derive the average S16AGN SED (see S16 and S17), finding the (1 σ ) error onthe mean L IR / νL ν (5100˚ A ) ratio to be 9.4 per cent. Bothof these are abscissa uncertainties, so we convert them toordinate uncertainties on φ IR , AGN using the gradient of theluminosity function. The error on the L IR / νL ν (5100˚ A ) ra-tio translates to a φ IR , AGN uncertainty in the range of 3–14 per cent for L IR , AGN < L ⊙ and 14–15 per cent at L IR , AGN > L ⊙ , whereas the L − / νL ν (5100˚ A ) ra-tio error translates to a φ IR , AGN uncertainty in the rangeof 3–14 per cent for L IR , AGN < L ⊙ and 14–26 per centfor L IR , AGN > L ⊙ . These are added in quadrature tothe A15 error on the functional form of φ IR , AGN in order toadjust the width of the φ IR , AGN σ boundaries. The data and functional forms of φ IR , AGN and φ IR are shownin Fig. 1 in 9 redshift bins within the 0 < z < . φ IR and φ IR , AGN are monotonically decreasing functions of L IR and L IR , AGN respectively (over the luminosity rangeconsidered here), and φ IR > φ IR , AGN . The 1 . < z < . z centre =1.35) and 1 . < z < z centre =1.75) redshift binsare taken from SP18 and the remaining redshift bins arepresented here for the first time. In the bins where the G13and A15 results do not cover exactly the same redshift range,we also evaluated the parametric model of the A15 LF atthe the centre of the G13 bins, finding the mean shift to benegligible at the bright end, so we use the original redshiftbins for φ IR , AGN in Fig. 1, as the AGN luminosity densitieswere calculated in those bins in A15.Fig. 1 shows that at low luminosities, φ IR and φ IR , AGN are offset by up to 2 dex, but this difference decreases withincreasing luminosity, and eventually φ IR and φ IR , AGN con-verge. For the sake of consistency in all redshift bins, wedefine L merge to be the luminosity at which the parametricforms of φ IR , AGN and φ IR meet. Note that although the datado not cover the L IR ∼ L merge parameter space in all bins,we are confident that L merge is a good approximation of theluminosity of convergence of the two LFs. In some redshiftbins one can see that the AGN and galaxy number densitiesare similar even before the parametric forms meet. More-over, optical QSO surveys like the SDSS which cover largeareas of sky to faint fluxes, have provided well-sampled AGNLFs to larger luminosities and smaller space densities thanprobed here. These show no change in the slope of the AGNLF down to space densities that are two orders of magnitudelower than probed by the A15 LF, and far beyond L merge (e.g. Croom et al. 2009). Although it is not possible to directly measure L IR , AGN (AGN emission only) and corresponding number densities,one can measure the number densities of AGN as a functionof L IR (host+AGN emission). The latter measurements arethen useful for comparing to a model of the former. In Fig2 we compare φ IR , AGN with the G13 AGN LF. G13 performSED fitting on their sample of IR-selected galaxies and builtthe AGN LF by selecting only the sources that get flagged in © , 1– ?? GN and star formation across cosmic time the SED fitting process as hosting an AGN. The G13 AGNLF thus represents the space densities of candidate AGNhosts, and L IR in this case is the emission from AGN andthe host. On the other hand, in our work, φ IR , AGN repre-sents the space densities of AGN as a function of L IR , AGN ,i.e. emission from the AGN only. Fig 2 shows that there isgood agreement between the G13 AGN LF and our φ IR . By integrating φ IR and φ IR , AGN we calculate the total in-frared luminosity density ( ρ IR and ρ IR , AGN respectively) as afunction of redshift. Subtracting ρ IR , AGN from ρ IR gives theIR luminosity density from star-formation ( ρ IR , SF ). Theseare plotted in Fig. 3. The shape of ρ IR and ρ IR , AGN looksimilar, with an initial increase up to z ∼ ρ IR is a factor of 19–64 higher than ρ IR , AGN and the contribution of AGN to the total infraredluminosity density ranges from ∼ z =0.15 to ∼ z = 2 .
25 (see table 1). The change in frac-tional AGN contribution with redshift is only significant atthe < σ level, thus there is no evidence that the contribu-tion of AGN to the total IR energy budget is dependent onredshift.Our results indicate that current estimates of the cosmicSFR density are only marginally affected by AGN contami-nation. This is slightly different to what is found by Grup-pioni et al. (2015), who show a small but significant AGNcontribution particularly at intermediate redshift (z ∼ ∼
20 per cent AGN inci-dence in a sample of IR-selected galaxies when examiningthe hardness ratio, mid-IR colours, optical and X-ray vari-ability, radio loudness and high excitation optical lines. Webelieve the difference in the AGN incidence rate is becausemulti-component SED fitting results in a larger fraction ofsources requiring some level of AGN contribution to theirtotal infrared luminosity.In any case both the Gruppioni et al. (2015) results andthe ones presented here consistently indicate that AGN arenot the primary contributors to ρ IR at any redshift. The ratio of φ IR , AGN to φ IR (hereafter referred to as F AGN )provides a simple estimate of the fraction of AGN-dominatedsources as a function of L IR (see also SP18 and SP19). Thisdefinition assumes that galaxies are either entirely AGN-powered or star-formation-powered (i.e. there is no mixing)and F AGN essentially represents n AGN / ( n AGN + n SF ), where n AGN is the number of AGN-powered galaxies and n SF is thenumber of star-formation-powered galaxies. Although thisdefinition has its limitations at low luminosities where theremight be substantial mixing between emission from starsand AGN, as we approach the high luminosity regime where Table 1. ρ IR , ρ IR , AGN and ρ IR , SF (in log[L ⊙ Mpc − ]) as shownin Fig. 3. The log 1 σ lower and upper values of ρ IR , ρ IR , AGN and ρ IR , SF are also listed. The last column shows the fractionalcontribution of AGN to ρ IR as a percentage. The redshifts arequoted at the middle of the bins.z log ρ IR log ρ IR , AGN log ρ IR , SF ρ IR , AGN / ρ IR (%)0.15 8.13 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . the luminosity functions start converging, L IR ∼ L IR , AGN ,i.e. the AGN infrared emission dominates the L IR . As aresult, we expect that F AGN adequately traces the AGN-dominated fraction of galaxies at least in the high luminosityregime.Fig. 4 shows F AGN as a function of L IR , calculated bydividing the φ IR , AGN parametric model by the φ IR paramet-ric model in each redshift bin. Note that at all redshifts, thecontribution of the AGN to the total infrared luminosity andhence the fraction of AGN-dominated sources is small at low L IR , but undergoes a rapid increase with increasing L IR , andat high L IR , the population becomes AGN dominated. Notethat the whole curve shifts rightwards with increasing red-shift, suggesting that the luminosity at which the infraredgalaxy population becomes AGN-dominated increases as afunction of redshift.In Fig. 5 we compare F AGN with the AGN incidencerate ( R AGN ) as reported in Hwang et al. (2010), Kartaltepeet al. (2010), Juneau et al. (2013) and Lemaux et al. (2014),aiming to compare the same redshift ranges as much as pos-sible. The different relations shown by these works are likelya result of the AGN selection criteria in the samples used.It is interesting to note that at a given L IR , the fractionof galaxies hosting AGN is much higher than the fractionof AGN-dominated galaxies, so the increase in the latter isvery easily accommodated by the increase in the former.This suggests that at L merge , almost all galaxies host AGN.This is consistent with what G13 also find, namely that thesources that make up the high luminosity tail of φ IR are con-sistently fitted with SED models that have a strong AGNcomponent. Earlier we defined L merge as the luminosity at which φ IR , AGN and φ IR meet and hence F AGN =1. We now also definethe mixing luminosity at F AGN =0.25 ( L mix25 ), F AGN =0.5( L mix50 ) and F AGN =0.75 ( L mix75 ) to be where the fractionof AGN-dominated sources is 25, 50 and 75 per cent respec-tively. Fig. 6 shows these quantities as a function of redshift,as well as the measurements for the local ( z < .
1) Universefrom SP19. The SP19 values of L mix25 , L mix50 , L mix75 and L merge at z < . © , 1– ?? M. Symeonidis and M. J. Page
Figure 4.
Plotted here is the ratio of φ IR , AGN to φ IR ( F AGN ) which provides a simple estimate of the fraction of AGN-dominatedsources as a function of L IR . The shaded outline to the curve represents the 1 σ uncertainty interval calculated from the uncertaintiesof the LFs in Fig. 1. The panels correspond to different redshift bins as indicated. The shaded vertical bands represent the ULIRG(10 < L IR < L ⊙ ) and HyLIRG ( L IR > L ⊙ ) regimes. these quantities at 0 < z < . z < . < z < . L mix25 , L mix50 , L mix75 and L merge increase with redshift,not surprising as both the AGN and IR LFs undergo redshiftevolution (Fig 1). It is interesting to note that at a given L IR the fraction of AGN-dominated sources is higher at lowredshift than it is at high redshift.In Fig. 7 we compare our results with the convergenceregion modelled by Hopkins et al. (2010), defined as the lo-cus of convergence between the galaxy and AGN LF, withthe width of this region representing the uncertainty in theconvergence point. Note that this is equivalent to our defini-tion of L merge and its corresponding uncertainties. Hopkinset al. derive their boundaries theoretically, using a semi-empirical approach, starting with a halo occupation modelconvolved with observables such as the stellar mass func- tion and then evolved using the prescriptions from hydro-dynamical simulations for the distribution of SFRs and L IR in obscured AGN, quiescent galaxies and merger-inducedstarbursts in order to construct LFs. They assume that itis only obscured AGN that make a significant contributionto the infrared, stating that only up to 5 per cent of thebolometric luminosity of unobscured AGN is emitted in thefar-IR. This fraction is consistent with what was proposedin S17, although the latter study showed that that it alsoapplies to unobscured AGN. It is interesting to note thatthe convergence region in the Hopkins et al. formulation isin broad agreement with our work, almost completely over-lapping with L merge until about z ∼ .
8. There is less pro-nounced overlap thereafter, however it has been noted thathydrodynamical simulations and semi-analytic models, of-ten underestimate the high-luminosity end of the IR LF andthe high-mass end of the mass function at high redshift (e.g.Gruppioni et al. 2015). As a result, it is possible that theHopkins et al. approach might be underestimating the con-vergence region with increasing redshift.In Fig. 7 we also show the Speagle et al. (2014) locus ofthe ‘main sequence of star-formation’ (SFR - M ⋆ relation) © , 1–, 1–
8. There is less pro-nounced overlap thereafter, however it has been noted thathydrodynamical simulations and semi-analytic models, of-ten underestimate the high-luminosity end of the IR LF andthe high-mass end of the mass function at high redshift (e.g.Gruppioni et al. 2015). As a result, it is possible that theHopkins et al. approach might be underestimating the con-vergence region with increasing redshift.In Fig. 7 we also show the Speagle et al. (2014) locus ofthe ‘main sequence of star-formation’ (SFR - M ⋆ relation) © , 1–, 1– ?? GN and star formation across cosmic time Figure 5.
The ratio of φ IR , AGN to φ IR ( F AGN ) in the 0 < z < . . < z < < z < R AGN , reported in Hwang et al. (2010; H10), Kartaltepe et al.(2010; K10), Juneau et al. (2013; J13) and Lemaux et al. (2014;L14) compared to F AGN in similar redshift ranges. evaluated in the log [ M ⋆ (M ⊙ )] = 10 . − . L IR . Inaddition we plot the L ⋆ of φ IR from G13, and the L ⋆ of the φ IR , AGN from A15 converted to the IR, although note thatthe two L ⋆ functions are not directly comparable becausethe two LFs are fitted with different parametric forms. Asexpected the region described by L mix25 , L mix50 , L mix75 and L merge is offset from the ‘knee’ ( L ⋆ ) of φ IR and φ IR , AGN . L mix25 is about 1.5-2 dex higher than the G13 L ⋆ ( L mix25 ∼ L ⋆ ) and L merge is offset by ∼ . L merge ∼ L ⋆ ).The large offset from L ⋆ and the ‘star-forming sequence’locus further illustrates the point that the AGN contributionto the total emission is not significant for the bulk of thestar-forming galaxy population.Note that our computed L mix25 , L mix50 , L mix75 and Figure 6.
The evolution of L mix25 (green), L mix50 (yellow), L mix75 (blue) and L merge (red) representing the fraction of AGN-dominated sources at the 25, 50, 70 and 100 per cent levels re-spectively. The corresponding hatched regions represent the 1 σ uncertainties on these quantities derived from the uncertaintiesin F AGN as shown in Fig 4. The symbols at z < . L mix25 , yellow asterisk for L mix50 , blueasterisk for L mix75 and red triangle for L merge . They are slightlyoffset in redshift for more clarity. L merge do not extend past z ∼ .
5. However, as they areall derived by dividing the luminosity functions, they arelinked to how the luminosity functions themselves evolveand hence it is reasonable to assume that they evolve in asimilar fashion to L ⋆ . We thus extrapolate L mix25 , L mix50 , L mix75 and L merge by evolving them in the same way as theG13 L ⋆ , namely L ∝ (1 + z ) . for z > .
85. The extrapo-lated quantities are shown as dotted lines in Fig. 7. L IR − z space Based on our results, we create a diagnostic diagram whichserves to separate the L − z space into a star-formation-dominated, a transition and an AGN-dominated region (Fig8). We define the AGN-dominated region as starting from L mix75 (Fig. 7), the transition region to be between L mix25 and L mix75 and the star formation dominated region at L IR < L mix25 . Note that this diagram is not designed forclassifying individual galaxies as AGN-dominated or star-formation-dominated, rather it reflects the dominance ofpopulations in L − z space. It is thus perfectly plausible thatsome sources in the star formation dominated region will beAGN-dominated in the IR. However, the more luminous agalaxy is the more likely it is that it will be AGN-dominated,and above a certain luminosity, it becomes a reasonable ex-pectation that individual galaxies can be assumed to be en-tirely AGN-powered.We populate Fig 8 with various samples from the lit-erature, selected to be (amongst) the most luminous at theredshifts probed. Fig 8 includes optically unobscured QSOsfrom Tsai et al. (2015; see also S17), intermediate redshift © , 1– ?? M. Symeonidis and M. J. Page
Figure 7.
The evolution of L mix25 (green), L mix50 (yellow), L mix75 (blue) and L merge (red) representing the fraction of AGN-dominated sources at the 25, 50, 75 and 100 per cent levels re-spectively. The corresponding hatched regions represent the 1 σ uncertainties on these quantities derived from the uncertaintiesin F AGN as shown in Fig 4. The dotted lines represent the ex-trapolated L mix25 , L mix50 , L mix75 and L merge σ boundaries upto z ∼
4, computed by evolving the luminosity by (1 + z ) . .The symbols at z < . L mix25 , yellow asterisk for L mix50 , blue asterisk for L mix75 andred triangle for L merge . They are slightly offset in redshift for clar-ity. The grey shaded region is taken from Hopkins et al. (2010)and indicates their modelled convergence region where objectschange from star-formation to AGN dominated. Also shown arethe L ⋆ from the Gruppioni et al. (2013) IR LF (solid turquoisecurve) and the L ⋆ from the AGN LF of A15 converted to the IR(vertical dashed blue curve). Finally, the evolution of the SFR-M ⋆ relation with redshift, evaluated at M ⋆ =10 . M ⊙ and M ⋆ =10 . M ⊙ , taken from Speagle et al. (2014), is plotted as a palebrown region. ULIRGs from Yang et al. (2007) and the
IRAS -selectedHyLIRGs from Rowan-Robinson et al. (2018). We also plotsources from the WISSH project (Bischetti et al. 2007) whichincludes WISE f > z > . µ m WISE bands but clearly detected at 12 and 22 µ m— they are also known as hot dust obscured galaxies (hotDOGs; Wu et al. 2012; Jones et al. 2014; Tsai et al. 2015,Fan et al. 2016). Table 2.
Data for Fig. 6, indicating the values of L mix25 , L mix50 , L mix75 and L merge at the middle of the redshift bins shown inFig. 4. Also included are the extrapolated L mix25 , L mix50 , L mix75 and L merge shown in Fig 7. The log 1 σ upper and lower values of L mix25 , L mix50 , L mix75 and L merge are also quoted.redshift log L mix25 log L mix50 log L mix75 log L merge (L ⊙ ) (L ⊙ ) (L ⊙ ) (L ⊙ ) < . a . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . b . . . . . . . . b . . . . . . . . . . . . . . . . c . . . . . . . . c . . . . . . . . c . . . . . . . . c . . . . . . . . Notes: a: data from SP19b: redshifts bins first explored in SP18 but data are from this workc: extrapolation (see Fig 7)
It is clear that the most luminous sources (currentlywith public data) accumulate in the transition or AGN-dominated regions, suggesting that their IR emission eitherhas a significant AGN contribution or it is entirely domi-nated by the AGN, a finding which is corroborated by thestudies from which they were taken. The hot DOGs arethought to be AGN powered based on several AGN signa-tures in the optical, mid-IR and X-rays (e.g. Wu et al. 2012;Stern et al. 2014; Tsai et al. 2015; Assef et al. 2015; Vito et al.2018) and so are the QSOs. The
IRAS
HyLIRGs, the samesources whose LF is shown in Fig 10 (see discussion in sec-tion 3.7), are unsurprisingly well within the AGN-dominatedregion.
SFRs are thought to be proportional to L IR (e.g. Kennicutt1998; 2009) and hence broadband infrared photometry isoften used to estimate galaxy SFRs. However, earlier weshowed that the AGN contribution increases as a functionof L IR , at any given redshift, suggesting that at some point L IR will stop tracing the SFR and instead will trace theAGN power. Using the relation between F AGN and L IR ateach redshift bin (see Fig 4), we compute the luminosityattributed to star-formation ( L IR , SF ) as follows: L IR , SF = L IR (1 − F AGN ) (2)Subsequently, we convert L IR , SF to SFR using the Kennicutt(1998) calibration, namely SFR = 4 . × − L IR , SF , where L IR , SF is in units of erg/s. Note that since F AGN representsthe fraction of AGN-dominated galaxies, not the fractionof AGN-powered IR emission in individual galaxies, L IR , SF represents the amount of IR emission that can be attributedto star-formation for a galaxy population in a given redshift– L IR bin and does not refer to individual galaxies. © , 1– ?? GN and star formation across cosmic time Figure 8.
Partitioning the L IR − z space into a star-formation-dominated, a transition and an AGN-dominated region. The transitionregion is within L mix25 and L mix75 (see Fig. 7). The AGN-dominated region is defined as being above L mix75 . Overplotted are varioussamples from the literature most of which are claimed to be amongst the most luminous at each redshift. Fig. 9 shows SFR plotted against L IR for each redshiftbin. Note that the SFR- L IR proportionality relation breaksdown at high L IR . At all redshifts, the turnover in the rela-tion occurs approximately when F AGN ∼ .
35 (indicated bythe horizontal dotted lines in Fig. 9), but the L IR at whichit happens increases with increasing redshift. The turnoverSFR (SFR turn ), although not a hard limit, represents thetypical maximum value of SFR that would be believable ifcomputed from the L IR at each redshift (listed in table 3).Higher SFRs would likely be overestimates. φ IR over 5 orders of magnitudein L IR As mentioned earlier, φ IR > φ IR , AGN and since φ IR declinesfaster than φ IR , AGN , there comes a point where they merge.Note that although the parametric models of the LFs inFig 1 seem to cross-over, this is simply the effect of ex-trapolating them. In reality the two LFs never cross overand the condition φ IR > φ IR , AGN always holds. At L merge ,the space densities of AGN and galaxies become consistentwithin the errors, suggesting that φ IR = φ IR , AGN . Beyond L merge , φ IR = φ IR , AGN still holds, hence φ IR should assumethe slope of φ IR , AGN as described by the A15 models. Join-
Table 3.
Table showing the SFR at the turnover point in theSFR- L IR relation, i.e. the maximum believable SFR that can becomputed from L IR at each redshift bin, as shown in Fig. 9. TheSFRs are rounded to the nearest decade. The redshifts are quotedin the middle of the bins.z SFR turn (M ⊙ /yr )0.15 2500.325 3200.5 3500.7 4700.9 9801.1 14601.45 23401.75 22002.25 3150 ing up the functional forms of φ IR and φ IR , AGN at L merge gives the shape that the functional form of φ IR should haveif we were able to measure it over 5 orders of magnitudein luminosity; see Fig. 10. Note that although the changeof slope at L IR = L merge seems abrupt, it is because weare crudely joining the parametric forms of the two LFs atthat point. If we were able to measure the space densities of © , 1– ?? M. Symeonidis and M. J. Page
Figure 9.
SFR as a function of L IR (solid lines) at each redshiftbin. The SFR is computed using equation 2. The dotted horizontallines denote the turnover in the SFR- L IR relation at each redshift,representing the typical maximum value of SFR that would bebelievable if computed from the L IR . sources around L merge we would expect the change of slopeto look smoother.The prediction that eventually φ IR assumes the slopeof φ IR , AGN was first made in SP18 for 1 < z <
2. Ob-jects in the hyperluminous infrared galaxy (HyLIRG) regime( L IR > L ⊙ ) are rare and in order to measure theirspace densities, an all sky survey, such as IRAS or WISE would be required. Using
IRAS data, Rowan-Robinson &Wang (2010; hereafter RRW10) estimated the HyLIRG LFat 0 . < z < < z <
2. SP18 showed that theHyLIRG space densities at 1 < z < . < z < IRAS galaxies and our mod-elled IR LF, confirms our prediction that at L IR > L merge , φ IR = φ IR , AGN hence the IR LF is essentially made up ofsources which derive the bulk of their IR power from AGNnot star-formation. This suggests that the most luminous in-frared emitters are AGN powered — at least up to z = 2 . φ IR can be compared with data, andplausibly at all redshifts. L IR − T dust relation It is well established that there is a relation between galax-ies’ L IR and their average dust temperature ( T dust ), withmore IR-luminous systems having higher T dust — hereafter,we refer to this as the L − T relation. This is observed in the local ( z < .
1) Universe (e.g. Dunne et al. 2000; Dale etal. 2001; Dale & Helou 2002; Chapman et al. 2003; Chapinet al. 2009) but also at higher redshifts (Hwang et al. 2010;Amblard et al. 2010; Calanog et al. 2013; Symeonidis et al.2013 — hereafter referred to as S13). The average increase ofdust temperature with luminosity is often attributed to thepresence of more intense starburst regions in the more lumi-nous sources. However, SP19 showed that infrared emissionin the local ULIRG population includes a substantial AGNcontribution, and thus they proposed that additional dustheating by the AGN could also play a role in increasing theaverage dust temperatures of these systems.Here, we provide a simple prescription in which we usethe computed F AGN to examine the effect of AGN dustheating as a function of L IR in a statistical manner, andsubsequently use this model to understand the local L − T relation. Since our approach is based on F AGN , as derived insection 3.3, it assumes a mix of AGN-dominated and star-formation dominated galaxies, rather than a scenario whereAGN and star-formation emission is mixed in individualgalaxies. While these two scenarios have different implica-tions for the variations in temperature between individualgalaxies at a given luminosity, we expect them to lead tosimilar average temperatures for the population in the wideluminosity bins we are considering.Since we know the AGN contribution as a function of L IR ( F AGN ; Fig 4), the average dust temperature of galaxiescan be approximated by the mixing of hot dust emissionfrom the AGN with cooler dust emission from stellar-heateddust, using F AGN to weigh the AGN and star-forming galaxydust temperatures as follows: T dust = F AGN T dust , AGN + (1 − F
AGN ) T dust , SF (3)where T dust , AGN is the assumed dust temperature of AGNand T dust , SF is the assumed dust temperature of star-forminggalaxies. To obtain T dust as a function of L IR we assume that T dust , SF is a function of L IR and that T dust , AGN is constant.To compute T dust , AGN we measure the dust temperature of each intrinsic AGN SED (see S17) that makes up the S16average intrinsic AGN SED used here, by fitting a grey-body function of the form B λ ( T ) λ − β (where β = 1 .
5) to60 and 100 µ m. This wavelength range was chosen so thatit is consistent with how the temperatures of local galax-ies were calculated in S13; see below. Averaging these AGNSED temperatures gives T dust , AGN of 57 K.For T dust , SF we need an L − T relation for star-forminggalaxies, clean from AGN contamination. For this purposewe use the L − T relation in S13 derived for a sample ofintermediate redshift ( z < . Herschel -selected galaxies.Implicit in this, is the assumption that AGN do not con-tribute to dust heating in the S13 sample and hence the S13 z < . L − T relation is solely the result of an increase inthe star-formation rate. Before using this relation, we exam-ine whether this is indeed the case, by computing the T dust we would expect with equation 3, assuming that T dust , SF isconstant at 29 K which is the temperature of the first binin the S13 L − T relation. T dust , AGN is taken to be 57 K, asabove. The results are shown in Fig. 11. The recomputed z < . L − T relation is flat, showing no increase with L IR suggesting that AGN cannot be responsible for the increasein dust temperature above the assumed baseline of 29 K. In-deed at the redshift and luminosity ranges probed by the © , 1– ?? GN and star formation across cosmic time Figure 10.
The shape of φ IR over 5 orders of magnitude in L IR , for the 9 φ IR redshift bins shown in Fig 1. The point showing an abruptchange in slope is L merge . At L IR < L merge the LF has the shape of φ IR as described by the G13 models, whereas at L IR > L merge , φ IR = φ IR , AGN so φ IR essentially assumes the slope of φ IR , AGN as described by the A15 models. The diamonds and asterisks show theIRAS HyLIRG luminosity function from Rowan-Robinson & Wang (2010) in the 0 . < z < < z < φ IR slopeat L IR > L merge , where the φ IR is essentially made up of AGN. S13 L − T relation, F AGN is at its baseline level of a fewper cent (Fig. 4). We can thus assume that the increase indust temperature seen in the S13 z < . L − T relation issolely a consequence of an increase in the SFR for the moreluminous sources.As mentioned earlier, our purpose is to examine theSP19 hypothesis that AGN dust heating plays a role in shap-ing the local L − T relation. Since we have just shown thatthe S13 z < . L − T relation is free from AGN contam-ination, we are in a position to use this as our model ofwhat the local L − T relation should look like in the absenceof AGN. To do this, we first re-normalise it to the baselinetemperature measured for local IR galaxies. This is 31.3 Kat log L IR /L ⊙ ∼
10, i.e. the first bin in the local L − T re-lation as measured by S13 (by fitting a greybody to the 60and 100 µ m data of local IR-luminous galaxies). The renor-malised L − T relation now represents what is expected forthe local Universe in the absence of AGN, i.e. for purely star-forming galaxies (see Fig. 12). Note that the measured dusttemperatures of local sources progressively diverge from the expected local L − T relation with increasing L IR , suggestingthat the increase in SFR alone cannot account for the rise indust temperature. We now investigate whether this discrep-ancy is the effect of the AGN contribution to dust heating.Taking equation 3 and substituting 57 K for T dust , AGN andthe expected local L − T relation for T dust , SF , we find that T dust is now consistent with the measured dust temperaturesof local galaxies. This suggests that AGN dust heating couldplay a significant role in shaping the local L − T relation. Note that, as mentioned above, our model assumes that T dust , AGN is constant, which might be an over-simplification.Indeed, T dust , AGN may be increasing with increasing L IR , asa result of an increase in the AGN radiation power heatingthe dust. However to measure the empirical relationship be-tween T dust , AGN and L IR , a much larger AGN sample wouldbe needed than the one available to us. In any case, an in-crease of T dust , AGN with L IR would serve to strengthen ourconclusions, in the sense that it would make the role of AGNdust heating in shaping the local L − T relation even morepronounced. φ IR , AGN
As mentioned in section 2, the derivation of φ IR , AGN wasbased on the S16 SED. Here, we examine the impact of thechoice of AGN SED, by recomputing φ IR , AGN with a rangeof diverse SEDs, chosen to be representative of the types ofunobscured AGN SEDs available in the literature. These arethe Xu et al. (2015) SED (hereafter Xu15 SED) taken fromLyu & Rieke (2017), the Mor & Netzer 2012 SED (here-after MN12 SED) extended into the far-IR as described inNetzer et al. (2016), and the Mullaney et al. (2011) SEDs(hereafter M11 SEDs). All are shown in Fig. 13. The MN12and Xu15 SEDs extend from the optical to the submm andin Fig 13 they are shown normalised to the S16 SED at0.51 µ m. One can see that, although they are less luminousin the far-IR, they are more luminous in the mid-IR and their © , 1– ?? M. Symeonidis and M. J. Page
Figure 11.
The L − T relation for z < . F AGN in the appropriate redshift range, we compute the expected T dust (black points and line), by assuming T dust , AGN =57 K and T dust , SF =29 K which is the dust temperature of the z = 0 . F AGN is at its baselinelevel of a few percent, indicating that AGN are not responsiblefor the rise in temperature seen in the Symeonidis et al. (2013) z < . L − T relation, suggesting that its shape is determined byan increase in SFR from the low to the high luminosity sources. L IR / νL ν, ratio is higher than that of the S16 SED. Forthe MN12 SED L IR / νL ν, =1.65 and for the Xu15 SED L IR / νL ν, =2.12, compared to L IR / νL ν, =1.54 for theS16 SED. On the other hand, the M11 SEDs do not extendto the optical, so in order to use them, we normalise them at20 µ m to the S16 SED and assume the S16 SED shape short-wards of 20 µ m. This is equivalent to using the S16 SED upto 20 µ m with a reduced far-IR emission ( > µ m), so in thisway we can conveniently examine the effect of the far-IR con-tribution in isolation. To cover the most extreme scenario,we chose the M11 SED with the lowest far-IR emission, outof their suite of three SEDs. The L IR / νL ν, ratio for ourchosen M11 SED is 1.22, indicating that reducing the far-IR emission alone only reduces L IR by about 20 per cent.This is because more than 90 per cent of the L IR in theaforementioned AGN SEDs (and unobscured AGN SEDs ingeneral) is made up by emission at λ < µm (e.g. see S17).This is also the reason why the Xu15 and MN12 SEDs havehigher L IR / νL ν, ratios than the S16 SED even thoughhave lower far-IR luminosity; it is because their mid-IR lu-minosity is higher.Figs 14 and 15 show the effect of the choice of AGN SEDin computing φ IR , AGN and F AGN respectively. Taking theconversion with the S16 SED as the reference point, we findthat other AGN SEDs introduce only a small change in our
Figure 12.
Luminosity and dust temperature measurements forlocal ( z < .
1) galaxies in five bins taken from Symeonidis etal. (2013) (red filled-in circles). The green line is the interme-diate redshift ( z < . L − T relation from Symeonidis et al.(2013) — see Fig. 11 — normalised to the first bin of the localmeasurements (log L IR /L ⊙ =11; 31.3 K), and represents the lo-cal L − T relation expected in the absence of AGN, i.e. for purelystar-forming galaxies. The blue curve and hatched 1 σ uncertaintyrepresents the local L − T relation expected including AGN, com-puted using equation 3.
Figure 13.
The Symeonidis et al. (2016) intrinsic AGN SED(black solid line) and 68 per cent confidence intervals (shadedregion), compared with: (i) the AGN SEDs from Mullaney et al.(2011) normalized to the S16 SED at 20 µ m (dashed-dot greencurves), (ii) the Xu et al. (2015) SED taken from Lyu & Rieke(2017), normalised to the S16 SED at 0.51 µ m (solid blue curve)and (iii) the Mor & Netzer 2012 SED extended into the far-IR asdescribed in Netzer et al. (2016), normalised to the S16 SED at0.51 µ m (vertical dash red curve). © , 1–, 1–
The Symeonidis et al. (2016) intrinsic AGN SED(black solid line) and 68 per cent confidence intervals (shadedregion), compared with: (i) the AGN SEDs from Mullaney et al.(2011) normalized to the S16 SED at 20 µ m (dashed-dot greencurves), (ii) the Xu et al. (2015) SED taken from Lyu & Rieke(2017), normalised to the S16 SED at 0.51 µ m (solid blue curve)and (iii) the Mor & Netzer 2012 SED extended into the far-IR asdescribed in Netzer et al. (2016), normalised to the S16 SED at0.51 µ m (vertical dash red curve). © , 1–, 1– ?? GN and star formation across cosmic time Figure 14.
A modification of Fig 1 in order to show the effect of the choice of AGN SED on φ IR , AGN . The black dashed curve andsurrounding shaded region (1 σ uncertainty) is the functional form of φ IR . The other shaded curve is the 1 σ uncertainty correspondingto φ IR , AGN with each coloured curve representing the functional form of φ IR , AGN derived with different AGN SEDs: the red solid curvecorresponds to the Symeonidis et al. (2016) SED, the orange dashed curve corresponds to the Mullaney et al. (2011) SED, the bluedashed curve corresponds to the Mor & Netzer (2012) SED and the green dash-dot curve corresponds to the Xu et al. (2015) SED. The1 σ φ IR , AGN uncertainty is computed with the Symeonidis et al. (2016) SED. results, shifting φ IR , AGN and F AGN by about ± . σ uncertainties. Moreover,it is clear that the S16 AGN SED represents a middle groundwithin the range of available AGN SEDs. For these reasonswe consider our results and conclusions robust to the choiceof AGN SED. We have compared the infrared galaxy LF ( φ IR ) as afunction of L IR (i.e. bolometric 8-1000 µ m emission fromdust heated by stars and AGN) to the infrared AGN LF( φ IR , AGN ) as a function of L IR , AGN (i.e. bolometric 8-1000 µ m emission from dust heated by AGN only) up to z = 2 .
5. We found that at low luminosities, φ IR and φ IR , AGN are offset by up to 2 dex, but this difference decreases withincreasing luminosity, and eventually φ IR and φ IR , AGN con-verge. Since the ratio of the two ( φ IR , AGN / φ IR ) is a proxyfor the fraction of AGN-dominated sources ( F AGN ) we foundthat AGN-powered galaxies constitute a progressively larger fraction of the total space density of IR-emitting sourceswith increasing L IR , until they take over as the dominantpopulation. This occurs at the point when the two LFs con-verge, L merge . At L IR > L merge , φ IR assumes the slope of φ IR , AGN : galaxies are now AGN-dominated — true at allredshifts. However, since the LFs evolve with redshift, sodoes the F AGN – L IR relation, and at a given L IR , the fractionof AGN-dominated sources is higher at low redshift than itis at high redshift.Comparing the AGN and galaxy IR LFs, and their evo-lution with redshift has allowed us to investigate the balanceof power between AGN and stars as a function of galaxy lu-minosity and cosmic time, and thus understand in more de-tail various aspects of galaxy evolution. These are discussedin more detail below. φ IR Since the 80s, when the IR LF was first computed using
IRAS data, it has been well established that φ IR has a flat- © , 1– ?? M. Symeonidis and M. J. Page
Figure 15.
A modification of Fig 4 in order to show the effect of the choice of AGN SED on the ratio of φ IR , AGN to φ IR ( F AGN ). Thecoloured curves represent F AGN derived using different AGN SEDs: the red solid curve corresponds to the Symeonidis et al. (2016) SED,the orange dashed curve corresponds to the Mullaney et al. (2011) SED, the blue dashed curve corresponds to the Mor & Netzer (2012)SED and the green dash-dot curve corresponds to the Xu et al. (2015) SED. The shaded 1 σ φ IR , AGN uncertainty is computed with theSymeonidis et al. (2016) SED. ter high-luminosity slope than what is prescribed by thetraditional Schechter (Schechter 1976) shape, unlike galaxyLFs in the UV and optical. Although bright AGN are regu-larly removed when building UV and optical galaxy luminos-ity functions, this is not the case in the infrared. We thuspropose that the reason for the shallower high-luminosityslope in φ IR at all redshifts is the increase in the space den-sity of AGN-dominated sources relative to SF-dominatedsources with increasing L IR (first discussed in SP19 for thelocal Universe). We find that at L IR > L ⋆ , the fraction ofAGN-dominated galaxies rises steeply — their relative spacedensity increases in a given L IR bin, flattening the slope of φ IR . G13 showed that at the highest luminosities probed intheir study, the IR LF is made up of galaxies which hostAGN. Here we show that the IR emission in these, is in factAGN-dominated, with the dust-reprocessed stellar emissionplaying a minor role. Our work is consistent with the G13 re-sults in the sense that the most luminous galaxies must hostAGN for their emission to be AGN-dominated. In particular,the comparison between the G13 AGN LF and our φ IR , AGN in Fig. 2 shows that the G13 SED fitting identifies a large proportion of luminous AGN and perhaps additional star-formation dominated sources, so the G13 AGN LF includesat least as many sources as our φ IR , AGN . At low AGN lumi-nosities, particularly below the LF ‘knee’, the comparison isperhaps not as straight-forward because AGN are often notthe dominant component in the IR and so absorbed AGNmight be hard to identify in the G13 SED fitting process.We note that the high-luminosity tail of φ IR undergoesa further flattening of slope when φ IR and φ IR , AGN convergeat L IR ∼ L merge . At L IR > L merge , the IR-luminous galax-ies population is predominantly AGN-powered and φ IR isessentially shaped by the space densities of AGN. Our pre-dictions regarding the high luminosity end are corroboratedby the measured space densities of galaxies from the IRAS all sky survey from RRW10, both at 0 . < z < < z < © , 1– ?? GN and star formation across cosmic time Our work has thrown light on the characteristic shapeof the IR LF (at z . L IR > L ⊙ .Moreover we have exposed that the true shape of the IRLF for star-formation is unknown at present, although weexpect it to have a steeper high luminosity slope than theIR LF currently measured, where the AGN contribution ismixed in with the star-formation contribution. Indeed cos-mological simulations, in aiming to reproduce galaxy LFs,will have to take into account that the IR LF is boosted athigh L IR due to AGN. For example, Katsianis et al. (2017)find that their models require less AGN feedback to matchthe IR LF than to match the UV observations. This is likelybecause the IR LF has a shallower high-luminosity slopethan the UV LF, but it is a contradictory result since AGNplay a much larger role in shaping the IR LF. There are many claims in the literature that a cold dustcomponent in galaxy SEDs is evidence for star-formationeven in cases where there is a confirmed AGN, so the far-IRis often used for SFR measurements (e.g. Hatziminaoglou etal. 2010; Rosario et al. 2013; Feltre et al. 2013; Ellison et al.2016; Duras et al. 2017). The SED analysis in S16 and S17,however, indicated otherwise: it was shown that luminousenough AGN can entirely drown the IR emission of theirhost galaxies even in the far-IR/submm, suggesting that forsources hosting sufficiently luminous AGN, L IR traces theAGN power rather than the star formation rate (true for allAGN types).Here we show that the SFR- L IR correlation ‘breaksdown’ (Fig. 9) once F AGN > .
35. Although F AGN refersto the fraction of AGN-dominated sources rather than theAGN contribution in a particular galaxy, the SFR- L IR cor-relation turn-over, nevertheless, implies that when a signifi-cant fraction of the population is AGN dominated in the IR,broadband IR photometry should be avoided as an indicatorof star formation in individual galaxies.What does this imply about a limit in galaxy SFRs?By the time the AGN dominate the infrared/submm partof the electromagnetic spectrum, they are already luminousenough to dominate the bolometric emission of their host,because only about a third of the AGN power comes outin the 8-1000 µ m range (e.g. Tsai et al. 2015; S16; S17). Asa result, the maximum believable SFRs we compute (Fig.9) might be quite close to the highest SFR that sourcesare likely to have at each cosmic epoch. Only with star-formation indicators independent of IR photometry will webe able to answer this conclusively. Nevertheless, our resultsshow that ‘extreme starbursts’ with SFRs of many thou-sands of M ⊙ /yr are much rarer than previously thought,in agreement with cosmological models, which fail to repro-duce such high SFRs even at the peak of a major merger(e.g. Narayanan et al. 2010; Narayanan et al. 2015). Galaxy evolution studies have long shown that high red-shift galaxies do not as a whole have the same propertiesas their lower redshift counterparts for a given luminosity.This is partly because of the availability of fuel which in-creases with increasing redshift, but here we show that there seems to be another important factor: the AGN fraction. Fora given L IR , the contribution of AGN to galaxies’ energybudget decreases as a function of redshift and the typicalfraction of AGN-dominated sources is higher at low redshiftthan it is at high redshift. This may be partly responsiblefor the luminosity evolution in the properties we observe inIR-luminous galaxies, i.e. high redshift ULIRGs being theanalogues of low redshift LIRGs and high-redshift HyLIRGsbeing the analogues of low-redshift ULIRGs.The current picture for the formation of massivespheroidals supports a scenario whereby a major merger in-duces the dust enshrouded phase of intense AGN and star-burst activity, followed by a blow-out phase of the dust andgas, leaving an optically unobscured QSO which eventu-ally turns into a ‘dead’ elliptical (e.g. Sanders et al. 1988;Hopkins et al. 2008; hereafter H08). Indeed the most IR-luminous obscured AGN, or hot DOGs as they are oftenreferred to (see section 3) are thought to be the progenitorsof optically-unobscured QSOs (e.g. Assef et al. 2015; Wu etal. 2018) and according to Bridge et al. (2013) perhaps eventhe short-lived ‘caught-in-the-act’ point where the AGN isexpelling gas and dust, a claim they base on their discoveryof extended Ly α emission in these sources.Our work (see Fig 8) suggests that (i) the most lumi-nous optically unobscured QSOs have substantial infraredemission on par with the most luminous IR-selected galax-ies and (ii) the IR emission of the most luminous sources isAGN dominated, irrespective of whether the AGN is opti-cally obscured or unobscured. This suggests that if the afore-mentioned scenario of evolution between optically-obscuredand optically-unobscured AGN is true, it must be accom-panied with a re-distribution of dust from a cocoon aroundthe central black hole to dust extended in the AGN narrowline region (NLR). The likely existence of dust in the AGNNLR was also examined in S17 who calculated that for theAGN to retain its optical colours and produce a substantialamount of IR emission, the dust must extend over kpc scalesand hence have low average dust temperature. Moreover, itwas shown that the dust mass estimates for the most lu-minous 2 < z < M ⊙ : see S17;also Ma & Yan 2015) are comparable with the dust massescalculated for hot DOGs (e.g. Fan et al. 2016).Since we find there are no galaxies whose luminosityfrom star-formation supercedes the most luminous AGN, ourresults are consistent with, although do not prove, the evolu-tionary scenario where the AGN quenches star-formation intheir host galaxies. The question that remains unanswered,however, is what are the SFRs of galaxies hosting the mostluminous AGN. Measuring these would be a critical step for-ward, if we are to understand AGN feedback in the contextof galaxy evolution. Indeed, JWST will give the opportunityto explore other indicators of star-formation such as poly-cyclic aromatic hydrocarbons (PAHs; F¨orster Schreiber etal. 2004; Peeters et al. 2004; Risaliti et al. 2006; Kennicuttet al. 2009), in the effort to move away from SFR measure-ments using broadband infrared photometry. L IR − T dust relation Many studies have reported the existence of intermediateredshift galaxies with lower T dust than local galaxies ofequivalent luminosities (e.g. Chapman et al. 2005; Coppin © , 1– ?? M. Symeonidis and M. J. Page et al. 2008; Symeonidis et al. 2009; Hwang et al. 2010; Mag-nelli et al. 2012; Casey et al. 2012; S13). Although in somecases their detection rate is linked to the selection biasesof submm surveys (e.g. Symeonidis et al. 2011) and hencedoes not reflect the average properties of the population,there is a measured ∼
10 K difference between the averagedust temperatures of local ULIRGs and their intermediateredshift counterparts (see S13). In other words, the interme-diate redshift L − T relation is flatter than the local one. Ithas been suggested before that this is a consequence of thelocal L − T relation evolving with redshift (e.g. Chapman etal. 2002; Lewis et al. 2005; Chapin et al. 2009) in the sameway that L ⋆ evolves. Symeonidis et al. (2009) looked intothis claim by de-evolving the luminosities of high-z ULIRGsby (1 + z ) , finding that they remained outside the local L − T relation. They concluded that this style of evolutionof the L − T relation cannot be responsible for the increasedpresence of cold ULIRGs in the distant Universe.Recently, SP19 proposed the idea that the local L − T relation could be driven by AGN. Here we demonstrate thatthis is indeed the case. Folding in the AGN contribution tothe L − T relation for star-forming galaxies, by mixing theAGN dust temperature and star-forming galaxy dust tem-perature in the ratio prescribed by F AGN , we successfullyreproduce the L − T relation measured in the local Uni-verse (Fig 12). We find that the dust temperatures of localULIRGs are higher than would be expected if the increase inSFR were the sole factor, hence we conclude that the differ-ence in average dust temperature between local ULIRGs andtheir less luminous counterparts is partly due to an increasedAGN fraction in the former group. Since F AGN increases asa function of L IR in a similar fashion (at least up to z ∼ . L − T relation at highredshift is flatter than the local L − T relation is becauseof a change in the fraction of AGN-dominated galaxies. Inother words, high redshift ULIRGs are cooler than their localcounterparts because they are predominantly star formationdominated, in contrast to local ULIRGs, many of which areAGN-powered (see Fig. 8). Note that this result does notcontradict the observed changes in galaxy properties, suchas sizes (e.g. Tacconi et al. 2006; Iono et al. 2009; Rujopakarnet al. 2011) as these are linked to the availability of cold gaswhich is more substantial at high redshift. We have described a phenomenological approach aimed to-wards understanding the balance of power between AGNand stars up to z ∼
4. Using the X-ray (converted to IR)AGN LF and the IR galaxy LF, we have investigated theimpact of AGN in measured galaxy properties such as L IR , SF R and T dust and interpreted the shape of two key observ-ables: the IR LF and the L − T relation.Our major findings and conclusions are listed below: • For the first time, we derive the shape of the pure AGNLF in the IR finding that it is responsible for shaping theIR LF at the highest luminosities. We find that star-forminggalaxies dominate the IR LF at L IR < L ⋆ , whereas AGNstart flattening the high-luminosity tail at L IR & L ⋆ .There is a further break in slope at L IR & L ⋆ where the IR LF becomes AGN-dominated at which point it takes onthe slope of the AGN LF. • The most IR-luminous and thus bolometrically lumi-nous sources at all redshifts are AGN-dominated. This,moreover, explains the reason why we can observe such lu-minous galaxies. If AGN did not exist, the space densities of L IR > L ⊙ galaxies would be orders of magnitude lowerthan what is currently measured, rendering such sourcesvery difficult to find in our observable Universe. • The range of maximum SFRs is likely between 1000and 4000 M ⊙ /yr at the peak of cosmic star formation his-tory (1 < z < • The AGN contribution in the IR can account for thedifferences in average dust temperatures between sources ofcomparable luminosity at different redshifts. Local ULIRGsare hotter than their intermediate redshift counterparts be-cause the AGN contribution in the former is up to 30 timeslarger. © , 1– ?? GN and star formation across cosmic time ACKNOWLEDGMENTS
MS and MJP acknowledge support by the Science and Tech-nology Facilities Council [ST/S000216/1].
DATA AVAILABILITY
The data underlying this article are either available in citedworks in the article, in the article itself or will be shared onreasonable request to the corresponding author.
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