What triggers black-hole growth? Insights from star formation rates
aa r X i v : . [ a s t r o - ph . C O ] N ov Mon. Not. R. Astron. Soc. , 1–12 (2013) Printed 15 October 2018 (MN L A TEX style file v2.2)
What triggers black-hole growth? Insights from star formation rates
Eyal Neistein, ⋆ Hagai Netzer Max-Planck-Institute for Extraterrestrial Physics, Giessenbachstrasse 1, 85748 Garching, Germany School of Physics and Astronomy, The Sackler Faculty of Exact Sciences, Tel-Aviv University, Tel-Aviv 69978, Israel
ABSTRACT
We present a new semi-analytic model for the common growth of black holes (BHs) andgalaxies within a hierarchical Universe. The model is tuned to match the mass function ofBHs at z = 0 and the luminosity functions of active galactic nuclei (AGNs) at z < . We use anew observational constraint, which relates the luminosity of AGNs to the star-formation rate(SFR) of their host galaxies. We show that this new constraint is important in various aspects:a) it indicates that BH accretion events are episodic; b) it favours a scenario in which BHaccretion is triggered by merger events of all mass ratios; c) it constrains the duration of bothmerger-induced star-bursts and BH accretion events. The model reproduces the observationsonce we assume that only 4 per cent of the merger events trigger BH accretion; BHs accretionis not related to secular evolution; and only a few per cent of the mass made in bursts goes intothe BH. We find that AGNs with low or intermediate luminosity are mostly being triggeredby minor merger events, in broad agreement with observations. Our model matches variousobserved properties of galaxies, such as the stellar mass function at z < and the clustering ofgalaxies at redshift zero. This allows us to use galaxies as a reliable backbone for BH growth,with reasonable estimates for the frequency of merger events. Other modes of BH accretion,such as disk-instability events, were not considered here, and should be further examined inthe future. Key words: galaxies: nuclei; galaxies: starburst; galaxies: haloes; galaxies: active; galaxies:bulges; cosmology: large-scale structure of Universe
Most massive galaxies in the local Universe host supermassiveblack holes (BHs) in their centres (Kormendy & Richstone 1995).Active periods of accretion onto such objects, seen as active galac-tic nuclei (AGNs), are observed in less than a few percent of theobjects. Consequently, models of BH evolution rely on assump-tions about the triggering of accretion events and the connection, ifany, with the host galaxy evolution. A key problem in such studiesrelates to the big difference in scale between the cold gas in thegalaxy (distributed over several kpc) and the inner disk around theBH (typically smaller than a parsec). Various suggestions have beenmade to bridge the gap between these scales, including: mergertriggered accretion, secular processes in the host galaxy includingdisk instabilities , mass loss from evolved stars, star formation (SF)activity in the central region, and more. ⋆ E-mail: [email protected] In this work we use the terms “secular evolution” and “secular processes”to indicate all types of internal processes within a galaxy. These includeevents of disk instability that might induce bursts of star-formation. Secularevolution does not include events related or triggered by galaxy mergers.
The merger scenario is motivated by two different lines of ev-idence. First, N -body and hydrodynamical simulations of merg-ing galaxies suggest that such events drive a large amount of coldgas into the centre of the merging system, resulting in the forma-tion of a large bulge or a spheroidal galaxy (Barnes & Hernquist1991; Mihos & Hernquist 1996; Cox et al. 2006; Robertson et al.2006; Di Matteo et al. 2007). Second, AGN activity is observed inlocal ultra-luminous infrared galaxies (ULIRGs), which are knownto be associated with energetic merger events (Sanders et al. 1988;Sanders & Mirabel 1996; Surace et al. 2000; Canalizo & Stockton2001; Veilleux et al. 2009). Observationally, an evidence for a di-rect connection between minor mergers and AGN activity is moredifficult to establish.Recent studies show that most galaxies at z < thathost a low-luminosity AGN do not show morphological evi-dence for major merger events in their recent history (Gabor et al.2009; Cisternas et al. 2011; Kocevski et al. 2012; Schawinski et al.2012). Only high-luminosity AGNs are related to major mergers(Treister et al. 2012). This has been taken to indicate that the role ofsecular processes in driving gas to the centre of galaxies and feed-ing the BH is important and very common at almost all redshifts(Efstathiou et al. 1982; Genzel et al. 2006; Elmegreen & Burkert c (cid:13) E. Neistein and H. Netzer
Herschel in the FIR, and are more reliable than UV-based SFRs. Accord-ing to Rosario et al. (2012), such SFRs are uncorrelated with theAGN luminosity at low and intermediate luminosities and at highredshift. However, high luminosity AGNs at low and intermediateredshifts do show a correlation with the SFRs of their host galaxies.In this paper we use a semi-analytic model (SAM) of galaxy-formation combined with BH evolution, in order to examine thecorrelations between SFRs and AGN luminosities. SAMs are nat-urally being used for this problem as they provide a statisticalsample of galaxies that is in general agreement with observations(Kauffmann & Haehnelt 2000; Croton et al. 2006; Bower et al.2006; Malbon et al. 2007; Monaco et al. 2007; Somerville et al.2008; Bonoli et al. 2009; Fanidakis et al. 2011; Fanidakis et al.2012; Hirschmann et al. 2012).Our study is different from previous SAMs in various as-pects. First, we use the SAM from Neistein & Weinmann (2010) and Wang et al. (2012) that fits the stellar mass function of galaxiesat < z < and the clustering of galaxies at low redshift. As a re-sult, the star-formation histories and merger-rates of galaxies withinthe model are in broad agreement with the observed Universe. Sec-ond, we do not attempt to model AGN feedback as a function ofeach specific AGN but rather assume that the galaxies within ourmodel experience an average AGN feedback that depends only onhalo mass. Third, we aim to match a wide range of AGN obser-vations, including the relation between SFR and AGN luminositymentioned above, and the fraction of host galaxies that are experi-encing major merger events.Various recent empirical models of BHs and AGNs evolutionare aimed to fit the BH mass function and AGN luminosity func-tions (e.g. Wyithe & Loeb 2003; Lapi et al. 2006; Hopkins et al.2006, 2007, 2008; Croton 2009; Shankar et al. 2009; Shankar 2010;Shankar et al. 2012; Pereira & Miranda 2011; Conroy & White2012; Draper & Ballantyne 2012). Here we choose to use SAMs,as they allow a more direct modelling of SFRs and merger fractionsof individual objects, in close contact with the formation history oftheir host haloes. These features play a key role in our model.This paper is organized as follows. In section 2 we describethe model ingredients and the details of computing all the proper-ties of galaxies and BHs. Section 3 includes a detailed compari-son between the model and observations. The results are summa-rized and discussed in section 4. This study is based on the cos-mological parameters that are used by the Millennium simulation: (Ω m , Ω Λ , σ , h ) = (0 . , . , . , . . Throughout the paperwe use log to denote log . The SAM used in this work is adopted from Wang et al. (2012),and is based on the formalism of Neistein & Weinmann (2010).The model follows galaxies inside the complex structure of subhalomerger-trees taken from a large N -body cosmological simulation(the Millennium simulation, Springel et al. 2005). This simulationfollows 2160 dark-matter particles inside a periodic box of length500 h − Mpc, with a minimum halo mass of . × h − M ⊙ .Our SAM includes the effects of cooling, star formation (SF),accretion, merging, and feedback. Unlike other SAMs, these lawsare simplified to be functions of only the host subhalo mass and red-shift. We have shown in Neistein et al. (2012) that this concept issufficient for the SAM to reproduce the gas and stellar mass contentof galaxies, on an object by object basis, as obtained from a hydro-dynamical simulation to an accuracy of 0.1 dex. Consequently, thisSAM is complex enough to accurately follow the SF histories ofgalaxies.The specific model used here was presented in Wang et al.(2012) as model 4. It is based on the SAM of De Lucia & Blaizot(2007), transformed to the language of Neistein & Weinmann(2010) and including the following modifications: • SF efficiency (the ratio between the SFR and the cold gas masswithin the disk) is lower in small mass haloes. • Satellite galaxies experience stripping of hot gas in propor-tion to the stripping of dark-matter, following the suggestion ofWeinmann et al. (2010) (see also Khochfar & Ostriker 2008). • Cooling is suppressed within haloes that are more massivethan . × h − M ⊙ , and there is no SF within haloes of mass > × h − M ⊙ at z < . . These ingredients are aimed to c (cid:13) , 1–12 hat triggers black-hole growth? mimic the feedback from AGNs, although they do not depend onthe specific AGN hosted by each galaxy. • The dynamical friction time is assumed to depend on the cos-mic time and is shorter at higher redshift. This behaviour is ob-tained by using the Chandrasekhar formula with a multiplicationfactor of × ( t/ . . , where t is the time in Gyr since thebig-bang. This dependence is motivated by a more radial infall ofsatellite galaxies towards the centre of their group at high redshifts(Hopkins et al. 2010; Weinmann et al. 2011). • The SFR in merger induced bursts depends on the halomass. In particular, it is lower than the approximation used byDe Lucia & Blaizot (2007) for haloes less massive than × h − M ⊙ . The specific implementation is described below.Galaxies in our model are embedded within dark-matter sub-haloes as extracted from the N -body simulation. We assume thatthe galaxies merge following the merging-time of their host sub-haloes, with an additional time-delay. This delay is estimated usingthe Chandrasekhar formula for dynamical friction (see Wang et al.2012). Mergers trigger SF bursts, with an efficiency that dependson the mass ratio of the two galaxies. The total stellar mass formedin the merger induced burst is: ∆ m s , burst = . (cid:16) m m (cid:17) . m cold if M h > M . (cid:16) m m (cid:17) . m cold M h M otherwise (1)where m , m are the baryonic masses of the central and satel-lite galaxy respectively (including both stellar and cold gas mass), m cold is the sum of the cold gas masses of the two galaxies, M h is the mass of the descendant subhalo, and M = 3 × h − M ⊙ . For high mass galaxies, this recipe follows the re-sults of hydrodynamical simulations by Mihos & Hernquist (1994)and Cox et al. (2008), and was adopted by various SAMs (e.g.Somerville et al. 2001; Croton et al. 2006; Khochfar & Silk 2009;Neistein & Weinmann 2010; Khochfar et al. 2011). For low massgalaxies this recipe is motivated by recent observations of SF effi-ciency (Wang et al. 2012). Note that mergers provide the only trig-ger for SF bursts in our model. The other mode of SF, by secularprocesses, describes the relatively slow conversion of cold gas intostars within disk galaxies.The specific model used here is able to fit the SF histo-ries of galaxies to a higher accuracy than most other SAMs (seeHenriques et al. 2012, for a recent success in this respect). As wasshown in Neistein & Weinmann (2010), our models reproduce boththe stellar mass function of galaxies up to z = 4 , and the distribu-tion of SFRs at z = 0 . In Wang et al. (2012) we further improvedthe model to reproduce the auto-correlation function of galaxies at z = 0 . These results are unique in comparison to other SAMs, al-lowing us to use reliable SF histories of galaxies as a basis for thework presented here which focuses on BH evolution. The modelfits observations to a level of 20-40 per cent, and is probably notthe only possible galaxy formation model. In particular, there is adegeneracy between the amount of stars formed in mergers inducedbursts, versus the amount of star formation due to secular processes.The duration of SF bursts has a negligible effect on the statis-tical properties of the model galaxies. This is because these eventsare rare, and hardly contribute to the total SFR density of the Uni-verse. However, in our current study, bursts are the only channelof BH growth, and their duration plays an important role in themodel. We assume that the shape of SF bursts follows a Gaussianas a function of time, with the following parameterization: d m s , burst d t = ∆ m s , burst σ b √ π exp (cid:20) − ( t − t ) σ b (cid:21) . (2)Here σ b determines the burst duration, t is the time in Gyr since thebig-bang, and t is the time of the peak in the SF burst. We assumethat t occurs σ b after the time the galaxies merge, to allow asmoothly rising peak of SFR (the burst of SF starts at the time ofmerging). We allow the burst to continue forming stars up to σ b after t , so the total duration of the burst is σ b .At higher redshifts galaxies have smaller radii, and time-scalesare shorter (the halo dynamical time is proportional to the cosmictime, t ). We therefore assume that σ b depends on t in the followingway: σ b = σ t . , (3)where σ is a free constant.An additional important ingredient of the model is the defini-tion of the bulge mass. We assume that galaxies can grow a bulgeaccording to two different channels. First, SF bursts that are trig-gered by mergers of any mass ratio are assumed to contribute theirstellar content to the bulge (i.e., ∆ m s , burst from Eq. 1 is addedto the bulge of the remnant galaxy). Second, once the mass ratio m /m is larger than 0.3, the total stellar mass of both galaxies ismoved to the bulge of the remnant galaxy. Therefore, the mass ofstars within the bulge might be larger than the total amount of starsformed within bursts. Our SAM assumes that BHs grow only during merger induced starbursts. The masses of seed BHs in this model are extremely smallin comparison to the mass added in the first merger event and makeno difference to the accumulated mass of BHs at relatively low red-shifts. We have tested that using BH seeds of mass M ⊙ doesnot change our model results significantly.When galaxies merge, we merge their corresponding BHs atthe same time. Following each merger event, a burst of SF occursaccording to Eqs. 1-3. We allow the remnant BH to grow in massaccording to: d m BH d t = (1 − η ) d m s , burst d t α acc with probability α p otherwise (4)Here η is the fraction of mass that is transformed into radiationand α acc is a free parameter, corresponding to the efficiency of BHaccretion with respect to the SF burst.In a Λ CDM universe, the fraction of galaxies with an active SFburst at any given time is high, especially due to the non-negligibleburst duration σ b . However, observations show that the number ofAGNs is significantly lower (e.g. Croom et al. 2009). Our modelassumes that only a fraction α p of the merger events induce ac-cretion into the BH. In practice, at each time-step of the SAM(with a typical duration of 10 Myr) and for each BH we generatea random number, distributed uniformly between zero and unity.We then allow accretion only if this random number is smallerthan α p . In practice, each merger event adds on average a massof α acc α p ∆ m s , burst to the BH.The bolometric luminosity of the AGN is defined as: L AGN = η − η ∆ m BH ∆ t c , (5)where ∆ t is the length of the time-step within the SAM ( ∼ c (cid:13) , 1–12 E. Neistein and H. Netzer
Myr), ∆ m BH is the total mass that is added to the BH within atime-step (i.e., the integration of Eq. 4), and c is the speed of light.The Eddington luminosity describes the limit at which radia-tion pressure balances the gravitational force of the BH L Edd = 1 . (cid:18) m BH M ⊙ (cid:19) erg s − , (6)where the factor 1.5 on the left is derived for solar metallicity gas.In our model, the accretion into the BH is determined by the SFburst, and might be above the Eddington limit. In addition, it is rea-sonable to assume that this limit will vary between different BHs.In order to use a practical accretion limit, we define λ Edd to bea log-normal random variable (i.e. its log value is normally dis-tributed) with a mean of λ Edd , and a standard deviation of σ Edd (in log). For each accretion event, we randomly choose a value for λ Edd and do not allow L AGN to exceed L Edd λ Edd . We will referto L Edd λ Edd as the Eddington threshold , since it is being used toactively limit the accretion onto BHs. We note that we do not usethe Eddington threshold for the first accretion event (i.e. when theBH mass equals zero).At low accretion rates we use the properties of ‘advectiondominated accretion flows’ (ADAFs). As in previous studies (e.g.Fanidakis et al. 2012) we model the ADAF limit by η ADAF = L AGN L Edd ηα ADAF (7)which is valid only for L AGN /L Edd < α
ADAF . By definition, η ADAF equals η when L AGN /L Edd = α ADAF . In this work wefix α ADAF to a value of 0.01.Some of the results presented here make use of the luminosityof AGNs in the B band. For the conversion between L AGN and B band we use the bolometric correction from Marconi et al. (2004): log ( ν B L ν B / L AGN ) = − . . L − . L +0 . L . (8)where L = log( L AGN /L ⊙ ) − . The absolute magnitude in theAB system is then given by M B = − . − . (cid:0) ν B L ν B / erg s − (cid:1) , (9)where B refers to a rest wavelength of 4400 ˚A.To summarize, our SAM includes all the ingredients fromWang et al. (2012) related to galaxies, with the following additionalparameters related to the evolution of BHs: η , α acc , α p , λ Edd , ,and σ Edd . These parameters are presented in Table 1 and their bestchosen values are justified in section 3. The ingredients used hereare similar to previous SAMs (e.g. Malbon et al. 2007), althoughwe do not include growth modes that are not due to bursts (e.g.Hirschmann et al. 2012).Finally, we note that the model is limited both in terms of theminimum BH mass that is properly resolved, and in terms of thelimited volume of our simulation box. These limitations originatefrom the limited dynamical range of the Millennium simulation thatis being used here, and will be discussed below.
In this work we treat the galaxies as priors and do not change theparameters that affect their evolution, except for the value of σ ,which has a negligible effect on the properties of galaxies. Conse-quently, there are only six free parameters in the model, as listed inTable 1. However, the low density of AGNs in the Universe forces Log M BH [ M ⊙ ] L og Φ [ M p c − d e x − ] Shankar et al. (2009)z=0.0z=1.0z=3.1resolutionlimit
Figure 1.
The mass function of BHs. The shaded region represents the ob-servational prediction from Shankar et al. (2009) based on the correlationbetween bulge and BH masses at low redshift. Different line types corre-spond to the model mass function at various redshifts as indicated. The grey dashed line shows the minimum BH mass that is reliably reproduced by themodel (due to a minimum subhalo mass of . × h − M ⊙ ). us to test each set of model parameters by using the full Millen-nium simulation, spending a few CPU hours on each run. In orderto achieve fast tuning, while still running our model on the fullsimulation box, we first save all the model results that are relatedto the evolution of galaxies. We then run the BH ingredients only,thus saving a large amount of computational time. Our tuning pro-cedure can evolve BHs over the full Millennium simulation in onlythree minutes (using one processor), allowing us to systematicallyexplore a large region of the parameter space.We use three different types of observations to constrain ourmodel parameters: the luminosity functions of AGNs at < z < ,the mass function of BHs at z = 0 , and the relation between SFRsand AGN luminosities. While we further compare the model toother observations in the following sections, these additional ob-servations were not used for tuning the model. We start by tuning the model parameters against two common ob-servations: the mass function of BHs at redshift zero, and the lu-minosity function of AGNs at z < . We apply a tuning proce-dure that systematically scans a range of the parameters α acc , α p , λ Edd , , σ Edd according to the range listed in Table 1. The value of σ can significantly affect the luminosity function of AGNs. How-ever, it is fixed here due to its effect on the relation between SFRsand AGN luminosities, that will be discussed in the next section.Using the prior value of σ = 0 . Gyr, we could not find a modelthat matches the data to a satisfying accuracy, while using constantvalues for all the parameters. We note that larger values of σ allowfor better models. Consequently, we choose to add a dependenceon time for α acc . It should be noted that a similar result as shownhere could arise from varying the parameter α p with time. We willdiscuss below the degeneracy in choosing the best solution, and itsrelation with the SFR values of our model galaxies. Our best model c (cid:13) , 1–12 hat triggers black-hole growth? Table 1.
The free parameters used to model BHs and AGNs.Parameter range best value description σ η α acc . t − . t + 0 . Accretion efficiency, Eq. 4, t = t/ . Gyr α p λ Edd , σ Edd −9−7−5−9−7−5 L og Φ [ M p c − d e x − ] −28−25−22−9−7−5 −28−25−22 M B −28−25−22 z=0.4−0.68 z=0.68−1.06 z=1.06−1.44z=1.44−1.82 z=1.82−2.20 z=2.20−2.60z=3.25 z=3.75 z=4.25 Figure 2.
The luminosity functions of AGNs. Each panel shows one redshift bin as indicated. Observational results from Croom et al. (2009) and Richards et al.(2006) are plotted in diamonds and squares symbols respectively. Following Eq. 2 and 3 from Croom et al. (2009), we add 0.587 and 0.817 magnitudes to M g and M i respectively, in order to convert them to M B (note that in these papers M g and M i are defined for rest wavelengths corresponding to z = 2 and hencerequire correction factors to compare with our computed B band at a wavelength of 4400 ˚A). Model results are plotted in solid lines. uses η = 0 . , consistent with a value of 0.057 obtained for non-rotating BHs.In Fig. 1 we show that the mass function of BHs from themodel at z = 0 agrees with the prediction from Shankar et al.(2009). The results from Shankar et al. (2009) are based on themass function of galaxies, combined with the correlation betweenthe bulge and the BH mass. It is therefore not a direct observa-tion, and should not be considered as a strong constraint. However,the mass function points to important features of the model and wechoose to use it as a constraint even though the actual values are notcertain. For example, the recent work by McConnell & Ma (2012)indicates that the ratio between the mass of bulges and BHs couldreach a level of ∼ at the high-mass end. Fig. 1 also shows themodel mass functions at higher redshifts, indicating that the num-ber of low mass BHs grows fast before z ∼ and changes onlyslightly at z < .As seen in Fig. 1, the computed mass function declines at log m BH / M ⊙ . . . We have tested a lower resolution modelby allowing BHs to grow only within subhaloes more massivethan h − M ⊙ . This mimics a low-resolution simulation withrespect to the actual minimum mass of the simulation ( . × h − M ⊙ ). Within this resolution test, the bend in the mass function occurs at a larger mass, indicating that our resolution limitis indeed the reason for the bend at log m BH / M ⊙ . . . Our lim-ited resolution has a negligible effect on other results shown in thiswork.Models based on high resolution merger trees could possi-bly solve the above resolution problem (e.g. Fanidakis et al. 2012).Since it is difficult to increase the mass resolution within cos-mological simulations, this issue could be addressed by usingMonte-Carlo algorithms for generating merger-trees of haloes (e.g.Somerville & Kolatt 1999; Parkinson et al. 2008; Neistein & Dekel2008). However, the merger-trees used here are based on subhaloes,and are more accurate than the theoretical merger trees based onhaloes. We plan to check the use of Monte-Carlo merger trees in afuture study.The luminosity functions (LFs) of AGNs are shown in Fig. 2where points are observations adopted from Croom et al. (2009),Richards et al. (2006) and solid lines are the model results. Thetheoretical LFs computed by the SAM are in broad agreement withthe observations. In case we use constant α acc the LFs at z < are higher than the observed ones. We choose to use only opticalLFs here since it was shown by previous studies that different LFs(e.g. based on bolometric luminosity or X-ray), do not add more c (cid:13) , 1–12 E. Neistein and H. Netzer constraints on the models (Hirschmann et al. 2012; Fanidakis et al.2012).Previous studies using the merger scenario as the main mecha-nism of feeding BHs, like the one presented in Marulli et al. (2008),had difficulties matching the AGN LF. Our model is different fromthese earlier attempts. In particular, it is based on improved SF his-tories which match the observed stellar mass functions over a largerange of redshifts. Such modifications alter the amount of cold gasavailable for bursts within mergers, and the number of major ver-sus minor mergers. Consequently, the AGN LF is different althoughthe mode of BH accretion is the same (see the Appendix for moredetails).It should be noted that our simulation volume is smaller thanthe observed volume at z & , giving rise to some of the deviationsseen at high luminosities at this redshift range. Furthermore, we donot take into account various effects that could change the model atthe level of ∼
30 per cent. For example, it is well known that someAGNs are obscured and would not be accounted for in the observedLFs. We have tested that using the slim-disk approximation for su-per Eddington accretion rates (e.g. Fanidakis et al. 2012) does notchange the model results. Lastly, re-tuning the ingredients relatedto galaxy-formation might further improve the model results. Weneglect all these effects in order to keep our model as simple aspossible.Most of the free parameters in our model have a simple effecton the LF. Since the SF bursts of galaxies are not modified, α acc behaves as a constant multiplication factor for the luminosity of allAGNs at a given redshift. Changing α acc thus induces a lateral shiftin the luminosity function. The value of α p changes the number ofbursts leading to BH activity, and therefore shifts the luminosityfunction along the Y-axis. Both α acc and α p are degenerated atsome level, yielding similar results for different combinations withthe same value of α acc α p . The value of η is similar in its effect to α acc . In addition, it changes the relations between mass growth (i.e.the mass function of BHs) and luminosity. The parameters of theEddington threshold, λ Edd , and σ Edd , change mostly the high-endpart of the luminosity functions, and also the mass function of BHs.These two parameters do not have a simple effect on the modelresults. When neglecting the Eddington threshold, the luminosityof AGNs only depends on the SFR within bursts, and not on theBH mass. In this simplified case, the LF of AGNs has the sameshape as the number-density of SFRs in the model.
In Fig. 3 we show the observed results from Rosario et al. (2012) ingrey dashed lines. Values along the X-axis correspond to the bolo-metric luminosity of X-ray selected AGNs. The original Y-axis ofthis plot corresponds to the rest-frame luminosity at a wavelengthof 60 µ m, stacking all galaxies that host AGNs with similar L AGN .In order to transform the IR luminosity into SFR, we use the rela-tion L IR = 3 . × SFR (erg s − ) and L µm = 0 . L IR , whereSFRs are given in units of M ⊙ yr − . The corresponding SFR val-ues are thus population averages for various redshift groups and donot represent individual objects.Interestingly, as discussed in Rosario et al. (2012), for z > there is hardly a correlation between the AGN luminosities andSFRs. At z < the correlation between SFRs and AGN luminosi-ties only exist for L AGN > erg s − . These findings seemsurprising, since we expect that AGN growth modes will be cou-pled to the properties of their host galaxies. A lack of correlationmight indicate that most AGNs are triggered by processes that are
40 42 44 46 48−1−0.500.511.522.5
Log L AGN [erg/s] L og S F R [ M ⊙ / y r ] z=0.0z=0.3z=0.5z=1.0z=2.1 Figure 3.
The average SFR for host galaxies of a given AGN luminosity.Observational results from Rosario et al. (2012) are shown in grey dashed lines, where thinner lines correspond to higher redshifts. The observed errorbars are typically at the level of ± . and ± . dex, for SFR and L AGN respectively. Model results using the same averaging scheme and the sameredshift bins are plotted in solid lines with redshifts as indicated. For refer-ence, we plot in dotted line the relation
SFR ∝ L . (the plot is referredto in the paper as the ‘rates diagram’).
40 42 44 46 48−2−1012
Log L AGN [erg/s] L og S F R [ M ⊙ / y r ] total SFRSFR from bursts (x<−1)SFR from bursts (x>−1)average SFRaverage L AGN z = 0.0
Figure 4.
The rates diagram: values of SFR versus L AGN at z = 0 . Cir-cles represent the SFRs and AGN luminosities of the model galaxies.
Cross and square symbols show the level of SFR for the same objects, when con-sidering contributions from SF bursts only (symbols are plotted for 20 percent of the objects). We use the variable x = ( t − t ) /σ b , where x < − corresponds to objects in the early stages of the burst. The thick solid lineshows the average SFR value for a given L AGN , as was computed in Fig. 3(i.e., based on the total SFRs). The dashed line corresponds to the averagevalue of L AGN , for a given value of total SFR. not related to the dominant mode of SF. In addition, it does notseem obvious that the correlation for bright AGNs only exist at lowredshifts. In what follows, we term this plot as the ‘rates diagram’,since it shows the relation between BH accretion rates , and SF rates of their host galaxies.An explanation for the rates diagram should take into accountthe various time-scales that are buried within this relation. First, c (cid:13)000
Cross and square symbols show the level of SFR for the same objects, when con-sidering contributions from SF bursts only (symbols are plotted for 20 percent of the objects). We use the variable x = ( t − t ) /σ b , where x < − corresponds to objects in the early stages of the burst. The thick solid lineshows the average SFR value for a given L AGN , as was computed in Fig. 3(i.e., based on the total SFRs). The dashed line corresponds to the averagevalue of L AGN , for a given value of total SFR. not related to the dominant mode of SF. In addition, it does notseem obvious that the correlation for bright AGNs only exist at lowredshifts. In what follows, we term this plot as the ‘rates diagram’,since it shows the relation between BH accretion rates , and SF rates of their host galaxies.An explanation for the rates diagram should take into accountthe various time-scales that are buried within this relation. First, c (cid:13)000 , 1–12 hat triggers black-hole growth? Log L AGN [erg/s] L og S F R [ M ⊙ / y r ]
40 42 44 46 48−1−0.500.511.522.5 −101234 ( t − t ) /σ b Figure 5.
The temporal location of AGNs with respect to the peak lumi-nosity of the burst. For each value of SFR and L AGN we plot the medianvalue of x = ( t − t ) /σ b (see Eq. 2). All AGNs are selected at redshiftzero. The dashed line follows the relation SFR ∝ L . . AGNs that arestarting their accretion episode lie on the right part of the diagram. the observations of SFRs are based on indicators that last ∼ ∼ Myr. Third, the duration of both the burst of SF and AGNactivity is σ b ≈ . t (see Eqs. 2 & 3).The time-averaged SFR is crucial to our main findings and itwas therefore tested under a different assumption. We have usedthe stellar bolometric luminosity as a function of time as a proxyof the FIR luminosity. The bolometric luminosity is obtained fromBruzual & Charlot (2003) for a delta function starburst. This hasresulted in only a minor change of the results. The reason is thatalthough the stellar bolometric luminosity starts to decrease afterabout years, it remains high enough to affect the integration ofthe SFR over several hundred Myrs.As a result of the SF time-scale, the observed value of the IRluminosity is affected by the secular SF that occurred before theburst. This luminosity is uncorrelated with the merger event andwith the AGN luminosity. High luminosity AGNs are those thatare observed at a time that is close to the peak of their accretionevent ( t from Eq. 2). In these cases the SF burst is significant, andconsists of most of the observed SFR value. This explains why thecorrelation between SFRs and AGN luminosities is only seen athigh AGN luminosities. At z = 2 , the secular SFR for star-forminggalaxies is high, reaching the same level of SFR due to bursts in themost luminous AGNs. This is the reason for the lack of correlationbetween SFR and AGN luminosity at these redshifts.At a given observed epoch t , different bursts have differentvalues of t and ∆ m s , burst only, as all other parameters do not varybetween different objects. Since the time-scale for averaging theAGN luminosity is short, objects with the same value of ∆ m s , burst and | t − t | will have the same values of L AGN . However, theseobjects will have very different SFRs because those with t > t will include the peak of SF within their SFRs, while for t < t theSFR will mostly include the secular SF. This effect is more severefor larger values of | t − t | , and once the burst duration is smallerthan the time-scale of SFR, contributing significantly to the scatterat low L AGN .In Fig. 4 we demonstrate these effects on our model galaxiesat z = 0 . We first plot individual SFRs and AGN luminosities fromthe model, and show how the average SFR is flat at L AGN < erg s − . We then plot for the same objects the SFRs that are cal-culated based on bursts only, taking out the contribution from thesecular SF mode. The SFR due to the bursts is more correlated withthe AGN luminosity. The remaining scatter between the bursty SFRand L AGN originates from the fact that AGNs can be selected bothbefore and after the peak (i.e. t can occur before or after the ob-servation). This changes the contribution to SFR from the burst it-self, although the AGN luminosity is left unchanged. In Fig. 4 weshow in different symbols AGNs that are selected before the peakof the burst, with ( t − t ) /σ b < − . For these objects, the correla-tion between SFR and AGN luminosity is strong, as expected. Thestrength of this last effect is smaller when σ b is higher (even whenusing σ = 0 . instead of the current value of 0.13, the scatter dueto different values of x becomes less dominant).Our model suggests that only σ and α acc affect the rates di-agram. Changing the value of σ results in modifying the averagelevel of SFR for low L AGN . On the other hand, α acc shifts thediagram along the X-axis. Unlike the behaviour of the luminosityfunction, there is no simple degeneracy between these parametershere. The value of σ = 0 . Gyr that is chosen for the best modelis obtained by matching the observed rates diagram.We have tested how other standard SF modes affect the ratesdiagram and found that the L AGN -SFR correlation is very sensi-tive to secular modes. For example, when using accretion into BHsthat is proportional to the secular SFR, there are no regions withuncorrelated SFR and AGN luminosity. This is apparent even incases where the BH growth in the secular mode is only − of theassumed SFR. As indicated by Fig. 4, the rates diagram originatesfrom two effects. First, there is hardly a correlation between the SFwithin the burst and the secular SF. Second, the episodic nature ofthe burst together with the integration time of the SFR indicator.These two effects do not exist in a secular mode that is based oncontinuous BH accretion mode. However, different types of secu-lar accretion, e.g. episodic events that were not tested by us, mightshow better agreement with the observed rates diagram.The rates diagram as shown here is defined as the average SFRat a given AGN luminosity, and is not affected by the number ofAGNs of different luminosities. However, once we compute the av-erage AGN luminosity as a function of SFR (dashed line in Fig. 4),we see a different trend, in which SFR and L AGN are always cor-related. This way of averaging hides the flat part of the diagram,occupied by low luminosity AGNs, and is more dependent on thenumber of low-luminosity AGNs (i.e. on sample selection). Sincethe flat part of the rates diagram is highly restricting the models,the average L AGN is less restrictive when comparing models to ob-servations.In Fig. 5 we plot for each value of SFR and AGN luminositythe median value of x ≡ ( t − t ) /σ b . According to Eq. 2, x is thelocation within the Gaussian of the burst, where negative values(down to -2) correspond to the burst starting point, and positivevalues (up to 4) correspond to the late episode of the burst. Eachburst starts on the left part of the rates diagram, with small AGNluminosity that is due to a value of x = − . As x increases towards0, both the SFR and L AGN rise. Later on, when x > L AGN goes c (cid:13) , 1–12 E. Neistein and H. Netzer
Log L AGN [erg/s] M a j o r f r a c t i on
40 42 44 46 4800.20.40.60.81 z=0.0z=1.0z=2.1Treister et al. (2012)Kocevski et al. (2012)
Figure 6.
The fraction of galaxies that host AGNs and are going throughmajor mergers (mass ratio is bigger than 0.3) out of all galaxies that hostAGNs.
Thick lines show the model results at various redshifts as indicated,after selecting all galaxies that host BHs with masses log m BH / M ⊙ > . . The thin dashed line shows the fitting function from Treister et al.(2012), obtained from a compilation of various studies at < z < .The grey boxy line shows the results from Kocevski et al. (2012), derived at z ∼ . down to its initial level, while the SFR stays a bit higher, due to theintegration over 150 Myr. As a result, the right part of the diagramis mostly populated with x < − , and the higher values of L AGN are related to x ∼ . This effect modifies the correlation of SFR ∝ L AGN (that is used by the model, Eq. 4) such that
SFR ∝ L . ,as observed by Netzer (2009). The main argument against a model of BH growth that is basedonly on mergers is the morphology of AGN hosts. As discussed inthe Introduction, numerous works show that most AGNs reside innormal disk galaxies, with no sign of interaction. Here we test theobservational constraint in this respect more closely.In Fig. 6 we show the fraction of galaxies that host AGNs andare participating in major merger events, out of all galaxies that hostAGNs. Major merger events are defined as those with mass ratiothat is bigger than 0.3. Note that in the SAM, if a galaxy have morethan one merger event, the mass ratio is determined by the eventwith the largest contribution to the SFR. A galaxy is considered tobe a part of a merger event throughout the burst.Fig. 6 shows that the results of the model are roughly consis-tent with those of Treister et al. (2012), although they deviate fromthe analysis of Kocevski et al. (2012). The model predicts that ma-jor mergers are associated with more luminous AGNs. There are afew limitations in this comparison that should be mentioned. First,we assume that the mass ratio for major mergers is 0.3, which issomewhat arbitrary. Second, we assume that the time-scale for de-tecting the morphological features within the galaxy is similar tothe assumed duration of the burst. Third, we do not allow for atime-delay between the change in morphology and the onset of ac-cretion into the BH. All these issues complicate the interpretationof the results.A different way to examine this issue is to compare galaxiesthat host AGNs to a control sample of galaxies with the same stellar −1 Mass ratio, r M e r g e r f r a c t i o n , d P / d r allAGN hosts, 10 The fraction of galaxies undergoing a merger event with a massratio r . d P /d r is the probability distribution of galaxies of different r values.All galaxies are selected at z = 2 . with stellar mass as indicated, in orderto avoid resolution issues. The solid line corresponds to all the galaxieswithin the model. The dashed line shows the fraction out of all the galaxiesthat host an AGN with < L AGN < erg s − , as were selectedby Kocevski et al. (2012). mass, that do not host AGNs. According to Kocevski et al. (2012),these two populations show similar fractions of galaxies that aredetected as going through merger events. In Fig. 7 we make thesame comparison with our model galaxies. This plot shows thefraction of galaxies going through a merger event of mass ratio r , after selecting only galaxies at z = 2 , and with stellar mass . < log( m s / M ⊙ ) < . The AGN sample includes galax-ies hosting an AGN with < L AGN < erg s − , similarlyto the sample of Kocevski et al. (2012). This result shows that thefraction of galaxies going through a merger event is larger by afactor of ∼ for galaxies that host AGNs. Unlike the comparisonmade in Fig. 6, here the uncertainty is due to the existence of atime-delay between changes in morphology and the BH accretionphase. In Fig. 8 we show the relation between bulge and BH mass in ourmodel. The ratio of the two masses depends on various factors.First, bulges can grow in major merger events by using the stellarmass from the disks of both progenitor galaxies. This effect willallow bulges to gain more mass than the total SFR during mergers,more than what is used for feeding the BH. In addition, the scatterbetween the bulge and BH masses should be a result of α p , whichallows for only a part of the burst events to feed the central BH.Our model agrees with the results of both H¨aring & Rix(2004) and Sani et al. (2011) at redshift zero. However, the recentstudy by McConnell & Ma (2012) shows that at a bulge mass of M ⊙ the BH mass is higher than what we get here, reaching M ⊙ . Our model BHs are less massive at the high mass endbecause we use the mass function from Shankar et al. (2009) forcalibrating the mass of BHs in our model. In addition, the modelpredicts a smaller scatter in the mass relation for more massive ob-jects in comparison to observations. c (cid:13) , 1–12 hat triggers black-hole growth? Log M bulge [ M ⊙ ] L og M B H [ M ⊙ ] Figure 8. The relation between the masses of bulges and BHs at z = 0 . Symbols correspond to the observational results from H¨aring & Rix (2004)and Sani et al. (2011). The thick solid line shows the median BH mass for agiven bulge mass, taken from the model galaxies. Dashed lines show the 5and 95 per cent levels of the BH distribution for each bulge mass. Log L AGN [erg/s] L og M B H [ M ⊙ ] 42 44 46 z=0.0 z=1.0z=2.0 z=4.0 Figure 9. The distribution of BH masses as a function of AGN luminositiesat various redshifts. The thick solid lines are the median values of the modelThe dashed lines show the 67 and 95 per cent levels of the distribution. Thethick straight line in each panel shows the Eddington luminosity, Eq. 6. The distribution of BH masses, for a given value of L AGN areshown in Fig. 9. The model predicts that most AGNs accretion isbelow the Eddington limit, especially at low redshift. At higher red-shifts and high L AGN the AGNs accretion is closer to the Edding-ton limit. The scatter we use for the Eddington threshold allow forsome objects to slightly exceed the formal Eddington limit, mostlyat high redshift. Log m s [ M ⊙ ] L og ( SS F R ) [ G y r − ] z = 0.0 Figure 10. The distribution of specific SFR (SSFR) versus stellar massat z = 0 . Thick contours represent the distribution of all the modelgalaxies, while thin lines show the distribution of galaxies that hostAGNs with L AGN > erg s − . Contour levels are at log P = − . , − . , − . , − . , . where the integral of P equals unity. Interestingly, our merger scenario naturally predicts that AGNsare hosted by massive star-forming galaxies. This can be seen inFig. 10. Observations of this type were done by Salim et al. (2007)and Bongiorno et al. (2012) using different SFR indicators. Thisdiagram is an extension of the rate diagram shown in Fig. 3, as itshows the full distribution of specific SFR, for each value of stellarmass. Results at higher redshifts are similar to what is shown herefor z = 0 . L AGN plane In Fig. 11 we show how other properties of AGNs depend on bothSFRs and AGN luminosities at z = 0 . We show that the modelpredicts a higher values of L AGN /L Edd at higher L AGN , withsmall dependence on SFRs. This is in spite of the lower values of x = ( t − t ) /σ b seen in Fig. 5 at high L AGN and low SFRs. Asa result, the Eddington ratio does not depend on x , the time withinthe burst. We have further tested that the Eddington threshold doesnot play a role at shaping the rates diagram at z = 0 .In the lower panel of Fig. 11 we show the median BH massat each value of SFR and L AGN . The scatter in masses around L AGN < erg s − depends on the SFR but other regions ofthe diagram include more uniform distribution of BH masses. This work presents a semi-analytic model (SAM) for the formationof galaxies and black holes (BHs) within a Λ CDM Universe. Ourmodel is built on a galaxy-formation model that matches variousobservations of galaxies. These include the stellar mass functionat < z < , the distribution of star-formation rates (SFRs) at z = 0 , and the auto-correlation function of galaxies at z = 0 . Theresults were developed in a previous study (Wang et al. 2012), andare adopted here with no further modifications to the properties ofgalaxies. When adding BHs to the model, we are interested in the c (cid:13) , 1–12 E. Neistein and H. Netzer Log L AGN [erg/s] L og S F R [ M ⊙ / y r ] 40 42 44 46 48−1−0.500.511.522.5 −6−5−4−3−2−1 Log L/L edd Log L AGN [erg/s] L og S F R [ M ⊙ / y r ] 40 42 44 46 48−1−0.500.511.522.5 77.588.59 BH mass Figure 11. SFR versus L AGN at z = 0 . The upper panel shows the medianEddington ratio, log L AGN /L Edd , at each bin. The lower panel representsthe median BH mass in units of log M ⊙ . Here we set BH masses to a min-imum value of M ⊙ . properties of BHs and active galactic nuclei (AGNs), and how theycorrelate with the properties of their host galaxies. We do no takeinto account the possible feedback from AGNs on the physics ofgas within galaxies.Our model assumes that BHs grow only during star-formationbursts, with a probability α p that is the same for all galaxies at allredshifts. The bursts in our model are only due to merger events;we do not model bursts from secular processes such as disk in-stability. When an event of BH accretion occurs, we assume thatthe gas mass that reaches the BH equals a fraction α acc of thestars made in the burst at the same time. We use two additionalparameters to describe the threshold on accretion due to the Ed-dington luminosity, in order to limit the accretion in case the burstis large and the BH mass is small. This model for the formationand evolution of BHs is therefore very simple, also in compari-son to previous SAMs (Kauffmann & Haehnelt 2000; Croton et al.2006; Bower et al. 2006; Malbon et al. 2007; Monaco et al. 2007;Somerville et al. 2008; Bonoli et al. 2009; Fanidakis et al. 2011;Fanidakis et al. 2012; Hirschmann et al. 2012).The observational constraints used here are the mass functionof BHs at redshift zero (Shankar et al. 2009), the luminosity func- tion of AGNs at z . (Richards et al. 2006; Croom et al. 2009),and the relation between SFRs and AGN luminosities (Shao et al.2010; Rosario et al. 2012). We specifically study the latter con-straint, as it was not tested by previous models. According toRosario et al. (2012), AGNs at low redshift are related to a con-stant level of SFR within their host galaxies for L AGN < ergs − . At higher AGN luminosity, where L AGN is larger than the lu-minosity of SFR, a power-law type correlation, SFR ∝ L . isseen (see also Netzer 2009). At z ∼ , AGNs of all luminositiesare hosted within galaxies of the same average SFR, at a level of ∼ 30 M ⊙ yr − . We term these results as the ‘rates diagram’, sinceit shows the relation between the star-formation rate, and the rateof BH growth.As was demonstrated in Figs. 3 & 4, our model fits well theobserved rates diagram. A necessary condition for the agreementis that we adopt the correct time scales for both SF and AGN ac-tivity. We therefore assume that the luminosity at µm used byRosario et al. (2012) represent an averaging of 150 Myr over theSFR of each galaxy, and that the AGN luminosity is instantaneous(i.e. using the minimum time-step of our model, ∼ Myr). Whenusing these time scales, we naturally reproduce the observed ratesdiagram. In our model, the lack of correlation between SFR andAGN luminosities is due to two main reasons: First, secular SF ingalaxies are not associated with BH activity. Second, BH accretionbefore and after the peak in SFR could have the same AGN lumi-nosity, but different SFR. A key assumption in the model is the lackof correlation between the properties of a galaxy prior to the mergerevent, and the amount of star-formation within the burst, which de-pends on the properties of both merging galaxies. We thus arguethat the rates diagram favours a mode of BH accretion that is dueto mergers.The rates diagram is used here for constraining the durationof the bursts in our model and for constraining the BH accretionfactor, α acc . The diagram is very sensitive to secular modes of BHgrowth (i.e. modes that do not depend on merger events). Even asmall level of BH accretion from the secular mode, which adds anegligible mass to BHs, can modify the rates diagram considerably.Although we do not model such scenarios here, more constraintscould be obtained by measuring the SFR in the central regions ofgalaxies (e.g. Stern & Laor 2012).Visual classification of AGN hosts indicates that most AGNsare located within normal disk galaxies, with no signs of merg-ers (Gabor et al. 2009; Cisternas et al. 2011; Kocevski et al. 2012;Schawinski et al. 2012; Treister et al. 2012). We show in Figs. 6& 7 that a similar result is obtained here, using a model with BHgrowth coming only from mergers. This is because most BH ac-cretion is associated with minor merger events, which are difficultto detect observationally. However, our model shows that a typicalgalaxy has roughly half the chance to experience a merger event incomparison to a galaxy of the same stellar mass that hosts an AGN.We do not test in this work the possibility of having a time-delaybetween the merger event and the episode of BH accretion. Such atime-delay will further decrease the amount of AGN hosts that areshowing morphological signs of interactions.The model parameters used here were tuned to fit the ob-served mass function of BHs at z = 0 , and the luminosity func-tion of AGNs at z . . In addition, our final model agrees withthe observed correlation between the mass of bulges and BHs(H¨aring & Rix 2004; Sani et al. 2011; McConnell & Ma 2012). Weshow in Fig. 10 that our model predicts that AGN hosts are rela-tively massive, and star-forming galaxies.Finally, we provide predictions for the mass of BHs, and their c (cid:13) , 1–12 hat triggers black-hole growth? Eddington ratios, within the rates diagram, as a function of bothSFR and L AGN . These predictions could be used to test the modelagainst new observations. ACKNOWLEDGMENTS The Millennium Simulation databases used in this paper and theweb application providing online access to them were constructedas part of the activities of the German Astrophysical Virtual Ob-servatory. EN acknowledges funding by the DFG via grant KH-254/2-1. We thank David Rosario, Eleonora Sani, and FrancescoShankar for sharing their data in electronic format; David Rosario,Francesco Shankar, Dieter Lutz, and Benny Trakhtenbrot for usefuldiscussions; and Sadegh Khochfar for reading an earlier draft andfor many helpful suggestions. REFERENCES Barnes J. E., Hernquist L. E., 1991, ApJ, 370, L65Best P. N., Kauffmann G., Heckman T. M., Brinchmann J., Char-lot S., Ivezi´c ˇZ., White S. D. M., 2005, MNRAS, 362, 25Bongiorno A., et al., 2012, ArXiv e-prints, 1209.1640Bonoli S., Marulli F., Springel V., White S. D. 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G., et al., 2000, AJ, 120, 1579 APPENDIX A: COMPARISON WITH PREVIOUSMODELS As was discussed in the main body of the paper, previous mod-els (e.g. Croton et al. 2006; De Lucia & Blaizot 2007; Marulli et al.2008) have obtained different results with models that are oftenbased on the same N -body simulation as is used here. In order toprovide more details on the difference between our model and pre-vious ones, we plot in Fig. A1 the mass functions of BHs from ourmodel, along with the results from the publicly avialable model ofDe Lucia & Blaizot (2007). It can be seen that our model builds themass of BH faster at high redshift than the previous model. This isprobably due to the difference in star-formation law that was imple-mented in our model (see Wang et al. 2012, for more details on ourmodel). In brief, our model uses lower SF efficiencies at high red-shift, and for low-mass galaxies. In this way, more cold gas is avail-able for SF during bursts, allowing much larger gas feeding into thecentral BH. It is shown in Wang et al. (2012) that the cold gas con-tent within our model is much higher than in De Lucia & Blaizot(2007). It should be mentioned that our model galaxies actuallyinclude more cold gas than what is allowed by observations. Thisissue, discussed in detail in Wang et al. (2012), should effect thechoice of our parameter α acc . Lastly, our merger rates (as a func-tion of galaxy mass) might differ from those of previous modelsdue to the difference in the stellar mass function. The diffferent BHmass function shown in Fig. A1 indicates that the relation betweenstellar mass and BH mass is also different in our model, giving riseto different merger rates per BH mass in comparison to previousmodels. Log M BH [ M ⊙ ] L og Φ [ M p c − d e x − ] Shankar et al. (2009)z=0.0z=1.0z=3.1resolutionlimit Figure A1. The mass function of BHs. The shaded region represents theobservational prediction from Shankar et al. (2009) based on the correla-tion between bulge and BH masses at low redshift. Different line types cor-respond to the model mass function at various redshifts as indicated. Thegrey dashed line shows the minimum BH mass that is reliably reproducedby the model (due to a minimum subhalo mass of . × h − M ⊙ ).We add in red lines results from the public model of De Lucia & Blaizot(2007) for comparison. c (cid:13)000