The X-Ray Luminosity Function of Active Galactic Nuclei
a r X i v :a s t r o -p h /9908295v 1 26 A u g 1999The X-Ray Luminosity Function of Active Galactic Nuclei M.Schmidt 1,R.Giacconi 2,G.Hasinger 3,J.Tr¨u mper 4,and G.Zamorani 5,6
1
California Institute of Technology,Pasadena,CA 91125,USA 2
European Southern Observatory,Karl-Schwarzschild-Str.1,85748Garching bei M¨u nchen,Germany 3
Astrophysikalisches Institut Potsdam,An der Sternwarte 16,14482Potsdam,Germany 4Max-Planck-Institut f¨u r extraterrestrische Physik,Karl-Schwarzschild-Str.2,85740Garching bei M¨u nchen,Germany 5Osservatorio Astronomico,Via Zamboni 33,40126Bologna,Italy 6Istituto di Radioastronomia del CNR,via Gobetti 101,I-40129,Bologna,Italy Abstract.We derive an X-ray luminosity function for active galactic nuclei (AGN)that accounts for the X-ray source counts in the 0.5–2.0and 2–10keV energy ranges,the redshift distribution of AGNs in the ROSAT Deep Survey (RDS),as well as the X-ray background (XRB)from 1–10keV.We emphasize the role of X-ray absorp-tion,which has a large e?ect on the faint end of the 2–10keV source counts,as well as on the integrated X-ray background.
2M.Schmidt et al.:The X-Ray Luminosity Function of Active Galactic Nuclei In deriving the redshift z max,the spectral energy dis-
tribution of the source plays an important role.This may
be characterized by one or more spectral indices,and ab-
sorption given by an e?ective hydrogen column(cf.Mor-
rison and McCammon1983).We assume that the energy
spectral index of AGNs is?1.3below1keV,and?0.7
above1keV(Schartel et al.1997).Information about the
distribution of absorptions in complete AGN samples is
very rare:the HEAO1-A2survey of X-ray sources at2–
10keV(Piccinotti et al.1982)is the only complete sam-
ple for which hydrogen columns of the AGNs are known
(Schartel et al.1997)at the present time.The survey con-
tains30AGNs to a limiting?ux of2.710?11cgs at2–10
keV over an area of27,020square degrees.We use the
Piccinotti survey as the generating sample,thus ensuring
that the observed properties of its sources,including the
individual absorptions,are precisely incorporated in the
derivation of the luminosity function.
Once the luminosity fuction is derived,we can predict
the source counts,redshift distributions and the integrated
contribution of the AGNs to the XRB.We then iterate the free parameters characterizing the density evolution by?tting to observed source counts from other complete samples and/or the XRB,as described in the next section.
3.Results
Since pure density evolution of the luminosity function leads to a severe overestimate of the XRB(see below),we assume that the density evolution depends on the X-ray2-10keV luminosity(HX),such that the co-moving density of sources varies with redshift as(1+z)k where k=k o for HX>=HX o k=k o+k1(log HX-log HX o)for HX
Our procedure is to set the free parameters character-izing the density evolution,k o,k1and HX o,such that we?t the number of AGNs in the RDS,as well as the XRB in the energy range1-2keV.The RDS covers0.162 sq.deg.to a limit of1.110?14cgs and0.136sq.deg.to 0.5510?14cgs.The sample contains42AGNs(Schmidt et al.1998;source36has since been identi?ed as an AGN at redshift1.52;sources14and84have been tentatively identi?ed with infrared objects in the K-band,presum-ably reddened AGNs).For the XRB,we use the results of a study by Miyaji et al.(1998b),recently updated by Miyaji et al.(1998c).
In iterating the free parameters for the density evolu-tion,we?rst explore the case of pure density evolution, i.e.,k1=0.In this case,the RDS number density is repro-duced for k o=4.75,but the predicted XRB at1–2
keV Fig.1.Predicted AGN source counts(thick curve)in the energy range0.5–2.0keV.The thin curves represent the counts(from top to bottom,on the right side)for sources with columns0,1021,1022,1023,and1024cm?2.The AGN counts in the RDS and the RBS are indicated(see text). for AGNs is twice the observed intensity.We conclude that pure density evolution with k1=0is untenable.
Through trial and error,we?nd that both the RDS source count and the1–2keV XRB can be?tted with k o=4.94,k1=3.00,and log HX o=44.00.This is the model that we discuss in the remainder of this paper.It predicts an RDS redshift distribution in the redshift in-tervals of0–1,1–2,2–3,>3of12.3,23.3,6.1,and0.4,re-spectively,where the observed numbers are16,20,4,and 0,with2unknown.Since luminosities and redshifts are strongly correlated in a?ux-limited sample,the excellent agreement shows that the rate of evolution for di?erent lu-minosities is essentially correct,con?rming the luminosity dependence of the evolution to?rst order.
We test the model on the ROSAT Bright Survey(RBS, Schwope et al.,1998),which is based on the ROSAT survey bright source catalogue(Voges et al.1995).The RBS contains194AGNs with0.5?2.0keV?uxes above 2.910?12cgs over an area of20,320sq.deg.Our model predicts193sources.Considering the small number of sources in our generating sample,the precise agreement is fortuitous,but it is encouraging that there is no dis-crepancy between these two large-area bright surveys in di?erent energy bands.Fig.1shows the predicted source counts at0.5-2keV,as well as the separate contributions from sources with di?erent columns N H.Further discus-sion of the N H distribution is given below.
M.Schmidt et al.:The X-Ray Luminosity Function of Active Galactic Nuclei
3
Fig.2.Predicted AGN source counts (thick curve)in the
energy range 2–10keV.The thin curves represent the
counts (from top to bottom,both at the extreme left and
right sides),for sources with columns 0,1022,1023,1021,
and 1024cm ?2.The HEAO1-A2AGN source count and a
total source count representative of the ASCA and Bep-
poSAX deep surveys (see text)are indicated.
Next,we turn to the source counts at 2–10keV.At the
bright end,the AGN source count is provided by the Pic-
cinotti survey,which is exactly re?ected in the model.At
the faint end,we represent the results of deep surveys with
ASCA (Cagnoni et al.1998)and BeppoSAX (Giommi et
al.1998)by a representative source density of 45deg ?2at
510?14cgs.Our model as presented so far yields only 23
deg ?2.
This discrepancy is a direct consequence of an apparent
incompatibility between the 2–10kev and the ROSAT 0.5–
2.0keV source counts.At a source count of,say,10deg ?2,
the 2–10keV ?ux from the ASCA counts (Cagnoni et al.
1998)and the 0.5–2.0keV ROSAT counts (Hasinger et
al.1998),if interpreted in terms of a single power law of
the spectral energy distribution,require a spectral index
of ?0.5.Typical observed spectral indices are ?0.7in the
2–10keV band,and ?1.3in the 0.5–2keV band (Schartel
et al.1997).The spectral discrepancy suggests the exis-
tence of some sources with a much harder spectrum or
larger absorption than those of the typical sources.The
distribution of the e?ective hydrogen columns for the Pic-
cinotti AGNs given by Schartel et al.(1997)is 18,3,5,and
4for columns 0,1021,1022,and 1023cm ?2,respectively.
We now explore the e?ect of adding one or two sources
with N H =1024to this sample.This ad hoc addition
is Fig.3.Predicted X-ray background from 1–10keV.The contributions from AGNs with di?erent N H values are in-dicated,and their sum is labeled “all AGN”.The curve la-beled “total”includes estimated contributions from galax-ies and clusters of galaxies.The dashed curve represents the observed XRB according to Miyaji et al.(1998b,c).statistically not unreasonable:the probability of missing two marked sources out of 32is around 13%.Speci?cally,we have added one hypothetical source to the Piccinotti sample,with a ?ux of 3.210?11cgs,a red-shift of 0.028and log N H =24.0.The e?ect of this ad-ditional source on the 0.5–2.0keV source counts is negli-gible,as shown by Fig.1,as is its e?ect on the 1–2keV XRB.Therefore,we can leave the evolution parameters k o ,k 1,and HX o unchanged.In contrast,the e?ect on the predicted 2–10keV source counts is dramatic:at 510?14cgs the addition of this one source doubles the predicted counts,which now agree with the observed counts.Fig.2shows that the log N H =24fraction of the counts rises with decreasing ?ux,reaches a maximum between 10?13and 10?14cgs and then declines again.This com-plex behavior is a consequence of the spectral properties of a heavily absorbed source moving through the 2–10keV band as its redshift increases.The redshift of 0.028for the hypothetical source was chosen to maximize the e?ect on the source counts.For redshifts of 0.024and 0.064,respec-tively,the e?ect on the 2–10keV source counts would be half as large,so two such sources would be required for the
4M.Schmidt et al.:The X-Ray Luminosity Function of Active Galactic Nuclei
same e?ect.There are10sources in the Piccinotti sample with redshifts in the range0.024–0.064.
The X-ray background is illustrated in Fig.3.The curve labeled”all AGN”is the sum of the?ve components with di?erent N H values.The”total”curve includes an estimate of the background expected from galaxies,and clusters of galaxies.The good?t to the observed XRB (Miyaji et al.1998b,c)at1-2keV is the result of our choice of k o and k1,see above.The log N H=24component,gen-erated by our hypothetical source,has a substantial e?ect on the predicted background above4keV,resulting in good agreement with the observed background at higher energies.
4.Discussion
We have succeeded in deriving a model of the AGN lumi-nosity function and its evolution that:
1.at0.5–
2.0keV reproduces the number of AGNs in the
RBS and the RDS,as well as the redshift distribution in the RDS;
2.at2–10keV reproduces the number and redshift dis-
tribution of AGNs in the HEAO1-A2survey,as well as the source counts in the deep ASCA and BeppoSax surveys
3.reproduces the observed XRB from1–10keV.
Essential ingredients of our derivation of the luminos-ity function are(a)the luminosity-dependent density evo-lution,with a cuto?at high redshift,and(b)evaluation of the e?ect of a realistic distribution of absorption columns. The success of our model analysis supports the proposals by Setti and Woltjer(1989),Madau et al.(1994),and oth-ers that the spectral di?erence between the XRB and the typical cosmic X-ray source(AGN)is a consequence of the internal absorption in AGNs,which makes the spectrum of the more absorbed AGNs e?ectively very hard.It ap-pears from our model that the high source counts at2–10 keV compared to those at0.5–2.0keV are caused by the same e?ect.
The small number of AGNs in the HEAO1-A2survey inherently limits the statistical accuracy of the model we have discussed here.The model predictions for the number of sources expected in the RBS,the RDS,etc.generally have a corresponding statistical error of around25%.At energies above2keV,the lack of statistics about the frac-tion of sources with log N H=24is a major source of un-certainty,as we discussed in Sec.3.Our attempt to repre-sent this component by a single hypothetical source in the Piccinotti sample that we used as a generating sample,al-lowed us to illustrate the e?ect of these sources.Statistical information on the frequency of high absorption columns will be required to con?rm or re?ne luminosity function models such as presented in this paper.Recent BeppoSAX observations of a sample of low luminosity AGNs selected on the basis of[O III]?uxes,assumed to be an isotropic luminosity indicator,show that the number of highly ab-sorbed sources is substantially higher than previously as-sumed on the basis of existing2–10keV data(Maiolino et al.1998).Once the statistical data on absorption columns are available,the question of how to take into account the wide variety of absorption spectra seen in AGN spectra (cf.Reichert et al.1985),which has been ignored in this paper,should also be addressed.
Further systematic surveys are desired,especially at higher energies,preferably beyond10keV,both shallow over a large sky area as well as deeper surveys over smaller areas.Optical identi?cations and redshifts for all sources, or well de?ned subsamples,are needed,as well as X-ray spectra of su?ciently large samples so that the distribu-tion of absorption columns to>1024cm?2can be deter-mined.
Acknowledgements.The ROSAT project is supported by the Bundesministerium f¨u r Forschung und Technologie(BMFT), by the National Aeronautics and Space Administration (NASA),and the Science and Engineering Research Council (SERC).The W.M.Keck Observatory is operated as a sci-enti?c partnership between the California Institute of Tech-nology,the University of California,and the National Aero-nautics and Space Administration.It was made possible by the generous?nancial support of the W.M.Keck Founda-tion.M.S.thanks the Alexander von Humboldt-Stiftung for a Humboldt Research Award for Senior U.S.Scientists in1990-91;and the directors of the Max-Planck-Institut f¨u r extrater-restrische Physik in Garching and of the Astrophysikalisches Institut Potsdam for their hospitality.We thank T.Miyaji for results on the X-ray background before publication.This work was supported in part by NASA grants NAG5-1531(M.S.), NAG8-794,NAG5-1649,and NAGW-2508(R.G.).G.H.ac-knowledges the DARA grant FKZ50OR94035.G.Z.ac-knowledges partial support by the Italian Space Agency(ASI) under contracts95-RS-152and ARS-96-70.We gratefully ac-knowledge the permission by the Springer Verlag to use their A&A L A T E X document class macro.
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