X-Ray Evolution of Active Galactic Nuclei and Hierarchical Galaxy Formation

0.31 MB·English

by  N. Menci

DraftversionFebruary2,2008
PreprinttypesetusingLATEXstyleemulateapjv.04/03/99
X-RAY EVOLUTION OF ACTIVE GALACTIC NUCLEI
AND HIERARCHICAL GALAXY FORMATION
N. MENCI1, F. FIORE1, G.C. PEROLA1,2, A. CAVALIERE3
Draft version February 2, 2008
ABSTRACT
We have incorporated the description of the X-ray properties of Active Galactic Nuclei (AGNs) into
a semi-analytic model of galaxy formation, adopting physically motivated scaling laws for accretion
triggered by galaxy encounters. Our model reproduces the level of the cosmic X-ray background at 30
4
keV; we predict that the largest contribution (around 2/3) comes from sources with intermediate X-ray
0
luminosity1043.5 <L /ergs−1 <1044.5,with50%ofthetotalspecificintensityproducedatz <2. The
0 X
2 predicted number density of luminous X-ray AGNs (LX > 1044.5 erg/s in the 2-10 keV band) peaks at
z ≈2withadeclineofaround3dextoz =0;forthelowluminositysources(1043 <LX/ergs−1 <1044)
n
it has a broader and less pronounced maximum around z ≈1.5. The comparisonwith the data shows a
a
generallygoodagreement. Themodelpredictionsslightlyexceedthe observednumberoflow-luminosity
J
AGNs at z ∼ 1.5, with the discrepancy progressively extending to intermediate-luminosity objects at
4
higher redshifts; we discuss possible origins for the mismatch. Finally, we predict the source counts
1
and the flux distribution at different redshifts in the hard (20-100 keV) X-ray band for the sources

1 contributing to the X- ray background.
v Subject headings: galaxies: active – galaxies: formation – X-rays: diffuse background– X-rays: galaxies
1 – galaxies: evolution – galaxies: interactions
6
2
1 1. INTRODUCTION On the other hand, the attempt by Kauffmann &
0 The X-ray emission of Active Galactic Nuclei (AGNs) Haehnelt (2000) to connect the BH accretion to the evo-
4 lution of galaxies in the hierarchical scenario was based
provides a unique probe into the history of the accretion
0 on a semi-analytic model (SAM) of galaxy formation of
on supermassive black holes (BHs) thought to power the
/ the kind introduced by Kauffmann et al. (1993) and Cole
hAGNs. In fact, the X-rays probe the accretion down to
et al. (1994) and progressively developed by several au-
pBH masses as small as mBH ∼ 107M⊙ and to bolomet- thors (Somerville & Primack 1999; Wu, Fabian & Nulsen
-ric luminosities as low as L ∼ 1043 erg/s. At redshifts
o 2000; Cole et al. 2000, Menci et al. 2002). Such a model
z > 0.5, these regimes of accretion are hardly accessible
r∼ assumed phenomenological and tunable scaling laws to
ttoopticalobservations,butmayprovidebothasignificant
s connect the gas accreted onto the BH with the cold gas
afraction of the total accretion power in the Universe and
fraction available in the galaxies left over by the star for-
:aconsiderablecontributiontothe observedCosmicX–ray
v mation. However, the model has been applied only to the
Background(CXB).
i brightquasar(QSOhereafter)population,yetithasfailed
X At higher z, constraints on the properties of the AGNs,
to reproduce the fast drop (by a factor ∼ 10−2) of their
rand hence on the history of accretion, have been derived
density observed from z ≈ 2 to the present. A later pa-
aby extrapolating local properties like the optical or X-ray
per by Nulsen & Fabian (2000)assumedthat the BHs are
luminosityfunctions,ortheX-rayspectralshapeofnearby
specifically fueled bythe coolingflows associatedwiththe
Seyfert galaxies. Based on these assumptions, several au-
hot gas during the process of hierarchical galaxy evolu-
thors (see Madau, Ghisellini & Fabian 1994; Comastri et
tion, the latter being described througha SAM. However,
al. 1995, 2001; Wilman & Fabian 1999) have constructed
such a model fails to account for the observed relation-
AGN synthesis models to account for the CXB; these au-
ship between the black hole and the spheroid masses (see
thors argued that most of the accretion power producing
Richstone et al. 1998); furthermore, it does not prop-
theCXBatenergiesbelow30keVisintrinsicallyabsorbed,
erlydescribethestatisticaldistributionofQSOproperties
as initially suggested by Setti & Woltjer (1989).
in that it over-predicts their low-z luminosity functions
The drawbacks of such an approach are constituted by
and under-predicts QSOs at high z. Other analytic (see,
the degeneracies between different possible extrapolations
e.g., Haiman & Loeb 1998; Wyithe & Loeb 2002; Hatz-
and hence between synthesis models that still reproduce
iminaoglou et al. 2003), semi-analytic (Volonteri, Hardt
the observed integrated AGN properties. Furthermore,
& Madau2003)orN-body (Kauffmann & Haehnelt 2002)
little directinsightcanbe gainedonthe physicallinksbe-
works are based on major merging events of dark mat-
tweenthe evolutionofAGNs andthat oftheir hostgalax-
ter haloes at high z as the only triggers for BH accretion,
ies. To now, the incorporation of the X-ray properties of
whichisrelatedtotheDMmassofthehaloeitheradopting
AGNs into a coherent picture of galaxy evolution is still
the locally observed relations or through phenomenologi-
lacking.
1INAF-OsservatorioAstronomicodiRoma,viadiFrascati33,00040Monteporzio, Italy
2DipartimentodiFisica,UniversitdiRomaTre,ViadellaVascaNavale84,I-00146Roma,Italy
3DipartimentoFisica,IIUniversita`diRoma,viaRicercaScientifica1,00133Roma,Italy
1
2
cal scaling laws; thus such models are suited to follow the to larger sizes through repeated merging events (at the
QSO evolution at high-intermediate z, but do not match rate given, e.g., in Lacey & Cole 1993). On the other
the observedsteep decline ofthe QSO density atredshifts hand,thelattermaycoalesceeitherwiththecentralgalaxy
z <1,arangeofcosmictimeofkeyinterestfortheactivity in the common halo due to dynamical friction, or with
∼
of AGNs observed in X-rays. other companion galaxies through binary aggregations.
Recently,Mencietal. (2003)developedamorephysical We Compute the probability for the latter processes to
modeltoconnecttheBHaccretiontothegalaxyevolution occur during the hierarchicalgrowth of the hosting struc-
in the hierarchical scenario. The accretion is triggered by ture yields, at any cosmic time t, and the differential dis-
galaxyencounters,notnecessarelyleadingtoboundmerg- tribution N(v,V,t) (per Mpc3) of galaxies with given v
ing,incommonhoststructureslikeclustersandespecially in hosts with circular velocity V. From this we derive
groups; these events destabilize part of the galactic cold the number N (V,t) of galaxies in a host halo (i.e., the
T
gas and hence feed the central BH, following the physi- membership), and the overall distribution of galaxy cir-
cal modelling developed by Cavaliere & Vittorini (2000, cular velocity N(v,t) irrespective of the host halo. To
CV00). The amountofthe coldgasavailable,the interac- each galactic circular velocity v, it is associated an aver-
tion rates, and the properties of the host galaxies are de- age galaxy tidal radius r (v); the average relative velocity
t
rivedthrough the SAM developed by Menci et al. (2002). V (V) of the galaxies in a common DM halo is computed
r
As a result, at high z the protogalaxies grow rapidly for each circular velocity V of the host halo.
by hierarchicalmerging; meanwhile,much fresh gas is im- The properties of the gas and stars contained in the
portedandalsodestabilized,sotheBHsarefueledattheir galactic DM clumps are computed as follows. Starting
full Eddington rates. At lower z, the dominant dynami- from an initial gas amount mΩ /Ω (m ∝ v3 being the
b
cal events are galaxy encounters in hierarchically growing DM mass of the galaxies)at the virial temperature of the
groups;now refueling peters out, as the residualgas is ex- galactic halos, we compute the mass m of cold baryons
c
hausted while the destabilizing encounters dwindle. With residing inregionsinteriorto the cooling radius. The disk
no parametertuning otherthan neededfor starformation associated to the cold baryons has radius r (v) and ro-
d
in canonical SAMs, the model naturally produces in the tation velocity v (v) computed after Mo, Mao & White
d
bright QSO population a rise for z >3, and for z <2.5 a (1998). From such a cold phase, stars are allowedto form
∼
drop as steep as observed. In addition, the results closely with rate m˙∗ = (mc/td)(v/200kms−1)−α∗ with the disk
reproduce the observed luminosity functions of the opti- dynamical time evaluated as t =r /v .
d d d
cally selected QSOs, their space density at different mag- Finally, a mass ∆mh = βm∗ is returned from the cool
nitudes from z ≈ 5 to z ≈ 0, and also the local m −σ to the hotgasphase due to the energy fedback by canon-
BH
relation. ical type II Supernovae associated to m∗. The feedback
Encouraged by the successes of the model, here we ex- efficiency is taken to be β =(v/v )αh; the values adopted
h
tend it to lower accretions and lower BH masses, in order for the free parameters α∗ = −1.5, αh = 2 and vh = 150
tostudythe X-raypropertiesofthe AGNs,andtopredict km/s fit both the local B-band galaxy LF and the Tully-
their contributionto the X-raybackground. We avoidthe Fisher relation, as illustrated by Menci et al. (2002). The
introductioninourmodelofdustandgasobscuration,and model also matches the bright end of the galaxy B-band
therefore conservatively we shall compare our predicted luminosity functions up to redshifts z ≈ 3 (see Poli et al.
CXB with the observations at energies E ≥ 30 keV, the 2003) and the resulting global star formation history is
spectral region not affected by photoelectric absorption. broadlyconsistentwiththatobserveduptoredshiftz ≈4
At lower energies we shall compare our predicted num- (Fontana et al. 1999).
ber and luminosity densities of AGNs with data already Ateachmergingevent,themassesofthedifferentbary-
corrected for dust and gas absorption. onic phases are replenished by those in the merging part-
The paper is organized as follows. In Sect. 2 we recall ner;thefurtherincrements∆mc,∆m∗,∆mhfromcooling,
the basic points of the galaxyevolutionarymodel we base star formation and feedback are recomputed on iterating
on. The specific modelling that relates the BH accretion the procedure described above.
to the galaxy encounters is recalled in Sect. 3, where we Thus, for each galactic circular velocity the star for-
also describe how we obtain the X-ray luminosities. The mation described above is driven by the cooling rate of
results concerning the X-ray properties of AGNs at low the hot gas and by the rate of replenishing the cold gas,
and high z are compared with observations in Sect. 4. which in turn is related to the progressive growth of the
The finalSect. 5 is devotedto discussionandconclusions. total galactic mass along the galaxy merging tree. The
integrated stellar emission S (v,t) at the wavelength λ is
λ
2. THEMODEL computed by convolving the star formation rate with the
spectral energy distribution φ obtained from population
2.1. The Semi-analytic Model for Galaxy Evolutiuon λ
synthesismodels(Bruzual&Charlot1993,andsubsequent
Thepropertiesofthegalaxieshostingthe AGNsarede- updates).
rived using the semi-analytic model described in detail in AllcomputationsaremadeinaΛ-CDMcosmologywith
Menci et al. (2003). Here we recall its basic points. Ω0 =0.3,Ωλ =0.7,abaryonfractionΩb =0.03,andHub-
Following the procedure usually adopted in SAMs, we ble constant h=0.7 in units of 100 km s−1 Mpc−1.
consider both the host dark matter (DM) halos (groups
2.2. The Accretion onto Supermassive BHs
and clusters of galaxies with mass M, virial radius R and
circular velocity V) containing the galaxies, and the DM Wefollowthe modelpresentedinMencietal. (2003)to
clumps (with circularvelocity v) associatedwith the indi- derive the fraction of the galactic cold gas accreted onto
vidual member galaxies. The former grow hierarchically thecentralBH.Galaxyencountersareexpectedtodestabi-
Menci et al. 3
lizepartofsuchgascausingittolooseangularmomentum cutoff at an energy E = 300 keV (see e.g. Perola et al.
c
(Mihos & Hernquist 1996; Barnes & Hernquist 1998; see 2002 and references therein); in view of the present data
also Mihos 1999), and thus triggering gas inflow. situation we shall keep this as our fiducial shape. The ef-
The fraction of cold gas destabilized in eachinteraction fect of the scatter in α and E will be discussed in Sect.
c
eventis computed in eq. A3 of CV00 in terms of the vari- 4.
ation∆j ofthe specific angularmomentumj ≈Gm/v of TheevolvingLFisderivedfromN(v,t)byapplyingthe
d
the gas, to read appropriate Jacobian given by eq. (3) with the appropri-
ate bolometric correction. The LF will include a factor
f(v,V)≈ 1 ∆j = 1 m′ rd vd . (1) τ/hτr(v)i < 1 since the luminosities in eq. (3) last for a
8(cid:12) j (cid:12) 8Dm b V E time τ and are rekindled after an average time τr. The
(cid:12) (cid:12)
(cid:12) (cid:12) result is
Here b = max[r ,R/N−1/3(V)] is the impact parameter, τ dv
d T N(L,t)=N(v,t) . (4)
m′isthemassofthepartnergalaxyintheinteraction,and hτri(cid:12)dL(cid:12)
the average runs over the probability of finding a galaxy (cid:12) (cid:12)
(cid:12) (cid:12)
with mass m′ in the same halo V where the galaxy m is As shown by Menci et al. (2003), the model produces
located. The prefactor accounts for the probability (1/2) a drop of the bright (MB < −24) QSOs as steep as ob-
of inflow rather than outflow related to the sign of ∆j. In served. Thisresultsfromthecombineddecreasewithtime
addition, the gas funneled inward may end up also in a of both the interaction rate τr−1 and the accreted fraction
nuclearstarburst;the relative amounthas been estimated f (see Fig. 1 in Menci et al. 2003). These in turn are
from 3/1 to 9/1 (see Sanders & Mirabel 1996; Frances- caused by the decrease of the encounter probability due
chini, Braito & Fadda 2002). Here we assume that 1/4 of to the decrease of the number density of galaxies inside
the inflow feeds the central BH, while the remaining frac- thehostgroups/clusters,andtothesimultaneousincrease
tion kindles circumnuclear starbursts, tackled in detail by of galaxy relative velocities Vr. For massive galaxies, the
Menci et al. (2004). above effects also combine with the decrease of the avail-
Therateofnearlygrazingencountersforagalactichalo able amount of cold gas, due to its rapid conversion into
withgivenv inside ahosthalo(grouporcluster)withcir- stars in the early phases of star formation.
cular velocity V, is given by τ−1 = n (V)Σ(v,V)V (V); The above effects concur to produce number densities
r T r
here n = N /(4πR3/3), and the cross section is and luminosity functions of QSOs in excellent agreement
T T
Σ(v,V)≈πh(r2+r′2)i is averagedover all partners with withtheobservationsinthefullrange0<z <6,asshown
tidal radius r′ itn thet same halo V. The membership N , in Menci et al. (2003). But comparison with optical data
and the distritbutions of v′, r′ and V are computed froTm allowsto probe the modelonly inthe medium-high accre-
t r tionregimes,correspondingtoopticalmagnitudesbrighter
the SAM as described in Sect. 2.
than M ≈ −24. Here we explore the predictions of our
The averagegasaccretionratetriggeredbyinteractions B
model down to accretion rates lower by a factor ∼ 10−1,
at z is given by (cf. CV00 eq. 5, and Menci et al. 2003)
which at present can only be probed by X-rays.
f(v,V) m (v)
m˙acc(v,z)= c , (2) 3. THEOVERALLPICTURE
D τr(v,V) E
Before presenting in detail our results and comparing
where the average is over all host halos with circular them with observations, we give an overview of the pic-
velocity V. The mass of the BH hosted in a galaxy ture concerning the BH accretion in evolving galaxies as
with given v at time t is updated after m (v,t) = it emerges from our model. In Fig. 1 we show the volume
BH
(1−η) t m˙ (v,t′)dt′,whereη ≈0.1(seeYu&Tremaine emissivity from the AGNs which at redshift z have lumi-
0 acc
2002)iRs the mass-energyconversionefficiency; here weas- nosity LX. Since our model links the evolution of AGNs
to that of the hierarchicallygrowinggalaxies,we cangain
sume inallgalaxiesinitialseedBHsofmassmuchsmaller
some insight also on the hosts of the AGNs contributing
than the active supermassive BHs (see Madau & Rees
to the accretionshistory of the Universe. So we also show
2001).
in the figure the evolutionary tracks of AGNs hosted in
Thebolometricluminositysoproducedbytheaccretion
galaxies with different masses.
onto a BH hosted in a galaxy with given v then reads
Atredshiftsfrom6to3arapidincreaseoftheaccretion
ηc2∆m issustainedbythecontinuousreplenishingofcoldgasdue
acc
L(v,t)= . (3)
tothefrequentgalaxymergingeventsandtothehighrate
τ
of encounters which destabilize it. The tradeoff bewteen
Here τ ≈ t ∼ 5107(t/t ) yrs is the duration of the ac- high luminosity and large number of sources determines
d 0
cretion episode, i.e., the timescale for the QSO to shine; a peak in the global emissivity at intermediate AGN lu-
∆m is the gas accreted at the rate given by eq. (2). minosities L ∼1044 erg/s, which are hosted typically in
acc X
The blue luminosity LB is obtained by applying a bolo- galaxies with DM mass 51010−31011M⊙.
metriccorrection13(Elvisetal. 1994),whilefortheunab- At later z the era of galaxy formation ends, the merg-
sorbed X-ray luminosity L (2-10 keV) we adopt a bolo- ing rate of galaxies drops, and the cold gas replenishing
X
metric correction c2−10 = 100 following Elvis, Risaliti & dwindles. The encounter rate of galaxies also decreases,
Zamorani(2002);forsimplicity,thisisassumedtobecon- and the galaxies enter a era of nearly passive evolution.
stant with z. The shape of the X-ray spectrum I(E) is The AGNs in the mostmassivegalaxies(with DM masses
assumed to be a power law with a slope α = 0.9 (see Co- M >1012M⊙) show the most dramatic decrease in lumi-
mastri 2000 and references therein), with an exponential nosity (see the leftmost track in Fig. 1), since their host
4
galaxieshavealreadyconvertedmostoftheirgasintostars for the spectrum (α = 0.9, Ec = 300 keV, c2−10 = 100,
at higher z. The decrease at z < 1.8 of the luminosities see Sect. 2.2) exceeds the value measured by HEAO1-A2
∼
of the AGN population produces the decrease in the total by no more than 50 %.
emissivity shown in Fig. 1. Atthepresentstateofourobservationalknowledge,the
Thelocationofthepeakinbothredshiftandluminosity, substantialagreementisveryencouraging,especiallyifthe
aswellasthespecificevolutionwithz oftheluminosityof following points are taken into account: a) the available
AGNshostedingalaxieswithdifferentmasses,stronglyaf- evidence (at E < 10 keV, Lumb et al. 2002; Vecchi et al.
fects the relative contributionof different classesof AGNs 1999) that the CXB normalization from the HEAO1-A2
to the CXB and the redshift distribution of their number experiment may be underestimated by as much as 30 %;
or luminosity density, as we show in detail below. b) the bolometric correction need take on the fixed value
we adopted for all values of L and L/L ; c) the inci-
edd
dence of a Compton thick phase along the active phase of
a galacticnucleus, as a function of L and z,is not known,
exceptthatlocallyitmayamountasmuchas50%(Risal-
iti,Maiolino&Salvati1999)oftheso-calledtype2AGNs,
namely those with a substantial obscuration both in the
opticalaswellasintheX-rayband. Theessentialfeatures
of our predictions are shown in figs. 2 and 3.
Fig. 1. - The overall X-ray emissivity contributed by AGNs with
given X-ray luminosity LX and redshift z. We also show the evo-
lutionary tracks of the luminisity of AGNs hosted in galaxies with
differentDM masses corresponding(from lefttoright) to 1013M⊙,
1012M⊙,2.51011M⊙,51010M⊙.
4. RESULTS
We compute the contributionto the CXB from the LFs
in eq. (4) as follows:
d2F(E) L2 I[L ,E(1+z)]
X
= dV dL N(L ,z) .
dEdω Z Z X X 4πd2
L1 L
(5)
HeredV isthecosmicvolumeelementperunitsolidangle
ω, d is the luminosity distance, and I(L,E) is the AGN
L Fig. 2. - The cumulative contruibution (multiplied by the energy
spectrum. This is normalized as to yield LX = L/c2−10 E0) to the predicted CXB at E0 = 30 keV, yielded by sources at
when integrated in the rest-frame energy range 2-10 keV.
progressively larger redshifts. The solid line shows the total CXB
We consider the contribution to the CXB from AGNs in
producedbysourceswithallluminosities. Theotherlinesshow the
specific luminosity ranges ∆L = [L1,L2]. The total CXB contributions of AGNs with luminosities Lx (in units of erg s−1
is obtained upon integrating over the full range of lumi-
in the band 2-10 keV) in the ranges 42 < logLX < 43.5 (dotted),
nosities 1042 <L /erg/s<51046 spanned by our SAM.
X 43.5<logLX <44.5(dotdashed),and44.5<logLX (long-dashed).
Since the model does not include obscuration, we shall The shaded strip is the value 43 keV cm−2 s−1 sr−1 measured by
directly compare the results from eq. 5 with the hard
HEAO1-A2(Gruberetal. 1999).
CXBobservedatE ≥30keVwherephotoelectricabsorp-
tion does not affect the observed fluxes. Nonetheless, we Fig. 2 shows that in our model the CXB is mainly con-
must be aware of the fact that, even at this energy, the tributed by AGNs with intermediate luminosities L =
X
value of the observed background is appreciabely affected 1043.5 − 1044.5 erg/s, which provide ≈ 50% of the total
by the presence of sources in a Compton thick phase of value. High luminosity (L > 1044.5 erg/s) and low lu-
X
obscuration. minosity (L < 1043 erg/s) sources contribute a fraction
X
In Fig. 2 we show the hard CXB at E = 30 keV ob- ∼ 25% each. The population with intermediate luminosi-
0
tained from eq. (5) by integrating the volume out to run- tiesstrikesthebesttradeoffbetweenlargerluminosityand
ning redshift z . We show both the global value, and the smallernumberofsources. Thus,inthispicturehighlumi-
fraction contributed by AGNs in three classes of luminos- nosityhighlyabsorbedobjects(theso-calledtype2QSOs)
ity. Thepredictedbackgroundwiththechosenparameters wouldnotgiveadominantcontributiontothe hardCXB.
Menci et al. 5
In fact, although recent XMM and Chandra surveys are This behavious can be regarded as a natural outcome in
providing a sizeable number of QSO2 (Barger et al. 2002, the framework of a hierarchical scenario, where at earlier
Fiore et al. 2003, Hasinger 2003), these are likely to con- times increasingly largeer numbers of small galaxies are
stitute a relatively minor fraction of sources down to the present, which later merge to form larger systems.
fluxes where the bulk of the hard CXB is resolved into Further insightinto the redshiftdistributionofthe con-
sources. tribution to the CXB at 30 keV is provided in Fig. 3,
which shows the z-derivative of the CXB in Fig. 2. The
contribution to the CXB from all sources peaks at z ≈ 2,
and so does the contribution of the intermediate luminos-
itysources. ThecontributionofhighluminosityAGNs,in-
stead,ismoresharplypeakedattheslightlylowerredshift,
z ≈1.7,while the contributionfromthe lowestluminosity
sources shows a broad z-distribution.
The CXB spectrum above 20 keV, computed with the
fixedvaluesofαandE givenabove,iscomparedwiththe
c
HEAO1-A2 data in Fig. 4. Apart from the normalization
mismatch commented previously, the predicted shape is
slightly softer than observed. We note however that, in a
more detailed modelling, the adoption of an appropriate
scatter in α and E is likely to yield a somewhat harder
c
shape.
Fig. 3. - It is shown the differential contruibution to the predicted
CXB at E0 =30 keV, for different ranges of luminosityof the con-
tributingsources. SymbolsareasinFig. 2
Fig. 5. -Top panel. The fluxdistributionof AGNs contributing to
theCXBatdifferentenergies (seelabelsinthebottom panel). The
fluxcorrespondstotheintrinsicemission(correctedforobscuration)
inthecurrentlyaccessibleenergyband2-10keV.Bottompanel. The
fraction of the CXB contributed by sources with fluxes larger than
theconsideredvalue.
Our model can provide guidelines for future observa-
tions. Fig. 5 shows the differential (upper panel) and
integral (lower panel) contribution to the CXB at various
energies (from 30 to 300 keV) provided by sources with
different 2-10 keV flux (corrected for obscuration). As a
Fig. 4. - The energy spectrum of the predicted CXB for E ≥ 30
function instead of their 20-100 keV flux, the panels in
keV, for different ranges of luminosity of the contributing sources.
Fig. 6 show the differential and the integralcontributions
SymbolsareasinFig. 1. DataarefromGruberetal. (1999).
to the CXB at 30 keV in various bins of redshifts, from
Note also that, while the contribution of the high lu- z = 0−1.5 to z > 3.5. This figure illustrates the pre-
minosity sources saturates already at z ≈ 2, that from dictions that the bulk of the CXB should be provided by
low luminosity ones continues to rise up to z ≈ 3 − 4. sources with fluxes around F20−100keV ≈10−14 ergs cm−2
6
s−1, placed at redshifts z ≈ 1.5 − 2.5. To observation- (Fiore et al. 2003). In particular, the latter authors com-
ally access this flux levels, high energy focussing optics is bined the results of the optical identification of the HEL-
required, a tchnological step forward which has become LAS2XMM 1dF survey with carefully selected identifica-
feasible and is included in current studies for further mis- tions from deep Chandra and XMM surveys to obtain a
sions, like, e.g., Constellation X 4 and NeXT (Tawara et well defined, flux limited sample of 317 hard X-ray se-
al. 2003). lected sources (2-10 keV), 70 % of them with a measured
redshift. These observations are performed in the 2−10
keV band; hence they imply generally small uncertainties
affecting the correctionfor line of sight obscurationin the
derivation of rest frame luminosity.
Total
z=0-1.5
z=1.5-2.5
z=2.5-3.5
z>3.5
Fig. 6. - Top panel. The 20-100 keV flux distribution of AGNs
contributingtotheCXBat30keVfordifferentbinsofredshift(see
labelsinthebottompanel). Bottompanel. ThefractionoftheCXB Fig. 7. - The source counts of hard X-ray AGNs contributing to
contributed by sources with brighter than the value inabscissa, for the CXB is shown for the band 13-80 keV, and compared with the
thedifferentredshiftshells. HEAO1-A4 data point (Levine et al. 1984). We also show the ex-
trapolation to the 13-80 keV band of the BeppoSAX HELLAS 5-
Fig. 7showsthesourcecountsexpectedinourmodelin
10 keV counts on assuming different absorbing column densities:
the 13-80keV band, to be comparedwith the HEAO1-A4 NH = 1021 cm−2 (short-dashed line), NH = 1023 cm−2 (long-
data point (Levine et al. 1984); . note that the predicted dashed line), NH = 1023.5 cm−2 (dot-dashed line), NH = 1024
counts agree very well with the bright flux point. We also cm−2 (dotted line)
compareour predictions with the extrapolationto the 13-
80keVbandofthe BeppoSAXHELLAS5-10keVcounts, In Fig. 8 we compare our predictions with the evolu-
assuming spectral shapes depending of different values of tion of the number and luminosity densities of AGNs in
theadoptedabsorbingcolumns. Thiscomparisonsuggests three luminosity bins, estimated by Fiore et al. (2003).
that the bulk of the hard X-ray selected sources with flux Note that the three luminosity bins adopted by Fiore et
at a few 10−13 erg cm−2 s−1 has a substantial absorbing al. (2003)for statistical reasonsdiffer from those adopted
column, of the order of N =1023 cm−2. in Fig. 2, which were chosen to single out the class of
H
So far we have compared the predictions of our model objectsproducing the dominantcontributiontothe CXB.
with integrated observations, i.e., the spectrum of the Allthepredicteddensitiesdropsubstantiallyfromz ≈2
CXB at energies higher than 30 keV and the hard X-ray to the present. The agreement with the data is excel-
counts. Wenowproceedtocomparethemodelwithobser- lent for the highest luminosity bin, not surprisingly since
vationsof differentialnature in redshiftandinluminosity, such objects are also sampled in the optical band, where
which can provide tighter constraints. Here the compari- the model was already successfully tested in Menci et al.
son is more critical due to the difficulty of obtaining well (2003). In addition, Fiore et al. (2003) find a nice agree-
defined,completesamplesofhighlyobscuredAGNsatred- ment between their data for high luminosity sources and
shifts z ≈ 2.5−3. The most recent results on the num- the evolution of optically selected AGNs with M < −24
B
ber and luminosity density of AGNs come from Chandra, estimated by Hartwick & Shade (1990). This agreement
XMM-Newton deep, pencil beam surveys: the North and confirms that, at least for the very luminous AGNs, the
South Chandra Deep Fields; Brandt et al. 2002; Barger bolometric corrections adopted in the B and in the X-ray
et al. 2002; Giacconi et al. 2002; Cowie et al. 2003; the band are fully consistent.
Lockman Hole survey (Hasinger 2003). We shall compare Atlowerluminosities,thedeclineforz <1−2islesspro-
with the wider but shallower surveys from XMM-Newton nounced in the predictions as well as in the observations.
4http://constellation.gsfc.nasa.gov/
Menci et al. 7
In the former, this is due to the larger quantity of galac- not be reduced by tuning the bolometric correction c2−10
tic cold gas left available for accretion in the less massive adoptedinourmodel,sincethelatteraffectsonlythenor-
galaxies. Thisis anaturalfeatureinhierachicalscenarios, malization of the luminosities.
since more massive potential wells originate from clumps
collapsedearlierinbiasedregionsoftheprimordialpertur-
bation field; the higher densities then prevailing allowed
for earlier condensation and hence enhanced star forma-
tion at high redshifts. Thus, at low z a larger fraction of
cold gas will have already been converted into stars, and
both star formation and BH accretion are considerably
suppressed. Wenote thoughthatthedecreaseofthe peak
redshift with decreasing luminosity appears to be signifi-
cantly smaller than indicated by the data. In particular,
at z= 1−2 the observed density of Seyfert-like AGNs is
a factor ≈2 lower than predicted by the model; a similar
difference is present also for the intermediate luminosity
objects (L2−10 = 1044−44.5 erg s−1) in the redshift bin
z =2−4.
Fig. 9. - The predicted LFs in the energy range 2-10 keV at low
redshifts 0.5 < z < 1 (dashed line) and high redshifts 2 < z < 4
(solidline)arecomparedwithobservationalvaluesderivedfromthe
same sample used in Fiore et al. (2003) to derive the densities in
Fig. 8.
5. DISCUSSION
Fig. 8. -Top: Theevolution ofthe number densityofX-rayAGNs
WehaveincorporatedthedescriptionoftheX-rayprop-
inthreebinsofluminosity(inunitsoferg/s,intheband2-10keV):
erties of AGNs into the hierarchicalpicture of galaxyevo-
43 < logLX < 44 (dotted line), 44 < logLX < 44.5 (solide line), lution. Our semi-analyticmodel, alreadyprovento match
44.5<logLX (dashedline). Thedatafortheaboveluminositybins theobservedevolutionofluminousopticallyselectedQSOs
(squares,triangles,andcircles,respectively)aretakenfromFioreet
over the redshift range 0 < z < 6 (Menci et al. 2003),
al. (2003). Bottom: The evolution of the X-rayluminosity density
is here extended to bolometric luminosities L a factor 10
forthesameluminositybins.
lower. So we describe the history of accretion down to
Thereasonforsuchadiscrepancycanbetracedbackto L∼1045 erg/s,forwhichthe mainobservationalinforma-
the shape ofthe high-z X-rayluminosity function. This is tion comes from the X-ray band.
shownin fig. 9, where we compare our model results with We have compared our model with X-ray observations
the observational LFs derived by Fiore et al. (2003, up- either corrected for gas obscuration, or performed in the
per panel) and by Ueda et al. (2003, lower panel), which hard (E > 30 keV) band not affected by photoelectric
are obtained from a combination of HEAO1, ASCA and absorption.
Chandradata,andextenddowntolowerluminosities. The We find that our model is encouragingly able to match
aboveobservationalresultsconcurtoindicatethattheLFs the level of the cosmic X-ray background (CXB) at 30
atz >2areappreciablyflatterthanatz =0.5−1. When keV (Fig. 2). We predict that the largest contribution
∼
the above data are compared to our results, a substantial (around 2/3) to the CXB comes from intermediate lumi-
agreementisfoundatlowz,whileatz >1.5−2themodel nosity sources 43.5 < log(L /ergs−1) < 44.5, and that
∼ X
overestimatesthe number of low luminosity objects found 50 % of its total specific intensity is produced at z < 2,
in both the observational analysis. Such a mismatch can see figs. 2, 3. The predicted 30−300 keV CXB spectrum
8
shown in Fig. 3 has been computed with the simplifying whose star formation is more smoothly distributed in z,
assumption of a fixed spectrum for all individual souces, and which retain even at z ≈0 an appreciable fraction of
and neglecting the absorption in Compton-thick sources. cold gas available for BH accretion.
If a spread in the spectral slope α and in the high-energy For z >2, the slight excess of the number and luminos-
∼
cutoff Ec is included, a harder spectrum would naturally ity densities of weak AGNs with LX < 1044.5 erg/s over
obtain. Concurrently,ifthedistributionofCompton-thick the observations may originate both in the observations
sources is skewed towards larger redshifts, the absorption and in the modelling.
would not affect the spectrum at large energies (E ∼> 100 Ontheonehand,dataincompletenessistobeexpected
keV), where the CXB is contributed mainly by low- red- at high z for low- luminosity objects. Althouh the data
shifts sources; this results in an effective flattening of the are corrected for absorption, the sources would be lost
spectrum. Since the inclusion of both these effects in the from the sample when heavily obscured below the detec-
model wouldlead to a harderspectrum, a confirmationof tionlimit. Also,theobservednumberandluminosityden-
theslopemasuredbyHEAO1-A4withfutureexperiments sities do not include Compton-thick sources whose contri-
would be of major interest. bution is instead included in the model predictions. If the
We also predict (figs. 6, 7) the number counts and the amountof obscuringgasincreasedwith redshift, as would
fluxdistributionatdifferentz inthehard(20-100keV)X- bethecaseifalargeamountofgasaccumulatesinthesur-
ray band for the sources contributing to the X- ray back- roundings of Eddington limited BHs, lower-z and higher
ground. We have shown that ∼ 50 % of the CXB at 30 luminosity sources would be effectively favoured. Future
keVisproducedbysourcesbrighterthan210−14ergcm−2 observations extended to harder bands will clarify the is-
s−1 in the 20-100keVband. Such predictions canprovide sue;inthe meanwhile,weplantoimprovethe comparison
guidelines for aimed observations and future experiments. between the model and the data through the inclusion in
When compared to the observed evolution of the num- the model of gas absorption and the computation of the
ber and luminosity density of AGNs with different L related effect of Compton thick sources. This in principle
X
(Fig. 8), our model agrees with the observations con- can be done self-consistently, since the amount of galactic
cerning all luminosities LX > 1043 erg/s for low or in- gas is predicted in our model (see fig. 1 in Menci et al.
termediate redshifts z < 1.5−2. Thus, adopting a uni- 2003).
∼
versal spectrum (and hence fixed bolometric corrections) On the other hand, the excess of predicted low-
our model matches the observations concerning both the luminosity AGNs at high z could originate from an in-
optical (see Menci et al. 2003) and the X-ray band, at complete modelling in the low mass regime at high z. For
least for objects with bolometric luminosities L > 1046 example, the mismatch may be lifted by a mean AGN
∼
erg/s; in particular, the density of luminous (L >1044.5 lifetime increasing with mass (see Yu & Tremaine 2002),
X
a feature that can be implemented in the developments
erg/s) AGNs peaks at z ≈ 2, while for the low luminos-
ity sources (1043 < L /ergs−1 < 1044) it has a broader of our present fiducial model, specifically through a mass
X
maximum around z ≈ 1.5; the decline from the maxi- dependence of τ in eqs. (3) and (4). Additional improve-
ments may concern the following sectors:
mum to the value at the present epoch is around 3 dex
for the former class, and 1.5 dex for the latter class. At i) The properties of the accretiondisks at low accretion
larger redshifts z > 2, the model still reproduces the ob- rates. Advection-dominated accretion flows might consti-
∼
tute an example of such a physics, though they ought to
servednumber and luminosity densities of AGNs stronger
than1044.5 erg/s,but at z=1−2 the predicted density of decreasethe emittedluminositypreferentiallyathighz to
Seyfert-like AGNs is a factor ≈ 2 larger than observed; a explain the excess.
similardifferenceispresentalsofortheintermediatelumi- ii) The regulation governing the amount of cool gas in
nosity objects (L2−10 = 1044−44.5 erg s−1) in the redshift low-masshostgalaxies,liketheSupernovaefeedback. This
bin z =2−4. We next discuss our interpretation of both still represents the most uncertain sector of all SAMs; it
the low-z and the high-z results. is known to play a key role in flattening the faint end of
For z < 2, the model results agree with the observed the optical galaxy luminosity functions, since large feed-
∼
number and luminosity densities in indicating a drop of backwoulddepletethecoldgasreservoirspreferentiallyin
the AGN population for z < 2 which is faster for the shallow potential wells.
strongest sources. In our picture the drop is due to the iii) The statistics of DM haloes. The most recent N-
combined effect of: 1) the decrease of the galaxy merging body simulations pointtowardamass function ofgalactic
and encounter rates which trigger the gas destabilization DM clumps somewhat flatter at the small-mass end than
andtheBHfeedingineachgalaxy;2)ofthedecreaseofthe previously assumed (see Sheth & Tormen 1999, Jenkins
et al. 2001). While this could contribute to solve the is-
galactic cold gas, which was already converted into stars
oraccretedonto the BH. The faster decline which obtains sue, the flattening is not large enough to explain out the
in massive galaxies (and hence for luminous AGNs) is re- observed excess.
All the abovepoints can concurrin determining the ex-
latedinparticulartothelattereffect. Indeed,inhierarchi-
calclusteringscenariosthestarformationhistoryoflarger cess of the predicted low-luminosity AGNs at high z. We
objects peaks at higher z, since massive objects originate note, however, that overprediction of the low-luminosity
sources is a long-standing problem which also affects the
from progenitors collapsed in biased regions of the Uni-
verse where/when the higher densities allowed for earlier number andluminosity distributionoffaint, high-z galax-
star formation; so, at low z such objects have already ex- ies. This would point toward an origin of the mismatch
in the physics of galaxy formation rather than in the de-
haustedmostoftheirgas. Ontheotherhand,lessmassive
galaxies are continuously enriched by low-mass satellites, scription of the accretion processes. If this is indeed the
Menci et al. 9
case, tuning the free parameters in the SAM (like, e.g., In sum, despite the uncertain origin of the overpredic-
the efficiency of the Supernovae feedback, the one which tion of faint X-ray sources at z > 2, the present model
∼
mainly suppress the AGN and star formation activity in providesagoodbaselineto includethe evolutionofgalax-
low mass systems) does not constitute a valid solution for ies andAGNs inthe sameglobalpicture, being supported
the excess of low- luminosity X-ray AGNs at high z; in by a remarkable agreement with the observations of its
fact,therequiredadjustmentswouldworsenthematching predictions for brighter sources in a wide range of red-
between the model results and the observed properties of shifts (from 0 < z < 6) and of wavelengths (from optical
galaxies,like,e.g., the Tully-Fisher relation. Onthe other to X-rays). The most distinctive feature of such a pic-
hand, implementing an ad hoc parametrical dependence ture is the dramatic decrease of the AGNs luminosities at
onz oftheSupernovaefeedbackcouldsignificantlyreduce z <2especially inmassivegalaxies(seeFig. 1), naturally
∼
theexcess;butintheabsenceofaphysicalmotivationthis resulting from to the exhaustion of cold gas necessary for
would not lead to a deeper insight into the galaxy-AGN feeding both the accretion and the star formation; relat-
connection. edly, massive galaxies are predicted to undergo a nearly
Thus, a real improvement in the modeling requires the passive evolution from z ≈ 2 to the present. The rele-
inclusionofadditionalphysicalprocessesintheSAM(and vance of such an exhaustion in determining the observed
inparticularin the sectorconcerningthe feedback)rather propertiesoftheAGNpopulation(inboththeopticaland
than the tuning of the parameters in the existing frame- the X-rays) is confirmed by recent N-body simulations
work. One such process could be well constituted by (Di Matteo et al. 2003). The above picture thus natu-
the inclusion into SAMs of the feedback produced by the rally explains the parallel evolution of BH accretion and
AGNs emission itself. Since the AGN activity strongly star formation in spheroidal systems; this, originally dis-
increases with redshift, this could significantly contribute cussed by Monaco, Salucci & Danese (2000) and Granato
to expell/reheat part of the galactic cold gas reservoir in et al. (2001), is supported by recent works (see Frances-
low-mass systems at high z. While the modeling of such chini, Hasinger, Miyaji, Malquori 1999; Haiman, Ciotti
impulsive processes is particulary delicate, some steps in & Ostriker 2003) which also enlightened its simultaneous
this direction have already been taken (see, e.g., Haen- consistence with the evolution of the optical and the X-
helt,Natarajan&Rees 1998;Silk &Rees 1998;Wyithe & ray luminosity functions of AGNs (Cattaneo & Bernardi
Loeb 2003; Cavaliere, Lapi & Menci 2002; and references 2003). The physical origin of such a parallel evolution is
therein). We shall investigatethe effects ofsuch processes here clarified and shown to arise as a natural outcome of
on the evolution of the AGN population in a next paper. hierarchical galaxy formation.
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