A&A 451, 443-456 (2006)
DOI: 10.1051/0004-6361:20053710
I. Matute1,2 - F. La Franca2 - F. Pozzi3,4 - C. Gruppioni4 - C. Lari5 - G. Zamorani4
1 - Max-Planck Institut für extraterrestrische Physik (MPE),
Giessenbachstrae, Postfach 1312,
85741 Garching, Germany
2 -
Dipartimento di Fisica, Università degli Studi
"Roma Tre'', via della Vasca Navale 84, 00146 Roma, Italy
3 -
Dipartimento di Astronomia, Università di Bologna,
via Ranzani 1, 40127 Bologna, Italy
4 -
INAF, Osservatorio Astronomico di Bologna, via Ranzani 1,
40127 Bologna, Italy
5 -
INAF, Istituto di Radioastronomia (IRA), via Gobetti 101,
40129 Bologna, Italy
Received 28 June 2005 / Accepted 30 December 2005
Abstract
Aims. We study the evolution of the luminosity function (LF) of type-1 and type-2 Active Galactic Nuclei (AGN) in the mid-infrared, derive the contribution of the AGN to the Cosmic InfraRed Background (CIRB) and the expected source counts to be observed by
at 24
m.
Methods. We used a sample of type-1 and type-2 AGN selected at 15m (ISO) and 12
m (IRAS), and classified on the basis of their optical spectra. Local spectral templates of type-1 and type-2 AGN have been used to derive the intrinsic 15
m luminosities. We adopted an evolving smooth two-power law shape of the LF, whose parameters have been derived using an un-binned maximum likelihood method.
Results. We find that the LF of type-1 AGN is compatible with a pure luminosity evolution (
L(z)=L(0)(1+z)kL) model where
.
A small flattening of the faint (
L15<L*15) slope of the LF with increasing redshift is favoured by the data. A similar evolutionary scenario is found for the type-2 population with a rate kL ranging from
1.8 to 2.6, depending significantly on the adopted mid-infrared spectral energy distribution. For type-2 AGN a flattening of the LF with increasing redshift is suggested by the data, possibly caused by the loss of a fraction of type-2 AGN hidden within the optically classified starburst and normal galaxies. The type-1 AGN contribution to the CIRB at 15
m is (4.2-12.1)
,
while the type-2 AGN contribution is (5.5-11.0)
.
We expect that
will observe, down to a flux limit of
mJy, a density of
1200 deg-2 type-1 and
1000 deg-2 type-2 optically classified AGN.
Conclusions. AGN evolve in the mid-infrared with a rate similar to the ones found in the optical and X-rays bands. The derived total contribution of the AGN to the CIRB (4-10%) and
counts should be considered as lower limits, because of a possible loss of type-2 sources caused by the optical classification.
Key words: cosmology: observations - infrared: galaxies - galaxies: active - surveys - galaxies: evolution
Active Galactic Nucleus (AGN hereafter) are expected to have played
an important role in the formation and evolution of the galaxies in the
Universe. An example is the observation of the correlation between the mass of
the central black holes (
)
and the mass of the bulges (Magorrian et al.
1998) or the velocity dispersion of gas and stars in the bulges of
galaxies (
-
relation; Ferrarese & Merritt 2000;
Tremaine et al. 2002). Thus, the measure of the history of the
density of AGN as a function of the luminosity (the luminosity function, LF
hereafter) can provide fundamental clues to explain the present day universe
(e.g. Balland et al. 2003; Menci et al. 2004; Granato et al. 2004; Di Matteo et al. 2005).
The LF will not only provide information on the census of AGN, but will also place constraints on the physical model of AGN, the origin and accretion history into supermassive black holes and the formation of structures in the early universe. Moreover, the measure of the AGN LF over the whole spectral range will provide information on the relative importance of accretion power in the overall energy budget of the universe.
AGN have been historically classified into two groups (type-1 and type-2),
depending on the presence or absence in their optical spectra of
broad emission lines (
). The unified model
for AGN assumes that the two types of sources are intrinsically the same
(Antonucci et al. 1993), and that the observed
differences in the optical spectra are explained by an orientation
effect. The presence of obscuring material (torus or warped
disc) around the central energy source and its orientation with respect to
the observer could prevent a direct view of the central region around
the nuclei responsible for the broad line emission observed in the optical
band. AGN are then classified in two groups: the un-obscured (type-1) and
obscured (type-2) sources depending on whether the line-of-sight intersects
the obscuring material or not. However, it seems clear that the
orientation-dependent model is a 0th-order approximation to
the true nature of AGN (e.g. Barger et al. 2005; La Franca et al.
2005).
The major efforts to understand the evolution of AGN historically have been concentrated in optical wavelengths and in recent years have produced the largest compilations of AGN from the Two Degree Field (2dF; Boyle et al. 2000; Croom et al. 2004) and the Sloan Digital Sky Survey (SDSS; York et al. 2000; Hao et al. 2005). However the optical bands have proved to be very inefficient in the selection of obscured sources and the assembly of unbiased samples of type-2 objects is difficult. In recent years many new windows have been opened at various wavelength bands for the observation of high redshift galaxies and AGN: sub-mm (SCUBA), Infrared (IRAS, ISO and Spitzer) and the X-ray (ROSAT, XMM and Chandra). Thanks to their smaller dependence on dust obscuration compared to the optical surveys, the Infrared and the hard X-ray wavelengths have proved to be much more efficient in the detection of type-2 sources.
X-ray observations so far have been consistent with population synthesis models based on the 0th-order unified AGN scheme (e.g. Comastri et al. 1995) or its modifications (Pompilio et al. 2000; Gilli et al. 2001; Ueda et al. 2003; La Franca et al. 2005). The hard spectrum of the X-ray background is explained by a mixture of absorbed and unabsorbed AGN, evolving with cosmic time. According to these models, most AGN spectra should be heavily obscured as the light produced by accretion is absorbed by gas and dust.
For this reason an important mid-infrared (4-40 m) thermal
emission is expected from reprocessed radiation by gas and
dust grains directly heated by the central black hole (e.g. Granato et al. 1997; Oliva et al. 1999; Nenkova et al.
2002). AGN in this case could be important contributors to the
Cosmic Infrared Background (CIRB). Indeed, IRAS has observed strong mid-IR
emission in all local (z<0.1) AGN (Miley et al. 1985; de Grijp et al. 1985; Neugebauer et al. 1986; Sanders et al.
1989). Complete and largely unbiased samples of AGN have been
produced at 12
m (Rush et al. 1993, RMS hereafter) and
25
m (Shupe et al. 1998) based on IRAS observations.
These samples provide an important insight into the infrared emission
from local galaxies and a firm basis with which to compare the properties of
galaxies in the local universe with the high redshift populations uncovered
by ISO (
)
and most recently by Spitzer (
).
Statistical studies of AGN in the mid-IR have been based on large but local samples from the IRAS observations (e.g. RMS, Shupe et al. 1998) and deep but small ISO fields in the Hubble Deep Field North (HDFN; Aussel et al. 1999a,b), South (HDFS; Oliver et al. 2002) and the Canada-France Redshift Survey (CFRS; Flores et al. 1999) that provided only a handful of objects.
Therefore, due to the small number of high redshift objects available, the
shape and evolution of the mid-IR LF of these objects at high redshift was
largely unknown. Only recently, large and highly complete 15m
spectroscopic samples, based on the European Large Area ISO
Survey (ELAIS hereafter; Oliver et al. 2000), have been released
(Rowan-Robinson et al. 2004; La Franca et al.
2004, FLF04 hereafter). Based on the analysis of the ISO
observations in the ELAIS-S1 field, Matute et al. (2002, M02
hereafter) derived the first estimate of the type-1 LF in the mid-IR
(15
m), finding an evolution similar to the ones observed in the optical
(Croom et al. 2004) and X-rays (e.g. Hasinger et al.
2005; La Franca et al. 2005). The evolution of the LF
for normal and starburst galaxies detected at 15
m in the southern ELAIS
fields (S1 and S2) has been derived and discussed by Pozzi et al.
(2004).
In this paper we investigate the separate evolution of type-1 and
type-2 AGN in the mid-IR and their contribution to the CIRB using: a)
the local IR population uncovered by IRAS; b) deep observations
from ISO fields and; c) the most recent spectroscopic
identifications of 15 m sources in the southern fields of the
ELAIS Survey (Pozzi et al. 2003; FLF04)
. The AGN sample
used in our work is described in Sect. 2. Section 3 introduces the
general method used to derive the parameters of the luminosity
function and presents the results. In Sect. 4 we discuss our results
and compare them with the LFs derived in the mid-IR by previous
analysis of mid-IR observations. The contribution to the CIRB and the
predicted counts in the mid-IR Spitzer band at 24
m are
computed and discussed in Sects. 5 and 6. Section 7 summarises the
main results.
A cosmology with H0=75 km s-1 Mpc-1 and
,
was adopted
for the work presented in this paper.
The mid-IR selected AGN sample used in this work has been extracted
from:
(i) the 15m ELAIS fields S1 and S2
(Lari et al. 2001; Pozzi et al. 2003),
(ii) the 15
m deep ISO surveys in the HDFN
(Aussel et al. 1999a,b), HDFS (Oliver et al.
2002) and CFRS (Flores et al. 1999),
(iii) the local IRAS 12
m sample of RMS.
The 15m catalogue in the ELAIS S1 field was released
by Lari et al. (2001). It covers an area of
4 deg2 centred at
,
and
includes 462
mid-IR sources down to a flux limit of 0.5 mJy. Mid-IR source counts based on this
catalogue have been presented and discussed by Gruppioni et al. (2002).
The analysis presented here is restricted to the more reliable subsample of
406 sources as described by FLF04. About 80
of these sources have been
optically identified on CCD exposures down to R
23, while spectral
classification has been obtained for 90
of the optically identified sample.
As discussed by FLF04, due to a different mid-IR flux limit coverage of the
ELAIS-S1 field, the total area has been divided into two regions: the central
and deepest region of S1 (S1-5) reaching mid-IR fluxes (S15 hereafter) of
0.5 mJy, and the outer region (S1-rest) with a 0.9 mJy flux limit. The S1-5 area
is spectroscopically complete at the 97
level down to R=21.6, while
S1-rest completeness reaches the 98
level down to R=20.5. In total 116 sources (29
of the total mid-IR sample) do not have a spectroscopic
identification due to incompleteness of the follow-up or to the lack of optical
counterpart brighter than R=23. A detailed description of the optical
identification, spectroscopic classification, size and completeness function of
the different areas used in the ELAIS-S1 sample are presented and discussed by
FLF04.
The S2 field is a smaller and deeper area centred at
,
covering
0.12 deg2. This region
includes 43 sources with S/N > 5 down to
S15=0.4 mJy
(Pozzi et al. 2003; Rowan-Robinson et al. 2004).
Photometry in the whole field
is available in the U, B, I and K
bands down
to 21.0, 24.5, 22.0 and 18.75 respectively (Vega magnitudes).
39 infrared sources have a counterpart in the I band. 22 of them have a
spectroscopic identification, while 8 sources are classified as stars since they
are associated with bright (I < 14) point-like sources in the optical
catalogue. To avoid large incompleteness due to the optical follow-up, only
sources with optical counterparts brighter than I = 20.6 were selected. Down
to this optical limit, the sample considered in S2 is then complete at the 95%
spectroscopic level for sources with
S15>0.7 mJy.
Classification for AGN dominated sources in the ELAIS fields was based on
their optical spectral signatures. Sources showing broad emission line
profiles (rest frame
km s-1) were classified as type-1.
Type-2 sources were selected following classic diagnostic diagrams (e.g. Tresse
et al. 1996; Osterbrock 1989; Veilleux & Osterbrock
1987) that included one or
more of the following line ratios: [NII]/H
,
SII/(H
+[NII]),
OI/H
,
[OIII]/H
and [OII]/H
when available,
depending on the redshift of the source (e.g. log([OIII]/H
) > 0.5
and log([NII]/H
) > -0.4).
In total, the southern ELAIS (S1+S2) AGN sample includes 27 (25+2) type-1 and
25 (23+2) type-2 AGN representing 16
(52/320) of the identified
infrared sources and
24
(52/221) of the extragalactic population.
Their distribution in the redshift-R-magnitude space is shown in Fig. 1. The
plotted lines represent a linear fit (
)
to the data (dotted
for type-1 AGN and dashed for type-2). Type-1 sources are detected up to
and show a quasi redshift-independent and narrow optical magnitude
distribution (
). On the other hand, type-2 sources show a larger
spread of optical magnitudes (
)
and a rather steep dependence on
the redshift up to
.
Constraints on the fainter population are provided by deep 15m
observations in the HDFN (Aussel et al. 1999a,b), HDFS
(Oliver et al. 2002) and in the 1452+52 field of the CFRS (Flores et al.
1999). These fields have a flux limit about an order of magnitude
deeper (
mJy) than the ELAIS-S fields but with sky coverages 100 to
500 times smaller. The multiwavelength follow-up in these fields has
identified a small fraction of sources as AGN (both type-1 and type-2).
In the HDFN, 41 15m sources have been detected over an area of 21.5 arcmin2. The sample is complete down to 0.1 mJy (Aussel et al.
1999a). 4 of these sources, with fluxes between 0.1 and 0.45 mJy, are
found to be AGN by Alexander et al. (2002), equally divided between
the two classes (Alexander et al., private communication). In the HDFS we use
the AGN identified by Franceschini et al. (2003) from a sample of 59 ISOCAM sources with
mJy selected over an area of 19.6 arcmin2. They have detected two secure AGN, one type-1 (
S15=0.288 mJy)
and one type-2 (
S15=0.518 mJy). The observations in the CFRS 1452+52 field
cover an area of
100 arcmin2. 41 sources with
mJy and
with
have been selected (Flores et al. 1999). The
spectroscopic follow-up identified one type-1 (
mJy) and one
type-2 (
mJy) source. In the abovementioned fields, a fraction
of the type-2 sources were not classified according to their optical spectra
but on the basis of the shape of their multiwavelength spectral energy
distribution (SED). For this reason only the selected type-1 population has been
used in our analysis.
We combined the ISOCAM data with the local IRAS sample of AGN from RMS.
The RMS Catalogue is a high galactic latitude (
),
colour selected (
/
)
and flux
limited (
Jy) sample extracted from the IRAS 12
m Faint Source Catalog, Version 2 (Moshir et al.
1991).
To avoid completeness uncertainties in the mid-IR sample, only sources
with
mJy were selected (see RMS).
In total 41 type-1 and 50 type-2 sources are found within this flux range.
The photometric and spectroscopic follow-up of the optical counterparts is
considered to be
100% complete for these sources and has been used in
our analysis as representative of the mid-IR selected population of AGN in
the local universe.
![]() |
Figure 1:
Distribution of ELAIS-S1 type-1 and -2 AGN in the
z-R-magnitude plane. Best fit linear solutions (![]() ![]() |
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In order to compare local sources with a higher redshift selected population and
to probe changes with cosmic time it is necessary to compare their intrinsic
physical properties. Our sample has been selected in the mid-IR and identified
in the optical band, therefore rest-frame luminosities, in the form of ,
at 15
m (L15) and in the R-band (LR) were
computed using well known SEDs for type-1 and 2 sources.
The compilation of Elvis et al. (1994) of 47 QSO, in the range of
1-20m,
was used as representative of the mid-IR emission for the type-1 population.
This composite SED agrees very well with spectroscopic observations of type-1
sources performed by ISO in the mid-IR (Clavel et al. 2000;
Spoon et al. 2002), showing a strong power-like continuum, very weak
or no PAH emission bands
and no evidence of the 10
m silicate absorption feature. Optical
luminosities for type-1 AGN were computed using the R-band k-correction by
Natali et al. (1998), which takes into account the large effect of
broad lines entering and leaving the passband.
Unlike type-1 sources, the mid-IR SED of type-2 objects vary greatly. They
range from starburst-like galaxy SEDs, as in the case of Circinus (Sturm
et al. 2000), showing a weak continuum, prominent emission from PAH molecules and a
deep silicate absorption feature at 10
m, to more power-like SEDs
dominated by hot dust directly heated by the active nucleus, as in NGC 1068
(Sturm et al. 2000). As a consequence, the mid-IR SED of NGC 1068 and
Circinus galaxies (Fig. 2) were used as representative of two extreme cases of
obscured AGN in the mid-IR. In order to derive the optical k-correction for
type-2 sources, an average spectrum was produced in the optical band
(3500-7000 Å) using our best type-2 spectra (Fig. 5 in FLF04).
In Fig. 3 we show the distributions in the L15-z plane of the total
sample used in our analysis, while Table 1 summarises the mean redshifts and
mid-IR luminosities, and corresponding 1
dispersion, measured for
the local (IRAS) and high redshift (ISO) sources.
The adopted shape of the luminosity function (LF) is a smooth two-power law
of the form:
![]() |
(1) |
![]() |
Figure 2: Adopted mid-IR spectral energy distributions (SEDs) for type-2 sources ( top panel) and the corresponding k-corrections as a function of redshift computed for the ISOCAM-LW3 filter ( bottom panel). |
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![]() |
Figure 3: Distribution in the L15- z space of the total sample of mid-IR type-1 and 2 AGN. The mid-IR luminosity for type-2 sources has been computed applying the Circinus k-correction (see text, Sect. 3.1). The dotted, dashed and dot-dashed lines represent the flux limits at 0.1, 1.0 and 300 mJy respectively. |
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The parameters for the luminosity function and the evolution have been
derived using an un-binned, maximum likelihood method (Marshall et al.
1983), as described by Matute et al. (2002). The
spectro-photometric
follow-up of the ELAIS southern fields was not deep enough to provide
an identification and a classification for all the sources detected in
the mid-IR sample. A factor depending on redshift and mid-IR luminosity was
therefore introduced in order to take into account the fraction of objects not
identified, due to the lack of an optical counterpart or to incompleteness of
the spectroscopic follow-up. We will refer to this factor as the
optical-completeness factor,
.
It represents
the probability that a source with a given redshift and mid-IR
luminosity
has an apparent R-band magnitude within the
spectroscopic limits of the samples, and was derived taking into
account both the average L15/LR ratio of the sources and its
observed natural spread. For any given mid-IR luminosity L15,
this probability has been computed assuming a Gaussian distribution of
log (
L15/LR) centred at its mean value and with a sigma equal to the
observed natural spread of the L15/LR relation (see next sections for
discussions on the adopted mean values and spreads of log (
L15/LR))
. Then, the
function to be minimised can be written as:
![]() |
(3) |
Table 1:
Mean redshift and luminosity (
)
of the mid-IR samples.
Confidence regions for each parameter have been obtained by computing
at a number of values around the best parameter (
),
while allowing the other parameters to float (see Lampton et al. 1976). A 68
confidence region for any single parameter
corresponds to
.
The goodness of the fit has been
verified using the bidimensional Kolmogorov-Smirnov test (2D-KS hereafter) in
the L15-z space (see Peacock 1983; Fasano & Franceschini
1987). The normalisation factor
is determined in such a
way to reproduce the observed total number of sources (ISO + IRAS).
For type-1 sources, the optical completeness factor,
,
has
been estimated using the mean value log (L15/LR) = 0.23 with a 1
dispersion of 0.25 (from the sample of Elvis et al. 1994). These
values are in rough agreement with the derived value for the IRAS local
sub-sample of type-1 AGN from Spinoglio et al. (1995; 0.05 with a
1
spread of 0.13). This ratio and its spread shows no significant
dependence on L15 over more than 4 decades of mid-IR luminosity and we
assumed them to be constant with redshift.
In order to find the best fit solutions to the LF we have considered:
In Fig. 4 we show the observed space density distribution and the
best fit models in two redshift intervals: z=[0,0.2], where the IRAS sources dominate, and
z=[0.2,2.2], mainly populated by ISO sources. The large interval at high redshifts (
z=[0.2,2.2])
was chosen only for representation purposes, to assure a significant
number of observed sources in each luminosity bin. In
order to correct for evolution within the redshift intervals, the
observed space density distribution is plotted following La Franca et al. (1997). The expected number of sources given by the model in each
bin (
)
is computed and compared to the observed number of
AGN in the bin (
). The ratio
/
for
each bin is then multiplied for the value of the LF at the
corresponding central luminosity and redshift value of the bin. The
plotted error bars correspond to the 1
Poisson distribution and
were estimated following Gehrels (1986). Space density upper limits are given
where sources are expected by the model but not observed. The 1
dispersion for the LF was computed according to the 1
uncertainties of
its parameters, and represented as a light-grey shaded area in Fig. 4.
Table 2: Parameter values of the fit of the luminosity function.
![]() |
Figure 4:
Type-1 AGN local (z=0.1, continuous line) and
high redshift (z=1.2, dash-dotted line) best fits to the 15![]() ![]() ![]() |
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Beside the natural statistical uncertainties due to the limited number of
sources used in our analysis, our fitting technique is affected by possible
errors due the assumed average value of the
L15/LR ratio used to correct
for the spectroscopic incompleteness of the samples. In order to estimate these
uncertainties we have recomputed the LF best fit solutions assuming two
extreme cases for the log(
L15/LR) ratio. In particular, we have used as
the average value of log (
L15/LR) our best estimate (0.23) plus or minus
the observed 1
dispersion (0.25). Even under these extreme assumptions,
the parameters of the LF result to be within the errors quoted in Table 2. The
dark-grey shaded areas in both panels of Fig. 4 show the corresponding
1
range of uncertainty introduced in the estimate of the space density
of type-1 AGN. As it is clearly seen in the figure, the statistical errors due
to the limited number of sources used in our analysis dominate over the
uncertainties due to the assumptions on the average value of the
log(
L15/LR) ratio. For example, the uncertainty introduced in the
estimated density of type-1 AGN by the assumed
L15/LR relation is
10% at
,
while the statistical uncertainty due
to the limited number of sources is larger than 20%. For these reasons, in
order to compute the errors over the parameters of the LF and any derived
quantity (e.g. integral counts and redshift distributions), we neglected the
uncertainties related to the assumptions on the average value of the
log(
L15/LR) ratio.
We observe that although the overall fit by the PLE model (model A in Table 2,
Fig. 4 bottom panel) is in reasonable agreement with the observed data, it
overpredicts by a small amount (1
), but systematically over 5
luminosity bins, the number of the low luminosity (
L15(z)<L15*)
and high redshift (z=1.2) type-1 AGN. This is the main reason why a
dependence of the faint slope on the redshift was included. The introduction
of this dependence translates into a luminosity dependent luminosity evolution
(LDLE) for the faint part of the LF (model B in Table 2). In this case, a
better agreement between the model and the data is obtained (Fig. 4, top
panel) as shown by the increment of the 2D-KS probability (0.35 vs. 0.11).
The measured rate of luminosity evolution (kL) is largely
independent of the adopted relation between
and z. The best fit
values,
,
are similar, within the errors, to those already found
for these objects in the optical and X-ray wavelengths, where the evolution
rate is between 2.5 and 3.5 (La Franca et al. 1997; Boyle et al.
2000; Miyaji et al. 2000 & 2001; Croom et al.
2004; La Franca et al. 2005; Hasinger et al.
2005). Therefore, according to this analysis, no difference is
found in the evolution of mid-IR selected type-1 AGN in comparison to the ones
selected in the optical and X-rays.
![]() |
Figure 5:
Left: mid-IR integral counts for type-1 AGN.
Shaded areas show the RMS and ELAIS observed counts, while symbols (triangle,
star and diamonds) represent the ISO-Deep surveys. The thick solid
line gives the predicted counts from the variable slope fit model ("B'').
Expectations from the fixed faint slope model ("A'') are plotted as a
dashed line. All errors in the observed distributions are quoted at the
1![]() ![]() |
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The 15m integral counts and the observed redshift distribution
for type-1 AGN can now be compared with the predictions derived from
the best fit models. The results of this comparison are presented in
the upper right and left panels of Fig. 5. The bottom panels show the
corresponding relative errors as derived from the 1
uncertainties on
the best fit parameters of the LF.
The expected integral counts (Fig. 5, left) given by both models
(dashed line for model "A'' and continuous line for model
"B'') provide a good representation of the observed data (shaded
areas) down to 2 mJy. At fluxes below
2 mJy the variable
slope model agrees better with the ELAIS data, while the PLE model is
more representative of the fainter population in the HDF and CFRS
fields. At the faintest fluxes (
S15=0.1 mJy) the variable slope
model underpredicts the observed counts by a factor
2.
The uncertainties on the predicted counts at this flux (
20%)
are not large enough to justify the observed discrepancy.
We also find an overall good agreement between the redshift distribution
of the observed data and the model predictions (Fig. 5, right).
The largest discrepancy between the models occurs at the lowest
redshift bin (z=[0,0.5]) where the fixed faint slope model (thin
lines) overpredicts the number of sources observed in the ISOCAM
fields by a factor 3 (4 observed vs.
12 expected), while
the variable faint slope model provides a better representation of
the observed distribution.
In summary, although the variable faint slope model provides a better
overall fit to the LF and reproduces better the z-distribution, it
underestimates the faint mid-IR counts (
S15<0.5 mJy) by a factor
of 4. As both models ("A'' fixed and "B'' variable faint slope)
are statistically acceptable, we conclude that given the presently
available statistics the two models are equivalent within the errors.
![]() |
Figure 6:
Observed and best fit LF for type-2 AGN at
![]() ![]() |
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M02 measured for the first time the evolution of type-1 AGN based on a
preliminary mid-IR catalogue from the ELAIS-S1 field. The values found
here for the fixed faint slope LF (model "A'') are in agreement
with what already found by M02 within 1
errors. The
only exception is for the bright slope (
), where the here derived value
is flatter (2.29
+0.36-0.16 vs. 2.89
+0.29-0.26).
This difference can be understood if we take into account the large
uncertainties in the brighter luminosity intervals (in both M02 and our sample)
due to the small number of sources. While the 2D-KS test gives a 11%
probability that the our sample of AGN is well represented by a non-evolving
faint slope (model "A''), this probability decreases to 5% if we use the
parameters values reported by M02 (Table 1 in M02).
As for type-1 AGN, a relation between the intrinsic 15m luminosity
(L15) and the optical luminosity (LR) for type-2 AGN is required to
correct for the optical incompleteness. FLF04 has shown that such a relation
exists and found it to be valid for the whole mid-IR population (excluding
type-1 sources) over more than 4 decades of mid-IR luminosity. In order to
derive this relationship, optical identifications from RMS, ELAIS-S fields, HDF
North (Aussel et al. 1999a,b) and South (Mann et al.
2002; Franceschini et al. 2003) were used. As opposed to
type-1 sources, the ratio
(L15/LR) has
a dependence on L15 which can be expressed in the linear form
The LF was computed in the luminosity range log L15=[42, 47] and in the redshift interval z=[0,0.7]. A total of 75 sources (25 from ELAIS and 50 from RMS) were used to derive the LF shape and evolution. Best fit values for the LF parameters, as well as the corresponding 2D-KS probabilities, can be found in Table 2 for each of the two representative mid-IR k-corrections assumed.
For type-2 AGN, we followed the same fitting sequence as for type-1
AGN. The results for a fixed faint slope (PLE model) are found on
Table 2 on rows labeled "C'' (for the NGC 1068 k-correction) and
"E'' (for the Circinus k-correction). In both cases, the value of
the 2D-KS test (
and 0.18 respectively) does not reject
the PLE model, but an important source overprediction is again present
in the model if compared to the observed data for the low luminosity
and moderate-z (z = [0.1, 0.6]) part of the sample. A better fit is
found by assuming an evolving faint slope of the LF parameterised as
specified in Sect. 3.2. In this case, in order to avoid unphysical
solutions due to the low statistics at high redshift, the
parameter was allowed to vary in the range [0,6], while the
parameter was allowed to vary in the range [0,2]. Indeed, both parameters
found a solution at the edges of the allowed ranges.
The results can be found in Table 2 and Fig. 6, fits labeled "D''
and "F'' for the NGC 1068 and Circinus k-corrections respectively.
![]() |
Figure 7: Left: observed and predicted integral counts for type-2 sources using the the two representative SED: NGC 1068 (thin dashed for the "C'' model and thin continuous for the "D'' model) and Circinus (thick dashed for the "E'' model and thick continuous for the "F'' model). Right: observed and predicted type-2 AGN redshift distribution for the different models mentioned before. Lines as in left panel. Symbols and shaded area in both panels as in Fig. 5. Errors reported in the lower section of both panels have been computed and plotted as described in Fig. 5. |
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Figure 6 shows the observed and predicted space density distribution of
the type-2 AGN in two representative redshift intervals, low-z(z=[0,0.1]) where the IRAS sources dominate and intermediate-z(
z=[0.1,0.6]), mainly populated by ISO
sources. The overall best solution found for the two representative SED,
NGC 1068 (left panel, model "D'') and Circinus (right panel,
model "F''), are plotted. The observed space density, errors,
upper limits and the 1
confidence regions for the LF have
been computed and plotted as described in Sect. 3.2. As observed for
type-1 AGN, the errors introduced by the low statistics (light
shaded area) are larger than the ones due to the assumptions on the
L15/LR relation (dark shaded area). For example, in this case,
while the error introduced by the assumed
L15/LR relation in
the determination of the density of type-2 AGN is
20% at the
break luminosity (L15*) of the LF, the limited statistics
introduce, instead, a
60% uncertainty. Therefore, also for
type-2 AGN, in order to compute the errors on the LF parameters and
on any derived quantity (counts and redshift distributions) the
uncertainties introduced by the assumptions on the value of the
L15/LR relation have been neglected.
The rate of evolution kL found for type-2 AGN depends strongly on
the assumed SED. If an NGC 1068 k-correction is adopted, the rate
of evolution is
,
lower than the one measured for
type-1 sources (
). On the other hand, an evolution
rate
is obtained if the Circinus SED is assumed,
closer to the one measured for type-1 AGN. These differences in kLare caused by the stronger k-correction introduced by the Circinus SED
(Fig. 1), which generates higher intrinsic luminosities in the redshift range
[0.1, 0.6] compared to those given by the NGC 1068
k-correction. In the other
hand, the impact of the assumed SED on all the other fitted parameters is small
(see Table 2 and Fig. 6).
For each best fit LF of the type-2 AGN, the predicted counts and
redshift distributions were derived and compared with the observed
data. Predictions at 15m for the integral counts are given in
the left panel of Fig. 7, while the derived redshift distribution is
shown in the right panel of the same figure. In both panels of
Fig. 7 a thick-dashed line represents the Circinus fixed slope
model ("E''), a thick-continuous line the Circinus variable slope
model ("F''), a thin-dashed line the NGC 1068 fixed slope model
("C'') and a thick-continuous line the NGC 1068 variable slope
model ("D'').
A good agreement, within the errors, between the models and the data
is observed. At variance with the solutions found for the type-1 AGN
(Sect. 3.2), although a higher 2D-KS probability is obtained using a
variable faint slope model, no major differences are observed in the
integral counts down the faintest ELAIS flux (1 mJy;
log
). The differences between the various models only
become significant at fainter fluxes (
mJy), especially
at the fluxes reached by the Spitzer space observatory
(
mJy; see Sect. 6). Indeed, the relative errors
are rather uniform, with mean values around 30-50%. Therefore, the
higher observed density of the deep ISO data (a factor
10)
is statistical significant. However, as previously mentioned
(Sect. 2), the higher density of AGN found in these fields is partly due to
the classification method used, which is not only based on a pure
optical spectral classification. The predicted redshift distributions
agree, within the errors, in the redshift interval where the LF was
computed (z=[0,0.7]). The different behaviour observed at z>0.7is understood by the different k-corrections obtained from the
adopted SED. The estimated errors range from a factor
1.3
at low redshift to
2.0 at the limiting redshift used to fit
the LF, and increase drastically when the predictions are extrapolated at
higher redshifts.
In the previous sections we have seen that a flattening with redshift of the
faint slope of both type-1 and type-2 luminosity functions is slightly
favoured by the data. This flattening would disappear if 7 additional
type-1 AGN, in the luminosity-redshift range log
L15=[42, 45] and
z=[0.2, 3.2], and
6 additional type-2 AGN within log
L15=[42, 44] and
z=[0.1, 0.7] were found. We briefly discuss now two possible origins of
incompleteness for the mid-IR AGN sample and their effects on the observed LF:
i) objects not identified due to the spectro-photometric limit of completeness
of the survey and; ii) possible misclassification of the objects.
The spectroscopic incompleteness at faint optical magnitudes of the
ELAIS sample is represented by the factor
(Sect. 3.1).
The corrections introduced through this term are represented in Fig. 8
as a function of redshift and mid-IR luminosity.
The shaded areas in the figure outline the region where type-1 (top)
and type-2 sources (bottom), fainter than the spectro-photometric
limit of the surveys, are expected to be found. A darker area in the
plot indicates that a higher fraction of correction has been applied
(i.e. higher number of lost sources) and it spans from
1%
(light-grey area) to
30% (darkest area) of the total sky area
available in a given interval of redshift and luminosity. The correction
computed corresponds to
4 type-1 and
1 type-2 sources in
the L15-z interval used in the minimisation process.
If the suggested flattening is really due to an incompleteness effect, then the
possibly missed objects are expected to follow an optical-mid-IR relation
different from the one measured for the identified fraction of the
high redshift ISO sources and in the local universe by IRAS
(z<0.1) and adopted in our estimate of
.
In the case of type-1 AGN, if the average value of the assumed
log(
L15/LR) relation is increased by 2.5 times the observed dispersion
of the relation (i.e.
0.86 instead of 0.23),
7 additional sources
would be expected at low luminosity and high redshifts, thus avoiding the
need for a flattening of the LF. This higher
L15/LR value could correspond,
for example, to sources with a significantly larger amount of gas and dust
with respect to the local samples of Elvis et al. (1994) and Spinoglio
et al. (1995). For type-2 AGN, the relation derived by La Franca
et al. (2004) implies that for the low luminosity
(
L15<L*15) and moderate redshift (
0.1-0.5) sources, all the
possible optical counterparts should have been observed. Only the high
luminosity (
L15>L*15), higher redshift (z>0.5) sources are affected
by incompleteness. Also in this case a significant higher value of the
L15/LR relation would be required in order to avoid the need
for a flattening of the LF.
![]() |
Figure 8:
Luminosity-redshift distribution of the type-1
( top) and type-2 ( bottom) AGN. Shaded areas represents
the fraction of incompleteness due to the optical spectroscopic limits.
Contours range from 75% (black) to 95% (light-gray) of the total
area lost and have a 5% step between them. For type-1 AGN ![]() ![]() ![]() |
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A second source of incompleteness could be spectroscopic mis-classification of the sources. The increase in the mean redshift of the ISO population with respect to the local IRAS sample (see Table 1) implies that a larger fraction of the host galaxy light is collected for a given size of the slit used for the optical spectroscopic identifications. The consequence is a dilution of AGN signatures that affects the measured equivalent widths (EW) and line ratios (see e.g. Moran et al. 2002). The effect is less significant for type-1 sources due to the presence of easily identified broad emission lines caused by a direct view of the central energy source with a low level of obscuration. The situation is more complicated for type-2 AGN since their higher degree of obscuration suppresses an important fraction of the optical light from the nuclei. The host galaxy would then naturally contribute with a larger fraction to the observed optical light from the nuclear source, sometimes even dominating it. The effect is maximised for the intrinsically faint AGN, whose optical features will be highly diluted into the host galaxy spectrum. This effect could be relevant in producing the observed flattening at high redshift of the luminosity function.
Observations with XMM and Chandra have uncovered a not
negligible number of AGN for which the classification given by their
optical spectra does not correspond to the X-ray classification of
the source (e.g. Fiore et al. 2000, 2003; Barger et al.
2005). In
their analysis of deep (70 Ks long) XMM observations on
ELAIS S1-5, La Franca et al. (in preparation) find that the fraction
of misclassified type-1 AGN appears to be negligible. Vice-versa, in
the case of type-2 AGN, the observations with XMM have revealed
that about 10-20% of the ISO counterparts optically classified
as no-AGN (i.e. normal and starburst galaxies) show X-ray luminosity
consistent with AGN activity. This fraction, in the case of ELAIS-S,
would imply that as many as 10 to 25 sources, classified in the
optical as starburst or normal galaxies, may harbour an AGN that can
contribute to the observed mid-IR flux. If this is the case, the
number of true type-2 AGN may be higher by a factor
than that used in this analysis and this would have important
consequences for the observed LF and its evolution.
We conclude that the observed flattening with redshift of the LF for low luminosity AGN can be explained if we assume that the incompleteness in the ELAIS sample was not properly modeled, for two possible reasons: (i) the unidentified fraction of sources may have a L15/LR ratio different from that of the identified AGN or, (ii) more likely, a relevant fraction of type-2 AGN could have been mis-classified due to dilution of the optical nuclear spectra by the hosting galaxy. These sources of incompleteness are probably almost negligible for type-1 AGN (especially the last one), while our measure of the density of type-2 AGN has instead to be considered a lower limit.
A local luminosity function (LLF) for type-1 and type-2 AGN was derived at
12m by RMS. Their results can be directly compared to our findings at
z=0. The values for the LF parameters reported by RMS and those computed by us
are summarised in Table 3.
Two parameters of the LF computed by RMS, the faint slope ()
and the
luminosity break (L15*), differ significantly from our solutions for both
the type-1 and the type-2 AGN. The difference in the value of the luminosity
break cannot be explained by the SEDs conversion factors from 12 to
15
m,
since they imply a small change in the intrinsic luminosity of the sources
(
log
m]
0.0 for type-1 and
0.1 for type-2
AGN). These discrepancies can instead be understood if we take into account
that: (i) the faint slope was fixed a priori in the fitting procedure by
RMS; (ii) the strong effect of evolution in the different luminosity bins was
not considered by RMS and; (iii) our best fit is obtained by taking into account
not only the local IRAS sources but also the high redshift ISOCAM
population.
Table 3: Parameter values of the fit of the mid-IR Luminosity Functions.
![]() |
Figure 9:
Comparison of LFs at 25![]() ![]() ![]() |
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A local combined (i.e. type-1 + type-2) AGN LF has been derived by Xu
et al. (2003) at 25m. It is based on an IRAS colour
selected (
)
sample obtained from a complete
catalog compiled by Shupe et al. (1998). Assuming a luminosity
evolution equal to the optical one (Boyle et al. 2000) and a set of
SEDs with a dependence on luminosity, Xu et al. (2003) were able to
derive the predictions for the AGN counts, the redshift distribution and
the contribution to the cosmic background from the UV to the sub-mm
wavelengths. A direct comparison of the two LFs can then be made by
translating our 15
m luminosities into 25
m luminosities,
using the adopted SEDs for each source class.
The results of this comparison, in two different redshift intervals,
can be found in Fig. 9 and Table 3. We find a good agreement between the
two LFs (dashed line for the 25
m selected sample;
continuous line for our type-1 + type-2 15
m LF) in the local
universe (z
0.1). The difference found at intermediate-z(z=0.6, the maximum z used to derive the type-2 LF) and low
luminosities L<L*) is mainly due to the observed decline in space
density at this redshift for the obscured sources.
The difference at higher luminosities (L>L*) can be explained by
the stronger evolutionary rate found by Boyle et al. (2000) for
optical selected type-1 AGN (
)
and used by Xu et al.
(2003) in their analysis with respect to the values found in this work,
depending on the AGN type. The difference in the LF induced by
these different kL parameters is already significant at
.
The deep observations carried out by the ISOCAM instrument on-board of ISO place interesting constraints on the shape and behaviour of the LF. For type-1 AGN they favour a PLE model scenario (dashed line in Fig. 5, left panel). This suggests that a small fraction of the low-luminosity ELAIS-S type-1 AGN may still be hidden within the rest of the mid-IR population. If this is the case, they do not follow the optical-mid-IR luminosity relation assumed for the rest of the type-1 sources as already discussed in Sect. 3.4.
The observations of type-2 sources in these fields indicate that all
our best fit solutions underestimate them by more than 1.5.
This result is not surprising since most of the type-2 sources
identified in these surveys have been classified using criteria
different from the pure optical spectral classification (i.e. SED
reconstruction, X-ray properties and radio emission). Indeed, this was
the reason why we did not consider these sources in our minimisation
process. A comparison between their observed space density and our
predictions has to be made with care due to the different classification
methods used.
Even if cosmic variance can increase the HDF-N, -S and CFRS quoted errors in Figs. 5 and 7 (by as much as 20-100% in such a small fields, Somerville et al. 2004), it cannot fully justify the observed difference since in all these fields the observed counts are found to be systematically higher than our predictions.
The contribution of AGN to the intensity of the Cosmic Background
light in the Infrared (CIRB) has been derived for all the models
presented in Table 2. The intensity of the CIRB at 15m for a
given population has been computed as,
![]() |
Figure 10:
The expected Spitzer MIPS integral counts
for AGN at 24![]() ![]() ![]() |
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The integrated light from type-1 AGN galaxies provides a contribution
of (4.2-12.1)
(in units
of
)
at 15
m. This value corresponds to (1.6-4.5)
of the
15
m background as reported by Elbaz et al. (2002) and confirmed
by Metcalfe et al. (2003,
)
using deep lensed observations with ISOCAM. Our predictions are in agreement
with what previously estimated by M02 (
).
The contribution of type-2 sources is found to be (5.5-14.6)
,
depending significantly on the
assumed SED and the parameterisation for the evolution of the faint
slope [
], and accounts for (2.0-5.4)% of the CIRB at
15
m. We note here that, even if the space density of
the obscured sources, up to redshift 0.7 (where type-2 AGN are
detected), is a factor 2-6 higher than that of the un-obscured ones
(in the luminosity range
,
around
,
where most of the CIRB is produced), their contributions to the
CIRB at 15
m are very similar. The main reason is that type-2
AGN have a strong k-correction imposed by the mid-IR SED. Moreover, the
effect is increased by a slightly lower evolution rate than
type-1 AGN, and a significant decline of the faint space density at higher z.
The total estimated contribution of AGN represents 4-10% of
the total light observed in the mid-IR. This fraction is about half of
the one ascribed to the AGN by M02. M02 study was limited to
type-1 AGN, and assumptions based on the unified model and the local
ratio of type-2 to type-1 (
4, Maiolino & Rieke 1995) were made
to derive their contribution. The smaller ratio of type-2 to type-1
found in our fields can explain the observed difference in our estimates.
Mid-IR studies based on IRAS and ISO observations have
indirectly estimated a contribution of AGN to the CIRB not larger than
5-10
(e.g. Malkan & Stecker 1998; Franceschini et al. 2001; Xu
et al. 2001, 2003). This is
the maximum room "left'' in their models by the strongly evolving
starburst population. The total contribution was in any case uncertain
since mid-IR selected type-2 AGN and starburst galaxies were treated
as a single population. Another estimate of this contribution comes
from the X-ray band (0.5-10 keV), which offers a better wavelength
regime where to select and identify obscured sources (unless the
sources are Compton-thick,
cm-2).
A cross-correlation of X-ray and IR sources detected by deep observations in
the Chandra Deep field North (CDFN; Brandt et al. 2001) and in
the Lockman Hole (Hasinger et al. 2001) allowed Fadda et al.
(2002) to estimate the maximum fraction of the CIRB produced by AGN.
This fraction is found to be of (
)%, a factor 2-4 higher than our
predictions.
On the basis of the hard X-ray determination of the LF and
semi-empirical SEDs (linking the X-ray to the Infrared),
Silva et al. (2004) have derived the contribution of AGN and their
host galaxy to the CIRB. For type-1 AGN, the agreement between
their results (
)
and
the ones presented here is very good.
There is instead a significant difference for type-2 sources. The predictions
from Silva et al. (2004,
)
are,
in the most favourable case (model "E''), at least a factor of 2 higher
than ours and closer to the numbers provided by Fadda et al. (2002).
The higher efficiency of the hard X-ray observations to select obscured AGN
can explain the discrepancy between our results and the ones presented by
Fadda et al. (2002) and Silva et al. (2004).
The conclusion drawn from the comparison with the above mentioned studies is that, as discussed in Sect. 3.4, it is likely that a significant fraction of type-2 AGN is hidden within the rest of the mid-IR selected population, the normal and starburst galaxies.
The Spitzer space telescope is currently performing several deep mid- and
far-infrared observations in selected areas of the sky. Following the results
presented in this paper we have estimated the expected number of AGN sources as
a function of the flux in the Spitzer mid-IR band. The derived integral
counts for the MIPS instrument at 24m are shown in Fig. 10. The
results are given in three panels that correspond to three different
combinations of type-1 and type-2 models (Table 2). Our estimates are compared
to the total contribution of AGN from the models of Xu et al. (2003) and
Silva et al. (2004). In the case of the Silva et al. (2004)
model the individual contributions from type-1 and type-2 AGN are also shown.
Best fit solutions with a redshift dependence on the faint slope are plotted in
the left panel. The central panel presents the expectations assuming the
best fits without any evolution for the faint slope of the LF. Finally, the
combination of type-1 and type-2 models that better fits the expectations from
Silva et al. (2004) is given in the right panel.
At a 24m flux of 0.01 mJy the total AGN counts given by our
best fit solutions underestimate the predictions by Silva et al.
(2004) and Xu et al. (2003) by a factor of
2-3
(Fig. 10, left). With these models we predict to find
1200
+420-300 type-1 and
1000
+350-250 type-2
optically classified AGN per sq. degree down to a Spitzer flux limit of
mJy.
If compared to the individual contributions of type-1 and type-2 AGN
given by the Silva et al. (2004) model, we note that the large
disagreement is mainly due to the low number of type-2 AGN expected in
our models (a factor
5 lower) and caused by the rapid flattening
with z of the faint LF slope. The large effect of the LF faint slope
decline in the counts is evident if compared to the PLE models
predictions plotted in the central panel. The PLE models
overestimate the 24
m counts by both Xu et al. (2003)
and Silva et al. (2004) below 0.06 mJy. A combination of the model
"B'' (variable LF faint slope for type-1 AGN) and model "E'' (fixed
faint slope model for type-2 AGN) produces the best approximation to
the counts derived by the Silva et al. (2004) model based on the AGN
hard X-ray LF (Fig. 10, right). If this is the case, then
1200
type-1 and
5600 type-2 AGN persq. degree are expected brighter
than 0.01 mJy at 24
m.
We want to note here that: i) although the expected Spitzer/24 m
integral counts derived by our different models differ by factors as large as
6-10, they are very similar down to the flux limits of the ELAIS-South
Surveys (shaded area in Fig. 10), responsible for the majority of the sources
observed at high redshift in our sample; ii) even if some of our models produce
counts comparable to the ones derived from X-ray LFs at
mJy (Fig. 10, central and right panels), they
are always lower at brighter fluxes. This second point explains the observed
difference (by a factor of
3) between our models and Silva et al.
(2004) in the contribution of AGN to the CIRB.
Combining ISO/15m observations in ELAIS fields, HDF-N, HDF-S and
the CFRS with the local IR population detected by IRAS at 12
m, we
have derived the evolution for the mid-IR selected and optically classified
AGN. While a similar study had been done for QSOs+Seyfert-1 sources
(Matute et al. 2002), we have presented here for the first time the
rate of evolution shown by obscured, type-2 AGN. Our results are:
Acknowledgements
The authors are grateful to the referee for helpful comments. This paper is based on observations collected at the European Southern Observatory, Chile (ESO No. 57.A-0752, 58.B-0511, 59.B-0423, 61.B-0146, 62.P-0457, 67.A-0092(A), 68.A-0259(A), 69.A-0538(A) and 70.A-0362(A). This research has been partially supported by ASI, INAF and MIUR grants. I.M. acknowledges a Ph.D. grant from CNAA/INAF.