Astronomy & Astrophysics manuscript no. ABongiorno c© ESO 2018
October 27, 2018
The VVDS type–1 AGN sample: The faint end of the luminosity
function
A. Bongiorno1, G. Zamorani2, I. Gavignaud3, B. Marano1, S. Paltani4,5, G. Mathez6, J.P. Picat6, M. Cirasuolo7, F.
Lamareille2,6, D. Bottini8, B. Garilli8, V. Le Brun9, O. Le Fèvre9, D. Maccagni8, R. Scaramella10,11, M. Scodeggio8, L.
Tresse9, G. Vettolani10, A. Zanichelli10, C. Adami9, S. Arnouts9, S. Bardelli2, M. Bolzonella2, A. Cappi2, S.
Charlot12,13, P. Ciliegi2, T. Contini6, S. Foucaud14, P. Franzetti8, L. Guzzo15, O. Ilbert16, A. Iovino15, H.J.
McCracken13,17, C. Marinoni18, A. Mazure9, B. Meneux8,15, R. Merighi2, R. Pellò6, A. Pollo9,19, L. Pozzetti2, M.
Radovich20, E. Zucca2, E. Hatziminaoglou21 , M. Polletta22, M. Bondi10, J. Brinchmann23, O. Cucciati15,24, S. de la
Torre9, L. Gregorini25, Y. Mellier13,17, P. Merluzzi20, S. Temporin15, D. Vergani8, and C.J. Walcher9
(Affiliations can be found after the references)
Received; accepted
Abstract
In a previous paper (Gavignaud et al. 2006), we presented the type–1 Active Galactic Nuclei (AGN) sample obtained from the first epoch data
of the VIMOS-VLT Deep Survey (VVDS). The sample consists of 130 faint, broad-line AGN with redshift up to z = 5 and 17.5 < IAB < 24.0,
selected on the basis of their spectra.
In this paper we present the measurement of the Optical Luminosity Function up to z = 3.6 derived from this sample, we compare our results with
previous results from brighter samples both at low and at high redshift.
Our data, more than one magnitude fainter than previous optical surveys, allow us to constrain the faint part of the luminosity function up to high
redshift.
By combining our faint VVDS sample with the large sample of bright AGN extracted from the SDSS DR3 (Richards et al., 2006b), we find that the
model which better represents the combined luminosity functions, over a wide range of redshift and luminosity, is a luminosity dependent density
evolution (LDDE) model, similar to those derived from the major X-surveys. Such a parameterization allows the redshift of the AGN space density
peak to change as a function of luminosity and explains the excess of faint AGN that we find at 1.0 < z < 1.5. On the basis of this model we find,
for the first time from the analysis of optically selected samples, that the peak of the AGN space density shifts significantly towards lower redshift
going to lower luminosity objects. This result, already found in a number of X-ray selected samples of AGN, is consistent with a scenario of “AGN
cosmic downsizing”, in which the density of more luminous AGN, possibly associated to more massive black holes, peaks earlier in the history of
the Universe, than that of low luminosity ones.
Key words. surveys-galaxies: high-redshift - AGN: luminosity function
1. Introduction
Active Galactic Nuclei (AGN) are relatively rare objects that ex-
hibit some of the most extreme physical conditions and activity
known in the universe.
A useful way to statistically describe the AGN activity along
the cosmic time is through the study of their luminosity func-
tion, whose shape, normalization and evolution can be used to
derive constraints on models of cosmological evolution of black
holes (BH). At z.2.5, the luminosity function of optically se-
lected type–1 AGN has been well studied since many years
(Boyle et al., 1988; Hewett et al., 1991; Pei, 1995; Boyle et al.,
2000; Croom et al., 2004). It is usually described as a double
power law, characterized by the evolutionary parameters L∗(z)
and Φ∗(z), which allow to distinguish between simple evolution-
ary models such as Pure Luminosity Evolution (PLE) and Pure
Density Evolution (PDE). Although the PLE and PDE mod-
els should be mainly considered as mathematical descriptions
of the evolution of the luminosity function, two different phys-
ical interpretations can be associated to them: either a small
Send offprint requests to: Angela Bongiorno, e-mail:
angela.bongiorno@oabo.inaf.it
fraction of bright galaxies harbor AGN, and the luminosities of
these sources change systematically with time (‘luminosity evo-
lution’), or all bright galaxies harbor AGN, but at any given time
most of them are in ‘inactive’ states. In the latter case, the frac-
tion of galaxies with AGN in an ‘active’ state changes with time
(‘density evolution’). Up to now, the PLE model is the preferred
description for the evolution of optically selected QSOs, at least
at low redshift (z < 2).
Works on high redshift type–1 AGN samples (Warren et al.,
1994; Kennefick et al., 1995; Schmidt et al., 1995; Fan et al.,
2001; Wolf et al., 2003; Hunt et al., 2004) have shown that the
number density of QSOs declines rapidly from z ∼ 3 to z ∼ 5.
Since the size of complete and well studied samples of QSOs
at high redshift is still relatively small, the rate of this decline
and the shape of the high redshift luminosity function is not yet
as well constrained as at low redshift. For example, Fan et al.
(2001), studying a sample of 39 luminous high redshift QSOs at
3.6 < z < 5.0, selected from the commissioning data of the Sloan
Digital Sky Survey (SDSS), found that the slope of the bright end
of the QSO luminosity function evolves with redshift, becoming
flatter at high redshift, and that the QSO evolution from z = 2
to z = 5 cannot be described as a pure luminosity evolution. A
similar result on the flattening at high redshift of the slope of
http://arxiv.org/abs/0704.1660v1
2 Bongiorno, A. et al.: The VVDS type–1 AGN sample: The faint end of the luminosity function
the luminosity function for luminous QSOs has been recently
obtained by Richards et al. (2006b) from the analysis of a much
larger sample of SDSS QSOs (but see Fontanot et al. (2007) for
different conclusions drawn on the basis of combined analysis of
GOODS and SDSS QSOs).
At the same time, a growing number of observations at differ-
ent redshifts, in radio, optical and soft and hard X-ray bands, are
suggesting that also the faint end slope evolves, becoming flat-
ter at high redshift (Page et al., 1997; Miyaji et al., 2000, 2001;
La Franca et al., 2002; Cowie et al., 2003; Ueda et al., 2003;
Fiore et al., 2003; Hunt et al., 2004; Cirasuolo et al., 2005;
Hasinger et al., 2005). This evolution, now dubbed as “AGN cos-
mic downsizing” is described either as a direct evolution in the
faint end slope or as “luminosity dependent density evolution”
(LDDE), and it has been the subject of many speculations since
it implies that the space density of low luminosity AGNs peaks
at lower redshift than that of bright ones.
It has been observed that, in addition to the well known
local scale relations between the black hole (BH) masses and
the properties of their host galaxies (Kormendy & Richstone,
1995; Magorrian et al., 1998; Ferrarese & Merritt, 2000), also
the galaxy spheroid population follows a similar pattern of “cos-
mic downsizing” (Cimatti et al., 2006). Various models have
been proposed to explain this common evolutionary trend in
AGN and spheroid galaxies. The majority of them propose that
the feedback from the black hole growth plays a key role in
determining the BH-host galaxy relations (Silk & Rees, 1998;
Di Matteo et al., 2005) and the co-evolution of black holes
and their host galaxies. Indeed, AGN feedback can shut down
the growth of the most massive systems steepening the bright
end slope (Scannapieco & Oh, 2004), while the feedback-driven
QSO decay determines the shape of the faint end of the QSO LF
(Hopkins et al., 2006).
This evolutionary trend has not been clearly seen yet with
optically selected type–1 AGN samples. By combining results
from low and high redshifts, it is clear from the studies of op-
tically selected samples that the cosmic QSO evolution shows a
strong increase of the activity from z ∼ 0 out to z ∼ 2, reaches a
maximum around z ≃ 2 − 3 and then declines, but the shape of
the turnover and the redshift evolution of the peak in activity as
a function of luminosity is still unclear.
Most of the optically selected type–1 AGN samples stud-
ied so far are obtained through various color selections of
candidates, followed by spectroscopic confirmation (e.g. 2dF,
Croom et al. 2004 and SDSS, Richards et al. 2002), or grism and
slitless spectroscopic surveys. These samples are expected to be
highly complete, at least for luminous type–1 AGN, at either
z ≤ 2.2 or z ≥ 3.6, where type–1 AGN show conspicuous colors
in broad band color searches, but less complete in the redshift
range 2.2 ≤ z ≤ 3.6 (Richards et al. 2002).
An improvement in the multi-color selection in optical bands
is through the simultaneous use of many broad and medium band
filters as in the COMBO-17 survey (Wolf et al., 2003). This sur-
vey is the only optical survey so far which, in addition to cov-
ering a redshift range large enough to see the peak of AGN ac-
tivity, is also deep enough to sample up to high redshift type–1
AGN with luminosity below the break in the luminosity func-
tion. However, only photometric redshifts are available for this
sample and, because of their selection criteria, it is incomplete
for objects with a small ratio between the nuclear flux and the
total host galaxy flux and for AGN with anomalous colors, such
as, for example, the broad absorption line (BAL) QSOs , which
have on average redder colors and account for ∼ 10 - 15 % of the
overall AGN population (Hewett & Foltz, 2003).
The VIMOS-VLT Deep Survey (Le Fèvre et al., 2005) is a
spectroscopic survey in which the target selection is purely flux
limited (in the I-band), with no additional selection criterion.
This allows the selection of a spectroscopic type–1 AGN sample
free of color and/or morphological biases in the redshift range
z > 1. An obvious advantage of such a selection is the possi-
bility to test the completeness of the most current surveys (see
Gavignaud et al., 2006, Paper I), based on morphological and/or
color pre-selection, and to study the evolution of type–1 AGN
activity in a large redshift range.
In this paper we use the type-1 AGN sample selected from
the VVDS to derive the luminosity function in the redshift range
1 < z < 3.6. The VVDS type–1 AGN sample is more than one
magnitude deeper than any previous optically selected sample
and allow thus to explore the faint part of the luminosity func-
tion. Moreover, by combining this LF with measurement of the
LF in much larger, but very shallow, surveys, we find an analyt-
ical form to dercribe, in a large luminosity range, the evolution
of type-1 AGN in the redshift range 0< z <4. The paper is or-
ganized as follows: in Section 2 and 3 we describe the sample
and its color properties. In Section 4 we present the method used
to derive the luminosity function, while in Section 5 we com-
pare it with previous works both at low and high redshifts. The
bolometric LF and the comparison with the results derived from
samples selected in different bands (from X-ray to IR) is then
presented in Section 6. The derived LF fitting models are pre-
sented in Section 7 while the AGN activity as a function of red-
shift is shown in Section 8. Finally in section 9 we summarize
our results. Throughout this paper, unless stated otherwise, we
assume a cosmology with Ωm = 0.3, ΩΛ = 0.7 and H0 = 70 km
s−1 Mpc−1.
2. The sample
Our AGN sample is extracted from the first epoch data of the
VIMOS-VLT Deep Survey, performed in 2002 (Le Fèvre et al.,
2005).
The VVDS is a spectroscopic survey designed to measure
about 150,000 redshifts of galaxies, in the redshift range 0 < z <
5, selected, nearly randomly, from an imaging survey (which
consists of observations in U, B, V, R and I bands and, in a
small area, also K-band) designed for this purpose. Full de-
tails about VIMOS photometry can be found in Le Fèvre et al.
(2004a), McCracken et al. (2003), Radovich et al. (2004) for
the U-band and Iovino et al. (2005) for the K-band. In this
work we will as well use the Galex UV-catalog (Arnouts et al.,
2005; Schiminovich et al., 2005), the u∗,g′,r′,i′,z′ photometry
obtained in the frame of the Canada-France-Hawaii Legacy
Survey (CFHTLS)1, UKIDSS (Lawrence et al., 2006), and the
Spitzer Wide-area InfraRed Extragalactic survey (SWIRE)
(Lonsdale et al., 2003, 2004). The spectroscopic VVDS survey
consists of a deep and a wide survey and it is based on a sim-
ple selection function. The sample is selected only on the basis
of the I band magnitude: 17.5 < IAB < 22.5 for the wide and
17.5 < IAB < 24.0 for the deep sample. For a detailed descrip-
tion of the spectroscopic survey strategy and the first epoch data
see Le Fèvre et al. (2005).
Our sample consists of 130 AGN with 0 < z < 5, selected
in 3 VVDS fields (0226-04, 1003+01 and 2217-00) and in the
Chandra Deep Field South (CDFS, Le Fèvre et al., 2004b). All
of them are selected as AGN only on the basis of their spectra,
1 www.cfht.hawaii.edu/Science/CFHLS
Bongiorno, A. et al.: The VVDS type–1 AGN sample: The faint end of the luminosity function 3
Figure 1. Distribution of absolute magnitudes and redshifts of
the total AGN sample. Open circles are the objects with am-
biguous redshift, shown at all their possible z values. The dotted
and dashed lines represent the magnitude limits of the samples:
IAB < 22.5 for the wide sample and IAB < 24.0 for the deep
sample.
irrespective of their morphological or color properties. In partic-
ular, we selected them on the basis of the presence of at least one
broad emission line. We discovered 74 of them in the deep fields
(62 in the 02h field and 12 in the CDFS) and 56 in the wide fields
(18 in the 10h field and 38 in the 22h field). This represents an
unprecedented complete sample of faint AGN, free of morpho-
logical or color selection bias. The spectroscopic area covered
by the First Epoch Data is 0.62 deg2 in the deep fields (02h field
and CDFS) and 1.1 deg2 in the wide fields (10h and 22h fields).
To each object we have assigned a value for the spectro-
scopic redshift and a spectroscopic quality flag which quantifies
our confidence level in that given redshift. As of today, we have
115 AGN with secure redshift, and 15 AGN with two or more
possible values for the redshift. For these objects, we have two
or more possible redshifts because only one broad emission line,
with no other narrow lines and/or additional features, is detected
in the spectral wavelength range adopted in the VVDS (5500 -
9500 Å) (see Figure 1 in Paper I). For all of them, however, a
best solution is proposed. In the original VVDS AGN sample,
the number of AGN with this redshift degeneracy was 42. To
solve this problem, we have first looked for the objects already
observed in other spectroscopic surveys in the same areas, solv-
ing the redshift for 3 of them. For the remaining objetcs, we
performed a spectroscopic follow-up with FORS1 on the VLT
Unit Telescope 2 (UT2). With these additional observations we
found a secure redshift for 24 of our AGN with ambiguous red-
shift determination and, moreover, we found that our proposed
best solution was the correct one in ∼ 80% of the cases. On the
basis of this result, we decided to use, in the following analysis,
our best estimate of the redshift for the small remaining fraction
of AGN with ambiguous redshift determination (15 AGN).
In Figure 1 we show the absolute B-magnitude and the
redshift distributions of the sample. As shown in this Figure,
our sample spans a large range of luminosities and consists of
both Seyfert galaxies (MB >-23; ∼59%) and QSOs (MB <-23;
∼41%). A more detailed and exhaustive description of the prop-
Figure 2. Composite spectra derived for our AGN with se-
cure redshift in the 02h field, divided in a “bright” (19 objects
at M1450 <-22.15, dotted curve) and a “faint” (31 objects at
M1450 >-22.15, dashed curve) sample. We consider here only
AGN with z > 1 (i.e. the AGN used in to compute the lumi-
nosity function). The SDSS composite spectrum is shown with
a solid line for comparison.
erties of the AGN sample is given in Paper I (Gavignaud et al.,
2006) and the complete list of BLAGN in our wide and deep
samples is available as an electronic Table in Appendix of
Gavignaud et al. (2006).
3. Colors of BLAGNs
As already discussed in Paper I, the VVDS AGN sample shows,
on average, redder colors than those expected by comparing
them, for example, with the color track derived from the SDSS
composite spectrum (Vanden Berk et al., 2001). In Paper I we
proposed three possible explanations: (a) the contamination of
the host galaxy is reddening the observed colors of faint AGN;
(b) BLAGN are intrinsically redder when they are faint; (c) the
reddest colors are due to dust extinction. On the basis of the sta-
tistical properties of the sample, we concluded that hypothesis
(a) was likely to be the more correct, as expected from the faint
absolute magnitudes sampled by our survey, even if hypotheses
(b) and (c) could not be ruled out.
In Figure 2 we show the composite spectra derived from the
sample of AGN with secure redshift in the 02h field, divided
in a “bright” and a “faint” sample at the absolute magnitude
M1450 = −22.15. We consider here only AGN with z > 1, which
correspond to the AGN used in Section 4 to compute the lumi-
nosity function. The choice of the reference wavelength for the
absolute magnitude, λ = 1450 Å, is motivated by our photo-
metric coverage. In fact, for most of the objects it is possible
to interpolate M1450 directly from the observed magnitudes. In
the same plot we show also the SDSS composite spectrum (solid
curve) for comparison. Even if also the ”bright” VVDS compos-
ite (dotted curve) is somewhat redder than the SDSS one, it is
clear from this plot that the main differences occur for faintest
objects (dashed curve).
A similar result is shown for the same sample in the upper
panel of Figure 3, where we plot the spectral index α as a func-
tion of the AGN luminosity. The spectral index is derived here
by fitting a simple power law f (ν) = ν−α to our photometric data
points. This analysis has been performed only on the 02h deep
4 Bongiorno, A. et al.: The VVDS type–1 AGN sample: The faint end of the luminosity function
Figure 3. Upper Panel: Distribution of the spectral index α as
a function of M1450 for the same sample of AGN as in Figure
2. The spectral index is derived here by fitting a simple power
law f (ν) = ν−α to our photometric data points. Asterisks are
AGN morphologically classified as extended and the grey point
is a BAL AGN. Bottom Panels: Distribution of the spectral in-
dex α for the same sample of AGN. All the AGN in this sample
are shown in the first of the three panels, while the AGN in the
“bright” and “faint” sub–samples are shown in the second and
third panel, respectively. The dotted curve in the second panel
corresponds to the gaussian fit of the bright sub–sample and it is
reported also in the third panel to highlight the differences in the
α distributions of the two sub-samples.
sample, since for the wide sample we do not have enough photo-
metric coverage to reliably derive the spectral index. Most of the
AGN with α > 1 are fainter than M1450 = −22.15, showing that,
indeed, the faintest objects have on average redder colors than
the brightest ones. The outlier (the brightest object with large α,
i.e. very red colors, in the upper right corner of the plot) is a BAL
The three bottom panels of Figure 3 show the histograms of
the resulting power law slopes for the same AGN sample. The
total sample is plotted in the first panel, while the bright and the
faint sub-samples are plotted in the second and third panels, re-
spectively. A Gaussian curve with < α >= 0.94 and dispersion
σ = 0.38 is a good representation for the distribution of about
80% (40/50) of the objects in the first panel. In addition, there
is a significant tail (∼ 20%) of redder AGN with slopes in the
range from 1.8 up to ∼ 3.0. The average slope of the total sample
(∼ 0.94) is redder than the fit to the SDSS composite (∼ 0.44).
Moreover, the distribution of α is shifted toward much larger val-
ues (redder continua) than the similar distribution in the SDSS
sample (Richards et al., 2003). For example, only 6% of the ob-
jects in the SDSS sample have α > 1.0, while this percentage is
57% in our sample.
The differences with respect to the SDSS sample can be
partly due to the differences in absolute magnitude of the two
samples (Mi <-22.0 for the SDSS sample (Schneider et al.,
2003) and MB <-20.0 for the VVDS sample). In fact, if we con-
sider the VVDS “bright” sub-sample, the average spectral index
< α > becomes ∼ 0.71, which is closer to the SDSS value (even
if it is still somewhat redder), and only two objects (∼8% of the
sample) show values not consistent with a gaussian distribution
with σ ∼0.32. Moreover, only 30% of this sample have α > 1.0.
Most of the bright SDSS AGNs with α > 1 are interpreted by
Richards et al. (2003) to be dust-reddened, although a fraction
of them is likely to be due to intrinsically red AGN (Hall et al.,
2006). At fainter magnitude one would expect both a larger frac-
tion of dust-reddened objects (in analogy with indications from
the X-ray data (Brandt et al., 2000; Mushotzky et al., 2000) and
a more significant contamination from the host galaxy.
We have tested these possibilities by examining the global
Spectral Energy Distribution (SED) of each object and fitting
the observed fluxes fobs with a combination of AGN and galaxy
emission, allowing also for the possibility of extinction of the
AGN flux. Thanks to the multi-wavelength coverage in the deep
field in which we have, in addition to VVDS bands, also data
from GALEX, CFHTLS, UKIDSS and SWIRE, we can study
the spectral energy distribution of the single objects. In particu-
lar, we assume that:
fobs = c1 fAGN · 10
−0.4·Aλ + c2 fGAL (1)
and, using a library of galaxy and AGN templates, we find the
best parameters c1, c2 and EB−V for each object. We used the
AGN SED derived by Richards et al. (2006a) with an SMC-
like dust-reddening law (Prevot et al., 1984) with the form
Aλ/EB−V = 1.39λ
µm , and a library of galaxies template by
Bruzual & Charlot (2003).
We found that for ∼37% of the objects, the observed flux
is fitted by a typical AGN power law (pure AGN), while 44%
of the sources require the presence of a contribution from the
host galaxy to reproduce the observed flux. Only 4% of the ob-
jects are fitted by pure AGN + dust, while the remaining 15%
of objects require instead both contributions (host galaxy con-
tamination and presence of dust). As expected, if we restrict the
analysis to the bright sample, the percentage of pure AGN in-
creases to 68%, with the rest of the objects requiring either some
contribution from the host galaxy (∼21%) or the presence of dust
oscuration (∼11%).
In Figure 4 we show 4 examples of the resulting fits: (i) pure
AGN; (ii) dust-extincted AGN; (iii) AGN contaminated by the
host galaxy; (iv) dust-extincted AGN and contaminated by the
host galaxy. The dotted line corresponds to the AGN template
before applying the extinction law, while the solid blue line cor-
responds to the same template, but extincted for the given EB−V ;
the red line corresponds to the galaxy template and, finally, the
black line is the resulting best fit to the SED. The host galaxy
contaminations will be taken into account in the computation of
the AGN absolute magnitude for the luminosity function.
Bongiorno, A. et al.: The VVDS type–1 AGN sample: The faint end of the luminosity function 5
Figure 4. Four examples of different decompositions of the ob-
served SEDs of our objects. Since for λ < 1216 Å, corresponding
to the Lyα line, the observed flux is expected to decrease because
of intervening absorption, all the photometric data at λ <1216 Å
are not considered in the fitting. The only requested constraint is
that they lie below the fit. The four fits shown in this Figure cor-
respond, from top to bottom, to pure-AGN, dust-extincted AGN,
AGN and host galaxy, dust-extincted AGN and host galaxy. The
dotted line corresponds to the AGN template before applying
the extinction law, while the solid blue line corresponds to the
same template, but extincted for the given EB−V . The red line
(third and fourth panel) corresponds to the galaxy template and,
finally, the black line is the resulting best fit to the SED. Arrows
correspond to 5σ upper limits in case of non detection in the IR.
4. Luminosity function
4.1. Definition of the redshift range
For the study of the LF we decided to exclude AGN with z ≤
1.0. This choice is due to the fact that for 0.5 ≤ z ≤ 1.0 the
only visible broad line in the VVDS spectra is Hβ (see Figure
1 of Paper I). This means that all objects with narrow or almost
narrow Hβ and broad Hα (type 1.8, 1.9 AGN; see Osterbrock
1981) would not be included in our sample, because we include
in the AGN sample all the objects with at least one visible broad
line. Since at low luminosities the number of intermediate type
AGN is not negligible, this redshift bin is likely to be under-
populated and the results would not be meaningful.
At z < 0.5, in principle we have less problems, because also
Hα is within the wavelength range of the VVDS spectra, but,
since at this low redshift, our sampled volume is relatively small
and QSOs rare, only 3 objects have secure redshifts in this red-
shift bin in the current sample. For these reasons, our luminosity
function has been computed only for z > 1.0 AGN. As already
mentioned in Section 2, the small fraction of objects with an am-
biguous redshift determination have been included in the compu-
tation of the luminosity function assuming that our best estimate
of their redshift is correct.
The resulting sample used in the computation of the LF consists
thus of 121 objects at 1< z <4.
4.2. Incompleteness function
Our incompleteness function is made up of two terms linked, re-
spectively, to the selection algorithm and to the spectral analysis:
the Target Sampling Rate (TSR) and the Spectroscopic Success
Rate (SSR) defined following Ilbert et al. (2005).
The Target Sampling Rate, namely the ratio between the ob-
served sources and the total number of objects in the photometric
catalog, quantifies the incompleteness due to the adopted spec-
troscopic selection criterion. The TSR is similar in the wide and
deep sample and runs from 20% to 30%.
The Spectroscopic Success Rate is the probability of a spec-
troscopically targeted object to be securely identified. It is a com-
plex function of the BLAGN redshift, apparent magnitude and
intrinsic spectral energy distribution and it has been estimated
by simulating 20 Vimos pointings, for a total of 2745 spectra.
Full details on TSR and SSR can be found in Paper I
(Gavignaud et al., 2006). We account for them by computing for
each object the associated weights wtsr = 1/TS R and wssr =
1/S S R; the total weighted contribution of each object to the
luminosity function is then the product of the derived weights
(wtsr × wssr).
4.3. Estimate of the absolute magnitude
We derived the absolute magnitude in the reference band from
the apparent magnitude in the observed band as:
M = mobs − 5log10(dl(z)) − 25 − k (2)
where M is computed in the band in which we want to compute
the luminosity function, mobs is the observed band from which
we want to calculate it, dl(z) is the luminosity distance expressed
in Mpc and k is the k-correction in the reference band. To make
easier the comparison with previous results in the literature, we
computed the luminosity function in the B-band.
To minimize the uncertainties in the adopted k-correction,
mobs for each object should be chosen in the observed band
which is sampling the rest-wavelength closer to the band in
which the luminosity function is computed. For our sample,
which consists only of z > 1 objects, the best bands to use to
compute the B-band absolute magnitudes should be respectively
the I-, J- and K-bands going to higher redshift. Since however,
the only observed band available for the entire sample (deep and
wide), is the I-band, we decided to use it for all objects to com-
pute the B-band magnitudes. This means that for z ∼
> 2, we
introduce an uncertainty in the absolute magnitudes due to the
k-correction. We computed the absolute magnitude considering
the template derived from the SDSS sample (Vanden Berk et al.,
2001).
As discussed in Section 3, the VVDS AGN sample shows
redder colors than those typical of normal, more luminous AGN
and this can be due to the combination of the host galaxy contri-
bution and the presence of dust. Since, in this redshift range, the
fractional contribution from the host galaxies is expected to be
more significant in the I-band than in bluer bands, the luminos-
ity derived using the I-band observed magnitude could, in some
cases, be somewhat overestimated due to the contribution of the
host galaxy component.
6 Bongiorno, A. et al.: The VVDS type–1 AGN sample: The faint end of the luminosity function
Figure 5. Real (full circles; AGN in the deep sample) and simu-
lated (open triangles; AGN in the wide sample) B-band absolute
magnitude differences as a function of MB(TOT) (upper panel)
and redshift (bottom panel). MB(TOT) is the absolute magnitude
computed considering the total observed flux, while MB(AGN)
is the absolute magnitude computed after subtracting the host-
galaxy contribution.
We estimated the possible impact of this effect on our re-
sults in the following way. From the results of the analysis of the
SED of the single objects in the deep sample (see Section 3) we
computed for each object the difference mI(TOT ) − mI(AGN)
and, consequently, MB(TOT ) − MB(AGN). This could allow us
to derive the LF using directly the derived MB(AGN), resolv-
ing the possible bias introduced by the host galaxy contami-
nation. These differences are shown as full circles in Figure
5 as a function of absolute magnitude (upper panel) and red-
shift (lower panel). For most of the objects the resulting dif-
ferences between the total and the AGN magnitudes are small
(∆M≤0.2). However, for a not negligible fraction of the faintest
objects (MB ≥-22.5, z ≤2.0) these differences can be signifi-
cant (up to ∼1 mag). For the wide sample, for which the more
restricted photometric coverage does not allow a detailed SED
analysis and decomposition, we used simulated differences to
derive the MB(AGN). These simulated differences have been de-
rived through a Monte Carlo simulation on the basis of the bi-
variate distribution ∆M(M,z) estimated from the objects in the
deep sample. ∆M(M,z) takes into account the probability distri-
bution of ∆M as a function of MB and z, between 0 and the solid
line in Figure 5 derived as the envelope suggested by the black
dots. The resulting simulated differences for the objects in the
wide sample are shown as open triangles in the two panels of
Figure 5.
The AGN magnitudes and the limiting magnitudes of the
samples have been corrected also for galactic extinction on the
basis of the mean extinction values E(B−V) in each field derived
from Schlegel et al. (1998). Only for the 22h field, where the ex-
tinction is highly variable across the field, we used the extinction
on the basis of the position of individual objects. The resulting
corrections in the I-band magnitude are AI ≃ 0.027 in the 2h and
10h fields and AI = 0.0089 in the CDFS field, while the average
value in the 22h field is AI = 0.065. These corrections have been
applied also to the limiting magnitude of each field.
4.4. The 1/Vmax estimator
We derived the binned representation of the luminosity function
using the usual 1/Vmax estimator (Schmidt, 1968), which gives
the space density contribution of individual objects. The lumi-
nosity function, for each redshift bin (z − ∆z/2 ; z + ∆z/2), is
then computed as:
Φ(M) =
M+∆M/2
M−∆M/2
wtsri w
Vmax,i
where Vmax,i is the comoving volume within which the i
th ob-
ject would still be included in the sample. wtsri and w
i are re-
spectively the inverse of the TSR and of the SSR, associated to
the ith object. The statistical uncertainty on Φ(M) is given by
Marshall et al. (1983):
√M+∆M/2
M−∆M/2
(wtsri w
V2max,i
We combined our samples at different depths using the
method proposed by Avni & Bahcall (1980). In this method it
is assumed that each object, characterized by an observed red-
shift zi and intrinsic luminosity Li, could have been found in any
of the survey areas for which its observed magnitude is brighter
than the corresponding flux limit. This means that, for our total
sample, we consider an area of:
Ωtot(m) = Ωdeep+Ωwide = 1.72 deg
2 for 17.5 < IAB < 22.5
Ωtot(m) = Ωdeep = 0.62 deg
2 for 22.5 < IAB < 24.0
The resulting luminosity functions in different redshift
ranges are plotted in Figure 6 and 7, where all bins which contain
at least one object are plotted. The LF values, together with their
1σ errors and the numbers of objects in each absolute magnitude
bin are presented in Table 1. The values reported in Table 1 and
plotted in Figures 6 and 7 are not corrected for the host galaxy
contribution. We have in fact a posteriori verified that, even if the
differences between the total absolute magnitudes and the mag-
nitudes corrected for the host galaxy contribution (see Section
4.3) can be significant for a fraction of the faintest objects, the
resulting luminosity functions computed by using these two sets
of absolute magnitudes are not significantly different. For this
reason and for a more direct comparison with previous works,
the results on the luminosity function presented in the next sec-
tion are those obtained using the total magnitudes.
5. Comparison with the results from other optical
surveys
We derived the luminosity function in the redshift range 1.0<
z <3.6 and we compared it with the results from other surveys at
both low and high redshift.
5.1. The low redshift luminosity function
In Figure 6 we present our luminosity function up to z = 2.1.
The Figure show our LF data points (full circles) derived in two
redshift bins: 1.0 < z < 1.55 and 1.55 < z < 2.1 compared with
the LF fits derived from the 2dF QSO sample by Croom et al.
(2004) and by Boyle et al. (2000), with the COMBO-17 sample
Bongiorno, A. et al.: The VVDS type–1 AGN sample: The faint end of the luminosity function 7
Figure 6. Our rest-frame B-band luminosity function, derived in the redshift bins 1.0 < z < 1.55 and 1.55 < z < 2.1, compared with
the 2dFQRS (Croom et al., 2004; Boyle et al., 2000), COMBO-17 data (Wolf et al., 2003) and with the 2dF-SDSS (2SLAQ) data
(Richards et al., 2005). The curves in the Figure show the PLE fit models derived by these authors. The thick parts of the curves
correspond to the luminosity range covered by the data in each sample, while the thin parts are extrapolations based on the best fit
parameters of the models.
by Wolf et al. (2003), and with the 2dF-SDSS (2SLAQ) LF fit
by Richards et al. (2005). In each panel the curves, computed
for the average z of the redshift range, correspond to a double
power law luminosity function in which the evolution with red-
shift is characterized by a pure luminosity evolution modeled as
M∗b(z) = M
b(0)−2.5(k1z+ k2z
2). Moreover, the thick parts of the
curves show the luminosity range covered by the data in each of
the comparison samples, while the thin parts are extrapolation
based on the the best fit parameters of the models.
We start considering the comparison with the 2dF and the
COMBO-17 LF fits. As shown in Figure 6, our bright LF data
points connect rather smoothly to the faint part of the 2dF data.
However, our sample is more than two magnitudes deeper than
the 2dF sample. For this reason, a comparison at low luminosity
is possible only with the extrapolations of the LF fit. At z > 1.55,
while the Boyle’s model fits well our faint LF data points, the
Croom’s extrapolation, being very flat, tends to underestimate
our low luminosity data points. At z < 1.55 the comparison is
worse: as in the higher redshift bin, the Boyle’s model fits our
data better than the Croom’s one but, in this redshift bin, our
data points show an excess at low luminosity also with respect to
Boyle’s fit. This trend is similar to what shown also by the com-
parison with the fit of the COMBO-17 data which, differently
from the 2dF data, have a low luminosity limit closer to ours: at
z > 1.55 the agreement is very good, but in the first redshift bin
our data show again an excess at low luminosity. This excess is
likely due to the fact that, because of its selection criteria, the
COMBO-17 sample is expected to be significantly incomplete
for objects in which the ratio between the nuclear flux and the
total host galaxy flux is small. Finally, we compare our data with
the 2SLAQ fits derived by Richards et al. (2005). The 2SLAQ
data are derived from a sample of AGN selected from the SDSS,
at 18.0 < g < 21.85 and z < 3, and observed with the 2-degree
field instrument. Similarly to the 2dF sample, also for this sam-
ple the LF is derived only for z < 2.1 and MB < −22.5. The plot-
ted dot-dashed curve corresponds to a PLE model in which they
fixed most of the parameters of the model at the values found
by Croom et al. (2004), leaving to vary only the faint end slope
and the normalization constant Φ∗. In this case, the agreement
with our data points at z < 1.55 is very good also at low lu-
minosity. The faint end slope found in this case is β = −1.45,
which is similar to that found by Boyle et al. (2000) (β = −1.58)
and significantly steeper than that found by Croom et al. (2004)
(β = −1.09). At z > 1.55, the Richards et al. (2005) LF fit tends
to overestimate our data points at the faint end of the LF, which
suggest a flatter slope in this redshift bin.
The first conclusion from this comparison is that, at low red-
shift (i.e. z < 2.1), the data from our sample, which is ∼2 mag
fainter than the previous spectroscopically confirmed samples,
are not well fitted simultaneously in the two analyzed redshift
bins by the PLE models derived from the previous samples.
Qualitatively, the main reason for this appears to be the fact that
our data suggest a change in the faint end slope of the LF, which
appears to flatten with increasing redshift. This trend, already
highlighted by previous X-ray surveys (La Franca et al., 2002;
Ueda et al., 2003; Fiore et al., 2003) suggests that a simple PLE
parameterization may not be a good representation of the evolu-
tion of the AGN luminosity function over a wide range of red-
shift and luminosity. Different model fits will be discussed in
Section 7.
8 Bongiorno, A. et al.: The VVDS type–1 AGN sample: The faint end of the luminosity function
Figure 7. Our luminosity function, at 1450 Å rest-frame, in the
redshift range 2.1<z<3.6, compared with data from other high-
z samples (Hunt et al. (2004) at z = 3; Combo-17 data from
Wolf et al. (2003) at 2.4 < z < 3.6; data from Warren et al.
(1994) at 2.2 < z < 3.5 and the SDSS data from Fan et al.
(2001)). The SDSS data points at 3.6< z <3.9 have been
evolved to z=3 using the luminosity evolution of Pei (1995) as
in Hunt et al. (2004). The curves show some model fits in which
the thick parts of the curves correspond to the luminosity range
covered by the data samples, while the thin parts are model ex-
trapolation. For this plot, anΩm = 1,ΩΛ = 0, h = 0.5 cosmology
has been assumed for comparison with the previous works.
5.2. The high redshift luminosity function
The comparison of our LF data points for 2.1< z <3.6 (full
circles) with the results from other samples in similar redshift
ranges is shown in Figure 7. In this Figure an Ωm = 1, ΩΛ = 0,
h = 0.5 cosmology has been assumed for comparison with pre-
vious works, and the absolute magnitude has been computed at
1450 Å. As before, the thick parts of the curves show the lu-
minosity ranges covered by the various data samples, while the
thin parts are model extrapolations. In terms of number of ob-
jects, depth and covered area, the only sample comparable to
ours is the COMBO-17 sample (Wolf et al., 2003), which, in
this redshift range, consists of 60 AGN candidates over 0.78
square degree. At a similar depth, in terms of absolute mag-
nitude, we show also the data from the sample of Hunt et al.
(2004), which however consists of 11 AGN in the redshift range
< z > ±σz =3.03±0.35 (Steidel et al., 2002). Given the small
number of objects, the corresponding Hunt model fit was de-
rived including also the Warren data points (Warren et al., 1994).
Moreover, they assumed the Pei (1995) luminosity evolution
model, adopting the same values for L∗ and Φ∗, leaving free to
vary the two slopes, both at the faint and at the bright end of
the LF. For comparison we show also the original Pei model
fit derived from the empirical luminosity function estimated
by Hartwick & Schade (1990) and Warren et al. (1994). In the
same plot we show also the model fit derived from a sample of
∼100 z ∼ 3 (U-dropout) QSO candidates by Siana et al. (pri-
vate comunication; see also Siana et al. 2006). This sample has
been selected by using a simple optical/IR photometric selec-
tion at 19< r′ <22 and the model fit has been derived by fix-
ing the bright end slope at z=-2.85 as determined by SDSS data
(Richards et al., 2006b).
In general, the comparison of the VVDS data points with
those from the other surveys shown in Figure 7 shows a satis-
factory agreement in the region of overlapping magnitudes. The
best model fit which reproduce our LF data points at z ∼ 3 is the
Siana model with a faint end slope β = −1.45. It is interesting to
note that, in the faint part of the LF, our data points appear to be
higher with respect to the Hunt et al. (2004) fit and are instead
closer to the extrapolation of the original Pei model fit. This dif-
ference with the Hunt et al. (2004) fit is probably due to the fact
that, having only 11 AGN in their faint sample, their best fit to
the faint-end slope was poorly constrained.
6. The bolometric luminosity function
The comparison between the AGN LFs derived from samples
selected in different bands has been for a long time a critical
point in the studies of the AGN luminosity function. Recently,
Hopkins et al. (2007), combining a large number of LF measure-
ments obtained in different redshift ranges, observed wavelength
bands and luminosity intervals, derived the Bolometric QSO
Luminosity Function in the redshift range z = 0 - 6. For each
observational band, they derived appropriate bolometric correc-
tions, taking into account the variation with luminosity of both
the average absorption properties (e.g. the QSO column density
NH from X-ray data) and the average global spectral energy dis-
tributions. They show that, with these bolometric corrections, it
is possible to find a good agreement between results from all
different sets of data.
We applied to our LF data points the bolometric corrections
given by Eqs. (2) and (4) of Hopkins et al. (2007) for the B-band
and we derived the bolometric LF shown as black dots in Figure
8. The solid line represents the bolometric LF best fit model de-
rived by Hopkins et al. (2007) and the colored data points cor-
respond to different samples: green points are from optical LFs,
blue and red points are from soft-X and hard-X LFs, respec-
tively, and finally the cyan points are from the mid-IR LFs. All
these bolometric LFs data points have been derived following
the same procedure described in Hopkins et al. (2007).
Our data, which sample the faint part of the bolometric lu-
minosity function better than all previous optically selected sam-
ples, are in good agreement with all the other samples, selected
in different bands. Only in the last redshift bin, our data are quite
higher with respect to the samples selected in other wavelength
bands. The agreement remains however good with the COMBO-
17 sample which is the only optically selected sample plotted
here. This effect can be attributed to the fact that the conversions
used to compute the Bolometric LF, being derived expecially for
AGN at low redshifts, become less accurate at high redshift.
Our data show moreover good agreement also with the
model fit derived by Hopkins et al. (2007). By trying various an-
alytic fits to the bolometric luminosity function Hopkins et al.
(2007) concluded that neither pure luminosity nor pure density
evolution represent well all the data. An improved fit can in-
stead be obtained with a luminosity dependent density evolution
model (LDDE) or, even better, with a PLE model in which both
the bright- and the faint-end slopes evolve with redshift. Both
Bongiorno, A. et al.: The VVDS type–1 AGN sample: The faint end of the luminosity function 9
Figure 8. Bolometric luminosity function derived in three
redshift bins from our data (black dots), compared with
Hopkins et al. (2007) best-fit model and the data-sets used in
their work. The central redshift of each bin is indicated in each
panel. Here, we adopted the same color-code as in Hopkins et al.
(2007), but for more clarity we limited the number of samples
presented in the Figure. Red symbols correspond to hard X-ray
surveys (squares: Barger et al. 2005; circles: Ueda et al. 2003).
Blue to soft X-ray surveys (squares: Silverman et al. 2005; cir-
cles: Hasinger et al. 2005). Cyan to infra-red surveys (circles:
Brown et al. 2006; squares: Matute et al. 2006). For the optical
surveys we are showing here, with green circles, the data from
the COMBO-17 survey (Wolf et al., 2003), which is comparable
in depth to our sample.
these models can reproduce the observed flattening with redshift
of the faint end of the luminosity function.
7. Model fitting
In this Section we discuss the results of a number of different fits
to our data as a function of luminosity and redshift. For this pur-
pose, we computed the luminosity function in 5 redshift bins at
1.0 < z < 4.0 where the VVDS AGN sample consists of 121
objects. Since, in this redshift range, our data cover only the
faint part of the luminosity function, these fits have been per-
formed by combining our data with the LF data points from the
SDSS data release 3 (DR3) (Richards et al., 2006b) in the red-
shift range 0 < z < 4. The advantage of using the SDSS sample,
rather than, for example, the 2dF sample, is that the former sam-
ple, because of the way it is selected, probes the luminosity func-
tion to much higher redshifts. The SDSS sample contains more
than 15,000 spectroscopically confirmed AGN selected from an
effective area of 1622 sq.deg. Its limiting magnitude (i < 19.1 for
z < 3.0 and i < 20.2 for z > 3.0) is much brighter than the VVDS
and because of this it does not sample well the AGN in the faint
part of the luminosity function. For this reason, Richards et al.
(2006b) fitted the SDSS data using only a single power law,
which is meant to describe the luminosity function above the
break luminosity. Adding the VVDS data, which instead mainly
sample the faint end of the luminosity function, and analyzing
the two samples together, allows us to cover the entire luminosity
range in the common redshift range (1.0 < z < 4.0), also extend-
ing the analysis at z < 1.0 where only SDSS data are available.
The goodness of fit between the computed LF data points
and the various models is then determined by the χ2 test.
For all the analyzed models we have parameterized the lu-
minosity function as a double power law that, expressed in lumi-
nosity, is given by:
Φ(L, z) =
(L/L∗)−α + (L/L∗)−β
whereΦ∗L is the number of AGN per Mpc
3, L∗ is the characteris-
tic luminosity around which the slope of the luminosity function
is changing and α and β are the two power law indices. Equation
5 can be expressed in absolute magnitude 2 as:
Φ(M, z) =
100.4(α+1)(M−M∗) + 100.4(β+1)(M−M∗)
7.1. The PLE and PDE models
The first model that we tested is a Pure Luminosity Evolution
(PLE) with the dependence of the characteristic luminosity de-
scribed by a 2nd-order polynomial in redshift:
M∗(z) = M∗(0) − 2.5(k1z + k2z
2). (7)
Following the finding by Richards et al. (2006b) for the SDSS
sample, we have allowed a change (flattening with redshift) of
the bright end slope according to a linear evolution in redshift:
α(z) = α(0) + A z. The resulting best fit parameters are listed
in the first line of Table 2 and the resulting model fit is shown
as a green short dashed line in Figure 9. The bright end slope α
derived by our fit (αVVDS=-3.19 at z=2.45) is consistent with the
one found by Richards et al. (2006b) (αSDSS = -3.1).
This model, as shown in Figure 9, while reproduces well the
bright part of the LF in the entire redshift range, does not fit the
faint part of the LF at low redshift (1.0 < z < 1.5). This appears
to be due to the fact that, given the overall best fit normalization,
the derived faint end slope (β =-1.38) is too shallow to reproduce
the VVDS data in this redshift range.
Richards et al. (2005), working on a combined 2dF-SDSS
(2SLAQ) sample of AGN up to z = 2.1. found that, fixing
all of the parameters except β and the normalization, to those
of Croom et al. (2004), the resulting faint end slope is β =
−1.45 ± 0.03. This value would describe better our faint LF at
low redshift. This trend suggests a kind of combined luminosity
and density evolution not taken into account by the used model.
2 Φ∗M = Φ
∣ln10−0.4
3 in their parameterization A1=-0.4(α + 1) =0.84
10 Bongiorno, A. et al.: The VVDS type–1 AGN sample: The faint end of the luminosity function
For this reason, we attempted to fit the data also including a term
of density evolution in the form of:
M(z) = Φ
M(0) · 10
k1Dz+k2Dz
In this model the evolution of the LF is described by both
a term of luminosity evolution, which affects M∗, and a term of
density evolution, which allows for a change in the global nor-
malization Φ∗. The derived best fit parameters of this model are
listed in the second line of Table 2 and the model fit is shown
as a blue long dashed line in Figure 9. This model gives a better
χ2 with respect to the previous model, describing the entire sam-
ple better than a simple PLE (the reduced χ2 decreases from ∼
1.9 to ∼ 1.35). However, it still does not satisfactorily reproduce
the excess of faint objects in the redshift bin 1.0 < z < 1.5 and,
moreover, it underestimates the faint end of the LF in the last
redshift bin (3.0 < z < 4.0).
7.2. The LDDE model
Recently, a growing number of observations at different red-
shifts, in soft and hard X-ray bands, have found evidences
of a flattening of the faint end slope of the LF towards high
redshift. This trend has been described through a luminosity-
dependent density evolution parameterization. Such a param-
eterization allows the redshift of the AGN density peak to
change as a function of luminosity. This could help in explain-
ing the excess of faint AGN found in the VVDS sample at
1.0 < z < 1.5. Therefore, we considered a luminosity depen-
dent density evolution model (LDDE), as computed in the major
X-surveys (Miyaji et al. 2000; Ueda et al. 2003; Hasinger et al.
2005). In particular, following Hasinger et al. (2005), we as-
sumed an LDDE evolution of the form:
Φ(MB, z) = Φ(M, 0) ∗ ed(z,MB) (9)
where:
ed(z,MB) =
(1 + z)p1 (z ≤ zc)
ed(zc)[(1 + z)/(1 + zc)]
p2 (z > zc)
. (10)
along with
zc(MB) =
zc,010
−0.4γ(MB−Mc) (MB ≥ Mc)
zc,0 (MB < Mc)
. (11)
where zc corresponds to the redshift at which the evolution
changes. Note that zc is not constant but it depends on the lu-
minosity. This dependence allows different evolutions at differ-
ent luminosities and can indeed reproduce the differential AGN
evolution as a function of luminosity, thus modifying the shape
of the luminosity function as a function of redshift. We also con-
sidered two different assumptions for p1 and p2: (i) both param-
eters constant and (ii) both linearly depending on luminosity as
follows:
p1(MB) = p1Mref − 0.4ǫ1 (MB − Mref) (12)
p2(MB) = p2Mref − 0.4ǫ2 (MB − Mref) (13)
The corresponding χ2 values for the two above cases are re-
spectively χ2=64.6 and χ2=56.8. Given the relatively small im-
provement of the fit, we considered the addition of the two fur-
ther parameters (ǫ1 and ǫ2) unnecessary. The model with con-
stant p1 and p2 values is shown with a solid black line in Figure
Figure 10. Evolution of comoving AGN space density with red-
shift, for different luminosity range: -22.0< MB <-20.0; -24.0<
MB <-22.0; -26.0< MB <-24.0 and MB <-26.0. Dashed lines
correspond to the redshift range in which the model has been
extrapolated.
9 and the best fit parameters derived for this model are reported
in the last line of Table 2.
This model reproduces well the overall shape of the luminos-
ity function over the entire redshift range, including the excess
of faint AGN at 1.0 < z < 1.5. The χ2 value for the LDDE model
is in fact the best among all the analyzed models. We found in
fact a χ2 of 64.6 for 67 degree of freedom and, as the reduced χ2
is below 1, it is acceptable 4.
The best fit value of the faint end slope, which in this model
corresponds to the slope at z = 0, is β =-2.0. This value is consis-
tent with that derived by Hao et al. (2005) studying the emission
line luminosity function of a sample of Seyfert galaxies at very
low redshift (0 < z < 0.15), extracted from the SDSS. They in
fact derived a slope β ranging from -2.07 to -2.03, depending on
the line (Hα, [O ii] or [O iii]) used to compute the nuclear lumi-
nosity. Moreover, also the normalizations are in good agreement,
confirming our model also in a redshift range where data are not
available and indeed leading us to have a good confidence on the
extrapolation of the derived model.
8. The AGN activity as a function of redshift
By integrating the luminosity function corresponding to our best
fit model (i.e the LDDE model; see Table 2), we derived the co-
moving AGN space density as a function of redshift for different
luminosity ranges (Figure 10).
The existence of a peak at z∼ 2 in the space density of bright
AGN is known since a long time, even if rarely it has been possi-
ble to precisely locate the position of this maximum within a sin-
gle optical survey. Figure 10 shows that for our best fit model the
peak of the AGN space density shifts significantly towards lower
4 We note that the reduced χ2 of our best fit model, which in-
cludes also VVDS data, is significantly better than that obtained by
Richards et al. (2006b) in fitting only the SDSS DR3 data.
Bongiorno, A. et al.: The VVDS type–1 AGN sample: The faint end of the luminosity function 11
Figure 9. Filled circles correspond to our rest-frame B-band luminosity function data points, derived in the redshift bins 1.0 < z <
1.5, 1.5 < z < 2.0, 2.0 < z < 2.5, 2.5 < z < 3.0 and 3.0 < z < 4.0. Open circles are the data points from the SDSS Data Release 3
(DR3) by Richards et al. (2006b). These data are shown also in two redshift bins below z = 1. The red dot-dashed line corresponds to
the model fit derived by Richards et al. (2006b) only for the SDSS data. The other lines correspond to model fits derived considering
the combination of the VVDS and SDSS samples for different evolutionary models, as listed in Table 2 and described in Section 7.
redshift going to lower luminosity. The position of the maximum
moves from z∼ 2.0 for MB <-26.0 to z∼ 0.65 for -22< MB <-20.
A similar trend has recently been found by the analysis
of several deep X-ray selected samples (Cowie et al., 2003;
Hasinger et al., 2005; La Franca et al., 2005). To compare with
X-ray results, by applying the same bolometric corrections
used is Section 6, we derived the volume densities derived
by our best fit LDDE model in the same luminosity ranges
as La Franca et al. (2005). We found that the volume density
peaks at z ≃ [0.35; 0.7; 1.1; 1.5] respectively for LogLX(2−10kev)
= [42–43; 43–44; 44–44.5; 44.5–45]. In the same luminosity
intervals, the values for the redshift of the peak obtained by
La Franca et al. (2005) are z ≃ [0.5; 0.8; 1.1; 1.5], in good agree-
ment with our result. This trend has been interpreted as evidence
of AGN (i.e. black hole) “cosmic downsizing”, similar to what
has recently been observed in the galaxy spheroid population
(Cimatti et al., 2006). The downsizing (Cowie et al., 1996) is a
term which is used to describe the phenomenon whereby lumi-
12 Bongiorno, A. et al.: The VVDS type–1 AGN sample: The faint end of the luminosity function
1.0 < z < 1.5 1.5 < z < 2.0
∆M Nqso LogΦ(B) ∆LogΦ(B) ∆M Nqso LogΦ(B) ∆LogΦ(B)
-19.46 -20.46 3 -5.31 +0.20 -0.38
-20.46 -21.46 11 -4.89 +0.12 -0.16 -20.28 -21.28 4 -5.29 +0.18 -0.30
-21.46 -22.46 17 -5.04 +0.09 -0.12 -21.28 -22.28 7 -5.18 +0.15 -0.22
-22.46 -23.46 9 -5.32 +0.13 -0.18 -22.28 -23.28 7 -5.54 +0.14 -0.20
-23.46 -24.46 3 -5.78 +0.20 -0.38 -23.28 -24.28 10 -5.34 +0.12 -0.17
-25.46 -26.46 1 -6.16 +0.52 -0.76 -24.28 -25.28 2 -5.94 +0.23 -0.53
2.0 < z < 2.5 2.5 < z < 3.0
∆M Nqso LogΦ(B) ∆LogΦ(B) ∆M Nqso LogΦ(B) ∆LogΦ(B)
-20.90 -21.90 1 -5.65 +0.52 -0.76
-21.90 -22.90 3 -5.48 +0.20 -0.38 -21.55 -22.55 3 -5.45 +0.20 -0.38
-22.90 -23.90 4 -5.76 +0.18 -0.30 -22.55 -23.55 4 -5.58 +0.19 -0.34
-23.90 -24.90 4 -5.81 +0.18 -0.30 -23.55 -24.55 3 -5.90 +0.20 -0.38
-24.90 -25.90 2 -5.97 +0.23 -0.53 -24.55 -25.55 2 -6.11 +0.23 -0.53
-25.90 -26.90 2 -6.03 +0.23 -0.55 -25.55 -26.55 1 -6.26 +0.52 -0.76
3.0 < z < 4.0
∆M Nqso LogΦ(B) ∆LogΦ(B)
-21.89 -22.89 4 -5.52 +0.19 -0.34
-22.89 -23.89 3 -5.86 +0.20 -0.40
-23.89 -24.89 7 -5.83 +0.14 -0.21
-24.89 -25.89 3 -6.12 +0.20 -0.38
Table 1. Binned luminosity function estimate for Ωm=0.3, ΩΛ=0.7 and H0=70 km · s−1 · Mpc−1. We list the values of Log Φ and
the corresponding 1σ errors in five redshift ranges, as plotted with full circles in Figure 9 and in ∆MB=1.0 magnitude bins. We also
list the number of AGN contributing to the luminosity function estimate in each bin
Sample - Evolution Model α β M∗ k1L k2L A k1D k2D Φ
∗ χ2 ν
VVDS+SDSS - PLE α var -3.83 -1.38 -22.51 1.23 -0.26 0.26 - - 9.78E-7 130.36 69
VVDS+SDSS - PLE+PDE -3.49 -1.40 -23.40 0.68 -0.073 - -0.97 -0.31 2.15E-7 91.4 68
Sample - Evolution Model α β M∗ p1 p2 γ zc,0 Mc Φ
∗ χ2 ν
VVDS+SDSS - LDDE -3.29 -2.0 -24.38 6.54 -1.37 0.21 2.08 -27.36 2.79E-8 64.6 67
Table 2. Best fit models derived from the χ2 analysis of the combined sample VVDS+SDSS-DR3 in the redshift range 0.0 < z < 4.0
assuming a flat (Ωm + ΩΛ = 1) universe with Ωm = 0.3.
nous activity (star formation and accretion onto black holes) ap-
pears to be occurring predominantly in progressively lower mass
objects (galaxies or BHs) as the redshift decreases. As such, it
explains why the number of bright sources peaks at higher red-
shift than the number of faint sources.
As already said, this effect had not been seen so far in the
analysis of optically selected samples. This can be due to the
fact that most of the optical samples, because of their limiting
magnitudes, do not reach luminosities where the difference in the
location of the peak becomes evident. The COMBO-17 sample
(Wolf et al., 2003), for example, even if it covers enough redshift
range (1.2 < z < 4.8) to enclose the peak of the AGN activity,
does not probe luminosities faint enough to find a significant
indication for a difference between the space density peaks of
AGN of different luminosities (see, for example, Figure 11 in
Wolf et al. (2003), which is analogous to our Figure 10, but in
which only AGN brighter than M ∼ -24 are shown). The VVDS
sample, being about one magnitude fainter than the COMBO-
17 sample and not having any bias in finding faint AGN, allows
us to detect for the first time in an optically selected sample the
shift of the maximum space density towards lower redshift for
low luminosity AGN.
9. Summary and conclusion
In the present paper we have used the new sample of AGN, col-
lected by the VVDS and presented in Gavignaud et al. (2006), to
derive the optical luminosity function of faint type–1 AGN.
The sample consists of 130 broad line AGN (BLAGN) se-
lected on the basis of only their spectral features, with no mor-
phological and/or color selection biases. The absence of these
biases is particularly important for this sample because the typ-
ical non-thermal AGN continuum can be significantly masked
by the emission of the host galaxy at the low intrinsic luminos-
ity of the VVDS AGN. This makes the optical selection of the
faint AGN candidates very difficult using the standard color and
morphological criteria. Only spectroscopic surveys without any
pre-selection can therefore be considered complete in this lumi-
nosity range.
Because of the absence of morphological and color selec-
tion, our sample shows redder colors than those expected, for
example, on the basis of the color track derived from the SDSS
composite spectrum and the difference is stronger for the intrin-
sically faintest objects. Thanks to the extended multi-wavelength
coverage in the deep VVDS fields in which we have, in addition
Bongiorno, A. et al.: The VVDS type–1 AGN sample: The faint end of the luminosity function 13
to the optical VVDS bands, also photometric data from GALEX,
CFHTLS, UKIDSS and SWIRE, we examined the spectral en-
ergy distribution of each object and we fitted it with a combina-
tion of AGN and galaxy emission, allowing also for the possi-
bility of extinction of the AGN flux. We found that both effects
(presence of dust and contamination from the host galaxy) are
likely to be responsible for this reddening, even if it is not pos-
sible to exclude that faint AGN are intrinsically redder than the
brighter ones.
We derived the luminosity function in the B-band for 1 <
z < 3.6, using the usual 1/Vmax estimator (Schmidt, 1968),
which gives the space density contributions of individual ob-
jects. Moreover, using the prescriptions recently derived by
Hopkins et al. (2007), we computed also the bolometric lumi-
nosity function for our sample. This allows us to compare our
results also with other samples selected from different bands.
Our data, more than one magnitude fainter than previous op-
tical surveys, allow us to constrain the faint part of the luminosity
function up to high redshift. A comparison of our data with the
2dF sample at low redshift (1 < z < 2.1) shows that the VVDS
data can not be well fitted with the PLE models derived by pre-
vious samples. Qualitatively, our data suggest the presence of
an excess of faint objects at low redshift (1.0 < z < 1.5) with
respect to these models.
Recently, a growing number of observations at different red-
shifts, in soft and hard X-ray bands, have found in fact evi-
dences of a similar trend and they have been reproduced with a
luminosity-dependent density evolution parameterization. Such
a parameterization allows the redshift of the AGN density peak
to change as a function of luminosity and explains the excess
of faint AGN that we found at 1.0 < z < 1.5. Indeed, by com-
bining our faint VVDS sample with the large sample of bright
AGN extracted from the SDSS DR3 (Richards et al., 2006b),
we found that the evolutionary model which better represents
the combined luminosity functions, over a wide range of red-
shift and luminosity, is an LDDE model, similar to those derived
from the major X-surveys. The derived faint end slope at z=0 is
β = -2.0, consistent with the value derived by Hao et al. (2005)
studying the emission line luminosity function of a sample of
Seyfert galaxies at very low redshift.
A feature intrinsic to these LDDE models is that the comov-
ing AGN space density shows a shift of the peak with luminos-
ity, in the sense that more luminous AGN peak earlier in the
history of the Universe (i.e. at higher redshift), while the density
of low luminosity ones reaches its maximum later (i.e. at lower
redshift). In particular, in our best fit LDDE model the peak of
the space density ranges from z ∼ 2 for MB < -26 to z∼ 0.65
for -22 < MB < -20. This effect had not been seen so far in the
analysis of optically selected samples, probably because most of
the optical samples do not sample in a complete way the faintest
luminosities, where the difference in the location of the peak be-
comes evident.
Although the results here presented appear to be already ro-
bust, the larger AGN sample we will have at the end of the still
on-going VVDS survey (> 300 AGN), will allow a better sta-
tistical analysis and a better estimate of the parameters of the
evolutionary model.
Acknowledgements. This research has been developed within the framework of
the VVDS consortium.
This work has been partially supported by the CNRS-INSU and its Programme
National de Cosmologie (France), and by Italian Ministry (MIUR) grants
COFIN2000 (MM02037133) and COFIN2003 (num.2003020150).
Based on data obtained with the European Southern Observatory Very Large
Telescope, Paranal, Chile, program 070.A-9007(A), 272.A-5047, 076.A-0808,
and on data obtained at the Canada-France-Hawaii Telescope, operated by the
CNRS of France, CNRC in Canada, and the University of Hawaii. The VLT-
VIMOS observations have been carried out on guaranteed time (GTO) allo-
cated by the European Southern Observatory (ESO) to the VIRMOS consortium,
under a contractual agreement between the Centre National de la Recherche
Scientifique of France, heading a consortium of French and Italian institutes,
and ESO, to design, manufacture and test the VIMOS instrument.
References
Arnouts, S., Schiminovich, D., Ilbert, O., et al. 2005, ApJ, 619, L43
Avni, Y. & Bahcall, J. N. 1980, ApJ, 235, 694A
Barger, A. J., Cowie, L. L., Mushotzky, R. F., et al. 2005, AJ, 129, 578
Boyle, B. J., Shanks, T., Croom, S. M., et al. 2000, MNRAS, 317, 1014
Boyle, B. J., Shanks, T., & Peterson, B. A. 1988, MNRAS, 235, 935
Brandt, W. N., Hornschemeier, A. E., Schneider, D. P., et al. 2000, AJ, 119, 2349
Brown, M. J. I., Brand, K., Dey, A., et al. 2006, ApJ, 638, 88
Bruzual, G. & Charlot, S. 2003, MNRAS, 344, 1000
Cimatti, A., Daddi, E., & Renzini, A. 2006, A&A, 453, L29
Cirasuolo, M., Magliocchetti, M., & Celotti, A. 2005, MNRAS, 357, 1267
Cowie, L. L., Barger, A. J., Bautz, M. W., Brandt, W. N., & Garmire, G. P. 2003,
ApJ, 584, L57
Cowie, L. L., Songaila, A., Hu, E. M., & Cohen, J. G. 1996, AJ, 112, 839
Croom, S. M., Smith, R. J., Boyle, B. J., et al. 2004, MNRAS, 349, 1397
Di Matteo, T., Springel, V., & Hernquist, L. 2005, Nature, 433, 604
Fan, X., Strauss, M. A., Schneider, D. P., et al. 2001, AJ, 121, 54
Ferrarese, L. & Merritt, D. 2000, ApJ, 539, L9
Fiore, F., Brusa, M., Cocchia, F., et al. 2003, A&A, 409, 79
Fontanot, F., Cristiani, S., Monaco, P., et al. 2007, A&A, 461, 39
Gavignaud, I., Bongiorno, A., Paltani, S., et al. 2006, ArXiv Astrophysics e-
prints
Hall, P. B., Gallagher, S. C., Richards, G. T., et al. 2006, AJ, 132, 1977
Hao, L., Strauss, M. A., Fan, X., et al. 2005, AJ, 129, 1795
Hartwick, F. D. A. & Schade, D. 1990, ARA&A, 28, 437
Hasinger, G., Miyaji, T., & Schmidt, M. 2005, A&A, 441, 417
Hewett, P. C. & Foltz, C. B. 2003, AJ, 125, 1784
Hewett, P. C., Foltz, C. B., Chaffee, F. H., et al. 1991, AJ, 101, 1121
Hopkins, P. F., Hernquist, L., Cox, T. J., et al. 2006, ApJ, 639, 700
Hopkins, P. F., Richards, G. T., & Hernquist, L. 2007, ApJ, 654, 731
Hunt, M. P., Steidel, C. C., Adelberger, K. L., & Shapley, A. E. 2004, ApJ, 605,
Ilbert, O., Tresse, L., Zucca, E., et al. 2005, A&A, 439, 863
Iovino, A., McCracken, H. J., Garilli, B., et al. 2005, A&A, 442, 423
Kennefick, J. D., Djorgovski, S. G., & de Carvalho, R. R. 1995, AJ, 110, 2553
Kormendy, J. & Richstone, D. 1995, ARA&A, 33, 581
La Franca, F., Fiore, F., Comastri, A., et al. 2005, ApJ, 635, 864
La Franca, F., Fiore, F., Vignali, C., et al. 2002, ApJ, 570, 100
Lawrence, A., Warren, S. J., Almaini, O., et al. 2006, ArXiv Astrophysics e-
prints
Le Fèvre, O., Mellier, Y., McCracken, H. J., et al. 2004a, A&A, 417, 839
Le Fèvre, O., Vettolani, G., Paltani, S., et al. 2004b, A&A, 428, 1043
Le Fèvre, O., Vettolani, G., Garilli, B., et al. 2005, A&A, 439, 845
Lonsdale, C., Polletta, M. d. C., Surace, J., et al. 2004, ApJS, 154, 54
Lonsdale, C. J., Smith, H. E., Rowan-Robinson, M., et al. 2003, PASP, 115, 897
Magorrian, J., Tremaine, S., Richstone, D., et al. 1998, AJ, 115, 2285
Marshall, H. L., Tananbaum, H., Avni, Y., & Zamorani, G. 1983, ApJ, 269, 35
Matute, I., La Franca, F., Pozzi, F., et al. 2006, A&A, 451, 443
McCracken, H. J., Radovich, M., Bertin, E., et al. 2003, A&A, 410, 17
Miyaji, T., Hasinger, G., & Schmidt, M. 2000, A&A, 353, 25
Miyaji, T., Hasinger, G., & Schmidt, M. 2001, A&A, 369, 49
Mushotzky, R. F., Cowie, L. L., Barger, A. J., & Arnaud, K. A. 2000, Nature,
404, 459
Osterbrock, D. E. 1981, ApJ, 249, 462
Page, M. J., Mason, K. O., McHardy, I. M., Jones, L. R., & Carrera, F. J. 1997,
MNRAS, 291, 324
Pei, Y. C. 1995, ApJ, 438, 623
Prevot, M. L., Lequeux, J., Prevot, L., Maurice, E., & Rocca-Volmerange, B.
1984, A&A, 132, 389
Radovich, M., Arnaboldi, M., Ripepi, V., et al. 2004, A&A, 417, 51
Richards, G. T., Croom, S. M., Anderson, S. F., et al. 2005, MNRAS, 360, 839
Richards, G. T., Fan, X., Newberg, H. J., et al. 2002, AJ, 123, 2945
Richards, G. T., Hall, P. B., Vanden Berk, D. E., et al. 2003, AJ, 126, 1131
Richards, G. T., Lacy, M., Storrie-Lombardi, L. J., et al. 2006a, ApJS, 166, 470
Richards, G. T., Strauss, M. A., Fan, X., et al. 2006b, AJ, 131, 2766
Scannapieco, E. & Oh, S. P. 2004, ApJ, 608, 62
Schiminovich, D., Ilbert, O., Arnouts, S., et al. 2005, ApJ, 619, L47
Schlegel, D. J., Finkbeiner, D. P., & Davis, M. 1998, ApJ, 500, 525
Schmidt, M. 1968, ApJ, 151, 393
14 Bongiorno, A. et al.: The VVDS type–1 AGN sample: The faint end of the luminosity function
Schmidt, M., Schneider, D. P., & Gunn, J. E. 1995, AJ, 110, 68
Schneider, D. P., Fan, X., Hall, P. B., et al. 2003, AJ, 126, 2579
Siana, B., Polletta, M., Smith, H. E., et al. 2006, ArXiv Astrophysics e-prints
Silk, J. & Rees, M. J. 1998, A&A, 331, L1
Silverman, J. D., Green, P. J., Barkhouse, W. A., et al. 2005, ApJ, 624, 630
Steidel, C. C., Hunt, M. P., Shapley, A. E., et al. 2002, ApJ, 576, 653
Ueda, Y., Akiyama, M., Ohta, K., & Miyaji, T. 2003, ApJ, 598, 886
Vanden Berk, D. E., Richards, G. T., Bauer, A., et al. 2001, AJ, 122, 549
Warren, S. J., Hewett, P. C., & Osmer, P. S. 1994, ApJ, 421, 412
Wolf, C., Wisotzki, L., Borch, A., et al. 2003, A&A, 408, 499
1 Università di Bologna, Dipartimento di Astronomia - Via Ranzani
1, I-40127, Bologna, Italy
2 INAF-Osservatorio Astronomico di Bologna - Via Ranzani 1, I-
40127, Bologna, Italy
3 Astrophysical Institute Potsdam, An der Sternwarte 16, D-14482
Potsdam, Germany
4 Integral Science Data Centre, ch. d’Écogia 16, CH-1290 Versoix
5 Geneva Observatory, ch. des Maillettes 51, CH-1290 Sauverny,
Switzerland
6 Laboratoire d’Astrophysique de Toulouse/Tabres (UMR5572),
CNRS, Université Paul Sabatier - Toulouse III, Observatoire Midi-
Pyriénées, 14 av. E. Belin, F-31400 Toulouse, France
7 Institute for Astronomy, University of Edinburgh, Royal
Observatory, Edinburgh EH9 3HJ
8 IASF-INAF - via Bassini 15, I-20133, Milano, Italy
9 Laboratoire d’Astrophysique de Marseille, UMR 6110 CNRS-
Université de Provence, BP8, 13376 Marseille Cedex 12, France
10 IRA-INAF - Via Gobetti,101, I-40129, Bologna, Italy
11 INAF-Osservatorio Astronomico di Roma - Via di Frascati 33, I-
00040, Monte Porzio Catone, Italy
12 Max Planck Institut fur Astrophysik, 85741, Garching, Germany
13 Institut d’Astrophysique de Paris, UMR 7095, 98 bis Bvd Arago,
75014 Paris, France
14 School of Physics & Astronomy, University of Nottingham,
University Park, Nottingham, NG72RD, UK
15 INAF-Osservatorio Astronomico di Brera - Via Brera 28, Milan,
Italy
16 Institute for Astronomy, 2680 Woodlawn Dr., University of
Hawaii, Honolulu, Hawaii, 96822
17 Observatoire de Paris, LERMA, 61 Avenue de l’Observatoire,
75014 Paris, France
18 Centre de Physique Théorique, UMR 6207 CNRS-Université de
Provence, F-13288 Marseille France
19 Astronomical Observatory of the Jagiellonian University, ul Orla
171, 30-244 Kraków, Poland
20 INAF-Osservatorio Astronomico di Capodimonte - Via
Moiariello 16, I-80131, Napoli, Italy
21 Institute de Astrofisica de Canarias, C/ Via Lactea s/n, E-38200
La Laguna, Spain
22 Center for Astrophysics & Space Sciences, University of
California, San Diego, La Jolla, CA 92093-0424, USA
23 Centro de Astrofsica da Universidade do Porto, Rua das Estrelas,
4150-762 Porto, Portugal
24 Universitá di Milano-Bicocca, Dipartimento di Fisica - Piazza
delle Scienze 3, I-20126 Milano, Italy
25 Università di Bologna, Dipartimento di Fisica - Via Irnerio 46,
I-40126, Bologna, Italy
	Introduction
	The sample
	Colors of BLAGNs
	Luminosity function
	Definition of the redshift range
	Incompleteness function
	Estimate of the absolute magnitude
	The 1/Vmax estimator
	Comparison with the results from other optical surveys
	The low redshift luminosity function
	The high redshift luminosity function
	The bolometric luminosity function
	Model fitting
	The PLE and PDE models
	The LDDE model
	The AGN activity as a function of redshift
	Summary and conclusion

  In a previous paper (Gavignaud et al. 2006), we presented the type-1 Active
Galactic Nuclei (AGN) sample obtained from the first epoch data of the
VIMOS-VLT Deep Survey (VVDS). The sample consists of 130 faint, broad-line AGN
with redshift up to z=5 and 17.5< I <24.0, selected on the basis of their
spectra. In this paper we present the measurement of the Optical Luminosity
Function up to z=3.6 derived from this sample, we compare our results with
previous results from brighter samples both at low and at high redshift. Our
data, more than one magnitude fainter than previous optical surveys, allow us
to constrain the faint part of the luminosity function up to high redshift. By
combining our faint VVDS sample with the large sample of bright AGN extracted
from the SDSS DR3 (Richards et al., 2006b) and testing a number of different
evolutionary models, we find that the model which better represents the
combined luminosity functions, over a wide range of redshift and luminosity, is
a luminosity dependent density evolution (LDDE) model, similar to those derived
from the major X-surveys. Such a parameterization allows the redshift of the
AGN space density peak to change as a function of luminosity and explains the
excess of faint AGN that we find at 1.0< z <1.5. On the basis of this model we
find, for the first time from the analysis of optically selected samples, that
the peak of the AGN space density shifts significantly towards lower redshift
going to lower luminosity objects. This result, already found in a number of
X-ray selected samples of AGN, is consistent with a scenario of "AGN cosmic
downsizing", in which the density of more luminous AGN, possibly associated to
more massive black holes, peaks earlier in the history of the Universe, than
that of low luminosity ones.

Introduction
Active Galactic Nuclei (AGN) are relatively rare objects that ex-
hibit some of the most extreme physical conditions and activity
known in the universe.
A useful way to statistically describe the AGN activity along
the cosmic time is through the study of their luminosity func-
tion, whose shape, normalization and evolution can be used to
derive constraints on models of cosmological evolution of black
holes (BH). At z.2.5, the luminosity function of optically se-
lected type–1 AGN has been well studied since many years
(Boyle et al., 1988; Hewett et al., 1991; Pei, 1995; Boyle et al.,
2000; Croom et al., 2004). It is usually described as a double
power law, characterized by the evolutionary parameters L∗(z)
and Φ∗(z), which allow to distinguish between simple evolution-
ary models such as Pure Luminosity Evolution (PLE) and Pure
Density Evolution (PDE). Although the PLE and PDE mod-
els should be mainly considered as mathematical descriptions
of the evolution of the luminosity function, two different phys-
ical interpretations can be associated to them: either a small
Send offprint requests to: Angela Bongiorno, e-mail:
angela.bongiorno@oabo.inaf.it
fraction of bright galaxies harbor AGN, and the luminosities of
these sources change systematically with time (‘luminosity evo-
lution’), or all bright galaxies harbor AGN, but at any given time
most of them are in ‘inactive’ states. In the latter case, the frac-
tion of galaxies with AGN in an ‘active’ state changes with time
(‘density evolution’). Up to now, the PLE model is the preferred
description for the evolution of optically selected QSOs, at least
at low redshift (z < 2).
Works on high redshift type–1 AGN samples (Warren et al.,
1994; Kennefick et al., 1995; Schmidt et al., 1995; Fan et al.,
2001; Wolf et al., 2003; Hunt et al., 2004) have shown that the
number density of QSOs declines rapidly from z ∼ 3 to z ∼ 5.
Since the size of complete and well studied samples of QSOs
at high redshift is still relatively small, the rate of this decline
and the shape of the high redshift luminosity function is not yet
as well constrained as at low redshift. For example, Fan et al.
(2001), studying a sample of 39 luminous high redshift QSOs at
3.6 < z < 5.0, selected from the commissioning data of the Sloan
Digital Sky Survey (SDSS), found that the slope of the bright end
of the QSO luminosity function evolves with redshift, becoming
flatter at high redshift, and that the QSO evolution from z = 2
to z = 5 cannot be described as a pure luminosity evolution. A
similar result on the flattening at high redshift of the slope of
http://arxiv.org/abs/0704.1660v1
2 Bongiorno, A. et al.: The VVDS type–1 AGN sample: The faint end of the luminosity function
the luminosity function for luminous QSOs has been recently
obtained by Richards et al. (2006b) from the analysis of a much
larger sample of SDSS QSOs (but see Fontanot et al. (2007) for
different conclusions drawn on the basis of combined analysis of
GOODS and SDSS QSOs).
At the same time, a growing number of observations at differ-
ent redshifts, in radio, optical and soft and hard X-ray bands, are
suggesting that also the faint end slope evolves, becoming flat-
ter at high redshift (Page et al., 1997; Miyaji et al., 2000, 2001;
La Franca et al., 2002; Cowie et al., 2003; Ueda et al., 2003;
Fiore et al., 2003; Hunt et al., 2004; Cirasuolo et al., 2005;
Hasinger et al., 2005). This evolution, now dubbed as “AGN cos-
mic downsizing” is described either as a direct evolution in the
faint end slope or as “luminosity dependent density evolution”
(LDDE), and it has been the subject of many speculations since
it implies that the space density of low luminosity AGNs peaks
at lower redshift than that of bright ones.
It has been observed that, in addition to the well known
local scale relations between the black hole (BH) masses and
the properties of their host galaxies (Kormendy & Richstone,
1995; Magorrian et al., 1998; Ferrarese & Merritt, 2000), also
the galaxy spheroid population follows a similar pattern of “cos-
mic downsizing” (Cimatti et al., 2006). Various models have
been proposed to explain this common evolutionary trend in
AGN and spheroid galaxies. The majority of them propose that
the feedback from the black hole growth plays a key role in
determining the BH-host galaxy relations (Silk & Rees, 1998;
Di Matteo et al., 2005) and the co-evolution of black holes
and their host galaxies. Indeed, AGN feedback can shut down
the growth of the most massive systems steepening the bright
end slope (Scannapieco & Oh, 2004), while the feedback-driven
QSO decay determines the shape of the faint end of the QSO LF
(Hopkins et al., 2006).
This evolutionary trend has not been clearly seen yet with
optically selected type–1 AGN samples. By combining results
from low and high redshifts, it is clear from the studies of op-
tically selected samples that the cosmic QSO evolution shows a
strong increase of the activity from z ∼ 0 out to z ∼ 2, reaches a
maximum around z ≃ 2 − 3 and then declines, but the shape of
the turnover and the redshift evolution of the peak in activity as
a function of luminosity is still unclear.
Most of the optically selected type–1 AGN samples stud-
ied so far are obtained through various color selections of
candidates, followed by spectroscopic confirmation (e.g. 2dF,
Croom et al. 2004 and SDSS, Richards et al. 2002), or grism and
slitless spectroscopic surveys. These samples are expected to be
highly complete, at least for luminous type–1 AGN, at either
z ≤ 2.2 or z ≥ 3.6, where type–1 AGN show conspicuous colors
in broad band color searches, but less complete in the redshift
range 2.2 ≤ z ≤ 3.6 (Richards et al. 2002).
An improvement in the multi-color selection in optical bands
is through the simultaneous use of many broad and medium band
filters as in the COMBO-17 survey (Wolf et al., 2003). This sur-
vey is the only optical survey so far which, in addition to cov-
ering a redshift range large enough to see the peak of AGN ac-
tivity, is also deep enough to sample up to high redshift type–1
AGN with luminosity below the break in the luminosity func-
tion. However, only photometric redshifts are available for this
sample and, because of their selection criteria, it is incomplete
for objects with a small ratio between the nuclear flux and the
total host galaxy flux and for AGN with anomalous colors, such
as, for example, the broad absorption line (BAL) QSOs , which
have on average redder colors and account for ∼ 10 - 15 % of the
overall AGN population (Hewett & Foltz, 2003).
The VIMOS-VLT Deep Survey (Le Fèvre et al., 2005) is a
spectroscopic survey in which the target selection is purely flux
limited (in the I-band), with no additional selection criterion.
This allows the selection of a spectroscopic type–1 AGN sample
free of color and/or morphological biases in the redshift range
z > 1. An obvious advantage of such a selection is the possi-
bility to test the completeness of the most current surveys (see
Gavignaud et al., 2006, Paper I), based on morphological and/or
color pre-selection, and to study the evolution of type–1 AGN
activity in a large redshift range.
In this paper we use the type-1 AGN sample selected from
the VVDS to derive the luminosity function in the redshift range
1 < z < 3.6. The VVDS type–1 AGN sample is more than one
magnitude deeper than any previous optically selected sample
and allow thus to explore the faint part of the luminosity func-
tion. Moreover, by combining this LF with measurement of the
LF in much larger, but very shallow, surveys, we find an analyt-
ical form to dercribe, in a large luminosity range, the evolution
of type-1 AGN in the redshift range 0< z <4. The paper is or-
ganized as follows: in Section 2 and 3 we describe the sample
and its color properties. In Section 4 we present the method used
to derive the luminosity function, while in Section 5 we com-
pare it with previous works both at low and high redshifts. The
bolometric LF and the comparison with the results derived from
samples selected in different bands (from X-ray to IR) is then
presented in Section 6. The derived LF fitting models are pre-
sented in Section 7 while the AGN activity as a function of red-
shift is shown in Section 8. Finally in section 9 we summarize
our results. Throughout this paper, unless stated otherwise, we
assume a cosmology with Ωm = 0.3, ΩΛ = 0.7 and H0 = 70 km
s−1 Mpc−1.
2. The sample
Our AGN sample is extracted from the first epoch data of the
VIMOS-VLT Deep Survey, performed in 2002 (Le Fèvre et al.,
2005).
The VVDS is a spectroscopic survey designed to measure
about 150,000 redshifts of galaxies, in the redshift range 0 < z <
5, selected, nearly randomly, from an imaging survey (which
consists of observations in U, B, V, R and I bands and, in a
small area, also K-band) designed for this purpose. Full de-
tails about VIMOS photometry can be found in Le Fèvre et al.
(2004a), McCracken et al. (2003), Radovich et al. (2004) for
the U-band and Iovino et al. (2005) for the K-band. In this
work we will as well use the Galex UV-catalog (Arnouts et al.,
2005; Schiminovich et al., 2005), the u∗,g′,r′,i′,z′ photometry
obtained in the frame of the Canada-France-Hawaii Legacy
Survey (CFHTLS)1, UKIDSS (Lawrence et al., 2006), and the
Spitzer Wide-area InfraRed Extragalactic survey (SWIRE)
(Lonsdale et al., 2003, 2004). The spectroscopic VVDS survey
consists of a deep and a wide survey and it is based on a sim-
ple selection function. The sample is selected only on the basis
of the I band magnitude: 17.5 < IAB < 22.5 for the wide and
17.5 < IAB < 24.0 for the deep sample. For a detailed descrip-
tion of the spectroscopic survey strategy and the first epoch data
see Le Fèvre et al. (2005).
Our sample consists of 130 AGN with 0 < z < 5, selected
in 3 VVDS fields (0226-04, 1003+01 and 2217-00) and in the
Chandra Deep Field South (CDFS, Le Fèvre et al., 2004b). All
of them are selected as AGN only on the basis of their spectra,
1 www.cfht.hawaii.edu/Science/CFHLS
Bongiorno, A. et al.: The VVDS type–1 AGN sample: The faint end of the luminosity function 3
Figure 1. Distribution of absolute magnitudes and redshifts of
the total AGN sample. Open circles are the objects with am-
biguous redshift, shown at all their possible z values. The dotted
and dashed lines represent the magnitude limits of the samples:
IAB < 22.5 for the wide sample and IAB < 24.0 for the deep
sample.
irrespective of their morphological or color properties. In partic-
ular, we selected them on the basis of the presence of at least one
broad emission line. We discovered 74 of them in the deep fields
(62 in the 02h field and 12 in the CDFS) and 56 in the wide fields
(18 in the 10h field and 38 in the 22h field). This represents an
unprecedented complete sample of faint AGN, free of morpho-
logical or color selection bias. The spectroscopic area covered
by the First Epoch Data is 0.62 deg2 in the deep fields (02h field
and CDFS) and 1.1 deg2 in the wide fields (10h and 22h fields).
To each object we have assigned a value for the spectro-
scopic redshift and a spectroscopic quality flag which quantifies
our confidence level in that given redshift. As of today, we have
115 AGN with secure redshift, and 15 AGN with two or more
possible values for the redshift. For these objects, we have two
or more possible redshifts because only one broad emission line,
with no other narrow lines and/or additional features, is detected
in the spectral wavelength range adopted in the VVDS (5500 -
9500 Å) (see Figure 1 in Paper I). For all of them, however, a
best solution is proposed. In the original VVDS AGN sample,
the number of AGN with this redshift degeneracy was 42. To
solve this problem, we have first looked for the objects already
observed in other spectroscopic surveys in the same areas, solv-
ing the redshift for 3 of them. For the remaining objetcs, we
performed a spectroscopic follow-up with FORS1 on the VLT
Unit Telescope 2 (UT2). With these additional observations we
found a secure redshift for 24 of our AGN with ambiguous red-
shift determination and, moreover, we found that our proposed
best solution was the correct one in ∼ 80% of the cases. On the
basis of this result, we decided to use, in the following analysis,
our best estimate of the redshift for the small remaining fraction
of AGN with ambiguous redshift determination (15 AGN).
In Figure 1 we show the absolute B-magnitude and the
redshift distributions of the sample. As shown in this Figure,
our sample spans a large range of luminosities and consists of
both Seyfert galaxies (MB >-23; ∼59%) and QSOs (MB <-23;
∼41%). A more detailed and exhaustive description of the prop-
Figure 2. Composite spectra derived for our AGN with se-
cure redshift in the 02h field, divided in a “bright” (19 objects
at M1450 <-22.15, dotted curve) and a “faint” (31 objects at
M1450 >-22.15, dashed curve) sample. We consider here only
AGN with z > 1 (i.e. the AGN used in to compute the lumi-
nosity function). The SDSS composite spectrum is shown with
a solid line for comparison.
erties of the AGN sample is given in Paper I (Gavignaud et al.,
2006) and the complete list of BLAGN in our wide and deep
samples is available as an electronic Table in Appendix of
Gavignaud et al. (2006).
3. Colors of BLAGNs
As already discussed in Paper I, the VVDS AGN sample shows,
on average, redder colors than those expected by comparing
them, for example, with the color track derived from the SDSS
composite spectrum (Vanden Berk et al., 2001). In Paper I we
proposed three possible explanations: (a) the contamination of
the host galaxy is reddening the observed colors of faint AGN;
(b) BLAGN are intrinsically redder when they are faint; (c) the
reddest colors are due to dust extinction. On the basis of the sta-
tistical properties of the sample, we concluded that hypothesis
(a) was likely to be the more correct, as expected from the faint
absolute magnitudes sampled by our survey, even if hypotheses
(b) and (c) could not be ruled out.
In Figure 2 we show the composite spectra derived from the
sample of AGN with secure redshift in the 02h field, divided
in a “bright” and a “faint” sample at the absolute magnitude
M1450 = −22.15. We consider here only AGN with z > 1, which
correspond to the AGN used in Section 4 to compute the lumi-
nosity function. The choice of the reference wavelength for the
absolute magnitude, λ = 1450 Å, is motivated by our photo-
metric coverage. In fact, for most of the objects it is possible
to interpolate M1450 directly from the observed magnitudes. In
the same plot we show also the SDSS composite spectrum (solid
curve) for comparison. Even if also the ”bright” VVDS compos-
ite (dotted curve) is somewhat redder than the SDSS one, it is
clear from this plot that the main differences occur for faintest
objects (dashed curve).
A similar result is shown for the same sample in the upper
panel of Figure 3, where we plot the spectral index α as a func-
tion of the AGN luminosity. The spectral index is derived here
by fitting a simple power law f (ν) = ν−α to our photometric data
points. This analysis has been performed only on the 02h deep
4 Bongiorno, A. et al.: The VVDS type–1 AGN sample: The faint end of the luminosity function
Figure 3. Upper Panel: Distribution of the spectral index α as
a function of M1450 for the same sample of AGN as in Figure
2. The spectral index is derived here by fitting a simple power
law f (ν) = ν−α to our photometric data points. Asterisks are
AGN morphologically classified as extended and the grey point
is a BAL AGN. Bottom Panels: Distribution of the spectral in-
dex α for the same sample of AGN. All the AGN in this sample
are shown in the first of the three panels, while the AGN in the
“bright” and “faint” sub–samples are shown in the second and
third panel, respectively. The dotted curve in the second panel
corresponds to the gaussian fit of the bright sub–sample and it is
reported also in the third panel to highlight the differences in the
α distributions of the two sub-samples.
sample, since for the wide sample we do not have enough photo-
metric coverage to reliably derive the spectral index. Most of the
AGN with α > 1 are fainter than M1450 = −22.15, showing that,
indeed, the faintest objects have on average redder colors than
the brightest ones. The outlier (the brightest object with large α,
i.e. very red colors, in the upper right corner of the plot) is a BAL
The three bottom panels of Figure 3 show the histograms of
the resulting power law slopes for the same AGN sample. The
total sample is plotted in the first panel, while the bright and the
faint sub-samples are plotted in the second and third panels, re-
spectively. A Gaussian curve with < α >= 0.94 and dispersion
σ = 0.38 is a good representation for the distribution of about
80% (40/50) of the objects in the first panel. In addition, there
is a significant tail (∼ 20%) of redder AGN with slopes in the
range from 1.8 up to ∼ 3.0. The average slope of the total sample
(∼ 0.94) is redder than the fit to the SDSS composite (∼ 0.44).
Moreover, the distribution of α is shifted toward much larger val-
ues (redder continua) than the similar distribution in the SDSS
sample (Richards et al., 2003). For example, only 6% of the ob-
jects in the SDSS sample have α > 1.0, while this percentage is
57% in our sample.
The differences with respect to the SDSS sample can be
partly due to the differences in absolute magnitude of the two
samples (Mi <-22.0 for the SDSS sample (Schneider et al.,
2003) and MB <-20.0 for the VVDS sample). In fact, if we con-
sider the VVDS “bright” sub-sample, the average spectral index
< α > becomes ∼ 0.71, which is closer to the SDSS value (even
if it is still somewhat redder), and only two objects (∼8% of the
sample) show values not consistent with a gaussian distribution
with σ ∼0.32. Moreover, only 30% of this sample have α > 1.0.
Most of the bright SDSS AGNs with α > 1 are interpreted by
Richards et al. (2003) to be dust-reddened, although a fraction
of them is likely to be due to intrinsically red AGN (Hall et al.,
2006). At fainter magnitude one would expect both a larger frac-
tion of dust-reddened objects (in analogy with indications from
the X-ray data (Brandt et al., 2000; Mushotzky et al., 2000) and
a more significant contamination from the host galaxy.
We have tested these possibilities by examining the global
Spectral Energy Distribution (SED) of each object and fitting
the observed fluxes fobs with a combination of AGN and galaxy
emission, allowing also for the possibility of extinction of the
AGN flux. Thanks to the multi-wavelength coverage in the deep
field in which we have, in addition to VVDS bands, also data
from GALEX, CFHTLS, UKIDSS and SWIRE, we can study
the spectral energy distribution of the single objects. In particu-
lar, we assume that:
fobs = c1 fAGN · 10
−0.4·Aλ + c2 fGAL (1)
and, using a library of galaxy and AGN templates, we find the
best parameters c1, c2 and EB−V for each object. We used the
AGN SED derived by Richards et al. (2006a) with an SMC-
like dust-reddening law (Prevot et al., 1984) with the form
Aλ/EB−V = 1.39λ
µm , and a library of galaxies template by
Bruzual & Charlot (2003).
We found that for ∼37% of the objects, the observed flux
is fitted by a typical AGN power law (pure AGN), while 44%
of the sources require the presence of a contribution from the
host galaxy to reproduce the observed flux. Only 4% of the ob-
jects are fitted by pure AGN + dust, while the remaining 15%
of objects require instead both contributions (host galaxy con-
tamination and presence of dust). As expected, if we restrict the
analysis to the bright sample, the percentage of pure AGN in-
creases to 68%, with the rest of the objects requiring either some
contribution from the host galaxy (∼21%) or the presence of dust
oscuration (∼11%).
In Figure 4 we show 4 examples of the resulting fits: (i) pure
AGN; (ii) dust-extincted AGN; (iii) AGN contaminated by the
host galaxy; (iv) dust-extincted AGN and contaminated by the
host galaxy. The dotted line corresponds to the AGN template
before applying the extinction law, while the solid blue line cor-
responds to the same template, but extincted for the given EB−V ;
the red line corresponds to the galaxy template and, finally, the
black line is the resulting best fit to the SED. The host galaxy
contaminations will be taken into account in the computation of
the AGN absolute magnitude for the luminosity function.
Bongiorno, A. et al.: The VVDS type–1 AGN sample: The faint end of the luminosity function 5
Figure 4. Four examples of different decompositions of the ob-
served SEDs of our objects. Since for λ < 1216 Å, corresponding
to the Lyα line, the observed flux is expected to decrease because
of intervening absorption, all the photometric data at λ <1216 Å
are not considered in the fitting. The only requested constraint is
that they lie below the fit. The four fits shown in this Figure cor-
respond, from top to bottom, to pure-AGN, dust-extincted AGN,
AGN and host galaxy, dust-extincted AGN and host galaxy. The
dotted line corresponds to the AGN template before applying
the extinction law, while the solid blue line corresponds to the
same template, but extincted for the given EB−V . The red line
(third and fourth panel) corresponds to the galaxy template and,
finally, the black line is the resulting best fit to the SED. Arrows
correspond to 5σ upper limits in case of non detection in the IR.
4. Luminosity function
4.1. Definition of the redshift range
For the study of the LF we decided to exclude AGN with z ≤
1.0. This choice is due to the fact that for 0.5 ≤ z ≤ 1.0 the
only visible broad line in the VVDS spectra is Hβ (see Figure
1 of Paper I). This means that all objects with narrow or almost
narrow Hβ and broad Hα (type 1.8, 1.9 AGN; see Osterbrock
1981) would not be included in our sample, because we include
in the AGN sample all the objects with at least one visible broad
line. Since at low luminosities the number of intermediate type
AGN is not negligible, this redshift bin is likely to be under-
populated and the results would not be meaningful.
At z < 0.5, in principle we have less problems, because also
Hα is within the wavelength range of the VVDS spectra, but,
since at this low redshift, our sampled volume is relatively small
and QSOs rare, only 3 objects have secure redshifts in this red-
shift bin in the current sample. For these reasons, our luminosity
function has been computed only for z > 1.0 AGN. As already
mentioned in Section 2, the small fraction of objects with an am-
biguous redshift determination have been included in the compu-
tation of the luminosity function assuming that our best estimate
of their redshift is correct.
The resulting sample used in the computation of the LF consists
thus of 121 objects at 1< z <4.
4.2. Incompleteness function
Our incompleteness function is made up of two terms linked, re-
spectively, to the selection algorithm and to the spectral analysis:
the Target Sampling Rate (TSR) and the Spectroscopic Success
Rate (SSR) defined following Ilbert et al. (2005).
The Target Sampling Rate, namely the ratio between the ob-
served sources and the total number of objects in the photometric
catalog, quantifies the incompleteness due to the adopted spec-
troscopic selection criterion. The TSR is similar in the wide and
deep sample and runs from 20% to 30%.
The Spectroscopic Success Rate is the probability of a spec-
troscopically targeted object to be securely identified. It is a com-
plex function of the BLAGN redshift, apparent magnitude and
intrinsic spectral energy distribution and it has been estimated
by simulating 20 Vimos pointings, for a total of 2745 spectra.
Full details on TSR and SSR can be found in Paper I
(Gavignaud et al., 2006). We account for them by computing for
each object the associated weights wtsr = 1/TS R and wssr =
1/S S R; the total weighted contribution of each object to the
luminosity function is then the product of the derived weights
(wtsr × wssr).
4.3. Estimate of the absolute magnitude
We derived the absolute magnitude in the reference band from
the apparent magnitude in the observed band as:
M = mobs − 5log10(dl(z)) − 25 − k (2)
where M is computed in the band in which we want to compute
the luminosity function, mobs is the observed band from which
we want to calculate it, dl(z) is the luminosity distance expressed
in Mpc and k is the k-correction in the reference band. To make
easier the comparison with previous results in the literature, we
computed the luminosity function in the B-band.
To minimize the uncertainties in the adopted k-correction,
mobs for each object should be chosen in the observed band
which is sampling the rest-wavelength closer to the band in
which the luminosity function is computed. For our sample,
which consists only of z > 1 objects, the best bands to use to
compute the B-band absolute magnitudes should be respectively
the I-, J- and K-bands going to higher redshift. Since however,
the only observed band available for the entire sample (deep and
wide), is the I-band, we decided to use it for all objects to com-
pute the B-band magnitudes. This means that for z ∼
> 2, we
introduce an uncertainty in the absolute magnitudes due to the
k-correction. We computed the absolute magnitude considering
the template derived from the SDSS sample (Vanden Berk et al.,
2001).
As discussed in Section 3, the VVDS AGN sample shows
redder colors than those typical of normal, more luminous AGN
and this can be due to the combination of the host galaxy contri-
bution and the presence of dust. Since, in this redshift range, the
fractional contribution from the host galaxies is expected to be
more significant in the I-band than in bluer bands, the luminos-
ity derived using the I-band observed magnitude could, in some
cases, be somewhat overestimated due to the contribution of the
host galaxy component.
6 Bongiorno, A. et al.: The VVDS type–1 AGN sample: The faint end of the luminosity function
Figure 5. Real (full circles; AGN in the deep sample) and simu-
lated (open triangles; AGN in the wide sample) B-band absolute
magnitude differences as a function of MB(TOT) (upper panel)
and redshift (bottom panel). MB(TOT) is the absolute magnitude
computed considering the total observed flux, while MB(AGN)
is the absolute magnitude computed after subtracting the host-
galaxy contribution.
We estimated the possible impact of this effect on our re-
sults in the following way. From the results of the analysis of the
SED of the single objects in the deep sample (see Section 3) we
computed for each object the difference mI(TOT ) − mI(AGN)
and, consequently, MB(TOT ) − MB(AGN). This could allow us
to derive the LF using directly the derived MB(AGN), resolv-
ing the possible bias introduced by the host galaxy contami-
nation. These differences are shown as full circles in Figure
5 as a function of absolute magnitude (upper panel) and red-
shift (lower panel). For most of the objects the resulting dif-
ferences between the total and the AGN magnitudes are small
(∆M≤0.2). However, for a not negligible fraction of the faintest
objects (MB ≥-22.5, z ≤2.0) these differences can be signifi-
cant (up to ∼1 mag). For the wide sample, for which the more
restricted photometric coverage does not allow a detailed SED
analysis and decomposition, we used simulated differences to
derive the MB(AGN). These simulated differences have been de-
rived through a Monte Carlo simulation on the basis of the bi-
variate distribution ∆M(M,z) estimated from the objects in the
deep sample. ∆M(M,z) takes into account the probability distri-
bution of ∆M as a function of MB and z, between 0 and the solid
line in Figure 5 derived as the envelope suggested by the black
dots. The resulting simulated differences for the objects in the
wide sample are shown as open triangles in the two panels of
Figure 5.
The AGN magnitudes and the limiting magnitudes of the
samples have been corrected also for galactic extinction on the
basis of the mean extinction values E(B−V) in each field derived
from Schlegel et al. (1998). Only for the 22h field, where the ex-
tinction is highly variable across the field, we used the extinction
on the basis of the position of individual objects. The resulting
corrections in the I-band magnitude are AI ≃ 0.027 in the 2h and
10h fields and AI = 0.0089 in the CDFS field, while the average
value in the 22h field is AI = 0.065. These corrections have been
applied also to the limiting magnitude of each field.
4.4. The 1/Vmax estimator
We derived the binned representation of the luminosity function
using the usual 1/Vmax estimator (Schmidt, 1968), which gives
the space density contribution of individual objects. The lumi-
nosity function, for each redshift bin (z − ∆z/2 ; z + ∆z/2), is
then computed as:
Φ(M) =
M+∆M/2
M−∆M/2
wtsri w
Vmax,i
where Vmax,i is the comoving volume within which the i
th ob-
ject would still be included in the sample. wtsri and w
i are re-
spectively the inverse of the TSR and of the SSR, associated to
the ith object. The statistical uncertainty on Φ(M) is given by
Marshall et al. (1983):
√M+∆M/2
M−∆M/2
(wtsri w
V2max,i
We combined our samples at different depths using the
method proposed by Avni & Bahcall (1980). In this method it
is assumed that each object, characterized by an observed red-
shift zi and intrinsic luminosity Li, could have been found in any
of the survey areas for which its observed magnitude is brighter
than the corresponding flux limit. This means that, for our total
sample, we consider an area of:
Ωtot(m) = Ωdeep+Ωwide = 1.72 deg
2 for 17.5 < IAB < 22.5
Ωtot(m) = Ωdeep = 0.62 deg
2 for 22.5 < IAB < 24.0
The resulting luminosity functions in different redshift
ranges are plotted in Figure 6 and 7, where all bins which contain
at least one object are plotted. The LF values, together with their
1σ errors and the numbers of objects in each absolute magnitude
bin are presented in Table 1. The values reported in Table 1 and
plotted in Figures 6 and 7 are not corrected for the host galaxy
contribution. We have in fact a posteriori verified that, even if the
differences between the total absolute magnitudes and the mag-
nitudes corrected for the host galaxy contribution (see Section
4.3) can be significant for a fraction of the faintest objects, the
resulting luminosity functions computed by using these two sets
of absolute magnitudes are not significantly different. For this
reason and for a more direct comparison with previous works,
the results on the luminosity function presented in the next sec-
tion are those obtained using the total magnitudes.
5. Comparison with the results from other optical
surveys
We derived the luminosity function in the redshift range 1.0<
z <3.6 and we compared it with the results from other surveys at
both low and high redshift.
5.1. The low redshift luminosity function
In Figure 6 we present our luminosity function up to z = 2.1.
The Figure show our LF data points (full circles) derived in two
redshift bins: 1.0 < z < 1.55 and 1.55 < z < 2.1 compared with
the LF fits derived from the 2dF QSO sample by Croom et al.
(2004) and by Boyle et al. (2000), with the COMBO-17 sample
Bongiorno, A. et al.: The VVDS type–1 AGN sample: The faint end of the luminosity function 7
Figure 6. Our rest-frame B-band luminosity function, derived in the redshift bins 1.0 < z < 1.55 and 1.55 < z < 2.1, compared with
the 2dFQRS (Croom et al., 2004; Boyle et al., 2000), COMBO-17 data (Wolf et al., 2003) and with the 2dF-SDSS (2SLAQ) data
(Richards et al., 2005). The curves in the Figure show the PLE fit models derived by these authors. The thick parts of the curves
correspond to the luminosity range covered by the data in each sample, while the thin parts are extrapolations based on the best fit
parameters of the models.
by Wolf et al. (2003), and with the 2dF-SDSS (2SLAQ) LF fit
by Richards et al. (2005). In each panel the curves, computed
for the average z of the redshift range, correspond to a double
power law luminosity function in which the evolution with red-
shift is characterized by a pure luminosity evolution modeled as
M∗b(z) = M
b(0)−2.5(k1z+ k2z
2). Moreover, the thick parts of the
curves show the luminosity range covered by the data in each of
the comparison samples, while the thin parts are extrapolation
based on the the best fit parameters of the models.
We start considering the comparison with the 2dF and the
COMBO-17 LF fits. As shown in Figure 6, our bright LF data
points connect rather smoothly to the faint part of the 2dF data.
However, our sample is more than two magnitudes deeper than
the 2dF sample. For this reason, a comparison at low luminosity
is possible only with the extrapolations of the LF fit. At z > 1.55,
while the Boyle’s model fits well our faint LF data points, the
Croom’s extrapolation, being very flat, tends to underestimate
our low luminosity data points. At z < 1.55 the comparison is
worse: as in the higher redshift bin, the Boyle’s model fits our
data better than the Croom’s one but, in this redshift bin, our
data points show an excess at low luminosity also with respect to
Boyle’s fit. This trend is similar to what shown also by the com-
parison with the fit of the COMBO-17 data which, differently
from the 2dF data, have a low luminosity limit closer to ours: at
z > 1.55 the agreement is very good, but in the first redshift bin
our data show again an excess at low luminosity. This excess is
likely due to the fact that, because of its selection criteria, the
COMBO-17 sample is expected to be significantly incomplete
for objects in which the ratio between the nuclear flux and the
total host galaxy flux is small. Finally, we compare our data with
the 2SLAQ fits derived by Richards et al. (2005). The 2SLAQ
data are derived from a sample of AGN selected from the SDSS,
at 18.0 < g < 21.85 and z < 3, and observed with the 2-degree
field instrument. Similarly to the 2dF sample, also for this sam-
ple the LF is derived only for z < 2.1 and MB < −22.5. The plot-
ted dot-dashed curve corresponds to a PLE model in which they
fixed most of the parameters of the model at the values found
by Croom et al. (2004), leaving to vary only the faint end slope
and the normalization constant Φ∗. In this case, the agreement
with our data points at z < 1.55 is very good also at low lu-
minosity. The faint end slope found in this case is β = −1.45,
which is similar to that found by Boyle et al. (2000) (β = −1.58)
and significantly steeper than that found by Croom et al. (2004)
(β = −1.09). At z > 1.55, the Richards et al. (2005) LF fit tends
to overestimate our data points at the faint end of the LF, which
suggest a flatter slope in this redshift bin.
The first conclusion from this comparison is that, at low red-
shift (i.e. z < 2.1), the data from our sample, which is ∼2 mag
fainter than the previous spectroscopically confirmed samples,
are not well fitted simultaneously in the two analyzed redshift
bins by the PLE models derived from the previous samples.
Qualitatively, the main reason for this appears to be the fact that
our data suggest a change in the faint end slope of the LF, which
appears to flatten with increasing redshift. This trend, already
highlighted by previous X-ray surveys (La Franca et al., 2002;
Ueda et al., 2003; Fiore et al., 2003) suggests that a simple PLE
parameterization may not be a good representation of the evolu-
tion of the AGN luminosity function over a wide range of red-
shift and luminosity. Different model fits will be discussed in
Section 7.
8 Bongiorno, A. et al.: The VVDS type–1 AGN sample: The faint end of the luminosity function
Figure 7. Our luminosity function, at 1450 Å rest-frame, in the
redshift range 2.1<z<3.6, compared with data from other high-
z samples (Hunt et al. (2004) at z = 3; Combo-17 data from
Wolf et al. (2003) at 2.4 < z < 3.6; data from Warren et al.
(1994) at 2.2 < z < 3.5 and the SDSS data from Fan et al.
(2001)). The SDSS data points at 3.6< z <3.9 have been
evolved to z=3 using the luminosity evolution of Pei (1995) as
in Hunt et al. (2004). The curves show some model fits in which
the thick parts of the curves correspond to the luminosity range
covered by the data samples, while the thin parts are model ex-
trapolation. For this plot, anΩm = 1,ΩΛ = 0, h = 0.5 cosmology
has been assumed for comparison with the previous works.
5.2. The high redshift luminosity function
The comparison of our LF data points for 2.1< z <3.6 (full
circles) with the results from other samples in similar redshift
ranges is shown in Figure 7. In this Figure an Ωm = 1, ΩΛ = 0,
h = 0.5 cosmology has been assumed for comparison with pre-
vious works, and the absolute magnitude has been computed at
1450 Å. As before, the thick parts of the curves show the lu-
minosity ranges covered by the various data samples, while the
thin parts are model extrapolations. In terms of number of ob-
jects, depth and covered area, the only sample comparable to
ours is the COMBO-17 sample (Wolf et al., 2003), which, in
this redshift range, consists of 60 AGN candidates over 0.78
square degree. At a similar depth, in terms of absolute mag-
nitude, we show also the data from the sample of Hunt et al.
(2004), which however consists of 11 AGN in the redshift range
< z > ±σz =3.03±0.35 (Steidel et al., 2002). Given the small
number of objects, the corresponding Hunt model fit was de-
rived including also the Warren data points (Warren et al., 1994).
Moreover, they assumed the Pei (1995) luminosity evolution
model, adopting the same values for L∗ and Φ∗, leaving free to
vary the two slopes, both at the faint and at the bright end of
the LF. For comparison we show also the original Pei model
fit derived from the empirical luminosity function estimated
by Hartwick & Schade (1990) and Warren et al. (1994). In the
same plot we show also the model fit derived from a sample of
∼100 z ∼ 3 (U-dropout) QSO candidates by Siana et al. (pri-
vate comunication; see also Siana et al. 2006). This sample has
been selected by using a simple optical/IR photometric selec-
tion at 19< r′ <22 and the model fit has been derived by fix-
ing the bright end slope at z=-2.85 as determined by SDSS data
(Richards et al., 2006b).
In general, the comparison of the VVDS data points with
those from the other surveys shown in Figure 7 shows a satis-
factory agreement in the region of overlapping magnitudes. The
best model fit which reproduce our LF data points at z ∼ 3 is the
Siana model with a faint end slope β = −1.45. It is interesting to
note that, in the faint part of the LF, our data points appear to be
higher with respect to the Hunt et al. (2004) fit and are instead
closer to the extrapolation of the original Pei model fit. This dif-
ference with the Hunt et al. (2004) fit is probably due to the fact
that, having only 11 AGN in their faint sample, their best fit to
the faint-end slope was poorly constrained.
6. The bolometric luminosity function
The comparison between the AGN LFs derived from samples
selected in different bands has been for a long time a critical
point in the studies of the AGN luminosity function. Recently,
Hopkins et al. (2007), combining a large number of LF measure-
ments obtained in different redshift ranges, observed wavelength
bands and luminosity intervals, derived the Bolometric QSO
Luminosity Function in the redshift range z = 0 - 6. For each
observational band, they derived appropriate bolometric correc-
tions, taking into account the variation with luminosity of both
the average absorption properties (e.g. the QSO column density
NH from X-ray data) and the average global spectral energy dis-
tributions. They show that, with these bolometric corrections, it
is possible to find a good agreement between results from all
different sets of data.
We applied to our LF data points the bolometric corrections
given by Eqs. (2) and (4) of Hopkins et al. (2007) for the B-band
and we derived the bolometric LF shown as black dots in Figure
8. The solid line represents the bolometric LF best fit model de-
rived by Hopkins et al. (2007) and the colored data points cor-
respond to different samples: green points are from optical LFs,
blue and red points are from soft-X and hard-X LFs, respec-
tively, and finally the cyan points are from the mid-IR LFs. All
these bolometric LFs data points have been derived following
the same procedure described in Hopkins et al. (2007).
Our data, which sample the faint part of the bolometric lu-
minosity function better than all previous optically selected sam-
ples, are in good agreement with all the other samples, selected
in different bands. Only in the last redshift bin, our data are quite
higher with respect to the samples selected in other wavelength
bands. The agreement remains however good with the COMBO-
17 sample which is the only optically selected sample plotted
here. This effect can be attributed to the fact that the conversions
used to compute the Bolometric LF, being derived expecially for
AGN at low redshifts, become less accurate at high redshift.
Our data show moreover good agreement also with the
model fit derived by Hopkins et al. (2007). By trying various an-
alytic fits to the bolometric luminosity function Hopkins et al.
(2007) concluded that neither pure luminosity nor pure density
evolution represent well all the data. An improved fit can in-
stead be obtained with a luminosity dependent density evolution
model (LDDE) or, even better, with a PLE model in which both
the bright- and the faint-end slopes evolve with redshift. Both
Bongiorno, A. et al.: The VVDS type–1 AGN sample: The faint end of the luminosity function 9
Figure 8. Bolometric luminosity function derived in three
redshift bins from our data (black dots), compared with
Hopkins et al. (2007) best-fit model and the data-sets used in
their work. The central redshift of each bin is indicated in each
panel. Here, we adopted the same color-code as in Hopkins et al.
(2007), but for more clarity we limited the number of samples
presented in the Figure. Red symbols correspond to hard X-ray
surveys (squares: Barger et al. 2005; circles: Ueda et al. 2003).
Blue to soft X-ray surveys (squares: Silverman et al. 2005; cir-
cles: Hasinger et al. 2005). Cyan to infra-red surveys (circles:
Brown et al. 2006; squares: Matute et al. 2006). For the optical
surveys we are showing here, with green circles, the data from
the COMBO-17 survey (Wolf et al., 2003), which is comparable
in depth to our sample.
these models can reproduce the observed flattening with redshift
of the faint end of the luminosity function.
7. Model fitting
In this Section we discuss the results of a number of different fits
to our data as a function of luminosity and redshift. For this pur-
pose, we computed the luminosity function in 5 redshift bins at
1.0 < z < 4.0 where the VVDS AGN sample consists of 121
objects. Since, in this redshift range, our data cover only the
faint part of the luminosity function, these fits have been per-
formed by combining our data with the LF data points from the
SDSS data release 3 (DR3) (Richards et al., 2006b) in the red-
shift range 0 < z < 4. The advantage of using the SDSS sample,
rather than, for example, the 2dF sample, is that the former sam-
ple, because of the way it is selected, probes the luminosity func-
tion to much higher redshifts. The SDSS sample contains more
than 15,000 spectroscopically confirmed AGN selected from an
effective area of 1622 sq.deg. Its limiting magnitude (i < 19.1 for
z < 3.0 and i < 20.2 for z > 3.0) is much brighter than the VVDS
and because of this it does not sample well the AGN in the faint
part of the luminosity function. For this reason, Richards et al.
(2006b) fitted the SDSS data using only a single power law,
which is meant to describe the luminosity function above the
break luminosity. Adding the VVDS data, which instead mainly
sample the faint end of the luminosity function, and analyzing
the two samples together, allows us to cover the entire luminosity
range in the common redshift range (1.0 < z < 4.0), also extend-
ing the analysis at z < 1.0 where only SDSS data are available.
The goodness of fit between the computed LF data points
and the various models is then determined by the χ2 test.
For all the analyzed models we have parameterized the lu-
minosity function as a double power law that, expressed in lumi-
nosity, is given by:
Φ(L, z) =
(L/L∗)−α + (L/L∗)−β
whereΦ∗L is the number of AGN per Mpc
3, L∗ is the characteris-
tic luminosity around which the slope of the luminosity function
is changing and α and β are the two power law indices. Equation
5 can be expressed in absolute magnitude 2 as:
Φ(M, z) =
100.4(α+1)(M−M∗) + 100.4(β+1)(M−M∗)
7.1. The PLE and PDE models
The first model that we tested is a Pure Luminosity Evolution
(PLE) with the dependence of the characteristic luminosity de-
scribed by a 2nd-order polynomial in redshift:
M∗(z) = M∗(0) − 2.5(k1z + k2z
2). (7)
Following the finding by Richards et al. (2006b) for the SDSS
sample, we have allowed a change (flattening with redshift) of
the bright end slope according to a linear evolution in redshift:
α(z) = α(0) + A z. The resulting best fit parameters are listed
in the first line of Table 2 and the resulting model fit is shown
as a green short dashed line in Figure 9. The bright end slope α
derived by our fit (αVVDS=-3.19 at z=2.45) is consistent with the
one found by Richards et al. (2006b) (αSDSS = -3.1).
This model, as shown in Figure 9, while reproduces well the
bright part of the LF in the entire redshift range, does not fit the
faint part of the LF at low redshift (1.0 < z < 1.5). This appears
to be due to the fact that, given the overall best fit normalization,
the derived faint end slope (β =-1.38) is too shallow to reproduce
the VVDS data in this redshift range.
Richards et al. (2005), working on a combined 2dF-SDSS
(2SLAQ) sample of AGN up to z = 2.1. found that, fixing
all of the parameters except β and the normalization, to those
of Croom et al. (2004), the resulting faint end slope is β =
−1.45 ± 0.03. This value would describe better our faint LF at
low redshift. This trend suggests a kind of combined luminosity
and density evolution not taken into account by the used model.
2 Φ∗M = Φ
∣ln10−0.4
3 in their parameterization A1=-0.4(α + 1) =0.84
10 Bongiorno, A. et al.: The VVDS type–1 AGN sample: The faint end of the luminosity function
For this reason, we attempted to fit the data also including a term
of density evolution in the form of:
M(z) = Φ
M(0) · 10
k1Dz+k2Dz
In this model the evolution of the LF is described by both
a term of luminosity evolution, which affects M∗, and a term of
density evolution, which allows for a change in the global nor-
malization Φ∗. The derived best fit parameters of this model are
listed in the second line of Table 2 and the model fit is shown
as a blue long dashed line in Figure 9. This model gives a better
χ2 with respect to the previous model, describing the entire sam-
ple better than a simple PLE (the reduced χ2 decreases from ∼
1.9 to ∼ 1.35). However, it still does not satisfactorily reproduce
the excess of faint objects in the redshift bin 1.0 < z < 1.5 and,
moreover, it underestimates the faint end of the LF in the last
redshift bin (3.0 < z < 4.0).
7.2. The LDDE model
Recently, a growing number of observations at different red-
shifts, in soft and hard X-ray bands, have found evidences
of a flattening of the faint end slope of the LF towards high
redshift. This trend has been described through a luminosity-
dependent density evolution parameterization. Such a param-
eterization allows the redshift of the AGN density peak to
change as a function of luminosity. This could help in explain-
ing the excess of faint AGN found in the VVDS sample at
1.0 < z < 1.5. Therefore, we considered a luminosity depen-
dent density evolution model (LDDE), as computed in the major
X-surveys (Miyaji et al. 2000; Ueda et al. 2003; Hasinger et al.
2005). In particular, following Hasinger et al. (2005), we as-
sumed an LDDE evolution of the form:
Φ(MB, z) = Φ(M, 0) ∗ ed(z,MB) (9)
where:
ed(z,MB) =
(1 + z)p1 (z ≤ zc)
ed(zc)[(1 + z)/(1 + zc)]
p2 (z > zc)
. (10)
along with
zc(MB) =
zc,010
−0.4γ(MB−Mc) (MB ≥ Mc)
zc,0 (MB < Mc)
. (11)
where zc corresponds to the redshift at which the evolution
changes. Note that zc is not constant but it depends on the lu-
minosity. This dependence allows different evolutions at differ-
ent luminosities and can indeed reproduce the differential AGN
evolution as a function of luminosity, thus modifying the shape
of the luminosity function as a function of redshift. We also con-
sidered two different assumptions for p1 and p2: (i) both param-
eters constant and (ii) both linearly depending on luminosity as
follows:
p1(MB) = p1Mref − 0.4ǫ1 (MB − Mref) (12)
p2(MB) = p2Mref − 0.4ǫ2 (MB − Mref) (13)
The corresponding χ2 values for the two above cases are re-
spectively χ2=64.6 and χ2=56.8. Given the relatively small im-
provement of the fit, we considered the addition of the two fur-
ther parameters (ǫ1 and ǫ2) unnecessary. The model with con-
stant p1 and p2 values is shown with a solid black line in Figure
Figure 10. Evolution of comoving AGN space density with red-
shift, for different luminosity range: -22.0< MB <-20.0; -24.0<
MB <-22.0; -26.0< MB <-24.0 and MB <-26.0. Dashed lines
correspond to the redshift range in which the model has been
extrapolated.
9 and the best fit parameters derived for this model are reported
in the last line of Table 2.
This model reproduces well the overall shape of the luminos-
ity function over the entire redshift range, including the excess
of faint AGN at 1.0 < z < 1.5. The χ2 value for the LDDE model
is in fact the best among all the analyzed models. We found in
fact a χ2 of 64.6 for 67 degree of freedom and, as the reduced χ2
is below 1, it is acceptable 4.
The best fit value of the faint end slope, which in this model
corresponds to the slope at z = 0, is β =-2.0. This value is consis-
tent with that derived by Hao et al. (2005) studying the emission
line luminosity function of a sample of Seyfert galaxies at very
low redshift (0 < z < 0.15), extracted from the SDSS. They in
fact derived a slope β ranging from -2.07 to -2.03, depending on
the line (Hα, [O ii] or [O iii]) used to compute the nuclear lumi-
nosity. Moreover, also the normalizations are in good agreement,
confirming our model also in a redshift range where data are not
available and indeed leading us to have a good confidence on the
extrapolation of the derived model.
8. The AGN activity as a function of redshift
By integrating the luminosity function corresponding to our best
fit model (i.e the LDDE model; see Table 2), we derived the co-
moving AGN space density as a function of redshift for different
luminosity ranges (Figure 10).
The existence of a peak at z∼ 2 in the space density of bright
AGN is known since a long time, even if rarely it has been possi-
ble to precisely locate the position of this maximum within a sin-
gle optical survey. Figure 10 shows that for our best fit model the
peak of the AGN space density shifts significantly towards lower
4 We note that the reduced χ2 of our best fit model, which in-
cludes also VVDS data, is significantly better than that obtained by
Richards et al. (2006b) in fitting only the SDSS DR3 data.
Bongiorno, A. et al.: The VVDS type–1 AGN sample: The faint end of the luminosity function 11
Figure 9. Filled circles correspond to our rest-frame B-band luminosity function data points, derived in the redshift bins 1.0 < z <
1.5, 1.5 < z < 2.0, 2.0 < z < 2.5, 2.5 < z < 3.0 and 3.0 < z < 4.0. Open circles are the data points from the SDSS Data Release 3
(DR3) by Richards et al. (2006b). These data are shown also in two redshift bins below z = 1. The red dot-dashed line corresponds to
the model fit derived by Richards et al. (2006b) only for the SDSS data. The other lines correspond to model fits derived considering
the combination of the VVDS and SDSS samples for different evolutionary models, as listed in Table 2 and described in Section 7.
redshift going to lower luminosity. The position of the maximum
moves from z∼ 2.0 for MB <-26.0 to z∼ 0.65 for -22< MB <-20.
A similar trend has recently been found by the analysis
of several deep X-ray selected samples (Cowie et al., 2003;
Hasinger et al., 2005; La Franca et al., 2005). To compare with
X-ray results, by applying the same bolometric corrections
used is Section 6, we derived the volume densities derived
by our best fit LDDE model in the same luminosity ranges
as La Franca et al. (2005). We found that the volume density
peaks at z ≃ [0.35; 0.7; 1.1; 1.5] respectively for LogLX(2−10kev)
= [42–43; 43–44; 44–44.5; 44.5–45]. In the same luminosity
intervals, the values for the redshift of the peak obtained by
La Franca et al. (2005) are z ≃ [0.5; 0.8; 1.1; 1.5], in good agree-
ment with our result. This trend has been interpreted as evidence
of AGN (i.e. black hole) “cosmic downsizing”, similar to what
has recently been observed in the galaxy spheroid population
(Cimatti et al., 2006). The downsizing (Cowie et al., 1996) is a
term which is used to describe the phenomenon whereby lumi-
12 Bongiorno, A. et al.: The VVDS type–1 AGN sample: The faint end of the luminosity function
1.0 < z < 1.5 1.5 < z < 2.0
∆M Nqso LogΦ(B) ∆LogΦ(B) ∆M Nqso LogΦ(B) ∆LogΦ(B)
-19.46 -20.46 3 -5.31 +0.20 -0.38
-20.46 -21.46 11 -4.89 +0.12 -0.16 -20.28 -21.28 4 -5.29 +0.18 -0.30
-21.46 -22.46 17 -5.04 +0.09 -0.12 -21.28 -22.28 7 -5.18 +0.15 -0.22
-22.46 -23.46 9 -5.32 +0.13 -0.18 -22.28 -23.28 7 -5.54 +0.14 -0.20
-23.46 -24.46 3 -5.78 +0.20 -0.38 -23.28 -24.28 10 -5.34 +0.12 -0.17
-25.46 -26.46 1 -6.16 +0.52 -0.76 -24.28 -25.28 2 -5.94 +0.23 -0.53
2.0 < z < 2.5 2.5 < z < 3.0
∆M Nqso LogΦ(B) ∆LogΦ(B) ∆M Nqso LogΦ(B) ∆LogΦ(B)
-20.90 -21.90 1 -5.65 +0.52 -0.76
-21.90 -22.90 3 -5.48 +0.20 -0.38 -21.55 -22.55 3 -5.45 +0.20 -0.38
-22.90 -23.90 4 -5.76 +0.18 -0.30 -22.55 -23.55 4 -5.58 +0.19 -0.34
-23.90 -24.90 4 -5.81 +0.18 -0.30 -23.55 -24.55 3 -5.90 +0.20 -0.38
-24.90 -25.90 2 -5.97 +0.23 -0.53 -24.55 -25.55 2 -6.11 +0.23 -0.53
-25.90 -26.90 2 -6.03 +0.23 -0.55 -25.55 -26.55 1 -6.26 +0.52 -0.76
3.0 < z < 4.0
∆M Nqso LogΦ(B) ∆LogΦ(B)
-21.89 -22.89 4 -5.52 +0.19 -0.34
-22.89 -23.89 3 -5.86 +0.20 -0.40
-23.89 -24.89 7 -5.83 +0.14 -0.21
-24.89 -25.89 3 -6.12 +0.20 -0.38
Table 1. Binned luminosity function estimate for Ωm=0.3, ΩΛ=0.7 and H0=70 km · s−1 · Mpc−1. We list the values of Log Φ and
the corresponding 1σ errors in five redshift ranges, as plotted with full circles in Figure 9 and in ∆MB=1.0 magnitude bins. We also
list the number of AGN contributing to the luminosity function estimate in each bin
Sample - Evolution Model α β M∗ k1L k2L A k1D k2D Φ
∗ χ2 ν
VVDS+SDSS - PLE α var -3.83 -1.38 -22.51 1.23 -0.26 0.26 - - 9.78E-7 130.36 69
VVDS+SDSS - PLE+PDE -3.49 -1.40 -23.40 0.68 -0.073 - -0.97 -0.31 2.15E-7 91.4 68
Sample - Evolution Model α β M∗ p1 p2 γ zc,0 Mc Φ
∗ χ2 ν
VVDS+SDSS - LDDE -3.29 -2.0 -24.38 6.54 -1.37 0.21 2.08 -27.36 2.79E-8 64.6 67
Table 2. Best fit models derived from the χ2 analysis of the combined sample VVDS+SDSS-DR3 in the redshift range 0.0 < z < 4.0
assuming a flat (Ωm + ΩΛ = 1) universe with Ωm = 0.3.
nous activity (star formation and accretion onto black holes) ap-
pears to be occurring predominantly in progressively lower mass
objects (galaxies or BHs) as the redshift decreases. As such, it
explains why the number of bright sources peaks at higher red-
shift than the number of faint sources.
As already said, this effect had not been seen so far in the
analysis of optically selected samples. This can be due to the
fact that most of the optical samples, because of their limiting
magnitudes, do not reach luminosities where the difference in the
location of the peak becomes evident. The COMBO-17 sample
(Wolf et al., 2003), for example, even if it covers enough redshift
range (1.2 < z < 4.8) to enclose the peak of the AGN activity,
does not probe luminosities faint enough to find a significant
indication for a difference between the space density peaks of
AGN of different luminosities (see, for example, Figure 11 in
Wolf et al. (2003), which is analogous to our Figure 10, but in
which only AGN brighter than M ∼ -24 are shown). The VVDS
sample, being about one magnitude fainter than the COMBO-
17 sample and not having any bias in finding faint AGN, allows
us to detect for the first time in an optically selected sample the
shift of the maximum space density towards lower redshift for
low luminosity AGN.
9. Summary and conclusion
In the present paper we have used the new sample of AGN, col-
lected by the VVDS and presented in Gavignaud et al. (2006), to
derive the optical luminosity function of faint type–1 AGN.
The sample consists of 130 broad line AGN (BLAGN) se-
lected on the basis of only their spectral features, with no mor-
phological and/or color selection biases. The absence of these
biases is particularly important for this sample because the typ-
ical non-thermal AGN continuum can be significantly masked
by the emission of the host galaxy at the low intrinsic luminos-
ity of the VVDS AGN. This makes the optical selection of the
faint AGN candidates very difficult using the standard color and
morphological criteria. Only spectroscopic surveys without any
pre-selection can therefore be considered complete in this lumi-
nosity range.
Because of the absence of morphological and color selec-
tion, our sample shows redder colors than those expected, for
example, on the basis of the color track derived from the SDSS
composite spectrum and the difference is stronger for the intrin-
sically faintest objects. Thanks to the extended multi-wavelength
coverage in the deep VVDS fields in which we have, in addition
Bongiorno, A. et al.: The VVDS type–1 AGN sample: The faint end of the luminosity function 13
to the optical VVDS bands, also photometric data from GALEX,
CFHTLS, UKIDSS and SWIRE, we examined the spectral en-
ergy distribution of each object and we fitted it with a combina-
tion of AGN and galaxy emission, allowing also for the possi-
bility of extinction of the AGN flux. We found that both effects
(presence of dust and contamination from the host galaxy) are
likely to be responsible for this reddening, even if it is not pos-
sible to exclude that faint AGN are intrinsically redder than the
brighter ones.
We derived the luminosity function in the B-band for 1 <
z < 3.6, using the usual 1/Vmax estimator (Schmidt, 1968),
which gives the space density contributions of individual ob-
jects. Moreover, using the prescriptions recently derived by
Hopkins et al. (2007), we computed also the bolometric lumi-
nosity function for our sample. This allows us to compare our
results also with other samples selected from different bands.
Our data, more than one magnitude fainter than previous op-
tical surveys, allow us to constrain the faint part of the luminosity
function up to high redshift. A comparison of our data with the
2dF sample at low redshift (1 < z < 2.1) shows that the VVDS
data can not be well fitted with the PLE models derived by pre-
vious samples. Qualitatively, our data suggest the presence of
an excess of faint objects at low redshift (1.0 < z < 1.5) with
respect to these models.
Recently, a growing number of observations at different red-
shifts, in soft and hard X-ray bands, have found in fact evi-
dences of a similar trend and they have been reproduced with a
luminosity-dependent density evolution parameterization. Such
a parameterization allows the redshift of the AGN density peak
to change as a function of luminosity and explains the excess
of faint AGN that we found at 1.0 < z < 1.5. Indeed, by com-
bining our faint VVDS sample with the large sample of bright
AGN extracted from the SDSS DR3 (Richards et al., 2006b),
we found that the evolutionary model which better represents
the combined luminosity functions, over a wide range of red-
shift and luminosity, is an LDDE model, similar to those derived
from the major X-surveys. The derived faint end slope at z=0 is
β = -2.0, consistent with the value derived by Hao et al. (2005)
studying the emission line luminosity function of a sample of
Seyfert galaxies at very low redshift.
A feature intrinsic to these LDDE models is that the comov-
ing AGN space density shows a shift of the peak with luminos-
ity, in the sense that more luminous AGN peak earlier in the
history of the Universe (i.e. at higher redshift), while the density
of low luminosity ones reaches its maximum later (i.e. at lower
redshift). In particular, in our best fit LDDE model the peak of
the space density ranges from z ∼ 2 for MB < -26 to z∼ 0.65
for -22 < MB < -20. This effect had not been seen so far in the
analysis of optically selected samples, probably because most of
the optical samples do not sample in a complete way the faintest
luminosities, where the difference in the location of the peak be-
comes evident.
Although the results here presented appear to be already ro-
bust, the larger AGN sample we will have at the end of the still
on-going VVDS survey (> 300 AGN), will allow a better sta-
tistical analysis and a better estimate of the parameters of the
evolutionary model.
Acknowledgements. This research has been developed within the framework of
the VVDS consortium.
This work has been partially supported by the CNRS-INSU and its Programme
National de Cosmologie (France), and by Italian Ministry (MIUR) grants
COFIN2000 (MM02037133) and COFIN2003 (num.2003020150).
Based on data obtained with the European Southern Observatory Very Large
Telescope, Paranal, Chile, program 070.A-9007(A), 272.A-5047, 076.A-0808,
and on data obtained at the Canada-France-Hawaii Telescope, operated by the
CNRS of France, CNRC in Canada, and the University of Hawaii. The VLT-
VIMOS observations have been carried out on guaranteed time (GTO) allo-
cated by the European Southern Observatory (ESO) to the VIRMOS consortium,
under a contractual agreement between the Centre National de la Recherche
Scientifique of France, heading a consortium of French and Italian institutes,
and ESO, to design, manufacture and test the VIMOS instrument.
References
Arnouts, S., Schiminovich, D., Ilbert, O., et al. 2005, ApJ, 619, L43
Avni, Y. & Bahcall, J. N. 1980, ApJ, 235, 694A
Barger, A. J., Cowie, L. L., Mushotzky, R. F., et al. 2005, AJ, 129, 578
Boyle, B. J., Shanks, T., Croom, S. M., et al. 2000, MNRAS, 317, 1014
Boyle, B. J., Shanks, T., & Peterson, B. A. 1988, MNRAS, 235, 935
Brandt, W. N., Hornschemeier, A. E., Schneider, D. P., et al. 2000, AJ, 119, 2349
Brown, M. J. I., Brand, K., Dey, A., et al. 2006, ApJ, 638, 88
Bruzual, G. & Charlot, S. 2003, MNRAS, 344, 1000
Cimatti, A., Daddi, E., & Renzini, A. 2006, A&A, 453, L29
Cirasuolo, M., Magliocchetti, M., & Celotti, A. 2005, MNRAS, 357, 1267
Cowie, L. L., Barger, A. J., Bautz, M. W., Brandt, W. N., & Garmire, G. P. 2003,
ApJ, 584, L57
Cowie, L. L., Songaila, A., Hu, E. M., & Cohen, J. G. 1996, AJ, 112, 839
Croom, S. M., Smith, R. J., Boyle, B. J., et al. 2004, MNRAS, 349, 1397
Di Matteo, T., Springel, V., & Hernquist, L. 2005, Nature, 433, 604
Fan, X., Strauss, M. A., Schneider, D. P., et al. 2001, AJ, 121, 54
Ferrarese, L. & Merritt, D. 2000, ApJ, 539, L9
Fiore, F., Brusa, M., Cocchia, F., et al. 2003, A&A, 409, 79
Fontanot, F., Cristiani, S., Monaco, P., et al. 2007, A&A, 461, 39
Gavignaud, I., Bongiorno, A., Paltani, S., et al. 2006, ArXiv Astrophysics e-
prints
Hall, P. B., Gallagher, S. C., Richards, G. T., et al. 2006, AJ, 132, 1977
Hao, L., Strauss, M. A., Fan, X., et al. 2005, AJ, 129, 1795
Hartwick, F. D. A. & Schade, D. 1990, ARA&A, 28, 437
Hasinger, G., Miyaji, T., & Schmidt, M. 2005, A&A, 441, 417
Hewett, P. C. & Foltz, C. B. 2003, AJ, 125, 1784
Hewett, P. C., Foltz, C. B., Chaffee, F. H., et al. 1991, AJ, 101, 1121
Hopkins, P. F., Hernquist, L., Cox, T. J., et al. 2006, ApJ, 639, 700
Hopkins, P. F., Richards, G. T., & Hernquist, L. 2007, ApJ, 654, 731
Hunt, M. P., Steidel, C. C., Adelberger, K. L., & Shapley, A. E. 2004, ApJ, 605,
Ilbert, O., Tresse, L., Zucca, E., et al. 2005, A&A, 439, 863
Iovino, A., McCracken, H. J., Garilli, B., et al. 2005, A&A, 442, 423
Kennefick, J. D., Djorgovski, S. G., & de Carvalho, R. R. 1995, AJ, 110, 2553
Kormendy, J. & Richstone, D. 1995, ARA&A, 33, 581
La Franca, F., Fiore, F., Comastri, A., et al. 2005, ApJ, 635, 864
La Franca, F., Fiore, F., Vignali, C., et al. 2002, ApJ, 570, 100
Lawrence, A., Warren, S. J., Almaini, O., et al. 2006, ArXiv Astrophysics e-
prints
Le Fèvre, O., Mellier, Y., McCracken, H. J., et al. 2004a, A&A, 417, 839
Le Fèvre, O., Vettolani, G., Paltani, S., et al. 2004b, A&A, 428, 1043
Le Fèvre, O., Vettolani, G., Garilli, B., et al. 2005, A&A, 439, 845
Lonsdale, C., Polletta, M. d. C., Surace, J., et al. 2004, ApJS, 154, 54
Lonsdale, C. J., Smith, H. E., Rowan-Robinson, M., et al. 2003, PASP, 115, 897
Magorrian, J., Tremaine, S., Richstone, D., et al. 1998, AJ, 115, 2285
Marshall, H. L., Tananbaum, H., Avni, Y., & Zamorani, G. 1983, ApJ, 269, 35
Matute, I., La Franca, F., Pozzi, F., et al. 2006, A&A, 451, 443
McCracken, H. J., Radovich, M., Bertin, E., et al. 2003, A&A, 410, 17
Miyaji, T., Hasinger, G., & Schmidt, M. 2000, A&A, 353, 25
Miyaji, T., Hasinger, G., & Schmidt, M. 2001, A&A, 369, 49
Mushotzky, R. F., Cowie, L. L., Barger, A. J., & Arnaud, K. A. 2000, Nature,
404, 459
Osterbrock, D. E. 1981, ApJ, 249, 462
Page, M. J., Mason, K. O., McHardy, I. M., Jones, L. R., & Carrera, F. J. 1997,
MNRAS, 291, 324
Pei, Y. C. 1995, ApJ, 438, 623
Prevot, M. L., Lequeux, J., Prevot, L., Maurice, E., & Rocca-Volmerange, B.
1984, A&A, 132, 389
Radovich, M., Arnaboldi, M., Ripepi, V., et al. 2004, A&A, 417, 51
Richards, G. T., Croom, S. M., Anderson, S. F., et al. 2005, MNRAS, 360, 839
Richards, G. T., Fan, X., Newberg, H. J., et al. 2002, AJ, 123, 2945
Richards, G. T., Hall, P. B., Vanden Berk, D. E., et al. 2003, AJ, 126, 1131
Richards, G. T., Lacy, M., Storrie-Lombardi, L. J., et al. 2006a, ApJS, 166, 470
Richards, G. T., Strauss, M. A., Fan, X., et al. 2006b, AJ, 131, 2766
Scannapieco, E. & Oh, S. P. 2004, ApJ, 608, 62
Schiminovich, D., Ilbert, O., Arnouts, S., et al. 2005, ApJ, 619, L47
Schlegel, D. J., Finkbeiner, D. P., & Davis, M. 1998, ApJ, 500, 525
Schmidt, M. 1968, ApJ, 151, 393
14 Bongiorno, A. et al.: The VVDS type–1 AGN sample: The faint end of the luminosity function
Schmidt, M., Schneider, D. P., & Gunn, J. E. 1995, AJ, 110, 68
Schneider, D. P., Fan, X., Hall, P. B., et al. 2003, AJ, 126, 2579
Siana, B., Polletta, M., Smith, H. E., et al. 2006, ArXiv Astrophysics e-prints
Silk, J. & Rees, M. J. 1998, A&A, 331, L1
Silverman, J. D., Green, P. J., Barkhouse, W. A., et al. 2005, ApJ, 624, 630
Steidel, C. C., Hunt, M. P., Shapley, A. E., et al. 2002, ApJ, 576, 653
Ueda, Y., Akiyama, M., Ohta, K., & Miyaji, T. 2003, ApJ, 598, 886
Vanden Berk, D. E., Richards, G. T., Bauer, A., et al. 2001, AJ, 122, 549
Warren, S. J., Hewett, P. C., & Osmer, P. S. 1994, ApJ, 421, 412
Wolf, C., Wisotzki, L., Borch, A., et al. 2003, A&A, 408, 499
1 Università di Bologna, Dipartimento di Astronomia - Via Ranzani
1, I-40127, Bologna, Italy
2 INAF-Osservatorio Astronomico di Bologna - Via Ranzani 1, I-
40127, Bologna, Italy
3 Astrophysical Institute Potsdam, An der Sternwarte 16, D-14482
Potsdam, Germany
4 Integral Science Data Centre, ch. d’Écogia 16, CH-1290 Versoix
5 Geneva Observatory, ch. des Maillettes 51, CH-1290 Sauverny,
Switzerland
6 Laboratoire d’Astrophysique de Toulouse/Tabres (UMR5572),
CNRS, Université Paul Sabatier - Toulouse III, Observatoire Midi-
Pyriénées, 14 av. E. Belin, F-31400 Toulouse, France
7 Institute for Astronomy, University of Edinburgh, Royal
Observatory, Edinburgh EH9 3HJ
8 IASF-INAF - via Bassini 15, I-20133, Milano, Italy
9 Laboratoire d’Astrophysique de Marseille, UMR 6110 CNRS-
Université de Provence, BP8, 13376 Marseille Cedex 12, France
10 IRA-INAF - Via Gobetti,101, I-40129, Bologna, Italy
11 INAF-Osservatorio Astronomico di Roma - Via di Frascati 33, I-
00040, Monte Porzio Catone, Italy
12 Max Planck Institut fur Astrophysik, 85741, Garching, Germany
13 Institut d’Astrophysique de Paris, UMR 7095, 98 bis Bvd Arago,
75014 Paris, France
14 School of Physics & Astronomy, University of Nottingham,
University Park, Nottingham, NG72RD, UK
15 INAF-Osservatorio Astronomico di Brera - Via Brera 28, Milan,
Italy
16 Institute for Astronomy, 2680 Woodlawn Dr., University of
Hawaii, Honolulu, Hawaii, 96822
17 Observatoire de Paris, LERMA, 61 Avenue de l’Observatoire,
75014 Paris, France
18 Centre de Physique Théorique, UMR 6207 CNRS-Université de
Provence, F-13288 Marseille France
19 Astronomical Observatory of the Jagiellonian University, ul Orla
171, 30-244 Kraków, Poland
20 INAF-Osservatorio Astronomico di Capodimonte - Via
Moiariello 16, I-80131, Napoli, Italy
21 Institute de Astrofisica de Canarias, C/ Via Lactea s/n, E-38200
La Laguna, Spain
22 Center for Astrophysics & Space Sciences, University of
California, San Diego, La Jolla, CA 92093-0424, USA
23 Centro de Astrofsica da Universidade do Porto, Rua das Estrelas,
4150-762 Porto, Portugal
24 Universitá di Milano-Bicocca, Dipartimento di Fisica - Piazza
delle Scienze 3, I-20126 Milano, Italy
25 Università di Bologna, Dipartimento di Fisica - Via Irnerio 46,
I-40126, Bologna, Italy
	Introduction
	The sample
	Colors of BLAGNs
	Luminosity function
	Definition of the redshift range
	Incompleteness function
	Estimate of the absolute magnitude
	The 1/Vmax estimator
	Comparison with the results from other optical surveys
	The low redshift luminosity function
	The high redshift luminosity function
	The bolometric luminosity function
	Model fitting
	The PLE and PDE models
	The LDDE model
	The AGN activity as a function of redshift
	Summary and conclusion
