1. No category

A Ks -band selected galaxy sample in GOODS-S: Catalogue
release and galaxy luminosity functions!
M. Salvato1 , A. Gabasch1,2 , N. Drory3 , G. Feulner1,2 , U. Hopp1,2 , M. Pannella1 , A. Rau1 , S. Seitz2 ,
R. Bender1,2 , and
1
2
3
Max–Planck–Institut f¨
ur extraterrestrische Physik, Giessenbachstraße 1, 85748 Garching, Germany
Universit¨
ats–Sternwarte M¨
unchen, Scheinerstraße 1, 81679 M¨
unchen, Germany
Department of Astronomy, University of Texas at Austin, University Station C1400, Austin, TX 78712
Received . . . / Accepted . . .
Abstract.
We present a deep Ks -selected galaxy catalogue constructed from public data in the centre of the GOODS-S
field. The sample of 3237 galaxies covers a total area of 50.64 arcmin2 and reaches a limiting magnitude of
Ks (AB) ∼ 25. We derive photometric redshifts with an accuracy of ∆z/(1 + z) ∼ 0.05. The catalogue with
multi-band photometry in U BV RIJHKs as well as the photometric redshifts are released to the public!! . A
comparison of Ks -band galaxy number counts to previously published results shows the quality of the sample.
We derive galaxy luminosity functions (LFs)in the rest-frame UV (1500˚
A) as well as in the rest-frame
optical (r ! ) and rest-frame near-infrared (Ks ) as a function of redshift. A comparison of the LFs in
the UV and the optical with deep I-band selected LFs shows the influence of the selection band:
The rest-frame UV LF from the Ks -selected GOODS-S sample has slightly larger characteristic
luminosity, a significantly lower characteristic density, but a similar faint-end slope. The rest-frame
optical LF shows good agreement at the bright end, but a significantly shallower faint-end slope.
This differences can be mainly attributed to the fact that some faint blue galaxies at lower redshifts
remain undetected in our near-infrared selected sample. The extrapolated rest-frame Ks -band LF
agrees with those based on Spitzer data. Considering the evolution of M ∗ and φ∗ we find relatively
good agreement with evolutionary trends found in the literature.
Key words. Galaxies: luminosity function – Galaxies: evolution – Galaxies: high-redshift – Galaxies:
fundamental parameters – Galaxies: distances and redshifts
1. Introduction
The advent of deep, large-area public surveys covering
a wide range of the electromagnetic spectrum from Xray to radio wavelengths enable us to study the evolution
of galaxies in unprecedented detail. Surveys like GOODS
(Giavalisco et al. 2004) and COSMOS (?)offer powerful
datasets to constrain the evolution of basic galaxy properties like the luminosity function (e.g. Caputi et al. 2006),
the stellar mass function (e.g. Bundy et al. 2005; Drory
et al. 2005), the star-formation history (e.g. Bunker et al.
2004; Gabasch et al. 2004b), and the specific star formation rate (e.g. Feulner et al. 2005; Juneau et al. 2005).
Send offprint requests to: M. Salvato [email protected]
!
Based on observations collected at the European Southern
Observatory, Chile (ESO programs 63.O-005, 64.O-0149, 64.O0158, 64.O-0229, 64.P-0150, 65.O-0048, 65.O-0049, 66.A-0547,
68.A-0013, 69.A-0014).
!!
http://www.mpe.mpg.de/opinas/goods-s/index.html
Moreover, the availability of high-resolution HST imaging
allows to trace the evolution of galaxy morphology over a
vast redshift range.
While galaxy surveys in the past have predominantly
been carried out at optical wavebands (see Colless 1997
for a review), the strong impulse to push the observational
frontier to ever higher redshifts, and the growing interest
in the build-up of stellar mass in galaxies over cosmic time
demands a selection at longer wavelengths. Especially the
near-infrared K-band offers the unique opportunity to
trace the massive part of the galaxy population out to
very high redshifts. Important near-infrared surveys include the Hawaii Deep Fields (Cowie et al. 1996), the
Las Campanas Infrared Survey (Marzke et al. 1999), K20
(Cimatti et al. 2002a), MUNICS (Drory et al. 2001), and
FIRES (Labb´e et al. 2003).
The purpose of this paper is to describe a deep Kselected galaxy catalogue on the central part of the
GOODS-S field with improved photometric calibration
and high-quality photometric redshifts. This catalogue
will be made publicly available and has already been used,
together with the FDF (Heidt et al. 2003), in Gabasch
et al. (2004b), Drory et al. (2005) and Feulner et al. (2005)
for deriving the star formation history, the evolution of
the stellar mass, and the specific star formation rate of
field galaxies within the redshift regime from 0.5 to 5.
Moreover, both samples have been used in Pannella et al.
(2006) to study the contribution of bulges and disks to the
evolution of the mass function up to z∼ 1.
This paper is organised as follows: Section 2 describes
the optical and near-infrared image dataset on which this
work is based. In Sect. 3 we discuss the source detection
method and the construction of the multi-band photometric catalogue. The photometric redshift technique used to
derive galaxy distances as well as its calibration and testing is detailed in Sect. 4. The resulting source catalogue
and galaxy number counts derived from it are described in
Sect. 5. Section 6 discusses the distribution of our objects
in redshift space. Galaxy luminosity functions at 1500˚
A
as well as in the r! and Ks bands are presented in Sect. 7,
before we summarise our results in Sect. 8.
Throughout this work we assume ΩM = 0.3, ΩΛ = 0.7,
H0 = 70 km s−1 Mpc−1 . Magnitudes are given in the AB
system.
2. Dataset
The study presented here is based on ground-based optical and near-infrared images obtained by ESO on the
GOODS-S field. Optical observations in the U, B, V, R and
I bands have been carried out with the Wide-Field Imager
(WFI) at the 2.2-m MPG/ESO telescope. The datasets
have been reduced by two different groups: U and I images
are taken from the field Deep2c of the GOODS/ESO Deep
Public Survey (Arnouts et al. 2001), and images in the B,
V and R bands have been provided by the Garching-Bonn
Deep Survey (Schirmer et al. 2003). U and I images have
a total exposure time of 13.2 and 7.47 hours, respectively.
The latter were obtained by stacking the images from
the GOODS/ESO Deep Public Survey and supplementing them with archival WFI images. Accordingly, total
exposure times of 15.8, 15.6 and 17.8 hours were reached
in the B, V and R bands, respectively. All optical observations were obtained under very similar seeing conditions
(1!! ) with a marginal spread of less than 5%.
The J, H and Ks -band data were observed with
ISAAC at the VLT and are part of the GOODS/ESO release 0.51 . The near-infrared observations are split into
eight subfields, with a size of 3! ×3! each (plate scale
0.!! 148/pixel). They cover the central part of the optical images which have a field of view of 30! ×30! (0.!! 238/pixel).
The nomenclature and the location of the near-infrared
subfields are shown in Fig. 1. The subfields are overlapping by ∼25!! , which reduces the total analysed area to
50.64 arcmin2 . The exposure times in each filter differ be1
Available at http://www.eso.org/science/goods/
Fig. 1. Mosaic Ks -band image showing the area covered by
the catalogue. Each of the eight subfields has a size of
3! ×3! . The nomenclature “FXX” corresponds to the original
GOODS/ESO naming scheme.
tween the eight subfields and range from 2.2 to 4.2, 3.9 to
5 and 5.8 to 7.9 hours in the J, H and Ks bands, respectively. Moreover, the seeing conditions varied significantly
for the eight sub-fields and between the three near-infrared
bands (see Tab. 1).
3. Source detection and multi-band photometry
Source detection and multi-band photometry was performed using YODA (Drory 2003). This package was
specifically designed for multi-band imaging surveys. It
takes into account that in mosaiced frames as well as in
dithered images the background noise is often inhomogeneous across the field. Furthermore, the frames do usually
not share a common coordinate system and/or pixel scale,
due to the use of multiple telescopes and imagers. This
is a severe issue, since re-sampling the images to a common coordinate system inevitably introduces considerable
noise, especially for faint sources. The methodology used
here is resembling the method described in Drory et al.
(2001). Below, details on the detection, image registration
and photometric measurements, specific for this analysis,
are given.
3.1. Detection
Source detection was performed in the Ks -band subimages. Because of the considerable seeing variability between the individual subfields this results in varying limiting depths for the sub-patches. Compared to a degradation
of the quality of all images to that with the worst point
spread function (PSF), this has the advantage of reaching
the optimum depth for each subfield.
Table 1. Seeing of the near-infrared images for the 8 subfields.
The completeness and surface brightness limits for the Ks band images are given as well.
Field
F09
F10
F11
F14
F15
F16
F20
F21
J
H
KS
50% compl.
s. b. lim.
!!
!!
!!
mag
mag/arcs2
0.36
0.51
0.46
0.45
0.47
0.41
0.46
0.40
0.43
0.57
0.48
0.42
0.67
0.60
0.50
0.49
0.39
0.45
0.44
0.48
0.49
0.55
0.39
0.39
24.71
24.45
24.73
24.95
24.69
24.12
25.04
24.98
24.47
24.57
24.54
24.78
24.75
24.32
24.60
24.68
The reliability of the source detection depends mainly
on three parameters, namely (i) the threshold level above
the background, (ii) the minimum number of connected
pixels above that threshold which define an object and
(iii) the minimum number of pixels above the detection
threshold in split objects.
For each Ks -band subfield, simulations were
done using a different combinations of the parameters. The combination for which we obtained the
maximum number of detections in the positive image and the minimum number detections in the
negative image (false detections) has been considered as optimal and used . Accordingly, the detection parameters were chosen as 3.5σ for the detection threshold, 7 pixels for the minimum number
of consecutive pixels, and, in case of a splitted object, 5 pixels. A source catalogue for each subfield
was thus generated.
Due to dithering, the borders of the images were
not homogeneously exposed thus leads to in numerous false detections andobjects with unreliable photometry. For this reason, all detections located
within 50 pixels from the borders were removed.
Nevertheless, an overlap of few arcseconds still
remains between neighbouring subfields. A cross
check between the 8 catalogues revealed the presence of
65 sources with multiple detections. For these sources only
the detection with the largest distance to the border of the
image was included into the final source lists. The resulting catalogues consist of 3294 sources split into 450 in F09,
461 in F10, 427 in F11, 409 in F14, 351 in F15, 336 in f16,
408 in F20 and 452 in F21.
The 50% completeness limits for point-sources were estimated following the procedure described in Snigula et al.
(2002). The resulting value for each subfield, together with
the surface brightness limit, is listed in Tab. 1. Note that
the quantities were computed after the tuning of the photometry as explained in Sect. 4.
3.2. Multi–band photometry
After source detection, all optical and near-infrared images were convolved to the worst seeing among the images in the dataset, namely to the 1!! seeing of the B-band
frame. In the next step, each convolved image was registered to the pixel coordinate system of the corresponding
un-convolved Ks -band image in which the detection was
performed.
After transforming the coordinates the fluxes in all filters were measured in fixed apertures of 1.!! 5 (i.e. 1.5 times
the seeing). Furthermore, the total magnitudes included in
Kron-like apertures (Kron 1980) were derived. The small
fixed aperture was chosen in order to avoid the flux contamination from neighbouring objects. As a further advantage the colour gradient of extended objects far from the
centre are ignored. Thus, later spectral energy distribution
(SED) fitting will not take into account colour gradients
outside of the aperture. The fluxes were measured with
both YODA and SExtractor (Bertin & Arnouts 1996), and
the values were found to be consistent. The preliminary
magnitudes of the sources were computed based on the
zero-points and associated uncertainties provided in the
image headers. More precise magnitudes were achieved after the tuning of the zero-points of the images as described
in the following section.
4. Photometric redshift
4.1. The method
Photometric redshifts for the detected sources were computed with the algorithm described in Bender et al. (2001)
and Gabasch et al. (2004a). In brief, semi-empirical SED
templates were fitted to the multi-band photometry data
and the best solution was determined via χ2 statistics.
The templates were obtained by grouping approximately
300 observed spectra of galaxies from the FORS Deep
Field (FDF; Heidt et al. 2003) and the Hubble Deep Field
North (HDF; Williams et al. 1996) according to their spectral properties and extending them by fitting a combination of different stellar population models by Maraston
(1998) with different ages and dust extinction values. As
a result, representative SED templates with variable starformation activity, age, metalicity, and dust extinction
were obtained. The complete set of 29 SED templates is
shown in Fig. 2.
For each object a redshift probability function P (z)
was determined by matching the redshifted galaxy templates to the multi-band source fluxes assuming no priors.
In addition, stellar SEDs from the Pickles compilation of
stars with solar abundance, metal-weak and metal-rich FK dwarf and G-K giant components (Pickles 1998) were
fitted.
4.2. The calibration
The photometric redshifts were calibrated using the observed spectra of 135 galaxies. 120 of these were taken from
Fig. 2. SED template library used for the photometric redshift determination. All templates are normalised to the flux
at λ = 5100˚
A.
the GOODS/EIS webpage available prior to the release of
the spectroscopic master catalogue2 . In addition 15 spectra of non-active galaxies were taken from the follow-up
of X-ray observations in the Chandra Deep Field South
(Szokoly et al. 2004). The redshift distribution of these
135 galaxies ranges from z = 0.2 to z = 6.0, with the
majority of them lying between z = 0.5 and z = 1.4.
The technique of photometric redshift is in general very sensitive to uncertainties in the photometry
(see Bolzonella et al. (2000) for a complete discussion).
Therefore, precise zero-points of the individual images are
mandatory. Unfortunately, the first release of the optical
GOODS/EIS images suffered from significant inaccuracies
of the zero–points in the U and I bands (see Arnouts et al.
2001; Manfroid & Selman 2001; Hildebrandt et al. 2005).
In addition, field-to-field variations of the order of 0.1 mag
in J and 0.2 mag in Ks were already noted when the data
were released. For the H-band data field-to-field variations
were not ruled out in the release.
Being aware of these uncertainties, we allowed for small
changes in the zero-points of the images in order to increase the accuracy of the photometric redshift solution.
In a given optical band, the same correction to the zeropoint was applied in all subfields, as single images cover
the whole area. In the near-infrared, new zero-points were
independently obtained for each of the eight subfields. The
zero-points were considered appropriate when for each object with an available spectrum (i) the photometric redshift was consistent with the spectroscopic one and (ii)
the selected galaxy template was resembling the actual
2
http://www.eso.org/science/goods/spectroscopy/
CDFS Mastercat/
Fig. 3. Template fitting to the photometric points for an example galaxy with R=23 mag (bottom panel). The best fit is
obtained with a late-type galaxy template at z = 1.02 ± 0.05.
The same galaxy with a spectroscopic redshift of z = 0.97 is
shown for comparison in the top panel (arbitrarily normalised)
with the continuum from the best fitting SED (dotted line) is
over-plotted.
spectrum. A typical example is shown in Fig. 3, were the
multi-band photometry of a galaxy at R=23 mag is plotted together with the best fitting SED template. The resulting photometric redshift of z=1.02±0.05 is consistent
with the spectroscopic redshift of z=0.97.
The final corrections to the zero-points in the B, V and
R bands are only marginal (from −0.02 to +0.08 mag),
while U and I required a systematic brightening of the
order of 0.25 magnitudes. In the J band the necessary
correction was on average −0.1 mag, while the H and Ks band zero-points needed a modification in a range of −0.45
to +0.19 mag depending on the subfield. Applying these
corrections, a set of new zero-points was computed for all
bands: U =21.10, B=24.61, V =24.15, R=24.54, I=22.88;
the zero-points for the J, H and Ks bands for each subfield
are listed in Tab. 2. The obtained values were used to
compute the actual surface brightness limits of the Ks band images and the aforementioned completeness limits
of the catalogues presented in Table 1.
Fig. 4 (left panel) shows the comparison between our
photometric redshift and thenow available spectroscopic
redshift for a sample of approximately 500 galaxies (i.
e. including the 135 used for the calibration: see
figure caption for details). Considering only galaxies
with highly reliable spectroscopic redshifts, an accuracy of
∆z/(1+z) = 0.05 is reached independent of redshift (middle panel), the highest precision achieved for this dataset
of images so far. The right panel shows the histogram of
the reduced χ2 of the photometric redshifts fit. The me-
Table 2. Correction to the zero-points of the images.
F09
F10
F11
F14
F15
F16
F20
F21
J
H
Ks
mag
mag
mag
25.08
24.89
24.88
25.1
25.06
24.55
25.03
25.08
24.48
24.68
24.66
24.53
24.44
24.81
24.55
24.82
24.14
24.08
23.92
24.16
23.93
23.83
24.27
24.35
dian value of the reduced χ2 is below 1.6 and demonstrates
that the galaxy templates describe the vast majority of
galaxies well.
4.3. Verification of the zero-points
Although the achieved accuracy of the photometric redshifts is a crucial test of our re-calibrated zero-points,
we performed additional tests using (i) detecxtion in
more than one subfield, (ii) the H-band catalogue of the
Las Campanas Infrared Survey (Chen et al. 2002) and
(iii) photometric redshifts provided by COMBO–17 (Wolf
et al. 2004).
As discussed above, 65 sources were detected in more
than one of the eight Ks -band images. For each of these
sources and for a given near-infrared band, the photometry of the multiple detections (after the zero-point correction) is in agreement within 0.05 mag or better. The
resulting values for the photometric redshifts of the individual sources are consistent within ∆zphot = 0.03.
Observations of the GOODS-S field in V , R, I, z and
H are also included in the Las Campanas Infrared Survey.
Chen et al. (2002) provide the H-band photometry for
sources brighter then H ∼ 20.8 mag in a fixed aperture
of 2!! . In order to allow a comparison with their results,
we recomputed the flux measurements in the H band using the same aperture. The magnitude difference ∆MH =
MH, Las Campanas − MH, this work for common sources, before and after the zero-point correction, are shown in the
left panel of Fig. 5. Using the original zero-points, the
distribution showed an offset of ∆MH = 0.04 mag and a
non-negligible asymmetry due to field-to-field variations.
With the new zero-points this asymmetry disappears and
the distribution is centred at ∆MH = 0.03 mag with an
RMS of 0.1 mag.
We further compared our photometric redshifts with
the results of COMBO–17 (Wolf et al. 2004), a survey
based on photometry in 17 optical filters, including 12
medium-band filters. These filters are sensitive to individual emission lines and therefore allow a photometric
redshift accuracy of up to 1% for sources brighter than
R = 21. The precision decreases for fainter objects, reaching 10% at R > 24. A total of 499 targets with photometric
redshifts and classified as galaxy in COMBO–17 are also
present in our catalogues. A comparison of the photometric redshifts is shown in the right panel of Fig. 5.
Following Wolf et al. we estimated the precision of
our photometric redshift in different magnitude intervals. For galaxies brighter than R = 21 an accuracy of
∆z = (z COMBO−17 − z this work )/(1 + z COMBO−17 ) ∼ 0.02
was achieved. This value corresponds to the intrinsic binning of our photometric redshift procedure. Sources with
21 < R < 23.5 have a ∆z of 0.05. For galaxies fainter
than R = 23.5, the photometric redshifts of COMBO–17
exhibit significant uncertainties. Therefore, these sources
could not be used for further verification of the quality of
our results.
5. Source catalogue
After removing the field-to-field variations of the
photometry and the verification of the photometric redshift accuracy, we applied our method to all
eight Ks -band source catalogues. The merged final catalogue can be accessed online at the URL
http://www.mpe.mpg.de/opinas/goods-s/index.html.
Additionally, information about sources can be accessed
by clicking on them in the images or querying by coordinates. For each source its identification, position,
photometry, photometric and spectroscopic (if available)
redshift, absolute magnitude in the B and Ks bands, and
its classification are presented. In addition thumbnail
images in all filter bands as well as the best fitting SED
model together with the photometric redshift probability
distribution are shown. The nature of a source is indicated
by a flag (galaxy=G, star=S, AGN=AGN). Below we
describe how stars are identified and how we treated
AGN for the subsequent analysis of the galaxy luminosity
function.
5.1. Stars
The catalogue contains 14 stars with known spectral type
provided by SIMBAD as well as 22 objects for which stellar spectra have been observed in the follow-up by VVDS,
VLT/FORS2 spectroscopy in GOODS-S and K20.
As demonstrated in Gabasch et al. (2004a), stars can be
also identified by the photometric redshift technique. We
classify as stars all objects for which the best fitting stellar SED gives a better match than any galaxy template (2
χ2star < χ2galaxy ). According to this criterion 41 stars were
selected, out of which ∼50% were also spectroscopically
confirmed.
5.2. AGN
The KS -band selection naturally does not distinguish between normal and active galaxies, thus also AGN and
quasars are contained in the final source catalogue. As
no specific AGN template is included in our photometric
Fig. 4. Left panel: Comparison between the photometric redshifts presented in this paper and publicly available spectroscopic
redshifts for galaxies in GOODS-S. This includes objects in common with the VVDS (Le F`evre et al. 2004), observed with
the VLT/FORS2 (Vanzella et al. 2005), from the spectroscopic follow-up of Chandra selected sources (Szokoly et al. 2004)
and from K20 (Mignoli et al. 2005). The filled circles indicate objects for which the spectroscopic redshifts were flagged as
highly reliable (flag(VVDS)=4, flag(VLT/FORS2)=A, flag(Szokoly)=2, flag(K20)=1). Empty circles mark galaxies with lower
reliability. Middle panel: Distribution of the uncertainties in the photometric redshift (solid histogram). It can be fitted by a
Gaussian distribution (dotted line) centred at ∆z/(1 + z) = 0.012 with a σ of 0.05. Right panel: Histogram of the reduced χ2
of the best template fit for all 3237 galaxies. The dotted vertical line indicates the median reduced χ2 of 1.6.
Fig. 5. Left panel: Histogram of magnitude differences between the H-band photometry from the Las Campanas Survey and this
work computed within a fixed aperture of 2!! . The dashed and solid lines show the distribution before and after the correction
of the zero-points, respectively. After the correction the asymmetry of the distribution disappears. Right panel: Comparison
between the photometric redshifts presented in this work and those provided by COMBO–17 for the galaxies in common.
Filled circles represent galaxies brighter than R =23.5 mag and empty circles mark fainter sources.
redshift code, a separate verification of the reliability of
the photometric redshift for those galaxies was required.
For this purpose, we compared the photometric redshifts for 36 X-ray selected sources from our catalogue
with secure spectroscopic redshifts provided by Szokoly
et al. (2004). 15 of those where classified as galaxies on
the base of their optical spectra and already used for the
calibration in Sect. 4.1. The remaining sources include 7
type-I and 14 type-II AGN.
We find a good match of the photometric and spectroscopic redshifts for all 36 sources with an accuracy of
∆z/(1 + z) = 0.05 (see Fig. 6). Irrespective of the small
sample size, the achieved precision excels those obtained
for previous X-ray selected samples, including those using
AGN templates (e.g., Zheng et al. 2004).
As no specific AGN SED templates were used to obtain the photometric redshifts, the accurate match with
the templates of normal and star-forming galaxies suggests
K [AB mag]
Fig. 6. Comparison of the photometric redshift presented in
this work with the spectroscopic redshift for 36 X-ray selected galaxies. Symbols are as defined in Zheng et al. (2004),
where open circles represent type-I AGN, open squares type-I
quasars, filled circles type-II AGN, filled squares type-II AGN
and triangles galaxies. The accuracy is ∆z/(1+z) ∼ 0.05. Note
that no specific AGN SED template was used. This suggests
that the light of the host galaxies dominates over the nuclear
emission.
that the optical emission of the X-ray selected sources is
dominated by the host galaxy rather than the central engine. Therefore, these galaxies remained included in the
final source catalogue used in the following for the study
of the luminosity functions. Only for two sources significant deviations between the photometric and spectroscopic redshifts were found, namely (ii) a normal galaxy,
and (iii) a type II AGN. In both cases the algorithm has
picked up the right redshift as second solution.
5.3. The final catalogue
After removal of the stars, the galaxy number counts for
the 3237 galaxies of the final catalogue have been computed (Tab. 3) and a good agreement has been found when
comparing the results to previous studies (Fig. 7). This is
the catalogue that has been already used, together with
the FDF, in Gabasch et al. (2004b), Drory et al. (2005),
Feulner et al. (2005) and ? for deriving the star formation
history, the evolution of the stellar mass, and the specific
star formation rate, the star formation history and evolution of galaxy morphology of field galaxies within a
vast redshift regime. In the following section we analyse
the redshift distribution and the luminosity functions.
Fig. 7. Galaxy number counts in the Ks band from our catalogue,not corrected for incompleteness (filled red circles) and
from previous studies (other symbols). Error bars indicate
Poisson errors.
Table 3. Differential Ks -band galaxy number counts in the
GOODS-S field.
Ks
[mag]
17.50
18.50
19.50
20.50
21.50
22.50
23.50
log N (K)
[mag−1 deg−1 ]
2.70
3.17
3.77
4.10
4.33
4.61
4.79
δ log N (K)
[mag−1 deg−1 ]
0.17
0.10
0.05
0.03
0.03
0.02
0.01
6. Redshift distribution
To better characterise the galaxy population probed by
our sample we study the distribution of the absolute Iband magnitude with redshift for the various SED templates (see left panel of Fig. 8). It confirms that early-type
galaxies are present out to relatively high redshifts of z ∼ 2
in a deep Ks -band selected catalogue (?). Later types can
be traced to even higher redshifts.
This trend can be seen also in the right panel of Fig. 8,
where we reproduce the redshift distribution of the sample galaxies as a function of their SED (as attributed by
the photo-z code). Galaxies classified as early type (red)
appear mostly at redshift less than 1.5, while those classified as intermediate type (green) reach redshifts up to
4. On the other hand, objects with a starburst/irregulartype SED (blue) span the full redshift range. Only in a few
Table 4. Schechter function fit to the luminosity function at
1500˚
A. A fixed value of α1500 =-1.07 has been used.
redshift bin
0.45 0.81
0.81 1.11
1.11 1.61
1.61 2.15
2.15 2.91
2.91 4.01
M∗1500
(mag)
φ∗1500
(Mpc−3 )
-18.72+0.22
−0.22
0.0072+0.0010
−0.0010
-19.61+0.26
−0.25
-19.72+0.28
−0.22
-20.34+0.20
−0.20
-20.80+0.43
−0.56
-21.27+0.29
−0.28
0.0041+0.0007
−0.0006
0.0036+0.0010
−0.0008
0.0028+0.0006
−0.0005
0.0011+0.0006
−0.0004
Table 6. Schechter function fit to Ks -band luminosity function
for a fixed value of αK = −1.15.
redshift bin
0.45 0.85
0.85 1.31
1.31 1.91
1.91 2.61
M∗Ks
(mag)
φ∗Ks
(Mpc−3 )
-23.54+0.37
−0.41
0.0028+0.0004
−0.0003
-23.20+0.25
−0.21
0.0013+0.0002
−0.0001
-23.52+0.24
−0.21
-23.39+0.24
−0.21
0.0017+0.0002
−0.0002
0.0009+0.0001
−0.0001
0.0008+0.0002
−0.0002
7. Luminosity function
Table 5. Schechter function fit to the r ! -band luminosity function for a fixed value of αr! = −1.07.
redshift bin
0.45 0.85
0.81 1.31
1.31 1.91
1.91 2.61
2.61 3.81
3.81 5.01
M∗r!
(mag)
φ∗r!
(Mpc−3 )
-22.38+0.22
−0.20
0.0047+0.0004
−0.0004
-22.63+0.18
−0.18
0.0019+0.0002
−0.0002
-22.90+0.21
−0.16
0.001+0.0002
−0.0001
-22.55+0.20
−0.17
-22.96+0.20
−0.20
-23.36+0.55
−0.56
0.003+0.0003
−0.0003
0.0013+0.0002
−0.0002
0.0002+0.0002
−0.0001
cases, the photo-z code has attributed an early-type SED
to objects at redshifts as high as 2.5. This can be naturally
explained as follows. The rest-frame UV-to-optical SED of
a heavily dust obscured starburst at these high redshifts is
very similar to that of an old, passively evolving galaxy, so
that the photometric redshift technique selects the wrong
SED. This is particularly true in absence of any prior on
the maximum redshift allowed for an early-type galaxy. In
fact, when early-type SEDs are forced not to characterise
galaxies at redshifts higher than 1.5, the new solutions of
the photo-z code for the previous objects do correspond
to a starburst-like SED. Furthermore, only 2% of these
objects have a new redshift that differs by more than 0.2
from the original one, the fraction of those with a difference in redshift larger than 0.5 being only 1%. In the
same panel, the total redshift distribution of the objects is
shown as a black line. Large scale structures spectroscopically detected at z ∼ 0.7 (Cimatti et al. 2002b; Gilli et al.
2003; Le F`evre et al. 2004), z ∼ 1.1 (Vanzella et al. 2002),
z ∼ 1.61 (Gilli et al. 2003), and z ∼ 3.5 (Caputi et al.
2006) can be also seen in the histogram of photometric
redshifts.
In this section we analyse the rest-frame UV, r! , and Ks band luminosity functions inferred from the Ks -selected
GOODS catalogue. The previously mentioned different limiting magnitudes of the sub-patches
are taken into account in the computation of the
luminosity functions. Following Gabasch et al. (2004a)
we derive the absolute rest-frame magnitudes by using the
best fitting SED determined by the photometric redshift
code. As the SED fits all observed-frame wave-bands
simultaneously, possible systematic errors which could
be introduced by using k-corrections applied to a single
observed magnitude are reduced. Since the photometric
redshift code works with 1.5!! aperture fluxes, we also need
to correct to total luminosities by applying an object
dependent scale factor. For this scale factor we used the
ratio of the Ks -band aperture flux to the total flux as
provided by YODA. To account for the fact that some
fainter galaxies are not visible in the whole survey volume
we perform a V /Vmax (Schmidt 1968) correction. To
derive reliable Schechter parameters we limit our analysis
of the luminosity function to the bins where the V /Vmax
correction contributes at most a factor of 3 (we also show
the uncorrected luminosity function in the various plots
as open circles). The errors of the LFs are calculated
by means of Monte-Carlo simulations and include the
photometric redshift error of every single galaxy as well
as the statistical error.
Rest-frame UV-band LF:
In Fig. 9 we show the UV LF as evaluated in a rectangular filter centred at 1500 ± 100 ˚
A in the redshift
range 0.5 < z < 4.0. The filled (open) symbols denote
the LF with (without) completeness correction. The
solid lines show the Schechter function fitted to the
luminosity function for a fixed slope α = −1.07. The
best fitting Schechter parameters, the redshift binning
as well as the reduced χ2 are also listed in each panel
of the figure and in Tab. 4. Since the slightly shallower
Ks -selected GOODS-S LF does not allow us to constrain
the faint-end slope to the same level as Gabasch et al.
(2004a) in the FDF (but is consistent with the faint
end slope determined for that field), we adopt this value
also for the GOODS-S sample. Furthermore, we also
Fig. 8. Left panel: Absolute I-band magnitude versus photometric redshift. Colour indicates the SED template, where red
corresponds to early types, and blue to late types. Note the lack of galaxies in the redshift range 0.2 to 0.6 (see inset). Right
panel: Redshift number distribution of all galaxies in the GOODS-S sample. The clustering visible at z ∼ 0.7, 1.1, and 1.6 is
spectroscopically confirmed.
show in the various panels the corresponding UV-band
Schechter function derived in the FDF. Compared to LF
parameters of the optically selected FDF sample, the
1500˚
A LF of the Ks -selected sample has slightly brighter
values of M∗ , significantly lower values in φ∗ and, within
the large errors, a similar faint-end slope α. As faint blue
galaxies at relatively low redshifts will certainly be missed
more likely in a Ks -selected sample than in an optical
selected one, the significantly lower values of φ∗ does
not come as a surprise (see also Fig. 11 and discussion
below). Moreover, we showed in Gabasch et al. (2004b)
that the UV luminosity density (directly proportional to
the SFR) derived in GOODS-S is similar in shape, but
systematically lower by ≈ 0.2 dex at z > 1 compared
to the FDF. This result originates from the lower density of M1500 > −19 galaxies in the Ks -selected catalogue.
Rest-frame r! -band LF:
The r! -band LFs together with the best fitting Schechter
parameter, the redshift binning as well as the reduced χ2
is shown in Fig. 10 and listed in Tab. 5. Although there
is a relatively good agreement between the slope of the
UV LF found in the FDF and GOODS-S, this is not the
case for the r! -band. A steep slope of αr! = −1.30 ± 0.05
as found for the r! -band FDF LF (Gabasch et al. 2006) is
not seen for the GOODS-S LF. Therefore, we investigate
the redshift evolution of the faint-end slope of the LF by
fitting a three parameter Schechter function (M ∗ , φ∗ , and
α). Under the assumption that α does not depend on redshift, the slope’s best error-weighted value in the redshift
range from %z& ∼ 0.65 to %z& ∼ 2.3 is αr! = −1.07 ± 0.12
(including also the higher redshift bins changes α only
marginally). The difference between the FDF and the
GOODS-S slope is hence on a 2σ level for the r’-band.
As already discussed above, faint blue galaxies will certainly be missed more likely in a Ks -selected sample
than in an I-selected one. This is illustrated best in
Fig. 11, where we show the absolute r! -band magnitude
of GOODS-S and FDF galaxies as a function of redshift
and sub-divided into four main SED types. The SEDs
are mainly grouped according to the UV−K colour (see
Gabasch et al. 2006, for more details): for increasing
spectral type (SED type 1 → SED type 4) the SEDs become bluer, i.e. the UV flux (and thus the recent star
formation rate) increases if compared to the K-band flux.
Furthermore, the rest-frame U − V colour lies in the range
between 2.3 – 1.9, 2.0 – 1.6, 1.6 – 0.9, and 0.9 – 0 for SED
type 1, 2, 3, and 4, respectively. Therefore, in a rough classification one can refer to SED types 1 and 2 (SED type
3 and 4) as red (blue) galaxies.
Fig. 10 clearly shows, that the Ks -selected GOODS-S
catalogue mainly misses faint SED type 4 galaxies,
whereas about the same number of type 1, 2 and 3
galaxies are detected. This deficit can not be compensated by the V /Vmax method, as it corrects only for the
phenomenon that a faint galaxy in the selection catalogue
might not be visible in the whole volume of the redshift
bin under consideration. The V /Vmax correction cannot
account for galaxy types which are not detected at all.
On the other hand, as we show in Gabasch et al. (2006)
at the depth of the FDF the faint-end of the r! -band
LF is always dominated by SED type 4 galaxies, while
˚ from low redshift ($z% = 0.65, upper left panel) to high redshift ($z% = 3.5, lower right
Fig. 9. Luminosity functions at 1500 A
panel). The filled (open) symbols show the luminosity function corrected (uncorrected) for V /Vmax . The corresponding Schechter
function derived in the FDF is also shown as dashed line in every panel with the shaded region roughly corresponding to the
associated 1σ error. The limiting magnitude of the FDF is indicated by the low-luminosity cut-off of the shaded region.
for the bright end SED type 1 galaxies dominate. As we
are able to detect in GOODS-S about the same amount
of type 1/2 galaxies (if compared to the FDF) but miss
a large fraction of faint type 4 galaxies, the overall LF
flattens. It also explains the relatively good agreement at
the bright end between the GOODS-S and FDF r! -band
LF up to redshift of about z ∼ 2.5.
Rest-frame Ks -band LF:
The rest-frame Ks -band LF in the redshift range
%z& = 0.65 to %z& = 2.3 is shown in Fig. 12 and listed in
Tab. 6. Computing the rest-frame Ks -band luminosity of
a galaxy at some redshift z > 0 is, in principle, an extrapolation since our reddest observed band is the Ks band
itself. However, Saracco et al. (2006) show that the RMS
error of this extrapolation is comparable to the typical
photometric errors as long as the observed Ks filter samples the part of the SED dominated by old stars, i.e. for
wavelengths λ > 4000˚
A. Hence we restrict our analysis of
the rest-frame Ks -band LF to redshifts z <
∼ 2.
In each panel of the Figure we also show the bestfitting Schechter parameters, the redshift binning as well
as the reduced χ2 . As the slope of the LF is relatively
uncertain, we decided to use a fixed slope of α = −1.15
which yields a relatively good χ2 in the various redshift
bins. Note that there is a hint for an upturn at the very
faint end of the LF at low redshift (see also Saracco et al.
2006).
In the second and third panel the corresponding LF
as presented recently in Caputi et al. (2006) is also shown
in red. Caputi et al. used Spitzer/IRAC data in addition
to the available optical and near-infrared photometry in
GOODS-S. Hence the relatively good agreement between
their and our LF shows that we do not suffer from large
extrapolation errors.
Furthermore in Fig. 13 we compare our Ks -band LF
to the one published by Saracco et al. (2006) for a very
deep, but ten times smaller survey. For this comparison
we computed our LF in the same redshift bins as Saracco
et al.. Both LFs are in very good agreement.
In the last two panels of Fig. 12 we compare our
best-fitting values for M ∗ and φ∗ (derived using a fixed
α = −1.1) at various redshifts with results from the literature (using the same value for α) showing reasonable
agreement. Considering the redshift evolution of φ∗ we
find that the characteristic number density drops by a
factor of ∼ 3 − 4 over the redshift range 0.65 < z < 2.3,
Fig. 10. r’-band luminosity functions from low redshift ($z% = 0.45, upper left panel) to high redshift ($z% = 5.1, lower right
panel). The filled (open) symbols show the luminosity function corrected (uncorrected) for V /Vmax . The corresponding
Schechter function derived in the FDF is also shown as dashed line in every panel together with the its limiting
magnitude, indicated by the low-luminosity cut-off of the shaded region.
which results in an decrease of the Ks -band luminosity
density with increasing redshift.
8. Conclusion
In this paper we have made use of publicly available
U BV RIJHKs images in the centre of the GOODS-S field
to construct a deep Ks -selected galaxy sample for evolution studies. Our catalogue of 3237 galaxies covers a total
area of 50.64 arcmin2 and reaches a limiting magnitude of
Ks ∼ 25 (50% completeness limit for point sources).
We describe in detail the construction and calibration
of the photometric catalogue. We lay special emphasis on
an improvement of the photometric calibration by making use of spectroscopic information. A comparison of
Ks -band galaxy number counts to previously published
results shows the quality of the galaxy sample. We derive photometric redshifts and estimate their accuracy of
∆z/(1 + z) ∼ 0.05 over the whole range up to z ∼ 5 by
comparing them to available high-quality spectra in the
field.
The resulting photometric catalogue as well as
the photometric redshifts are released to the pub-
lic. It can be accessed at the following web address:
http://www.mpe.mpg.de/opinas/goods-s/index.html.
We derive galaxy luminosity functions in the restframe UV (1500˚
A) as well as in the rest-frame optical (r! )
and rest-frame near-infrared (Ks ) as a function of redshift.
Compared to the UV LF derived from the I-band selected
FDF sample (Gabasch et al. 2004a), the LF from the Ks selected GOODS-S sample has slightly brighter values of
M∗ , significantly lower values in φ∗ but, within the large
errors, a similar faint-end slope α.
This difference can be mainly attributed to the fact
that faint blue galaxies at lower redshifts will certainly be
missed more likely in a near-infrared selected sample than
in an optically selected survey.
For the rest-frame r! -band LF we find relatively good
agreement with the LF derived in the optically selected
FDF at the bright end, but a significantly shallower faintend slope for the Ks -selected GOODS-S sample, again
likely caused by the non-detection of extremely starforming galaxies in a near-infrared selected catalogue.
The rest-frame Ks -band LF agrees reasonably well
with previously published results (Caputi et al. 2006;
Saracco et al. 2006). Considering the evolution of φ∗
we find good agreement with the evolutionary model of
Fig. 11. Absolute r’-band magnitude as a function of redshift and SED type. The open red symbols are derived from the FDF
I-selected catalogue whereas the filled black symbols stem from this work (see text for details).
Caputi et al. (2006) as well as with the results of Feulner
et al. (2003) and Saracco et al. (2006). We find that the
characteristic number density drops by a factor of ∼ 3 − 4
over the redshift range 0.65 < z < 2.3. For M ∗ we can neither confirm nor exclude the evolution in the characteristic
luminosity due to the badly constrained bright end of the
LF in the small volume probed by our survey at lower
redshifts. At higher redshifts, however, our values for M ∗
agree very well with the literature.
Acknowledgements. We are grateful to A. Cimatti,
B. Vandame, and G. Szokoly for they availability. M. S.
thanks C. Maraston and D. Pierini for their help during
the preparation of the paper. The authors would like to
thank N. Metcalfe for making number count data available in
electronic form. We acknowledge funding by the DFG (SFB
375). This research has made use of NASA’s ADS Abstract
Service.
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