Spheroid's Panchromatic Investigation in Different Environmental Regions (SPIDER) - I. Sample and galaxy parameters in the grizYJHK wavebands

Abstract

This is the first paper of a series presenting a Spheroid's Panchromatic Investigation in Different Environmental Regions (SPIDER). The sample of spheroids consists of 5,080 bright (Mr<-20) Early-Type galaxies (ETGs), in the redshift range of 0.05 to 0.095, with optical (griz) photometry and spectroscopy from SDSS-DR6 and Near-Infrared (YJHK) photometry from UKIDSS-LAS (DR4). We describe how homogeneous photometric parameters (galaxy colors and structural parameters) are derived using grizYJHK wavebands. We find no systematic steepening of the CM relation when probing the baseline from g-r to g-K, implying that internal color gradients drive most of the mass-metallicity relation in ETGs. As far as structural parameters are concerned we find that the mean effective radius of ETGs smoothly decreases, by ~30%, from g through K, while no significant dependence on waveband is detected for the axis ratio, Sersic index, and a4 parameters. Also, velocity dispersions are re-measured for all the ETGs using STARLIGHT and compared to those obtained by SDSS. We compare our (2DPHOT) measurements of total magnitude, effective radius, and mean surface brightness with those obtained as part of the SDSS pipeline (Photo). Significant differences are found and reported, including comparisons with a third and independent part. A full characterization of the sample completeness in all wavebands is presented, establishing the limits of application of the characteristic parameters presented here for the analysis of the global scaling relations of ETGs. Comment: Accepted for Publication in MNRAS

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arXiv:0912.4547v2 [astro-ph.CO] 3 Jun 2010
Mon. Not. R. Astron. Soc. 000, 1–20 (2010) Printed 4 June 2010(MN LATEX style file v2.2)
Spheroid’s Panchromatic Investigation in Different Environmental
Regions (SPIDER) – I. Sample and galaxy parameters in the
grizYJHK wavebands.
F. La Barbera1⋆, R.R. de Carvalho2, I.G. de la Rosa3, P.A.A. Lopes4,
J.L.Kohl-Moreira5and H.V. Capelato2
1INAF – Osservatorio Astronomico di Capodimonte, Napoli, Italy
2Instituto Nacional de Pesquisas Espaciais/MCT, S. J. dos Campos, Brazil
3Instituto de Astrofisica de Canarias, Tenerife, Spain
4Observat´ orio do Valongo/UFRJ, Rio de Janeiro, Brazil
5Observat´ orio Nacional/MCT, Rio de Janeiro, Brazil
Submitted on 2009 December 22
ABSTRACT
This is the first paper of a series presenting a Spheroid’s Panchromatic Investigation in Dif-
ferent Environmental Regions (SPIDER). The sample of spheroids consists of 5,080 bright
(Mr< −20) Early-Type galaxies (ETGs), in the redshift range of 0.05 to 0.095, with optical
(griz) photometry and spectroscopy from SDSS-DR6 and Near-Infrared (YJHK) photometry
from UKIDSS-LAS (DR4). We describe how homogeneous photometric parameters (galaxy
colors and structural parameters) are derived using grizY JHK wavebands. We find no sys-
tematic steepening of the CM relation when probing the baseline from g-r to g-K, implying
that internal color gradients drive most of the mass-metallicity relation in ETGs. As far as
structural parameters are concerned we find that the mean effective radius of ETGs smoothly
decreases, by 30%, from g through K, while no significant dependence on waveband is de-
tected for the axis ratio, Sersic index, and a4parameters. Also, velocity dispersions are re-
measured for all the ETGs using STARLIGHT and compared to those obtained by SDSS.
The velocity dispersions are re-derivedusing a combinationof simple stellar populationmod-
els as templates, hence accounting for the kinematics of different galaxy stellar components.
We compare our (2DPHOT) measurements of total magnitude, effective radius, and mean
surface brightness with those obtained as part of the SDSS pipeline (Photo). Significant dif-
ferences are found and reported, including comparisons with a third and independent part. A
full characterization of the sample completeness in all wavebands is presented, establishing
the limits of application of the characteristic parameters presented here for the analysis of the
global scaling relations of ETGs.
Key words: galaxies: fundamental parameters – formation – evolution
1 INTRODUCTION
We have witnessed tremendous advances in our ability to measure
galaxy properties with unprecedented accuracy over the past two
decades. Thegreatest leapforward wasthe advent of theCCD, with
anorder of magnitude increase insensitivity over photographic film
and the ability to easily make quantitative measurements. Today,
surveys like the Sloan Digital Sky Survey (SDSS) and UKIRT In-
frared Deep Sky Survey (UKIDSS) provide access to high qual-
ity data covering a large wavelength range, probing different astro-
⋆E-mail:
valho2008@gmail.com(RRdC)
labarber@na.astro.it(FLB);rrdecar-
physical aspects of the galaxies. These advances have been imme-
diately applied to examining the global properties of galaxies.
Understanding the formation and evolution of galaxies re-
quires probing them over a long time (redshift) baseline to establish
the physical processes responsible for their current observed prop-
erties. It is far easier to measure nearby ETGs as opposed to their
counterparts at high redshift, and this must be borne in mind when
comparing samples at opposite distance extremes. Almost as soon
as high quality data became available for nearby samples of ETGs
it was recognized that they occupy a 2-dimensional space, the fun-
damental plane (FP), represented by the quantities radius, velocity
dispersion, and surfacebrightness R- σ -µ. Brosche(1973) wasthe
first to examine ETGsusing multi-variate statistical techniques, ap-
plying Principal Component Analysis (PCA) to the relatively poor

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F. La Barbera et al.
dataavailable. Although hisresultswerenot fullyappreciated atthe
time, it drew the attention of other researchers who further studied
the implications of the FP (Djorgovski 1987; Dressler et al. 1987).
Brosche’s fundamental contribution was to show that we should
be looking for sets of data with the smallest number of significant
principal components when starting from a large number of input
parameters. In this way we reduce a high-dimensional dataset to
only those quantities that are likely to have physical meaning. Sev-
eral studies followed Brosche’s: Bujarrabal, Guibert & Balkowski
(1981), Efstathiou & Fall (1984), Whitmore (1984), and Okamura
et al. (1984).
The fundamental plane is a bivariate scaling law between R,
σ, and I, where µ = -2.5 log I, expressed as R ∼ σAIB. In order to
obtain accurate and meaningful coefficients that can be compared
to theoretical expectations (such as those from the Virial Theorem,
which implies A = 2 and B= -1) we need to not only have a ho-
mogeneous sample of ETGs, but also to understand the selection
effects in defining the sample and to properly measure the photo-
metric and spectroscopic quantities involved. Several contributions
in the past have met most of these requirements (Graham & Colless
1997; Jørgensen et al. 1996). However, the lack of homogeneous
data covering a large wavelength baseline while also probing the
entire range of environments (local galaxy density) impeded fur-
ther progress. Bernardi et al. (2003a,b), Bernardi et al. (2006), and
Bernardi et al. ( 2007) were the first to fill this gap and set strong
constraints on the FP coefficients and their implications, though
limited to the optical regime (see also Hyde & Bernardi 2009).
Another important and often overlooked aspect of such studies is
the impact of different techniques and implementations for mea-
suring R - σ - µ and their respective errors, which ultimately will
be propagated and compared to the distribution of residuals around
the FP (Prugniel & Simien 1996; Gargiulo et al. 2009).
This is the first paper of a series presenting the Spheroid’s
Panchromatic Investigation in Different Environmental Regions
(SPIDER) survey. SPIDER utilizes optical and Near-Infrared
(NIR) photometry in the grizY JHK wavebands as well as
spectroscopic data. Spectroscopy and optical photometry are
taken from SDSS DR6, while the Y JHK data are obtained
from the UKIDSS-LAS DR4. In the present work (Paper I),
we describe how the sample of ETGs is selected, how the
photometric and spectroscopic parameters are derived for each
galaxy, and derive an accurate estimate of the completeness
of the sample in each band. The grizY JHK galaxy images
have been homogeneously analyzed using 2DPHOT, an auto-
matic software designed to obtain both integrated and surface
photometry of galaxies in wide-field images (La Barbera et
al. 2008a). We present a detailed comparison of the 2DPHOT
output quantities (magnitudes and structural parameters) to those
provided by the SDSS Photo pipeline (Stoughton et al. 2002).
We have also re-computed central velocity dispersions from the
SDSS spectra using the software STARLIGHT (Cid Fernandes
et al. 2005), and compared these new estimates to those from
SDSS. Velocity dispersions are re-derived using a combination
of simple stellar population models as templates. This procedure
minimizes the well known template mismatch problem, accounting
for the different kinematics of various stellar components in a
galaxy. All the photometric and spectroscopic measurements
presented here are made available through an ascii table at
http://www.lac.inpe.br/bravo/arquivos/SPIDER data paperI.ascii.1
1The file is mirrored at http://www.na.astro.it/ labarber/SPIDER/.
The complete SPIDER data-set is also made available, on request,
through a database structure which allows the user to easily retrieve
all information by issuing SQL queries.
In Sec. 2, we describe how the galaxy sample is selected.
Sec. 3 describes how grizY JHK-band images are analyzed to
derive integrated photometry and the structural parameters, with
corresponding uncertainties. Secs. 4 and 5 compare the overall in-
tegrated and structural properties of ETGs from g through K, de-
riving color–magnitude relations and presenting the distribution of
structural parameters in all wavebands. Sec. 6 compares the struc-
tural parameters derived from 2DPHOT with those from SDSS. In
Sec. 7, we describe the measurement of central velocity disper-
sions, comparing them to those from SDSS. The completeness of
the sample is studied in Sec. 8. A summary is provided in Sec. 9.
Throughout the paper, we adopt a cosmology with H0 =
75kms−1Mpc−1, Ωm=0.3, and ΩΛ=0.7.
2SAMPLE SELECTION
2.1Sample Definition
The sample of ETGs is selected from SDSS-DR6, following a pro-
cedure described in La Barbera et al. (2008b) and La Barbera & de
Carvalho (2009), selecting galaxies in the redshift range of 0.05 to
0.095, with0.1Mr< − 20, where0.1Mr is the k-corrected SDSS
Petrosian magnitude in r-band. The k-correction is estimated using
the software kcorrect (version 4 1 4; Blanton et al. 2003a, here-
after BL03), through a restframe r-band filter blue-shifted by a fac-
tor (1+z0) (see also Sec. 3.1). As in previous works (e.g. Hogg et
al. 2004), we adopt z0 = 0.1. The lower redshift limit of the sam-
ple is chosen to minimize the aperture bias (G´ omez et al. 2003),
while the upper redshift limit guarantees (1) a high level of com-
pleteness (according to Sorrentino et al. 2006) and (2) allows us
to define a volume-limited sample of bright early-type systems. In
fact, ETGs follow two different trends in the size–luminosity di-
agram (Capaccioli, Caon & D’Onofrio 1992; Graham & Guzm´ an
2003). The separation between the two families of bright and or-
dinary ellipticals occurs at an absolute B-band magnitude of −19,
corresponding to the magnitude limit of Mr ∼ −20 we adopt here.
At the upper redshift limit of z = 0.095, the magnitude cut of
−20 also corresponds approximately to the magnitude limit where
the SDSS spectroscopy is complete (i.e. a Petrosian magnitude of
mr ∼ 17.8). Following Bernardi et al. (2003a), we define ETGs
using the SDSS spectroscopic parameter eClass, that indicates the
spectral type of a galaxy on the basis of a principal component
analysis, and the SDSS photometric parameter fracDevr, which
measures the fraction of galaxy light that is better fitted by a de
Vaucouleurs (rather than an exponential) law. In this contribution,
ETGs are those systems with eClass < 0 and fracDevr > 0.8.
We select only galaxies with central velocity dispersion, σ0, avail-
able from SDSS-DR6, in the range of 70 and 420 kms−1, and with
no spectroscopic warning on (i.e. zWarning attribute set to zero).
These constrains imply retrieving only reliable velocity dispersion
measurements from SDSS. All the above criteria lead to a sample
of 39,993 ETGs.
The sample of ETGs with optical data is then matched to the
fourth data release (DR4) of UKIDSS–Large Area Survey (LAS).
UKIDSS–LAS DR4 provides NIR photometry in the Y JHK
bands over ∼ 1000 square degrees on the sky, withsignificant over-
lap with SDSS (Lawrence et al. 2007). The Y HK-band data have
a pixel scale of 0.4′′/pixel, matching almost exactly the resolu-
tion of the SDSS frames (0.396′′/pixel). J band observations are

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SPIDER I – Sample and data analysis
3
Figure 1. Distribution in RA and DEC of the SPIDER sample. Black
points mark the optical griz data, while red and blue symbols denote the J
and Y JHK data, respectively. .
carried out with a resolution of 0.4′′/pixel, and then interleaved to
a subpixel grid. This procedure results into stacked frames with a
better resolutionof 0.2′′/pixel.TheY JHK stacked images(mul-
tiframes) have average depths2of 20.2, 19.6, 18.8, and 18.2 mags,
respectively. The matching of SDSS to UKIDSS data was done
with the CrossID interface of the WFCAM Science Archive web-
site3. For each ETG in the SDSS sample, we searched for the near-
est UKIDSS detection within a radius of 1”, by considering only
UKIDSS frames with better quality flag (ppErrBits < 16). The
matching result was very insensitive to the value of the searching
radius. In fact, changing it to 0.5” leads to decrease the sample with
galaxies having Y JHK data available by only five objects. The
number of matched sources is maximum in J band, with 7,604
matches, while amounts to 5,698, 6,773, and 6,886 galaxies in Y ,
H, and K bands, respectively. Considering ETGs simultaneously
matched with two UKIDSS bands, H+K provides the maximum
number of objects (6,575). For any possible set of three bands, the
number of matches varies between 5,228 (Y + J + K) to 5,323
(J + H + K), which is not significantly larger than the number of
5,080 ETGs having photometry available in all the Y JHK bands.
For this reason, we have retrieved NIR data for only those galaxies
with available photometry in either J (7,604), or H+K (6,575),
or Y JHK wavebands (5,080). The completeness in magnitude of
each sample is characterized in Sec. 8.
In summary, the SPIDER sample includes 39,993 galaxies
with available photometry and spectroscopy from SDSS-DR6. Out
of them, 5,080 galaxies have NIR photometry in DR4 of UKIDSS-
LAS. The distribution of galaxies with optical and NIR data on the
sky is illustrated in Fig. 1.
2defined by the detection of a point source at 5σ within a 2′′aperture.
3See http://surveys.roe.ac.uk/wsa/index.html for details.
2.2Contamination by Faint Spiral Structures
Specification of a given family of systems means setting a property
(or properties) that isolates systems that presumably went through
similar evolutionary processes. However, when we select as ETGs
systems with SDSS parameters eClass<0 and fracDevr>0.8
weexpect a certainamount of contamination by galaxies exhibiting
faint structures resembling spiral arms or other non-systemic mor-
phologies. Although several morphological indicators have been
proposed from the parameters of the SDSS pipeline (e.g. Strat-
eva et al. 2001), the eyeball classification is still considered one
of the most reliable indicator despite its evident subjectivity (Wein-
mann et al. 2009). We have visually inspected a subsample of 4,000
randomly chosen galaxies from our sample, classifying them into
three groups: ETGs (featureless spheroids); face-on LTGs - late
type galaxies (a bulge surrounded by an obvious disk); and edge-
on LTGs (a bulge with a prominent disk). This classification is then
used to evaluate the ability of the different morphological indica-
tors to distinguish edge-on and face-on galaxies from the bonafide
ETGs.
Five SDSS morphological indicators are considered as shown
in Figs. 2(a-e): (i) The r-band Inverse Concentration Index (ICIr),
defined by the ratio of the 50% to the 90%-light Petrosian radii
(see Shimasaku et al. 2001); (ii) The parameter fracDeVr, cor-
responding to the fraction of the total fitted model accounted for
the de Vaucouleurs component. Notice that the total fit is not a
bulge+disk decomposition but a re-scaled sum of the best-fitting
de Vaucouleurs and exponential components (Bernardi et al. 2006);
(iii) The eClass indicator (see Sec. 2.1); (iv) The fractional likeli-
hood of a de Vaucouleurs model fit (fLDeVr), defined as:
fLDeVr =
lnLDeVr
(lnLDeVr+ lnLexpr+ lnLstar)
(1)
where LDeV , Lexp and Lstar are the probabilities of achiev-
ing the measured chi-squared for the de Vaucouleurs, exponential
and PSF fits, respectively; and (v) The projected axis ratio (b/a)r
of a deVaucouleurs fit (deVABr - an SDSS attribute). From Fig. 2
fLDeVr and (b/a)r are the two better performance indicators dis-
criminating ETGs from face-on LTGs (see Maller et al. 2009).
Based on the visual inspection, we define two cutoff values (see
panel f in the Figure), one for each morphology indicator, defin-
ing a region where the contamination rate is ∼5%. We notice that
this contamination rate is ∼2.5 times smaller than that for the sam-
ple of 4,000. The selected values for the cutoffs are 0.04 and 0.4
for fLDeVrand (b/a)r, respectively. The same constraints imposed
to the entire ETG sample, define a sub-sample of 32,650 bonafide
ETGs. We flag 7,343 objects as lying in the non-bonafide ETGs
region defined by (b/a)r < 0.4 or fLDeVr > 0.04, so that we
can study the impact of contaminants on the global properties of
bonafide ellipticals.
3PHOTOMETRY
For each ETG, we retrieved the corresponding best-calibrated
frames from the SDSS archive and the multiframes from the WF-
CAM Science Archive. In the case of SDSS, only the griz images
were analyzed, since the signal-to-noise of the u-band data is too
low to measure reliable structural parameters. The resulting photo-
metric system, consisting of the grizY JHK wavebands, is shown
in Fig. 3, where we plot, for each band, the corresponding overall
transmission curve. Regarding photometric calibration, the zero–
point of each image was retrieved from the corresponding SDSS or

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F. La Barbera et al.
Figure 2. Different morphological indicators are plotted as a function of the central velocity dispersion of the galaxy for a subsample of 4,000 ETGs (panels
a-e). Panel (f) plots the two optimal indicators and the dashed lines indicate the region where the contamination is ∼6% ((b/a)r > 0.4 and fLDeVr < 0.04.
Face-on LTGs are indicated in black, edge-on LTGs in blue and bonafide ETGs in red, as shown in the upper-right corner of panel (d).
UKIDSS archives. As a result of the different conventions adopted
in the two surveys, the SDSS photometry is in the AB photomet-
ric system4, while UKIDSS data are calibrated into the Vega sys-
tem (Lawrence et al. 2007).
3.1Integrated properties
We have measured both aperture and total galaxy magnitudes with
different methods, homogeneously for both the optical and NIR
data. Aperture magnitudes are estimated with S-Extractor (Bertin
& Arnout 1996). For each galaxy, several apertures are measured,
spanning the 2 to 250 pixels diameter range. A set of adaptive aper-
ture magnitudes is also measured. The adaptive apertures have di-
4We actually apply small offsets to the griz zero-points in order
to produce a better match between the SDSS and AB systems (see
www.sdss.org/dr6/algorithms/fluxcal.html#sdss2ab).
ameters of dk = k · rKr,i, where k = 3,4,5,6 is a multiplicative
factor, and rKr,iis the Kron radius (Kron 1998) in the i-band, as
estimated with S-Extractor. The rKr,iis measured in i-band since
thisisapproximately in themiddle of the SPIDERphotometric sys-
tem (Fig. 3). For k = 3, the median value of dkis ∼ 5.8′′, which
is more than five times larger than the typical FWHM in all wave-
bands (see Sec. 3.2). More than 95% of all the ETGs have a value
of d3 larger than ∼ 4.8′′, and a ratio of d3 to the seeing FWHM
value larger than 3. This makes the adaptive aperture magnitudes
essentially independent of the seeing variation from g through K
(see Sec. 3.2). Different types of total magnitudes are adopted. For
the optical wavebands, we retrieve both petrosian and model mag-
nitudes, mp and mdev, from the SDSS archive (see Stoughton
et al. 2002). For each waveband, the Kron magnitude, mKr, is also
measured independently for all galaxies, within an aperture of three
times the Kron radius in that band. The Kron magnitudes are ob-
tained from MAG AUTO parameter as estimated in S-Extractor.

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SPIDER I – Sample and data analysis
5
Figure 3. Transmission curves, τ(λ), for the grizY JHK filters. Each
curve has been normalized to an area of one.
Finally, each galaxy has the estimate of total magnitude, mT, from
the corresponding two-dimensional fitting model (see Sec. 3.2).
To obtain homogeneous measurements from g through K,
magnitudes are k-corrected and dereddened for galactic extinc-
tion by re-computing both corrections with the same procedure in
all wavebands, rather than retrieving them, when available, from
the SDSS and UKIDSS archives. For each galaxy, the amount
of extinction is estimated from the reddening maps of Schlegel,
Finkbeiner, and Davis (1998), applying the correction of Bonifa-
cio, Monai & Beers (2000) that reduces the color excess value,
E(B − V ), in regions of high extinction (E(B − V ) > 0.1).
This correction is not included in the SDSS database, and only a
very small fraction of ETGs (< 1%) is found in the high extinction
regions. We computed k-corrections using the software kcorrect
(BL03), through restframe filters obtained by blue-shifting the
throughput curves in Fig. 3 by a factor (1 + z0). For z0 = 0, one
recovers the usual k-correction. For galaxies at redshift z = z0, the
k-correction is equal to −2.5log(1 + z0), independent of the filter
and the galaxy spectral type. We have adopted z0 = 0.0725 which
is the median redshift of the ETG sample. According to BL03,
this choice allows uncertainties on the k-corrections to be mini-
mized5. We have tested how the waveband coverage can affect the
k-corrections. For the sample of 5,080 galaxies with available data
in all grizY JHK bands, we have estimated the k-corrections in
griz for two cases, where we used (i) all the eight wavebands and
(ii) only the SDSS bands. k-corrections turned out to be very stable
with respect to the adopted waveband’s set, with the standard de-
viation of k-correction differences being smaller than 0.01mag for
all the griz wavebands.
5The value of z0 = 0.0725 is smaller than that of z0= 0.1 adopted for
sample selection (Sec. 2). The value of z0= 0.1 makes the selection more
similar to that performed from previous SDSS studies, while the choice of
z0= 0.0725 minimizes the errors in k-corrections.
3.2 Structural parameters
The grizY JHK images were processed with 2DPHOT (La Bar-
bera et al. 2008a) (hereafter LdC08), an automated software envi-
ronment that allows several tasks, such as catalog extraction (us-
ing S-Extractor), star/galaxy separation, and surface photometry to
be performed. The images were processed using two Beowulf sys-
tems. The optical images were processed at the INPE-LAC clus-
ter facility, running 2DPHOT simultaneously on 40 CPUs. A num-
ber of 31,112 best-calibrated frames were processed in each of
the griz wavebands, requiring ∼ 2 days per band. The UKIDSS
frames were processed at the Beowulf system available at INAF-
OAC. A total of 12,963 multiframes were processed by running
2DPHOT on 32 CPUs, simultaneously. The processing took half a
day for each band.
A complete description of the 2DPHOT package can be found
in LdC08; here we only outline the basic procedure followed to
measure the relevant galaxy parameters. Both the optical and NIR
images were processed with the same 2DPHOT setup to guar-
antee a homogeneous derivation of structural parameters from g
through K. For each frame, the so-called sure stars are identi-
fied from the distribution of all the detected sources in the FWHM
vs. signal-to-noise, S/N, diagram. This procedure allows an es-
timate of the average seeing FWHM of the image to be obtained
(see sec. 3 of LdC08). For each ETG, a local PSF model is con-
structed by fitting the four closest stars to that galaxy with a sum
of three two-dimensional Moffat functions. Deviations of the PSF
from the circular shape are modeled by describing the isophotes
of each Moffat function with Fourier-expanded ellipses. Galaxy
images were fitted with PSF-convolved Sersic models having el-
liptical isophotes plus a local background value. For each galaxy,
the fit provides the following relevant parameters: the effective
(half-light) radius, re, the mean surface brightness within that ra-
dius, < µ >e,, the Sersic index (shape parameter) n, the axis ra-
tio b/a, and the position angle of the major axis, PA. The total
(apparent) magnitude, mT, of the model is given by the definition
mT = −2.5log(2π) − 5log(re)+ <µ>e. Mean surface bright-
ness values are k-corrected and corrected for galactic extinction as
described inSec. 3.1. Moreover, cosmological dimming isremoved
by subtracting the term 10log(1 + z), where z is the SDSS spec-
troscopic redshift.
The characterization of the galaxy isophotal shape is done
through the two-dimensional fitting of each ETG in the gri wave-
bands, where Sersic models having isophotes described by Fourier-
expanded ellipses are adopted. Only the fourth order cos term of
the expansion, a4, is considered (boxiness - a4 < 0 and disky-
ness - a4 > 0, see e.g. Bender & M¨ ollenhoff 1987, hereafter
BM87). Only the gri band images are analyzed, since a4 is usu-
ally measured in the optical wavebands. Since the models are PSF-
convolved, the method above provides a global deconvolved esti-
mate of a4. This estimate is somewhat different from the definition
of BM87, where the peak value of a4 is derived in a given radial
range, with the minimum radius being set to four times the see-
ing FWHM and the maximum radius to twice the effective radius.
Since many galaxies in the SPIDER sample have effective radii
comparable to a few times the seeing FWHM value (see below),
the BM87 procedure is not applicable.
Fig. 4 shows the distribution of the average seeing FWHM
value for all the retrieved images from g through K. The seeing
FWHM was estimated from the sure star locus (see above). For
each band, we estimate the median of the distribution of FWHM
values, and the corresponding width values, using the bi-weight

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F. La Barbera et al.
Figure 4. Distribution of seeing FWHM values for all the grizY JHK
frames (from left to right and top to bottom). The median value, µ, of each
distribution is marked by the dashed line in each panel. Both the value of µ
and the width, σ, of the distributions are reported in the top-right corner of
each plot.
statistics (Beers, Flynn, & Gebhardt 1990). The median and width
values are reported in Fig. 4 for each band. As expected, the me-
dian FWHM value tends to smoothly decrease from the blue to
NIR wavebands, varying from 1.24′′in g-band to 0.82′′in K-band.
This variation corresponds to a relative change of ∼ 34% (with re-
spect to g band). Notice also that in Y JHK (griz) bands almost
all frames have seeing FWHM values better than 1.5′′(1.8′′), with
90% of the values being smaller than 1.2′′(1.5′′). This decreasing
of the seeing FWHM from g through K matches almost exactly the
relative change of effective radii from optical to NIR wavebands
(see below), making the ratio of FWHM to realmost constant from
g to K.
Fig. 5 compares the distribution of χ2values obtained from
the two-dimensional fitting of galaxies in each band. The peak and
width values of the distributions are computed by the bi-weight
statistics and reported in the figure. The χ2is computed as fol-
lows. For each galaxy, we select only pixels 1σ above the local sky
background value. The intensity value of each pixel is computed
from the two-dimensional seeing-convolved Sersic model. For the
selected pixels, we compute the χ2as the rms of residuals between
the galaxy image and the model. Residuals are normalized to the
expected noise in each pixel, accounting for both background and
photon noise. Notice that this χ2computation is somewhat differ-
ent from that of the two-dimensional fitting procedure, where the
sum of square residuals over all the galaxy stamp image is min-
imized (see LdC08). This explains the fact that all the peak val-
ues in Fig. 5 are slightly larger than one. An eye inspection of the
residual maps, obtained by subtracting the models to the galaxy
images, shows that the above χ2estimate is better correlated to
the presence of faint morphological features (e.g. spiral arms, disk,
etc...), that are not accounted for by the two-dimensional model.
This is shown in Figs. 6 and 7. Both figures show residual maps in
the r-band. Fig. 6 displays cases where the χ2is close to the peak
Figure 5. Same as Fig. 4 for the χ2distributions.
value (χ2< 1.5), while Fig. 7 exhibits cases with higher χ2value
(1.5 < χ2< 2.0). In most cases, as the χ2value increases, we can
see some faint features to appear in the residual maps. We found
that the percentage of galaxies with χ2> 1.5 is not negligible,
amounting to ∼ 17% in r-band. Most of the morphological fea-
tures are expected to be caused by young stellar populations, hence
disappearing when moving to NIR bands, where the galaxy light is
dominated by the old, quiescent stars. From Fig. 5, one can actu-
ally see that NIR bands exhibit a less pronounced tail of positive
χ2values with respect to the optical. This is also confirmed by a
Kolmogorov-Smirnov (KS) test. For instance, in the case of r and
K bands, the KS test gives a probability smaller than 1% for the
corresponding χ2distributions to be drawn from the same parent
distribution.
3.3 Uncertainty on structural parameters
We estimate the uncertainties on structural parameters by compar-
ingthedifferencesinlogre,<µ>e,andlogn betweencontiguous
wavebands. To obtain independent estimates of the uncertainties
on SDSS and UKIDSS parameters, the comparison is performed
for the r and i bands, and the J and H bands, respectively. The
variation of logre, < µ >e, and logn with waveband depends
on the measurement errors on structural parameters as well as on
the intrinsic variation of stellar population properties (e.g. age and
metallicity) across the galaxy, which implies a change of the light
profile with waveband. As it is well known, this change is responsi-
ble for the existence of radial color gradients inside ETGs (Peletier
et al. 1990). The basic assumption here is that the r and i (J and
H) bands are close enough that the variation of galaxy properties
from one band to the other is dominated by the measurement er-
rors. Tab. 1 shows that this is the case. In this table we report the
sensitivity of color indices with respect to age and metallicity be-
tween contiguous wavebands for a Simple Stellar Population (SSP)
model. The sensitivities to age and metallicities, indicated as ∆t
and ∆Z, are defined as the derivatives of the color indices with

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SPIDER I – Sample and data analysis
7
Figure 6. Two-dimensional fit results for galaxies in r-band with typical
χ2value (χ2< 1.5). Each plot shows the galaxy stamp (left) and the
residual map (right) after model subtraction, using the same gray scale of
intensity levels. The spatial scale is shown in the bottom-left corner of the
left plots. For each galaxy image, the corresponding celestial coordinates
(right ascension, RA, and declination, DEC, in degrees) and χ2value are
reported in the upper-left corner.
Figure 7. Same as Fig. 6 but for galaxies with high χ2value (1.5 < χ2<
2.0 in r-band).
Table 1. Sensitivity of color indices of an
SSP model to age and metallicity.
color index
∆Z
∆t
g-r
r-i
i-z
z-Y
Y-J
J-H
H-K
0.313
0.079
0.107
0.238
0.239
0.017
0.134
0.268
0.108
0.131
0.116
0.076
0.030
0.049
respect to logt and logZ, where t and Z are the age and metal-
licity, respectively. The derivatives are estimated as in La Barbera
& de Carvalho (2009). We use an SSP from the Bruzual & Charlot
(2003) synthesis code, withsolar metallicity, ScaloIMF, and an age
of t = 10.6 Gyr, corresponding to aformation redshift of zf = 3 in
the adopted cosmology. For the SDSS wavebands, the sensitivities
reach a minimum in r−i, while they have a maximum in g − r, as
expected bythefact thatthiscolor encompasses the4000˚ A breakin
the spectrum of ETGsat the median redshift of the SPIDER sample
(z = 0.0725). The values of ∆t and ∆Z can be used to estimate
the expected intrinsic waveband variation of structural parameters.
As shown by Spolaor et al. (2009), bright ETGs have a large dis-
persion in their radial metallicity gradients, ∇Z, with ∇Z varying
in the range of about 0 to −0.6 dex. On the contrary, age gradients
play a minor role (La Barbera & de Carvalho 2009). Even consid-
ering a dispersion of 0.3 dex in the metallicity gradients of ETGs,
from Tab. 1, one can see that the corresponding scatter in the r − i
internal color gradients would be only 0.079 · 0.3 ∼ 0.024mag.
FollowingSparks &J¨ orgensen (1993), for ade Vaucouleurs profile,
this implies an intrinsic scatter in the difference of r- and i-band ef-
fective radii of only ∼ 2.4%, hence much smaller than the typical
measurement error on re(see below). For the UKIDSS wavebands,
the lowest sensitivities to age and metallicity are obtained in J−H,
being even smaller than those of the optical colors.
The errors on structural parameters are expected to be mainly
driven by two parameters, the FWHM + pixel scale of the image
(with respect to the galaxy size) and the signal-to-noise ratio, SN.
Consequently, we bin the differences in logre, <µ>e, and logn
between r and i (J and H) bands with respect to the logarithm of
the mean effective radius, logre, and the SN per unit area of the
galaxy image, SN/r2
tween the two bands, of the inverse of the uncertainties on Kron
magnitudes. Each bin is chosen to have the same number of galax-
ies. In a given bin, we estimate the measurement errors on logre,
< µ >e, and logn from the mean absolute deviation of the cor-
responding differences in that bin. We refer to the measurement
uncertainties as σlog re, σ< µ >e, and σlog n, respectively. Since the
errors on effective parameters are strongly correlated, we also de-
rive the corresponding covariance terms, COVY,X, in each bin,
where X and Y are two of the three quantities logre, < µ >e,
and logn. For each pair of X and Y , we perform a robust linear
fit6of the differences in Y as a function of the corresponding dif-
ferences in X. The quantity COVY,X is obtained from the slope,
s, of the fitted relation as COVY,X = s × σ2
|COVY,X| ? σY×σX, and COVY,X = COVX,Y. Fig. 8plots the
e. The SN is defined as the mean value, be-
X, with the constraints
6The robust regression is performed by minimizing the sum of absolute
residuals of the Y vs. the X differences.

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8
F. La Barbera et al.
Figure 8. Errors on optical effective parameters as a function of the logarithm of the signal-to-noise (SN) per pixel. In the left panels, from top to bottom, we
plot the uncertainty on the effective radius, the effective mean surface brightness, and the Sersic index. The left panels, from top to bottom, plot the covariance
terms of the uncertainties on logre, < µ >e, and logn. Different colors show different bins of the effective radius as shown in upper-right of the top-left
panel. For a given color, the points shows the values of the uncertainties and the covariance terms obtained in different bins of the logarithm of the SN per
pixel. The dashed curves are the best-fit functional forms used to model the dependence of the uncertainties on SN (see the text).
quantities σlog re, σ< µ >e, and σlog nas well as the relevant covari-
ance terms as a function of log(SN/r2
errors on effective parameters are strongly correlated to the SN per
unit area. For log(SN/r2
decreases, the errors tend to become larger. For log(SN/r2
all galaxies have effective radii comparable or even smaller than
the pixel scale, with large values of log(SN/r2
smaller effective radii. As a result, the error on the effective param-
eters tends to increase as well. The σlog nexhibits a similar behav-
ior to that of σlog reand σ< µ >e, though with a larger dispersion at
given log(SN/r2
σ< µ >e, and COVlog re,< µ >e) and Sersic index (σlog n), the trends
e), for the r and i bands. The
e)? <2, as the signal-to-noise per unit area
e)? >2,
e) corresponding to
e). For the errors on effective parameters (σlog re,
exhibited in Fig. 8 are well described by the following, empirical
functional form:
y = P2(x) +
|c1|
(x − 5)c2,
(2)
wherey isoneof thequantitiesσlog re,σ< µ >e,andCOVlog re,< µ >e,
x = log(SN/r2
c1 and c2 are two parameters describing the increase of the error
values at high SN per unit area. For the quantities COV< µ >e,log n
and COVlog n,log re, the trends in Fig. 8 can be modeled by a fourth
order polynomial function. We have fitted the corresponding func-
tional forms by minimizing the sum of absolute residuals in y. The
best-fit curves are exhibited in Fig. 8.
Fig. 9 plots the errors on structural parameters as derived with
e), P2is a second order polynomial function, while

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SPIDER I – Sample and data analysis
9
Figure 9. Same as Fig. 8 but comparing J and H band structural parameters.
the above procedure for the J and H bands. The trends are simi-
lar to those obtained for the optical parameters, but with a larger
dispersion, at given SN per unit area, which is likely explained
by the fact that the number of galaxies in each bin with available
photometry in J and H is smaller (by a factor of ∼ 8) than that
in r and i. The uncertainties on the NIR parameters are on average
larger than those in the optical. For instance, at log(SN/r2
the uncertainty on logre is ∼ 0.06 dex in the optical, increasing
to ∼ 0.1 dex in the NIR. The median errors on logre, < µ >e,
and logn, amount to ∼ 0.1, ∼ 0.5 mag/arcsec2, and ∼ 0.1, re-
spectively, in the optical, and to ∼ 0.15, ∼ 0.6 mag/arcsec2, and
∼ 0.12 in the NIR. This difference can be qualitatively explained
by the fact that (i) the stars used for the PSF modeling have, on av-
erage, a lower signal-to-noise ratio in the NIR than in the optical,
and (ii) that the ratio of galaxy effective radii to the pixel scale of
the images is smaller in the NIR than in the optical. The trends in
e) = 2,
Fig. 9 are modeled with the same functional forms as for the optical
data.
We use the above analysis to assign errors to the structural
parameters to each galaxy in the SPIDER sample, for each wave-
band. For a given galaxy, we first calculate its SN per unit area and
then use the best-fitting functional forms to assign σlog re, σ< µ >e,
σlog n, and the corresponding covariance terms. For the gri bands,
we adopt the functional forms obtained from the r −i comparison,
while for the JHK bands we adopt the values obtained from the
comparison of J- and H-band parameters. In the z and Y bands,
we apply both the optical and NIR functional forms, and then de-
rive the errors by interpolating the two error estimates with respect
to the effective wavelength of the passbands.

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10
F. La Barbera et al.
4COLOR-MAGNITUDE RELATIONS
As a first step in the comparison of optical to NIR properties of
ETGs, we start to analyze the differences in their integrated proper-
ties, i.e. the color indices. The goal is comparing total Sersic mag-
nitudes in the different wavebands, in order to (i) characterize the
completeness of the SPIDER sample in the space of the (Sersic)
effective parameters (Sec. 8), and (ii) select suitable samples of
ETGs for the analysis of the FP (see papers II and III). Thus, we
estimate the color indices using the Sersic total magnitudes, rather
thanaperturemagnitudes asinmost ofprevious studies, andreferto
them also as the total galaxy colors. This is by itself an important
issue that will be addressed in a future contribution dealing with
the different ways of measuring colors (de Carvalho et al. 2010, in
preparation) which certainly goes beyond the scope of this paper.
The comparison of color indices is performed by construct-
ing the color–magnitude diagrams for different pairs of wavebands.
Since the ETG sample has photometry available in eight wave-
bands, we can derive seven different color–magnitude relations. We
consider galaxy colors in the form of g−X with X = rizY JHK,
and we write the color magnitude relations as:
g − X = agX+ bgXX,
(3)
where agXand bgXare the offsets and slopes of the relations. To
simplify the notations, we also set agg = 0 and bgg= 0. Fig. 10
plots the CM diagrams for all the 5,080 ETGs with available data
in all wavebands. In order to derive agXand bgX, we first bin each
g − X vs. X diagram with respect to the magnitude X. We adopt
N = 15 bins, with each bin including the same number of galax-
ies. Varying the number of bins in the range of 15 to 25 changes the
slope and offset values by less than 1%. For each bin, we derive the
peak of the corresponding distribution of galaxy colors by applying
the bi-weight location estimator (Beers, Flynn, & Gebhardt 1990).
The uncertainty of the peak value is estimated as the standard de-
viation of the peak values obtained in 1000 bootstrap iterations.
This procedure has the advantage of being insensitive to outliers in
the color distribution. The binning is performed up to a magnitude
limit X, obtained by transforming the 2DPHOT r-band complete-
ness limit of −20.55 (Sec. 8.1) through the median values of the
g − X total colors. The values of agXand bgXare then derived by
fitting the binned values of g − X vs. X, with an ordinary least-
squares fitting procedure with g − X as dependent variable. The
uncertainties on agXand bgXare obtained by randomly shifting
(N = 1000 times) the binned values of g − X according to their
uncertainties. Thevalues of agXand bgXareexhibited in Fig.10. It
is interesting to notice that, using total colors, the CM relations are
essentially flat, with the slopes bgXbeing mostly consistent with
zero within the corresponding uncertainties. In particular, the value
of bgXis consistent with zero at less than 2σ in g−r, g−i, g−J,
g −H, and g−K, while in g −z and g−Y the slopes differ from
zero at ∼ 3σ and ∼ 5σ levels, respectively. We do not find here
any systematic steepening of the CM relation when enlarging the
waveband baseline from g−r to g−K, as expected if the total CM
relation would be purely driven by a mass–metallicity relation in
ETGs. Following Scodeggio (2001), we can explain this surprising
result by the fact that we use total color indices. ETGs have neg-
ative color gradients, with color indices becoming bluer from the
galaxy center to its periphery. As a result, when adopting colors in
a fixed aperture, one is measuring the color inside a smaller region
(with respect to re) for the brightest (hence larger) galaxies than for
faintest galaxies in the sample. This leads to a misleading steepen-
ing of the CM relation. We notice that using de Vaucouleurs model
Table 2. Median peak values, ag−X, of the
distributions of total colors, g − X (X =
rizY JHK). The uncertainties are 1σ stan-
dard errors on the median values.
colorpeak value
g − r
g − i
g − z
g − Y
g − J
g − H
g − K
0.852 ± 0.007
1.274 ± 0.004
1.589 ± 0.008
2.282 ± 0.012
2.806 ± 0.012
3.472 ± 0.012
3.854 ± 0.018
magnitudes from SDSS would essentially lead to the same effect,
as model magnitudes are estimated in a fixed aperture for all the
SDSS wavebands (see Stoughton et al. 2002), and the SDSS effec-
tive radii tend to be more underestimated (with respect to the Ser-
sic re) for brighter than for fainter galaxies (see Fig. 16 of Sec. 6).
Sincethevalues ofbgX= 0aremostlyconsistent withzeroand our
aim here is that of relating total magnitudes among different wave-
bands (rather than performing a detailed study of CM relations), we
have decided to set bgX= 0, and derive ag−Xas the median of the
g − X peak values in the different magnitude bins. The values of
ag−X, together with the corresponding uncertainties, are listed in
Tab. 2. The uncertainties are the errors on the median values. They
are estimated from the width of the distribution of median values
for 200 bootstrap iterations.
Fixing the limiting magnitude of the ETG’s sample in a given
band, W (W = grizY JHK), one can use the CM relations
to map that limit into equivalent magnitude limits, Xlim (X =
grizY JHK), in all wavebands. From Eq. 3, one obtains:
Xlim=agW− agX
1 + bgX
+1 + bgW
1 + bgX
Wlim.
(4)
In the particular case of bgX= 0, one obtains the simplified ex-
pressions, Xlim = agY− agX+ Y , which is used in paper II to
analyze the FP relation for color–selected samples of ETGs.
5DISTRIBUTION OF STRUCTURAL PARAMETERS
FROM g THROUGH K
Figures11 to13 exhibit the distributionsof 2DPHOT Sersicparam-
eters from g through K. For each band, we select all the galaxies
availableinthatband(seeSec.2).Eachdistributionischaracterized
by its median value, µ, and the width, σ, estimated by the bi-weight
statistics (Beers, Flynn, & Gebhardt 1990). Both values, µ and σ,
are reported in the plots.
Fig. 11 compares the distributions of effective radii. The most
noticeable feature is that the median value of logre decreases
smoothly from the optical to the NIR, varying from ∼ 0.53 dex
(re ∼ 3.4′′) in g to ∼ 0.38 dex in K (re ∼ 2.4′′). This change
of ∼ 0.15 dex corresponds to a relative variation of ∼ 35% in
re, and is due to the fact that ETGs have negative internal color
gradients, with the light profile becoming more concentrated in the
center as one moves from shorter to longer wavelengths. Had we
used the peak values of the distributions, estimated with the bi-
weight statistics, rather than median values, the relative variation in
re would have been ∼ 31% (∼ 0.13 dex) instead of ∼ 35%. The
optical–NIR difference in logre is in agreement with the value of

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SPIDER I – Sample and data analysis
11
Figure 10. Color–magnitude relations for all the 5,080 galaxies with photometry available in grizY JHK. From left to right and top to bottom, galaxy colors
in the form of g −X, with Z = rizY JHK, are considered. For each panel: the slope and offset of the CM relation are reported in the upper-left corner, with
the corresponding 1σ standard uncertainties; the colored circles mark the peak of the color distribution in magnitude bins, with the corresponding 1σ error
bars; the solid line shows the best-fitting CM relation; the dashed line mark the magnitude cut ion that band that corresponds to a magnitude limit of −20.55
in the r-band (see text).
∼ 0.125 dex (∼ 29%) reported by Ko & Im (2005) for the sam-
ple of 273 ETGs from Pahre (1999), between the V and K bands.
Notice also that the relative change in re fortuitously matches the
improvement in average seeing FWHM between the g- and K-band
images (Sec. 3.2), which makes the measurement of structural pa-
rameters across the SPIDERwavelength baseline even more homo-
geneous.
Fig. 12 compares the distributions of values of the axis ra-
tio, b/a, of the best-fitting Sersic models. The median as well as
the width values of b/a turn out to be essentially constant from g
through K, amounting to ∼ 0.7 and ∼ 0.2, respectively. The con-
sistency of the b/a distributions with wavebands is in agreement
with that found by Hyde & Bernardi (2009) when comparing g-
and r- bands b/a values from SDSS. As expected, the fraction of
ETGs decreases dramatically at low values of b/a with only a few
percent of galaxies having axis ratios as low as 0.3.
Fig. 13compares thedistributionsof theSersicindex, n. Since
we have selected bulge-dominated galaxies (fracDevr > 0.8,
see Sec. 2), all the objects exhibit a Sersic index value larger than
one, i.e. no galaxy has an exponential (disk-like) light profile. In
particular, the fraction of ETGs becomes significantly larger than
zero above the value of n ∼ 2, which, according to Blanton et al.
(2003b), roughly corresponds to the separation limit between blue
and redgalaxiesintheSDSS.Thedistributionsshow alargescatter,
with n ranging from ∼ 2 to ∼ 10. The median value of n is around
6 for all wavebands, without any sharp wavelength dependence.
On the other hand, wesee some marginal change in the shape of the
distribution with waveband. In the optical griwavebands, a peak in
the distribution is evident around n ∼ 4. The distributions become
essentially flat in the other (NIR) wavebands, with the exception
of J where a peak is still present at n ∼ 4. Some caution goes in
interpreting these changes in shape. First, notice that observations
and data reduction in the J-band of UKIDSS-LASare carried out in
a somewhat different manner with respect to the other wavebands
Figure 11. Distributions of logre for all the grizY JHK wavebands
(from left to right and top to bottom). The median value, µ, of each dis-
tribution is marked by the vertical dashed line. The µ and width values
(see the text) are reported in the upper–right corner of each panel.
(see Warren et al.2007). A micro-stepping procedure, with integer
pixel offsets between dithered exposures is performed. Images are
interleaved to a subpixel grid and then stacked. This procedure re-
sults in a better image resolution of 0.2′′/pixel, with a better ac-
curacy of the astrometric solution (useful for proper motion’s mea-
surements). We cannot exclude that this difference in data reduc-

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12
F. La Barbera et al.
Figure 12. Same as Fig. 11 for the distribution of axis ratios.
Figure 13. Same as Fig. 11 for the distribution of Sersic indices.
tion affects the J-band distribution of n values. Moreover, as seen
in Sec. 3.3, uncertainties on structural parameters change from g
through K, hence preventing a straightforward comparison of the
shape of the distributions among different wavebands.
In order toanalyze thewaveband dependence of thea4param-
eter, we compare the a4 values among contiguous wavebands for
the sample of 39,993 ETGs. The comparison is performed using
only the gri wavebands, where the a4 estimates are derived (see
Sec. 3.2). Fig. 14 plots the differences in a4, δa4, between g and r,
and r and i, as a function of the median a4value, < a4 >. The δa4
values are binned with respect to < a4 >, with each bin including
Figure 14. Differences of a4 estimates between r − i (upper panel) and
g − r (lower panel) as a function of the median a4 value, < a4 >, in
the gri wavebands. The blue dashed line marks the value of zero. The red
curves are obtained by binning the data with respect to < a4>.
the same number (N = 200) of galaxies. For a given bin, the me-
dian difference of δa4 values is computed. The median values are
plotted as a continuous curve in Fig. 14, showing that there is no
systematic trend of a4from g through i.
6 COMPARISON OF SDSS AND 2DPHOT STRUCTURAL
PARAMETERS
Wecompare the effective parameters measured with2DPHOT with
those derived from the SDSS photometric pipeline Photo, that fits
galaxy images with two-dimensional seeing convolved de Vau-
couleurs models (Stoughton et al. 2002). From now on, the dif-
ferences are always in the sense of SDSS−2DPHOT. The com-
parison is done in r-band, by using the entire SPIDER sample
of 39,993 ETGs (Sec. 2). Effective radii along the galaxy ma-
jor axis are retrieved from the SDSS archive, and transformed
to equivalent (circularized) effective radii, re, with the axis ra-
tio values listed in SDSS. The effective mean surface brightness,
<µ>e, is then computed from the circularized effective radii and
the de Vaucouleurs model magnitude, mdev,r, using the definition
< µ >e=mdev,r+5log(re) + 2.5log(2π). All magnitudes are
dereddened for galactic extinction and k-corrected (see Sec. 3.1).
For both 2DPHOT and Photo, we denote the effective parameters
as re and <µ>e, saying explicitly when we refer to either one or
the other source.
In order to compare the method itself to derive re and <
µ>e(rather than the kind of model, i.e. Sersic vs. de Vaucouleurs),
we start by comparing the effective parameters of galaxies for
which2DPHOTgives aSersicindex of n ∼ 4. Tothiseffect,wese-
lect all the ETGs with n in the range of 3.7 to 4.3, considering only

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SPIDER I – Sample and data analysis
13
Figure 15. Differences in total magnitude, δ mag (upper panel), effective
radius, δre/re(middle panel), and FP parameter, δFP (lower panel), be-
tween SDSS and 2DPHOT, as a function of the SDSS r-band model mag-
nitude. All values refer to the r-band. Red curves are obtained by bin-
ning the differences with respect to mdev,r(see the text). The blue bars
mark the range of expected differences due to the sky overestimation effect
present in the SDSS parameters estimation. The size of the blue bars has
been estimated from fig. 6 of Abazajian et al. (2009) for δmag and fig. 3
of Adelman-McCarthy et al. (2008) for δre/re.
galaxies with better quality images (seeing FWHM < 1.5′′). This
selection results into a subsample of 4,525 ETGs. Fig. 15 plots the
differences in the total magnitude, effective radius, and FP param-
eter as a function of mdev,r, where FP =logre−0.3< µ >e is
the combination of logre and < µ >e entering the FP relation
(Saglia et al. 2001). For the re, we normalize the differences to the
Photo re values. For each quantity, the differences are binned with
respect to mdev,r, each bin including the same number (N = 200)
of galaxies. In a given bin, the peak value of the distribution of
differences (red curves in the figure) is computed by the bi-weight
statistics (Beers, Flynn, & Gebhardt 1990). The SDSS total magni-
tudes and effective radii differ systematically from those obtained
with 2DPHOT, with total magnitudes (effective radii) being fainter
(smaller) with respect to those of 2DPHOT. This effect tends to
disappear for faint galaxies: the absolute differences in total mag-
nitude decrease from ∼ 0.15mag (∼ 20%) at mdev,r∼ 15 to
∼ 0.1mag (6%) at mdev,r∼ 17.7. These differences are in the
same sense as those reported from previous studies (e.g. Bernardi
et al. 2007, Lauer et al. 2007), and can at least partly be accounted
by the sky overestimation problem affecting SDSS model parame-
ters (Adelman-McCarthy et al. 2008; Abazajian et al. 2009). Photo
tends to overestimate the sky level near large bright galaxies, lead-
ing to underestimate both total fluxes and effective radii. The effect
has been quantified from the SDSS team by adding simulated r1/4
seeing-convolved models to SDSS images, and recovering their in-
put parameters through Photo. Fig. 15 compares the range of val-
ues for differences between input and output parameters from the
SDSS simulations (blue bars), with what we find here. For re, the
average Photo-2DPHOT differences are only marginally consistent
Figure 16. Comparison of SDSS and 2DPHOT parameters as a function of
the 2DPHOT Sersic index (left panels), and the SDSS total model magni-
tude (right panels). From top to bottom, the same quantities as in Fig. 15
are compared. The red curves are obtained by binning the data as in Fig. 15,
but with each bin including 400 galaxies.
with those expected from the simulations. For the total magnitudes,
we find larger systematic differences, with 2DPHOT magnitudes
being brighter, by a few tenths of mag, than what expected from
the simulation’s results. We should notice that larger differences in
magnitude (and perhaps in re), in the same sense as we find here,
have also been reported by D’Onofrio et al. (2008) when compar-
ing their effective parameters with those from SDSS. Moreover,
the SDSS simulations have been performed by assuming a given
luminosity–size relation for ETGs, which might be slightly differ-
ent for ETG’ssamplesselected according todifferent criteria.Since
one main goal of the SPIDER project is that of analyzing the FP re-
lation, we have to point out that, although the differences in re and
mT are significant, the FP quantity is in remarkable good agree-
ment when comparing Photo to 2DPHOT. The average difference
in the FP is less than a few percent and does not depend on the
magnitude. As a consequence (see paper II), the FP coefficients
change by only a few percent when using either 2DPHOT or Photo
effective parameters.
Fig. 16 compares differences between Photo and 2DPHOT
parameters as a function of the Sersic index, n, as well as the
(SDSS) absolute model magnitude in r band,0.07Mdev,r. Differ-
ences are binned as in Fig. 15, considering only the N = 39,091
galaxies with better image quality (see above). The comparison
reveals large systematic differences, that strongly correlate with
the Sersic index n. As n increases, Sersic total magnitudes be-
come brighter – while Sersic effective radii become larger – than
the SDSS values. The former trend is consistent with that reported

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14
F. La Barbera et al.
byGraham et al.(2005). Similar,but weaker, trends arealsopresent
as a function of the galaxy magnitude, when moving from fainter
to brighter galaxies. This is somewhat expected, as ETGs exhibit a
luminosity-Sersic index relation, with brighter galaxies having on
average larger n (Caon, Capaccioli & D’Onofrio 1993). The trends
of Fig. 16 are similar to those obtained by D’Onofrio et al. (2008)
(see their fig. 1), when comparing Sersiceffective parameters to the
Photo quantities. As noticed above, the FP parameters are more
stable with respect to the fitting procedure than the other quantities.
In particular, the quantity FP shows only a weak dependence on
galaxy magnitude (see lower-right panel of Fig. 16), with an end-
to-end average variation of only 0.02 dex (∼ 5%). Since the FP
can be seen as a linear relation between the FP quantity and veloc-
ity dispersion (or galaxy magnitude7, through the Faber–Jackson
relation), the weak dependence of the FP quantity with magnitude
implies that the coefficients of the FP are expected not to change
significantly when using either 2DPHOT or SDSS parameters (see
paper II).
7 SPECTROSCOPY
7.1 Velocity dispersions from SDSS and STARLIGHT
We have re-computed central velocity dispersions for all the ETGs
in the SPIDER sample. Velocity dispersions are usually measured
by comparing the observed galaxy spectrum with single spectral
templates, which are assumed to describe the dominant stellar pop-
ulation of the galaxy. For ETGs, the spectra of red giant stars are
usually adopted. On the other hand, ETGs frequently show mixed
stellar populations, and this might significantly affect the σ0 es-
timate for some fraction of the ETG’s population. We derive the
σ0’s with the same procedure as in the SDSS-DR6 pipeline, i.e.
the direct fitting of galaxy spectra (see Adelman-McCarthy et al.
2008), but instead of using single spectral templates as in the SDSS
pipeline, we construct a mixed-population spectral template for
each galaxy. This is done as part of the automatic procedure de-
scribed in STARLIGHT(Cid Fernandes et al. 2005) where velocity
dispersion and stellar population parameters are determined simul-
taneously. Hence, the new velocity dispersion values should be vir-
tually unaffected by the different kinematics of the various stellar
components.
For each galaxy, we run the spectral fitting code STARLIGHT
(Cid Fernandes et al. 2005) to find the combination of single stel-
lar population (SSP) models that, normalized and broadened with
a given sigma, best matches the observed spectrum (also normal-
ized), which is first de-redshifted and corrected for extinction. We
use SSP models from the MILES galaxy spectral library, with a
Salpeter Initial Mass Function truncated at lower and upper cut-
off mass values of 0.01 and 120 M⊙, respectively (Vazdekis et
al. 2010). These models are based on the MILES stellar library
(S´ anchez-Bl´ azquez et al. 2006), which has an almost complete cov-
erage of stellar atmospheric parameters at a relatively high and
nearly constant spectral resolution of 2.3˚ A (FWHM). This reso-
lution is better than that of SDSS spectra, allowing us to suitably
degrade the spectral models to match the resolution of the observed
spectra (see below).
One main issue for the estimate of velocity dispersions from
7Notice that the Sersic ”n” is also correlated with velocity dispersion (Gra-
ham 2002), but the correlation exhibits a large dispersion.
Figure 17. Wavelength dependent instrumental resolution for the SDSS
spectra of five randomly selected ETGs. The resolution values are taken
from the fits spectral files in the SDSS archive. The dashed line shows
the resolution variation for the MILES SSP-models, which have a nearly
constant value of 2.3˚ A (FWHM). For each galaxy, we degrade the MILES
models (dashed curve) to match the corresponding wavelength dependent
resolution (solid curves; see the text).
SDSS is the wavelength variation of the SDSS spectral resolu-
tion. For the ETG’s spectra of the SPIDER sample, we found that
the median value of the resolution varies from ∼ 2.8˚ A (FWHM)
(σinst ∼ 90 km/s) in the blue (4000˚ A) up to ∼ 3.7˚ A (FWHM)
(σinst ∼ 55 km/s) in the red (8000˚ A). Resolution also varies sig-
nificantly among different spectra, as seen in Fig. 17, where we
plot the σinst as a function of wavelength for the spectra of five
randomly selected ETGs. Bernardi et al. (2003a) have accounted
for the wavelength dependence of the SDSS spectral resolution by
modeling it with a simple linear relation. On the contrary, in the
present study, we do not perform any modeling of σinst. For each
galaxyintheSPIDERsample, wedegrade theSSPmodels tomatch
the wavelength-dependent resolution, σinst(λ), of the correspond-
ing spectrum. The σinst is measured from the SDSS pipeline by
using a set of arc lamps, and provided in one fits extension of the
spectrum fits file (see Stoughton et al. 2002). The MILES models
are degraded by the transformation:
?
Ms(λ) =M(x)G(x − λ)dx
(5)
where M(λ) is a given SSP model, Ms(λ) is the smoothed model,
and the function G(λ) is a Gaussian kernel whose width is ob-
tained by subtracting in quadrature the MILES resolution to the de-
redshifted resolution σinst(λ/(1+z)), where z is the galaxy spec-
troscopic redshift. The integral is performed by discrete integra-
tion. Notice that Eq. 5 reduces to a simple convolution in the case
where σinst is a constant. For each galaxy, we run STARLIGHT
using the corresponding smoothed MILES models. We use a set
of SSP models covering a wide range of age and metallicity val-
ues (with fixed solar [α/Fe]=0 abundance ratio). Age values range
from 0.5 to ∼ 18 Gyr, while metallicity values of logZ/Z⊙ =
−1.68,−1.28,−0.68,−0.38,0.,0.2 are considered, resulting in a

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SPIDER I – Sample and data analysis
15
Figure 18. Example of the advantage in using mixed-population templates
to derive the galaxy central velocity dispersion. The upper panel shows an
example ETG spectrum from SDSS (J154615.45-001025.4) and the best-
matching synthetic models obtained by running STARLIGHT (i) with a set
of 132 different SSP MILES models (red color), and (ii) with a single SSP
model, having an age of 12.6 Gyr and solar metallicity (blue color). The
σ0 values obtained in the two cases are reported in the upper panel. The
lower panel shows the residuals obtained by subtracting the models to the
observed spectrum. The gray bands in the upper panel show the masked
windows we use to exclude from the fitting those regions possibly contam-
inated by emission lines (see the arrows in the plot) as well as corrupted
pixels (e.g. those corresponding to bad-columns).
total of 132 SSP models. Fig. 18 illustrates the advantage of using
a mixed-population rather than a single stellar population template.
In order to exacerbates the difference between the two approaches,
we selected the spectrum of one ETG for which STARLIGHTmea-
sures a significant contribution from young (age< 2 Gyr) stellar
populations. The Figure plots a portion of the spectrum, along with
two best-fittingmodels obtained by either the mixed-population ap-
proach (in red) or by running STARLIGHT with a single old stellar
population templatehaving an age of 12.6 Gyr and solar metallicity
(in blue). Residuals are plotted for both cases. It is evident that the
mixed-population model yields a better description of the contin-
uum and the absorption features in the galaxy spectrum. In particu-
lar, one may notice that the Mgb band (λ ∼ 5170˚ A), which is one
of the main spectral features to measure the σ0, shows significantly
smaller residuals in the case of the mixed-population fit. In fact, the
σ0 value (reported in the upper panel of Fig. 18) changes dramat-
ically from one case to the other. Fig. 18 also shows the masked
regions used to avoid either corrupted spectral regions (e.g., bad
columns) or regions possibly contaminated by nebular emission. In
particular, we show three masked regions. The ones at λ ∼ 4850
and 4980 ˚ A avoid the Hβ (4861˚ A) and [OIII] (4959 and 5007)
emission lines, respectively, while the one at ∼5220 ˚ A excludes
pixels contaminated by a bad-column, as flagged in the SDSS spec-
trum.
Fig. 19 compares velocity dispersion values obtained from the
SDSS spectroscopic pipeline with those measured in this work us-
ing STARLIGHT. A good agreement is found, with only a small
systematic trend at the low (< 90km/s) and high (> 280km/s) ends
Figure 19. Differences in logσ0 between STARLIGHT and SDSS as a
function of the SDSSvelocity dispersion value. Curves with different colors
are obtained by binning the data with respect to σ0(DR6), and taking for
each bin the corresponding median value (red), the location value estimated
through the the bi-weight statistics (magenta), and the 2.5σ clipped mean
value (green). Notice that the trend with σ is essentially the same for all
the three estimators. The horizontal blue dashed line marks the value of
zero, corresponding to a null difference between SDSS and STARLIGHT
σ0values.
of the σ0 range. In particular, for σ0 < 90km/s, the STARLIGHT
velocity dispersions are slightly higher, by a few percent, with re-
spect to those of the SDSS. It is important to emphasize that al-
though STARLIGHT does not normalize the spectrum by the con-
tinuum, which isdone by thedirect fittingmethod used inthe SDSS
pipeline, the good agreement found here is likely reflecting the ex-
cellent quality of flux calibration obtained in DR6 (see Figure 7
of Adelman-McCarthy et al. 2008).The impact of the above sys-
tematic difference in σ0on the scaling relations of ETGs is investi-
gated in paper II.
7.2Uncertainties on the velocity dispersions
To estimate the uncertainties on the STARLIGHT σ0 values, we
looked for ETGs in the SPIDER sample having spectra with re-
peated observations in SDSS. Out of all the 39,993 galaxies, we
found 2,313 cases with a duplicate spectrum available. For all these
duplicate spectra, we measure the σ0 with STARLIGHT, with the
same setup and set of model templates as for the primary spec-
tra. In each case, we compute the relative difference of σ0 as
δσ/σ = (σ0,2− σ0,1)/σ0,1, where the indices 1 and 2 refer to the
spectra with higher and lower S/N ratios. Fig. 20 plots the δσ/σ as
a function of the minimum S/N ratio, min(S/N), of each pair of
duplicate spectra. The S/N is computed from the median S/N ratio
in the spectral region of the Hβfeature, within a window of 100˚ A,
centered at λ = 4860˚ A. We bin the δσ/σ values with respect to
min(S/N), with each bin including 30 galaxies. For each bin, we
compute the median and rms values of δσ/σ. As the Fig. 20 shows,
the median values (red color) are fully consistent with zero, imply-
ingthat,asexpected (seeSec.2), theS/Nratioof thespectraislarge