A&A 557, A54 (2013)
DOI: 10.1051/0004-6361/201321463
c
ESO 2013
Astronomy
&
Astrophysics
The VIMOS Public Extragalactic Redshift Survey (VIPERS)
⋆
Galaxy clustering and redshift-space distortions at
z ≃ 0.8
in the first data release
S. de la Torre
1
, L. Guzzo
2,3
, J. A. Peacock
1
, E. Branchini
4,5,6
, A. Iovino
2
, B. R. Granett
2
, U. Abbas
7
, C. Adami
8
,
S. Arnouts
9,8
, J. Bel
10
, M. Bolzonella
11
, D. Bottini
12
, A. Cappi
11,13
, J. Coupon
14
, O. Cucciati
11
, I. Davidzon
11,15
,
G. De Lucia
16
, A. Fritz
12
, P. Franzetti
12
, M. Fumana
12
, B. Garilli
12,8
, O. Ilbert
8
, J. Krywult
17
, V. Le Brun
8
,
O. Le Fèvre
8
, D. Maccagni
12
, K. Małek
18
, F. Marulli
15,11,19
, H. J. McCracken
20
, L. Moscardini
15,11,19
, L. Paioro
12
,
W. J. Percival
21
, M. Polletta
12
, A. Pollo
22,23
, H. Schlagenhaufer
24,25
, M. Scodeggio
12
, L. A. M. Tasca
8
, R. Tojeiro
21
,
D. Vergani
26
, A. Zanichelli
27
, A. Burden
21
, C. Di Porto
11
, A. Marchetti
28,2
, C. Marinoni
10
, Y. Mellier
20
,
P. Monaco
29,16
, R. C. Nichol
21
, S. Phleps
25
, M. Wolk
20
, and G. Zamorani
11
(Affiliations can be found after the references)
Received 13 March 2013 / Accepted 10 July 2013
ABSTRACT
We present the general real- and redshift-space clustering properties of galaxies as measured in the first data release of the VIPERS survey.
VIPERS is a large redshift survey designed to probe in detail the distant Universe and its large-scale structure at 0.5 < z < 1.2. We describe in this
analysis the global properties of the sample and discuss the survey completeness and associated corrections. This sample allows us to measure the
galaxy clustering with an unprecedented accuracy at these redshifts. From the redshift-space distortions observed in the galaxy clustering pattern
we provide a first measurement of the growth rate of structure at z = 0.8: f σ
8
= 0.47 ± 0.08. This is completely consistent with the predictions of
standard cosmological models based on Einstein gravity, although this measurement alone does not discriminate between different gravity models.
Key words. cosmology: observations – large-scale structure of Universe – galaxies: high-redshift – galaxies: statistics
1. Introduction
Over the past decades galaxy redshift surveys have provided a
wealth of information on the inhomogeneous universe, mapping
the late-time development of the small metric fluctuations that
existed at early times, and whose early properties can be viewed
in the cosmic microwave background (CMB). The growth of
structure during this intervening period is sensitive both to the
type and amount of dark matter, and also to the theory of gravity,
so there is a strong motivation to make precise measurements of
the rate of growth of cosmological structure (e.g.
Jain & Khoury
2010).
Of course, galaxy surveys do not image the mass fluctua-
tions directly, unlike gravitational lensing. But the visible light
distribution does have some advantages as a cosmological tool
in comparison with lensing. The number density of galaxies is
⋆
Based on observations collected at the European Southern
Observatory, Cerro Paranal, Chile, using the Very Large Telescope
under programmes 182.A-0886 and partly 070.A-9007. Also based
on observations obtained with MegaPrime/MegaCam, a joint project
of CFHT and CEA/DAPNIA, at the Canada-France-Hawaii Telescope
(CFHT), which is operated by the National Research Council (NRC)
of Canada, the Institut National des Sciences de l’Univers of the
Centre National de la Recherche Scientifique (CNRS) of France, and
the University of Hawaii. This work is based in part on data prod-
ucts produced at TERAPIX and the Canadian Astronomy Data Centre
as part of the Canada-France-Hawaii Telescope Legacy Survey, a
collaborative project of NRC and CNRS. The VIPERS web site is
http://www.vipers.inaf.it/
sufficiently high that the density field of luminous matter can
be measured with a finer spatial resolution, probing interesting
non-linear features of the clustering pattern with good signal-
to-noise. The price to be paid for this is that the complicated
biasing relation between visible and dark matter has to be con-
fronted; but this is a positive factor in some ways, since under-
standing galaxy formation is one of the main questions in cos-
mology. Redshift surveys provide the key information needed to
meet this challenge: global properties of the galaxy population
and their variation with environment and with epoch.
The final advantage of redshift surveys is that the radial in-
formation depends on cosmological expansion and is corrupted
by peculiar velocities. Although the lack of a simple method to
recover true distances can be frustrating at times, it has come to
be appreciated that this complication is in fact a good thing. The
peculiar velocities induce an anisotropy in the apparent cluster-
ing, from which the properties of the peculiar velocities can be
inferred much more precisely than in any attempt to measure
them directly using distance estimators. The reason peculiar ve-
locities are important is that they are related to the underlying
linear fractional density perturbation δ via the continuity equa-
tion:
˙
δ = −∇ · u, where u is the peculiar velocity field. This can
be expressed more conveniently in terms of the dimensionless
scale factor, a(t), and the Hubble parameter, H(t), as
∇ · u = −H f δ; f ≡
dln δ
dln a
· (1)
The growth rate can be approximated in most models by f (a) ≃
Ω
m
(a)
γ
, where γ ≃ 0.545 in standard Λ-dominated models, but
Article published by EDP Sciences A54, page 1 of 19
A&A 557, A54 (2013)
where models of non-standard gravity display a growth rate in
which the effective value of γ can differ by 30% (Linder & Cahn
2007).
The possibility of using the redshift-space distortion signa-
ture as a probe of the growth rate of density fluctuations, together
with that of using the Baryonic Acoustic Oscillations (BAO) as
a standard ruler to measure the expansion history, is one of the
main reasons behind the recent burst of activity in galaxy redshift
surveys. The first paper to emphasise this application as a test of
gravity theories was the analysis of the VVDS survey by Guzzo
et al. (2008), and subsequent work especially by the SDSS LRG
(Samushia et al. 2012), WiggleZ (Blake et al. 2012; Contreras
et al. 2013), 6dFGS (Beutler et al. 2012) and BOSS (Reid et al.
2012) surveys has exploited this method to make measurements
of the growth rate at z < 1.
Surveys such as SDSS LRG, WiggleZ, or BOSS are char-
acterised by a large volume (0.5−2 h
−3
Gpc
3
), and a rela-
tively sparse galaxy population with number density of about
10
−4
h
3
Mpc
−3
. Statistical errors are in this case minimised
thanks to the large volume probed, at the expenses of select-
ing a very specific galaxy population (e.g. blue star form-
ing or very massive galaxies), often with a complex selec-
tion function. The goal of the VIMOS Public Extragalactic
Redshift Survey
1
(VIPERS) has been that of constructing a sur-
vey with broader science goals and properties comparable to lo-
cal general-purpose surveys such as the 2dFGRS. The adopted
strategy has been to optimise the features of the ESO VLT multi-
object spectrograph VIMOS in order to measure about 400 spec-
tra at I
AB
< 22.5 over an area of 200 square arcmin, in a sin-
gle exposure of less than 1 hour. The survey is being performed
as a “Large Programme” within the ESO general user frame-
work and aims at measuring redshifts for about 10
5
galaxies at
0.5 < z < 1.2.
The prime goal of VIPERS is an accurate measurement of
the growth rate of large-scale structure at redshift around unity.
The survey should enable us in particular to use techniques
aimed at improving the precision on the growth rate (
McDonald
& Seljak 2009
) thanks to its high galaxies sampling of about
10
−2
h
3
Mpc
−3
. In general, VIPERS is intended to provide ro-
bust and precise measurements of the properties of the galaxy
population at an epoch when the Universe was about half its cur-
rent age, representing one of the largest spectroscopic surveys
of galaxies ever conducted at these redshifts. Examples can be
found in the parallel papers that are part of the first science re-
lease (
Marulli et al. 2013; Malek et al. 2013; Davidzon et al.
2013).
This paper presents the initial analysis of the real-space
galaxy clustering and redshift-space distortions in VIPERS, to-
gether with the resulting implications for the growth rate. The
data are described in Sect. 2; Sect. 3 describes the survey selec-
tion effects; Sect. 4 describes our methods for estimating cluster-
ing, which are tested on simulations in Sect. 5; Sect. 6 presents
the real-space clustering results; Sect. 7 gives the redshift-
space distortions results, and Sect. 8 summarises our results and
concludes.
Throughout this analysis, if not specified otherwise, we
assume a fiducial Λ-cold dark matter (ΛCDM) cosmological
model with (Ω
m
, Ω
k
, w, σ
8
, n
s
) = (0.25, 0, −1, 0.8, 0.95) and a
Hubble constant of H
0
= 100 h km s
−1
Mpc
−1
.
1
http://vipers.inaf.it
2. Data
The VIPERS galaxy target sample is selected from the optical
photometric catalogues of the Canada-France-Hawaii Telescope
Legacy Survey Wide (CFHTLS-Wide,
Goranova et al. 2009).
VIPERS covers 24 deg
2
on the sky, divided over two areas within
the W1 and W4 CFHTLS fields. Galaxies are selected to a limit
of i
′
AB
< 22.5, applying a simple and robust gri colour pre-
selection to efficiently remove galaxies at z < 0.5. Coupled with
a highly optimised observing strategy (
Scodeggio et al. 2009),
this allows us to double the galaxy sampling rate in the redshift
range of interest, with respect to a pure magnitude-limited sam-
ple. At the same time, the area and depth of the survey result in
a relatively large volume, 5 × 10
7
h
−3
Mpc
3
, analogous to that
of the Two Degree Field Galaxy Redshift Survey (2dFGRS) at
z ≃ 0.1 (Colless et al. 2001, 2003). Such a combination of sam-
pling rate and depth is unique amongst current redshift surveys
at z > 0.5. VIPERS spectra are collected with the VIMOS multi-
object spectrograph (
Le Fèvre et al. 2003) at moderate resolu-
tion (R = 210) using the LR Red grism, providing a wavelength
coverage of 5500–9500 Å and a typical radial velocity error of
σ
v
= 175(1+ z) km s
−1
. The full VIPERS area of 24 deg
2
will be
covered through a mosaic of 288 VIMOS pointings (192 in the
W1 area, and 96 in the W4 area). A discussion of the survey data
reduction and management infrastructure is presented in
Garilli
et al.
(2012). An early subset of the spectra used here is analysed
and classified through a Principal Component Analysis (PCA)
in Marchetti et al. (2013). A complete description of the survey
construction, from the definition of the target sample to the ac-
tual spectra and redshift measurements, is given in the parallel
survey description paper (Guzzo et al. 2013).
The dataset used in this and the other papers of the early sci-
ence release, will represent the VIPERS Public Data Release 1
(PDR-1) catalogue. It will be publicly available in the fall of
2013. This catalogue includes 55 358 redshifts (27 935 in W1
and 27 423 in W4) and corresponds to the reduced data frozen
in the VIPERS database at the end of the 2011/2012 observ-
ing campaign; this represents 64% of the final survey in terms
of covered area. A quality flag has been assigned to each ob-
ject in the process of determining their redshift from the spec-
trum, which quantifies the reliability of the measured redshifts.
In this analysis, we use only galaxies with flags 2 to 9 inclusive,
corresponding to a sample with a redshift confirmation rate of
98%. The redshift confirmation rate and redshift accuracy have
been estimated using repeated spectroscopic observations in the
VIPERS fields (see
Guzzo et al. 2013, for details). The cata-
logue, which we will refer to just as the VIPERS sample in the
following, corresponds to a sub-sample of 45 871 galaxies with
reliable redshift measurements.
The redshift distribution of the sample is presented in Fig.
1.
We can see in this figure that the survey colour selection allows
an efficient removal of galaxies below z = 0.5. It is important
to notice that the colour selection does not introduce a sharp cut
in redshift but a redshift window function which has a smooth
transition from zero to one in the redshift range 0.4 < z < 0.6,
with respect to the full population of i
′
< 22.5 galaxies. This
effect on the radial selection of the survey, which we refer to as
the colour sampling rate (CSR) in the following, is only present
below z = 0.6. Above this redshift, the colour selection has no
impact on the redshift selection and the sample becomes purely
magnitude-limited at i
′
< 22.5 (
Guzzo et al. 2013). If we weight
the raw redshift distribution by the global survey completeness
function described in the next sections, one obtains the N(z) rep-
resented by the empty histogram in Fig.
1. For convenience, we
A54, page 2 of 19
S. de la Torre et al.: Galaxy clustering and redshift-space distortions in VIPERS
0
50
100
150
200
250
300
350
400
0.4 0.6 0.8 1 1.2 1.4
Number [deg
-2
(∆z=0.03)
-1
]
z
W1+W4
W1+W4 cor.
Analytical fit
Fig. 1. Redshift distribution of the combined W1+W4 galaxy sam-
ple when including only reliable redshifts (filled histogram) and that
corrected for the full survey completeness (empty histogram) scaled
down by 40% (see text). The curve shows the best-fitting template red-
shift distribution given by Eq. (
2) applied to the uncorrected observed
distribution.
scaled down the corrected N(z) by 40%, the average effective
survey sampling rate, to aid the comparison between the shapes
of the two distributions. The difference in shape between these
two N(z) shows the effect of incompleteness in the survey, which
is only significant at about z > 0.9 (see also
Davidzon et al.
2013).
The observed redshift distribution in the sample can be well
described by a function of the form
N(z) = A
z
z
0
!
α
exp
−
z
z
0
!
β
CS R(z), (2)
in units of deg
−2
· (∆z = 0.03)
−1
and where (A, z
0
, α, β) =
(3.103, 0.191, 8.603, 1.448). The CSR is the incompleteness in-
troduced by the VIPERS colour selection. It is primarily a func-
tion of redshift and can be estimated from the ratio between the
number of galaxies with i
′
< 22.5 satisfying the VIPERS colour
selection and the total number of galaxies with i
′
< 22.5 as a
function of redshift. We calibrated this function using the VLT-
VIMOS Deep Survey Wide spectroscopic sample (VVDS-Wide,
Garilli et al. 2008) which has a CFHTLS-based photometric cov-
erage and depth that is similar to that of VIPERS, but which is
free from any colour selection (see Guzzo et al. 2013, for de-
tails). The CSR is well described by a function of the form
CSR(z) =
"
1
2
−
erf
(
b(z
t
− z)
)
2
#
, (3)
with (b, z
t
) = (17.465, 0.424).
The fitting of N(z) is important in measuring galaxy cluster-
ing: the form of the mean redshift distribution must be followed
accurately, but features from large-scale structure must not be al-
lowed to bias the result. We discuss this issue in detail in Sect.
5.
3. Angular completeness
3.1. Slit assignment and footprint
To obtain a sample of several square degrees with VIMOS, one
needs to perform a series of individual observations or point-
ings. The VIPERS strategy consists in covering the survey area
with only one pass. This has been done in order to maximise
the volume probed. The survey strategy and the fact that the
VIMOS field-of-view is composed of four quadrants delimited
by an empty cross, create a particular footprint on the sky which
is reproduced in Figs.
4 and 5. In each pointing, slits are as-
signed to a number of potential targets which meet the survey
selection criteria. This is shown in Fig. 2, which illustrates how
the slits are positioned in the pointing W1P082. Given the sur-
face density of the targeted population, the multiplex capabil-
ity of VIMOS, and the survey strategy, a fraction of about 45%
of the parent photometric sample can be assigned to slits. We
define the fraction of target which have a measured spectrum
as the target sampling rate (TSR) and the fraction of observed
spectra with reliable redshift measurement as the spectroscopic
sampling rate (SSR). The number of slits assigned per pointing is
maximised by the SSPOC algorithm (
Bottini et al. 2005), but the
elongated size of the spectra means that the resulting sampling
rate is not uniform inside the quadrants. The dispersion direc-
tion of the spectra in VIPERS are aligned with the Dec direction
and consequently, the density of spectra along this direction is
lower with respect to that along the RA direction. This partic-
ular sampling introduces an observed anisotropic distribution of
pair separation, which has to be accounted for to measure galaxy
clustering correctly.
The two empty stripes between the four quadrants in each
pointing introduce a particular pattern in the measured correla-
tion functions if not accounted for. We correct for that by apply-
ing detailed binary masks of the spectroscopic observations to a
random sample of unclustered objects, so that both data and ran-
dom catalogues contain no objects in these stripes. These masks
account for the detailed VIMOS field-of-view geometry as well
as for the presence of vignetted areas at the boundaries of the
pointings. On top of these spectroscopic masks, we apply a set
of photometric masks which discard areas where the parent pho-
tometry is affected by defects such as large stellar haloes and
where the survey selection is compromised (see
Guzzo et al.
2013).
3.2. Small-scale incompleteness
We can characterise the amount of missing small-scale angular
pairs induced by the VIPERS spectroscopic strategy, by measur-
ing the angular pair completeness as a function of angular sep-
aration. This quantity, defined as the ratio between the number
of pairs in the spectroscopic sample and that in the parent pho-
tometric sample, can be written in terms of angular two-point
correlation functions as (Hawkins et al. 2003)
1
w
A
(θ)
=
1 + w
s
(θ)
1 + w
p
(θ)
, (4)
where w
s
(θ) and w
p
(θ) are respectively the angular correlation
function of the spectroscopic and parent samples. This function
is shown in Fig.
3. No significant difference is seen between the
W1 and W4 fields, as expected. The amount of missing angular
pairs is only significant below θ = 0.03 deg, which corresponds
to a transverse comoving scale of about 1 h
−1
Mpc at z = 0.8.
This fraction varies with redshift, although in practice we
cannot measure it at different redshifts since we do not have a
A54, page 3 of
19
A&A 557, A54 (2013)
Q1 Q2
Q4 Q3
7.0'
8.0'
2.4'
2.0'
N
E
Fig. 2. Illustration of the slit assignment in
pointing W1P082. The slits are shown in red
and associated rectangles represent the typical
dispersion of the spectra. All objects meeting
the survey selection criteria (potential spectro-
scopic targets) are represented by black circles.
measured redshift for all galaxies in the parent sample. For this
reason we use the global w
A
(θ) (averaged over all observed red-
shifts) to correct for the small-scale angular incompleteness ef-
fect. We will show in Sect.
5 that the level of systematic error
introduced by using w
A
(θ) instead of w
A
(θ|z) is very small, of
the order of a few percent. When measuring the angular cor-
relation functions, we include the completeness weights intro-
duced in the following section, in a similar way as for the three-
dimensional correlation function estimation.
It is important to mention that the small-scale angular incom-
pleteness effect is a general issue for large galaxy redshift sur-
veys, in which one has to deal with the mechanical constraints
of multi-object spectrographs and survey strategy. The incom-
pleteness due to slit assignment in VIPERS is to some extent
similar to the fibre collision problem in surveys using fibre spec-
troscopy such as 2dFGRS or SDSS, while the magnitude of the
effect is much more severe in our case. Recently, a new method
has been developed to accurately correct for fibre collision (
Guo
et al. 2012). Although this method is quite general, it is not ap-
plicable here. The exclusion between spectroscopically observed
objects in VIPERS is essentially uni-directional, meaning that
not all close pairs are excluded. Therefore calculations such as
that shown in Fig.
4 are possible from the set of one-pass ob-
servations, whereas the correction scheme of
Guo et al. (2012)
can only be used for SDSS where overlapping observations are
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
0.001 0.01 0.1 1
0.1 1 10
[1+w
s
(
θ
)] / [1+w
p
(
θ
)]
θ
[deg]
r
p
(z=0.8) [h
-1
Mpc]
W1
W4
Fig. 3. Completeness fraction of angular galaxy pairs due to the slit-
spectroscopy strategy in the W1 and W4 fields for all galaxies at
0.5 < z < 1.0. This has been obtained from the parent and spectro-
scopic sample angular correlation function.
A54, page 4 of
19
S. de la Torre et al.: Galaxy clustering and redshift-space distortions in VIPERS
Fig. 4. Variations of the target success rate (TSR) with quadrants. The TSR quantifies our ability of obtaining spectra from the potential tar-
gets meeting the survey selection in the parent photometric sample. The quadrants filled in black correspond to failed observations where no
spectroscopy has been taken.
Fig. 5. Variations of the spectroscopic success rate (SSR) with quadrants. The SSR quantifies our ability of determining galaxy redshifts from
observed spectra. The quadrants filled in black correspond to failed observations where no spectroscopy has been taken.
included. Thus we need to revise the correction methods devel-
oped for such surveys to apply them to VIPERS.
3.3. Large-scale incompleteness
In addition to the non-uniform sampling inside the pointings, the
survey has variations of completeness from quadrant to quad-
rant. This incompleteness is the combined effect of the TSR and
SSR. The latter, which characterises our ability of determining
a redshift from a galaxy spectrum, is determined empirically as
the ratio between the number of reliable redshifts and the total
number of observed spectra. The TSR and SSR in each quad-
rant are shown in in Figs.
4 and 5. From these figures one can
see clearly that both TSR and SSR functions vary according to
the position on the sky, although the SSR tends to have stronger
variations. The variations of TSR reflect the changes in angu-
lar galaxy density in the parent catalogue. Indeed, because of
the finite maximum number of slits that can be assigned and the
fact that each quadrant has a different number of potential tar-
gets, the less dense quadrants tend to be better sampled than the
denser ones. On the other hand, variations in observational con-
ditions from pointing to pointing induce changes in SSR. These
different observational conditions translate into variations of the
signal-to-noise of the measured spectra and so in our ability of
extracting a redshift measurement from them. These effects are
taken into account in the clustering estimation by weighting each
galaxy according to the reciprocal of the TSR and SSR.
4. Clustering estimation
We characterise the galaxy clustering in the VIPERS sample by
measuring the two-point statistics of the spatial distribution of
galaxies in configuration space. We estimate the two-point cor-
relation function ξ(r) using the
Landy & Szalay (1993) estimator
ξ(r) =
GG(r) − 2GR(r) + RR(r)
RR(r)
, (5)
where GG(r), GR(r), and RR(r) are respectively the normalised
galaxy-galaxy, galaxy-random, and random-random number of
pairs with separation inside [r − ∆r/2, r + ∆r/2]. Note that here
r is a general three-dimensional galaxy separation, not specifi-
cally the real-space separation. This estimator minimises the es-
timation variance and circumvent discreteness and finite volume
A54, page 5 of
19