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Photometric selection of emission-line galaxies, clustering analysis and a search for the integrated Sachs–Wolfe effect

Identifieur interne : 000F26 ( Istex/Corpus ); précédent : 000F25; suivant : 000F27

Photometric selection of emission-line galaxies, clustering analysis and a search for the integrated Sachs–Wolfe effect

Auteurs : Rich Bielby ; T. Shanks ; U. Sawangwit ; S. M. Croom ; Nicholas P. Ross ; D. A. Wake

Source :

RBID : ISTEX:508B804A396A7674F820FBC1AB655389185A7103

Abstract

We investigate the use of simple colour cuts applied to the Sloan Digital Sky Survey (SDSS) optical imaging to perform photometric selections of emission-line galaxies (ELGs) out to z < 1. Our selection is aimed at discerning three separate redshift ranges: 0.2 ≲z≲ 0.4, 0.4 ≲z≲ 0.6 and 0.6 ≲z≲ 1.0, which we calibrate using data taken by the COMBO-17 survey in a single field (S11). We thus perform colour cuts using the SDSS g, r and i bands and obtain mean photometric redshifts of and . We further calibrate our high-redshift selection using spectroscopic observations with the AAOmega spectrograph on the 4-m Anglo-Australian Telescope, observing ≈50–200 galaxy candidates in four separate fields. With just 1 h of integration time and seeing of ≈ 1.6 arcsec, we successfully determined redshifts for ≈65 per cent of the targeted candidates. We compare our spectroscopic redshifts to the photometric redshifts from the COMBO-17 survey and find reasonable agreement between the two. We calculate the angular correlation functions of these samples and find correlation lengths of r0= 2.78 ± 0.08, 3.71 ± 0.11 and 5.50 ± 0.13 h−1 Mpc for the low-, mid- and high-redshift samples, respectively. Comparing these results with predicted dark matter clustering, we estimate the bias parameter for each sample to be b= 0.72 ± 0.02, b= 0.93 ± 0.03 and b= 1.43 ± 0.03. We calculate the two-point redshift-space autocorrelation function at z≈ 0.6 and find a clustering amplitude of so= 6.4 ± 0.8 h−1 Mpc. Finally, we use our photometric sample to search for the integrated Sachs–Wolfe signal in the Wilkinson Microwave Anisotropy Probe (WMAP) 5-yr data. We cross-correlate our three redshift samples with the WMAP W, V, Q and K bands and find an overall trend for a positive signal similar to that expected from models. However, the signal in each is relatively weak, with the results in the WMAP W band being wTg(<100 arcmin) = 0.25 ± 0.27, 0.17 ± 0.20 and 0.17 ± 0.16 μK for the low-, mid- and high-redshift samples, respectively. Combining all three galaxy samples, we find a signal of wTg(<100 arcmin) = 0.20 ± 0.12 μK in the WMAP W band, a significance of 1.7σ. However, in testing for systematics where the WMAP data are rotated with respect to the ELG sample, we found similar results at several different rotation angles, implying the apparent signal may be produced by systematic effects.

Url:
DOI: 10.1111/j.1365-2966.2009.16219.x

Links to Exploration step

ISTEX:508B804A396A7674F820FBC1AB655389185A7103

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<div type="abstract">We investigate the use of simple colour cuts applied to the Sloan Digital Sky Survey (SDSS) optical imaging to perform photometric selections of emission-line galaxies (ELGs) out to z < 1. Our selection is aimed at discerning three separate redshift ranges: 0.2 ≲z≲ 0.4, 0.4 ≲z≲ 0.6 and 0.6 ≲z≲ 1.0, which we calibrate using data taken by the COMBO-17 survey in a single field (S11). We thus perform colour cuts using the SDSS g, r and i bands and obtain mean photometric redshifts of and . We further calibrate our high-redshift selection using spectroscopic observations with the AAOmega spectrograph on the 4-m Anglo-Australian Telescope, observing ≈50–200 galaxy candidates in four separate fields. With just 1 h of integration time and seeing of ≈ 1.6 arcsec, we successfully determined redshifts for ≈65 per cent of the targeted candidates. We compare our spectroscopic redshifts to the photometric redshifts from the COMBO-17 survey and find reasonable agreement between the two. We calculate the angular correlation functions of these samples and find correlation lengths of r0= 2.78 ± 0.08, 3.71 ± 0.11 and 5.50 ± 0.13 h−1 Mpc for the low-, mid- and high-redshift samples, respectively. Comparing these results with predicted dark matter clustering, we estimate the bias parameter for each sample to be b= 0.72 ± 0.02, b= 0.93 ± 0.03 and b= 1.43 ± 0.03. We calculate the two-point redshift-space autocorrelation function at z≈ 0.6 and find a clustering amplitude of so= 6.4 ± 0.8 h−1 Mpc. Finally, we use our photometric sample to search for the integrated Sachs–Wolfe signal in the Wilkinson Microwave Anisotropy Probe (WMAP) 5-yr data. We cross-correlate our three redshift samples with the WMAP W, V, Q and K bands and find an overall trend for a positive signal similar to that expected from models. However, the signal in each is relatively weak, with the results in the WMAP W band being wTg(<100 arcmin) = 0.25 ± 0.27, 0.17 ± 0.20 and 0.17 ± 0.16 μK for the low-, mid- and high-redshift samples, respectively. Combining all three galaxy samples, we find a signal of wTg(<100 arcmin) = 0.20 ± 0.12 μK in the WMAP W band, a significance of 1.7σ. However, in testing for systematics where the WMAP data are rotated with respect to the ELG sample, we found similar results at several different rotation angles, implying the apparent signal may be produced by systematic effects.</div>
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<surname>Bielby</surname>
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<email>bielby@iap.fr</email>
<affiliation>Department of Physics, Durham University, South Road, Durham DH1 3LE</affiliation>
<affiliation>Institut d'Astrophysique de Paris, UMR 7095 CNRS, Université Pierre et Marie Curie, 98bis boulevard Arago, 75014 Paris, France</affiliation>
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<forename type="first">Nicholas P.</forename>
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<p>We investigate the use of simple colour cuts applied to the Sloan Digital Sky Survey (SDSS) optical imaging to perform photometric selections of emission-line galaxies (ELGs) out to z < 1. Our selection is aimed at discerning three separate redshift ranges: 0.2 ≲z≲ 0.4, 0.4 ≲z≲ 0.6 and 0.6 ≲z≲ 1.0, which we calibrate using data taken by the COMBO-17 survey in a single field (S11). We thus perform colour cuts using the SDSS g, r and i bands and obtain mean photometric redshifts of and . We further calibrate our high-redshift selection using spectroscopic observations with the AAOmega spectrograph on the 4-m Anglo-Australian Telescope, observing ≈50–200 galaxy candidates in four separate fields. With just 1 h of integration time and seeing of ≈ 1.6 arcsec, we successfully determined redshifts for ≈65 per cent of the targeted candidates. We compare our spectroscopic redshifts to the photometric redshifts from the COMBO-17 survey and find reasonable agreement between the two. We calculate the angular correlation functions of these samples and find correlation lengths of r0= 2.78 ± 0.08, 3.71 ± 0.11 and 5.50 ± 0.13 h−1 Mpc for the low-, mid- and high-redshift samples, respectively. Comparing these results with predicted dark matter clustering, we estimate the bias parameter for each sample to be b= 0.72 ± 0.02, b= 0.93 ± 0.03 and b= 1.43 ± 0.03. We calculate the two-point redshift-space autocorrelation function at z≈ 0.6 and find a clustering amplitude of so= 6.4 ± 0.8 h−1 Mpc. Finally, we use our photometric sample to search for the integrated Sachs–Wolfe signal in the Wilkinson Microwave Anisotropy Probe (WMAP) 5-yr data. We cross-correlate our three redshift samples with the WMAP W, V, Q and K bands and find an overall trend for a positive signal similar to that expected from models. However, the signal in each is relatively weak, with the results in the WMAP W band being wTg(<100 arcmin) = 0.25 ± 0.27, 0.17 ± 0.20 and 0.17 ± 0.16 μK for the low-, mid- and high-redshift samples, respectively. Combining all three galaxy samples, we find a signal of wTg(<100 arcmin) = 0.20 ± 0.12 μK in the WMAP W band, a significance of 1.7σ. However, in testing for systematics where the WMAP data are rotated with respect to the ELG sample, we found similar results at several different rotation angles, implying the apparent signal may be produced by systematic effects.</p>
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<article-title>Photometric selection of emission-line galaxies, clustering analysis and a search for the integrated Sachs–Wolfe effect</article-title>
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<contrib-group>
<contrib contrib-type="author">
<name>
<surname>Bielby</surname>
<given-names>Rich</given-names>
</name>
<xref ref-type="aff" rid="a1">1</xref>
<xref ref-type="aff" rid="a2">2</xref>
<xref ref-type="corresp" rid="c1">*</xref>
</contrib>
<contrib contrib-type="author">
<name>
<surname>Shanks</surname>
<given-names>T.</given-names>
</name>
<xref ref-type="aff" rid="a1">1</xref>
</contrib>
<contrib contrib-type="author">
<name>
<surname>Sawangwit</surname>
<given-names>U.</given-names>
</name>
<xref ref-type="aff" rid="a1">1</xref>
</contrib>
<contrib contrib-type="author">
<name>
<surname>Croom</surname>
<given-names>S. M.</given-names>
</name>
<xref ref-type="aff" rid="a3">3</xref>
</contrib>
<contrib contrib-type="author">
<name>
<surname>Ross</surname>
<given-names>Nicholas P.</given-names>
</name>
<xref ref-type="aff" rid="a1">1</xref>
<xref ref-type="aff" rid="a4">4</xref>
</contrib>
<contrib contrib-type="author">
<name>
<surname>Wake</surname>
<given-names>D. A.</given-names>
</name>
<xref ref-type="aff" rid="a1">1</xref>
</contrib>
</contrib-group>
<aff id="a1">
<label>1</label>
Department of Physics, Durham University, South Road, Durham DH1 3LE</aff>
<aff id="a2">
<label>2</label>
Institut d'Astrophysique de Paris, UMR 7095 CNRS, Université Pierre et Marie Curie, 98bis boulevard Arago, 75014 Paris, France</aff>
<aff id="a3">
<label>3</label>
Sydney Institute for Astronomy, School of Physics, University of Sydney, NSW 2006, Australia</aff>
<aff id="a4">
<label>4</label>
Department of Astronomy and Astrophysics, Pennsylvania State University, 525 Davey Laboratory, University Park, PA 16802, USA</aff>
<author-notes>
<corresp id="c1">*E-mail:
<email>bielby@iap.fr</email>
</corresp>
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<pub-date pub-type="ppub">
<day>11</day>
<month>04</month>
<year>2010</year>
</pub-date>
<pub-date pub-type="epub">
<day>01</day>
<month>04</month>
<year>2010</year>
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<volume>403</volume>
<issue>3</issue>
<fpage>1261</fpage>
<lpage>1273</lpage>
<history>
<date date-type="received">
<day>27</day>
<month>11</month>
<year>2009</year>
</date>
<date date-type="accepted">
<day>14</day>
<month>12</month>
<year>2009</year>
</date>
</history>
<copyright-statement>© 2010 The Authors. Journal compilation © 2010 RAS</copyright-statement>
<copyright-year>2010</copyright-year>
<abstract>
<p>We investigate the use of simple colour cuts applied to the Sloan Digital Sky Survey (SDSS) optical imaging to perform photometric selections of emission-line galaxies (ELGs) out to
<italic>z</italic>
< 1. Our selection is aimed at discerning three separate redshift ranges: 0.2 ≲
<italic>z</italic>
≲ 0.4, 0.4 ≲
<italic>z</italic>
≲ 0.6 and 0.6 ≲
<italic>z</italic>
≲ 1.0, which we calibrate using data taken by the COMBO-17 survey in a single field (S11). We thus perform colour cuts using the SDSS
<italic>g</italic>
,
<italic>r</italic>
and
<italic>i</italic>
bands and obtain mean photometric redshifts of
<inline-formula>
<inline-graphic xlink:href="mnras0403-1261-mu1.gif"></inline-graphic>
</inline-formula>
and
<inline-formula>
<inline-graphic xlink:href="mnras0403-1261-mu2.gif"></inline-graphic>
</inline-formula>
. We further calibrate our high-redshift selection using spectroscopic observations with the AAOmega spectrograph on the 4-m Anglo-Australian Telescope, observing ≈50–200 galaxy candidates in four separate fields. With just 1 h of integration time and seeing of ≈ 1.6 arcsec, we successfully determined redshifts for ≈65 per cent of the targeted candidates. We compare our spectroscopic redshifts to the photometric redshifts from the COMBO-17 survey and find reasonable agreement between the two. We calculate the angular correlation functions of these samples and find correlation lengths of
<italic>r</italic>
<sub>0</sub>
= 2.78 ± 0.08, 3.71 ± 0.11 and 5.50 ± 0.13
<italic>h</italic>
<sup>−1</sup>
Mpc for the low-, mid- and high-redshift samples, respectively. Comparing these results with predicted dark matter clustering, we estimate the bias parameter for each sample to be
<italic>b</italic>
= 0.72 ± 0.02,
<italic>b</italic>
= 0.93 ± 0.03 and
<italic>b</italic>
= 1.43 ± 0.03. We calculate the two-point redshift-space autocorrelation function at
<italic>z</italic>
≈ 0.6 and find a clustering amplitude of
<italic>s
<sub>o</sub>
</italic>
= 6.4 ± 0.8
<italic>h</italic>
<sup>−1</sup>
Mpc. Finally, we use our photometric sample to search for the integrated Sachs–Wolfe signal in the
<italic>Wilkinson Microwave Anisotropy Probe</italic>
(
<italic>WMAP</italic>
) 5-yr data. We cross-correlate our three redshift samples with the
<italic>WMAP</italic>
<italic>W</italic>
,
<italic>V</italic>
,
<italic>Q</italic>
and
<italic>K</italic>
bands and find an overall trend for a positive signal similar to that expected from models. However, the signal in each is relatively weak, with the results in the
<italic>WMAP W</italic>
band being
<italic>w</italic>
<sub>Tg</sub>
(<100 arcmin) = 0.25 ± 0.27, 0.17 ± 0.20 and 0.17 ± 0.16 μK for the low-, mid- and high-redshift samples, respectively. Combining all three galaxy samples, we find a signal of
<italic>w</italic>
<sub>Tg</sub>
(<100 arcmin) = 0.20 ± 0.12 μK in the
<italic>WMAP W</italic>
band, a significance of 1.7σ. However, in testing for systematics where the
<italic>WMAP</italic>
data are rotated with respect to the ELG sample, we found similar results at several different rotation angles, implying the apparent signal may be produced by systematic effects.</p>
</abstract>
<kwd-group>
<kwd>galaxies: general</kwd>
<kwd>galaxies: photometry</kwd>
<kwd>galaxies: spiral</kwd>
<kwd>cosmic microwave background</kwd>
<kwd>large-scale structure of Universe</kwd>
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<body>
<sec id="ss1">
<title>1 INTRODUCTION</title>
<p>Imaging surveys are currently in the process of mapping out a vast region of the Universe over a large range of the electromagnetic spectrum. The pacesetter in recent years is the Sloan Digital Sky Survey (SDSS;
<xref ref-type="bibr" rid="b59">York et al. 2000</xref>
), which now provides [as of data release 6 (DR6);
<xref ref-type="bibr" rid="b1">Adelman-McCarthy et al. 2008</xref>
] photometric data for approximately 230 million distinct sources over an area of 8240 deg
<sup>2</sup>
. Current and future wide- and deep-field surveys such as SWIRE (
<xref ref-type="bibr" rid="b27">Irwin & Lewis 2001</xref>
;
<xref ref-type="bibr" rid="b36">McMahon et al. 2001</xref>
;
<xref ref-type="bibr" rid="b45">Rowan-Robinson et al. 2008</xref>
), UKIDSS (
<xref ref-type="bibr" rid="b33">Lawrence et al. 2007</xref>
), CFHTLS (
<xref ref-type="bibr" rid="b6">Cabanac et al. 2007</xref>
;
<xref ref-type="bibr" rid="b35">McCracken et al. 2008</xref>
), Pan-STARRS (
<xref ref-type="bibr" rid="b30">Kaiser et al. 2005</xref>
), LSST (
<xref ref-type="bibr" rid="b55">Sweeney et al. 2009</xref>
), VST ATLAS, the VISTA Hemisphere Survey and the SDSS itself will continue to add to the mapping of the Universe around us presenting increasing amounts of data at a variety of wavelengths. Given this enormous effort in the collection of photometric data, and the expense of subsequent spectroscopic surveys, the filtering of galaxies by type and redshift via their photometric properties is a vital and powerful tool for the effective use of the large quantities of photometric data available to us. Selecting distinct galaxy populations in this way offers a relatively cheap route to large galaxy and quasi-stellar object (QSO) surveys, either through using photometric redshifts or by using broader photometric constraints to select specific galaxy populations for subsequent spectroscopic surveys.</p>
<p>A key example of the success of this process over recent years has been the photometric selection of luminous red Galaxies (LRGs) at redshifts up to
<italic>z</italic>
≈ 0.8 (
<xref ref-type="bibr" rid="b16">Eisenstein et al. 2001</xref>
;
<xref ref-type="bibr" rid="b38">Padmanabhan et al. 2005a</xref>
;
<xref ref-type="bibr" rid="b60">Blake et al. 2009</xref>
;
<xref ref-type="bibr" rid="b11">Collister et al. 2007</xref>
). LRGs offer a simple route to photometric selection of different redshift samples due to the 4000 Å break feature, which passes through the optical wavelength bands from redshifts of
<italic>z</italic>
= 0 out to
<italic>z</italic>
= 1. Such selections have been used in a range of key cosmological applications, and perhaps most significant amongst these is the detection of the baryon acoustic oscillation (BAO) signature in analyses of large-scale structure. This was measured by
<xref ref-type="bibr" rid="b17">Eisenstein et al. (2005)</xref>
using spectroscopic redshifts of >40 000 LRGs selected from the SDSS using photometric constraints based on the progression of the 4000-Å break. The measurement of the BAO signal should also be possible using suitably accurate photometric redshifts as the BAO galaxy clustering features are on scales of the order of 100
<italic>h</italic>
<sup>−1</sup>
Mpc (
<xref ref-type="bibr" rid="b16">Eisenstein et al. 2001</xref>
;
<xref ref-type="bibr" rid="b9">Cole et al. 2005</xref>
;
<xref ref-type="bibr" rid="b17">Eisenstein et al. 2005</xref>
).</p>
<p>One significant use of photometrically selected galaxies is the study of the integrated Sachs–Wolfe (ISW) effect, in which cosmic microwave background (CMB) photons are subjected to shifts in energy as they pass through the gravitational potential wells of galaxies and clusters in an accelerating Universe (
<xref ref-type="bibr" rid="b46">Sachs & Wolfe 1967</xref>
). This has been studied by a number of authors using the
<italic>WMAP</italic>
public DRs in combination with photometrically selected galaxy populations. Aside from the use of simple magnitude-limited galaxy samples (e.g.
<xref ref-type="bibr" rid="b19">Fosalba, Gaztañaga & Castander 2003</xref>
;
<xref ref-type="bibr" rid="b18">Fosalba & Gaztañaga 2004</xref>
;
<xref ref-type="bibr" rid="b42">Rassat et al. 2007</xref>
), this work is again dominated by the use of LRGs. For example,
<xref ref-type="bibr" rid="b39">Padmanabhan et al. (2005b)</xref>
use photometrically selected LRGs from the SDSS (covering a redshift range of 0.2 <
<italic>z</italic>
< 0.6) to make a 2.5σ detection of the ISW effect in
<italic>WMAP</italic>
first-year data, whilst
<xref ref-type="bibr" rid="b7">Cabré et al. (2006)</xref>
combine a
<italic>z</italic>
≈ 0.5 SDSS LRG sample with the
<italic>WMAP</italic>
third-year data to claim a detected ISW signal of 3σ. More recently
<xref ref-type="bibr" rid="b22">Giannantonio et al. (2008)</xref>
performed a combined analysis using a number of galaxy and QSO catalogues, incorporating Two Micron All Sky Survey data (
<xref ref-type="bibr" rid="b28">Jarrett et al. 2000</xref>
), SDSS DR6 galaxies, SDSS MegaZ LRGs (
<xref ref-type="bibr" rid="b11">Collister et al. 2007</xref>
), NRAO VLA Sky Survey radio data (
<xref ref-type="bibr" rid="b12">Condon et al. 1998</xref>
),
<italic>HEAO</italic>
X-ray data (
<xref ref-type="bibr" rid="b4">Boldt 1987</xref>
) and the SDSS DR6 QSO catalogue (
<xref ref-type="bibr" rid="b43">Richards et al. 2009</xref>
). By combining the results from these data sets,
<xref ref-type="bibr" rid="b22">Giannantonio et al. (2008)</xref>
report a 4.5σ detection of the ISW effect and go on to use this to test a number of cosmological models. In particular, their ISW result places constraints on the mass density of Ω
<sub>m</sub>
= 0.26
<sup>+0.09</sup>
<sub>−0.07</sub>
, assuming a flat Λ cold dark matter (ΛCDM) cosmology.</p>
<p>As an alternative to the recent dominance of LRGs for large redshift surveys, we now look at the photometric selection and clustering of emission-line galaxies (ELGs). The key advantage of using ELGs in this application is the ability to identify galaxies through spectroscopic observations with relatively short exposure times, due to the emission lines with which they are most easily identified.
<xref ref-type="bibr" rid="b60">Blake et al. (2009)</xref>
have successfully used this to their advantage to undertake the WiggleZ spectroscopic survey of ELGs with the aim of measuring the BAO signal at
<italic>z</italic>
≈ 0.7. They select ELGs in the redshift range 0.5 <
<italic>z</italic>
< 1 using a combination of GALEX far- and near-ultraviolet imaging with
<italic>g, r</italic>
and
<italic>i</italic>
-band optical imaging from SDSS and the second Red Cluster Sequence project (
<xref ref-type="bibr" rid="b58">Yee et al. 2007</xref>
). In this case, the GALEX data allow them to select
<italic>z</italic>
> 0.5 galaxies using the Lyman-break technique, whilst the SDSS optical data allows them to limit their sample to just blue emission-line objects. They then perform spectroscopic observations using the AAOmega instrument at the 4-m Anglo-Australian Telescope (AAT), with exposure times of <1 h required for successful identification.</p>
<p>In this paper, we attempt to refine a number of photometric selections of ELGs in different redshift ranges, using optical data from the SDSS. In making greater use of the ELG population in studies of large-scale structure, we may maximize the use of the available data from such large-scale surveys as the SDSS and the upcoming VST ATLAS and Pan-STARRS surveys. We use COMBO-17 photometric redshift data in combination with SDSS data to perform a calibration of our photometric selections (
<xref ref-type="sec" rid="ss2">Section 2</xref>
). We go on to outline and review our observation programme at the AAT, which was aimed at providing a spectroscopic catalogue with which to further calibrate the photometric selections. In
<xref ref-type="sec" rid="ss3">Section 3</xref>
, we then evaluate the clustering properties of the galaxy populations contained in our photometric selections using SDSS data. We then use the full samples of >600 000 galaxies selected from the SDSS to perform a search for the ISW effect in
<italic>WMAP</italic>
5-yr data (
<xref ref-type="sec" rid="ss4">Section 4</xref>
). We present our summary and conclusions in
<xref ref-type="sec" rid="ss5">Section 5</xref>
. Throughout this paper, we assume a λCDM cosmology with Ω
<sub>M</sub>
= 0.3, Ω
<sub>Λ</sub>
= 0.7 and
<italic>H</italic>
<sub>0</sub>
= 100
<italic>h</italic>
km s
<sup>−1</sup>
Mpc.</p>
</sec>
<sec id="ss2">
<title>2 PHOTOMETRIC SELECTION</title>
<sec id="ss2-1">
<title>2.1 Data and selection</title>
<p>Using SDSS imaging data, our aim is to develop a set of photometric selection criteria using the SDSS filter bands (
<xref ref-type="bibr" rid="b21">Fukugita et al. 1996</xref>
) alone to isolate ELGs in three separate redshift ranges of approximately
<italic>z</italic>
< 0.4, 0.4 <
<italic>z</italic>
< 0.6 and
<italic>z</italic>
> 0.6. At these redshifts, the 4000 Å break is a key feature in the observed optical spectra of both red and blue galaxies as it moves through the
<italic>g</italic>
and
<italic>r</italic>
SDSS filters with increasing redshift. In ELGs however, the break is somewhat weaker than in the spectra of LRGs, whilst the continuum at wavelengths greater than 4000 Å remains lower compared with the LRG spectrum due to the dominance of young blue stars in the ELGs. These contrasts in the spectra of LRGs and ELGs inherently allow us to separate the two in colour space, whilst simultaneously facilitating photometric selections of galaxies at different redshifts.</p>
<p>With this in mind, we have used the Bruzual & Charlot stellar population synthesis code (
<xref ref-type="bibr" rid="b5">Bruzual & Charlot 2003</xref>
) to model the evolution of a typical ELG in the
<italic>gri</italic>
(AB) colour plane. We used a Salpeter IMF with a galaxy formed at
<italic>z
<sub>f</sub>
</italic>
= 7.9 (i.e. with an age of 12.82Gyr at
<italic>z</italic>
= 0) and a τ= 9 Gyr exponential star formation rate (SFR). The resultant
<italic>gri</italic>
colour evolution track from
<italic>z</italic>
= 1.0 to
<italic>z</italic>
= 0 is shown in
<xref ref-type="fig" rid="f1">Fig. 1</xref>
(dashed black line). Here, we see a clear evolution in the
<italic>gri</italic>
colour space around which we may build a selection regime for identifying candidates in our desired redshift ranges. We also plot a track (dot–dashed line) for an elliptical galaxy using a τ= 1 Gyr exponential SFR and a redshift of formation of
<italic>z
<sub>f</sub>
</italic>
= 7.9 (with solar metallicity and Salpeter IMF).</p>
<fig position="float" id="f1">
<label>Figure 1</label>
<caption>
<p>Galaxies in the COMBO-17 S11 field plotted in the
<italic>gri</italic>
colour plane using SDSS magnitudes. The cyan diamonds, green triangles and red squares show galaxies with photometric redshifts in the ranges 0.2 <
<italic>z</italic>
< 0.4, 0.4 <
<italic>z</italic>
< 0.6 and
<italic>z</italic>
> 0.6, respectively. The labelled black tracks show the evolution of an ELG, from
<italic>z</italic>
= 1.2 to 0, and an elliptical galaxy, from
<italic>z</italic>
= 0.6 to 0. Our photometric selections are marked by the solid blue, green and red boxes for our low-, mid- and high-redshift bins.</p>
</caption>
<graphic xlink:href="mnras0403-1261-f1.gif"></graphic>
</fig>
<p>We calibrate our selections using the photometric redshift data published by the COMBO-17 team (
<xref ref-type="bibr" rid="b57">Wolf et al. 2003</xref>
;
<xref ref-type="bibr" rid="b53">Simon et al. 2009</xref>
). The data we use are from the COMBO-17 S11 field, which covers an area of
<inline-formula>
<inline-graphic xlink:href="mnras0403-1261-mu3.gif"></inline-graphic>
</inline-formula>
centred at
<inline-formula>
<inline-graphic xlink:href="mnras0403-1261-mu4.gif"></inline-graphic>
</inline-formula>
(J2000) and the entirety of which is covered by SDSS imaging. These data provide accurate [d
<italic>z</italic>
/(1 +
<italic>z</italic>
) = 0.02] photometric redshifts for a total of 7248 galaxies based on broad- and narrow-band imaging using 17 different optical and near-infrared filters. We match the positions of COMBO-17 galaxies to the equivalent objects in the SDSS data, thus combining the SDSS
<italic>ugriz</italic>
magnitudes with the COMBO-17 photometric redshifts. The S11 objects are shown in the (SDSS)
<italic>g</italic>
<italic>r</italic>
,
<italic>r</italic>
<italic>i</italic>
colour plane in
<xref ref-type="fig" rid="f1">Fig. 1</xref>
. For the purposes of clarity, we only plot those galaxies classified as blue spirals by the COMBO-17 team in this figure; however, the location of red-sequence galaxies is indicated by the LRG evolution track (dot–dashed line). The COMBO-17 galaxies have been split into three populations for the purposes of this plot based on their assigned photometric redshift from COMBO-17: 0.2 <
<italic>z</italic>
< 0.4 (blue diamonds), 0.4 <
<italic>z</italic>
< 0.6 (green triangles) and 0.6 <
<italic>z</italic>
< 1.0 (red squares).</p>
<p>Based on the distribution of the photometric redshifts and the ELG evolution track presented in the above plot, there is a clear progression in the
<italic>gri</italic>
colour plane based on ELG redshift. Further to this, areas of the plot can be isolated that should minimize the number of red-sequence galaxies, whilst maximizing the numbers of either
<italic>z</italic>
< 0.4 or
<italic>z</italic>
> 0.6 ELGs. The medium redshift range does however present significant problems. The ELG evolution track appears to pass through a region populated by both lower and higher redshift ELGs as well as low-redshift red-sequence galaxies in the 0.4 <
<italic>z</italic>
< 0.6 range.</p>
<p>From the above observations we construct three sets of colour cuts to preferentially select three redshift ranges. These are shown in
<xref ref-type="fig" rid="f1">Fig. 1</xref>
by the dotted blue box (low-redshift cut), solid green box (medium redshift cut) and dash–double-dotted red box (high-redshift cut). As discussed above, the mid-redshift range is significantly exposed to contamination from both ELGs at unwanted redshifts and red-sequence galaxies. To minimize the numbers of these, we have therefore added colour cuts to this sample based on the
<italic>r</italic>
<italic>i</italic>
,
<italic>i</italic>
<italic>z</italic>
and
<italic>u</italic>
<italic>g</italic>
colours of the selected galaxies. These additional cuts have also been calibrated using the COMBO-17 photometric redshifts. The details of our three selections, including the additional mid-redshift colour cuts, are given explicitly in
<xref ref-type="table" rid="t1">Table 1</xref>
. These cuts have been tailored to produce sky densities of candidates of ≈100 deg
<sup>−2</sup>
for each of the three redshift ranges in order to provide candidate numbers suitable for wide-field spectroscopic surveys performed with instruments such as the 2dF/AAOmega spectrograph.</p>
<table-wrap id="t1">
<label>Table 1</label>
<caption>
<p>Selection criteria chosen to identify galaxies in our three redshift ranges: 0.2 <
<italic>z</italic>
< 0.4, 0.4 <
<italic>z</italic>
< 0.6 and 0.6 <
<italic>z</italic>
< 1.0 using SDSS
<italic>ugriz</italic>
AB magnitudes.</p>
</caption>
<table frame="hsides" rules="groups">
<thead>
<tr>
<th align="left">Low redshift</th>
<th align="left">Mid-redshift</th>
<th align="left">High redshift</th>
</tr>
</thead>
<tbody>
<tr>
<td align="left">19.0 <
<italic>i</italic>
< 20.0</td>
<td align="left">19.0 <
<italic>i</italic>
< 20.2</td>
<td align="left">19.5 <
<italic>i</italic>
< 20.5</td>
</tr>
<tr>
<td align="left">
<italic>r</italic>
<italic>i</italic>
< 0.3</td>
<td align="left">
<italic>g</italic>
<italic>r</italic>
> 1.2(
<italic>r</italic>
<italic>i</italic>
) + 0.1</td>
<td align="left">
<italic>r</italic>
<italic>i</italic>
> 0.5</td>
</tr>
<tr>
<td align="left">
<italic>g</italic>
<italic>r</italic>
< 1.2(
<italic>r</italic>
<italic>i</italic>
) + 0.9</td>
<td align="left">
<italic>g</italic>
<italic>r</italic>
< 1.2(
<italic>r</italic>
<italic>i</italic>
) + 0.9</td>
<td align="left">
<italic>g</italic>
<italic>r</italic>
< 1.2(
<italic>r</italic>
<italic>i</italic>
) + 0.06</td>
</tr>
<tr>
<td align="left">
<italic>g</italic>
<italic>r</italic>
> −1.2(
<italic>r</italic>
<italic>i</italic>
) + 0.75</td>
<td align="left">
<italic>g</italic>
<italic>r</italic>
> −1.2(
<italic>r</italic>
<italic>i</italic>
) + 1.65</td>
<td align="left">
<italic>g</italic>
<italic>r</italic>
> 1.2(
<italic>r</italic>
<italic>i</italic>
) − 0.6</td>
</tr>
<tr>
<td rowspan="4" valign="top">
<italic>g</italic>
<italic>r</italic>
< −1.2(
<italic>r</italic>
<italic>i</italic>
) + 1.3</td>
<td align="left">
<italic>g</italic>
<italic>r</italic>
< −1.2(
<italic>r</italic>
<italic>i</italic>
) + 1.95</td>
<td align="left">
<italic>g</italic>
<italic>r</italic>
< −1.2(
<italic>r</italic>
<italic>i</italic>
) + 2.2</td>
</tr>
<tr>
<td>
<italic>r</italic>
<italic>i</italic>
> −(
<italic>i</italic>
<italic>z</italic>
) + 0.5</td>
<td></td>
</tr>
<tr>
<td>−2.0 <
<italic>u</italic>
<italic>g</italic>
< 1.0</td>
<td></td>
</tr>
<tr>
<td>
<italic>i</italic>
<italic>z</italic>
> 0.55</td>
<td></td>
</tr>
</tbody>
</table>
<table-wrap-foot>
<fn id="t1_note24">
<p>
<italic>Note</italic>
. These are illustrated in the
<italic>ugr</italic>
colour plane in
<xref ref-type="fig" rid="f1">Fig. 1</xref>
.</p>
</fn>
</table-wrap-foot>
</table-wrap>
<p>The photometric redshift distribution for our three samples is shown in
<xref ref-type="fig" rid="f2">Fig. 2</xref>
. This plot includes all the selected galaxies from the S11 field, including those identified as being part of the red sequence (these making up ≈4 per cent of the total selected across all three selections). The three selections are characterized by mean redshifts of
<inline-formula>
<inline-graphic xlink:href="mnras0403-1261-mu5.gif"></inline-graphic>
</inline-formula>
and
<inline-formula>
<inline-graphic xlink:href="mnras0403-1261-mu6.gif"></inline-graphic>
</inline-formula>
, with standard deviations of σ
<sub>low</sub>
= 0.05, σ
<sub>low</sub>
= 0.08 and σ
<sub>hi</sub>
= 0.21.</p>
<fig position="float" id="f2">
<label>Figure 2</label>
<caption>
<p>Redshift distributions of our three photometric selections based on photometric redshifts from the COMBO-17 data in the S11 field. The three samples give mean redshifts of
<inline-formula>
<inline-graphic xlink:href="mnras0403-1261-mu23.gif"></inline-graphic>
</inline-formula>
and
<inline-formula>
<inline-graphic xlink:href="mnras0403-1261-mu24.gif"></inline-graphic>
</inline-formula>
.</p>
</caption>
<graphic xlink:href="mnras0403-1261-f2.gif"></graphic>
</fig>
<p>For the purposes of this paper, we now use our three selections to create three data sets from the SDSS galaxy catalogue. We apply the selections to the SDSS DR6 taking our data from the PhotObjAll table available on the SDSS Catalog Archive Server Jobs System (CASJOBS) at
<ext-link ext-link-type="uri" xlink:href="http://casjobs.sdss.org">http://casjobs.sdss.org</ext-link>
. Aside from the colour–magnitude criteria given in
<xref ref-type="table" rid="t1">Table 1</xref>
, we reject objects which do not meet the following criteria:</p>
<p>
<list id="l1" list-type="roman-lower">
<list-item>
<p>TYPE=3 (i.e. classified as a galaxy);</p>
</list-item>
<list-item>
<p>NCHILD=0;</p>
</list-item>
<list-item>
<p>Flagged as BINNED1, BINNED2 and BINNED3;</p>
</list-item>
<list-item>
<p>90° < RA < 270°.</p>
</list-item>
</list>
</p>
<p>We also limit our selection to the main SDSS region, rejecting stripes 40–43. Stripe 26 is also rejected as this appears to show some contamination and spurious density fluctuations. The photometric selections are performed using the SDSS model magnitudes with the appropriate extinction values subtracted. The total numbers of candidates given by each selection are 892 528, 620 020 and 734 566 for the low-, mid- and high-redshift selections, respectively. These numbers give sky densities of 103 deg
<sup>−2</sup>
, 71.9 deg
<sup>−2</sup>
and 85.1 deg
<sup>−2</sup>
.</p>
</sec>
<sec id="ss2-2">
<title>2.2 Observations</title>
<p>An important element of this work is the calibration of the photometric selection samples with spectroscopic observations to confirm the achievable redshift distribution of our selections. To this end, we have performed spectroscopic observations of our
<italic>z</italic>
≈ 0.7 sample using the AAOmega spectrograph at the AAT (
<xref ref-type="bibr" rid="b47">Saunders et al. 2004</xref>
;
<xref ref-type="bibr" rid="b51">Sharp et al. 2006</xref>
). AAOmega is a double beam spectrograph fed by 2.1 arcsec diameter fibres, which allows the simultaneous observations of up to ≈360 objects in a circular field of view of diameter 2°.</p>
<p>Observations were taken on the AAOmega instrument at the Anglo-Australian Observatory (AAO) on the nights of 2006 March 4 and 6. The spectrograph was configured using the 5700 Å dichroic, with the 580V grating mounted in the blue-arm and the 385R grating in the red arm. The 580V grating gives a wavelength coverage of 370 to 580 nm, with a pixel size of 0.1 nm pixel
<sup>−1</sup>
and the 385R a coverage of 560 to 880 nm, with a pixel size of 0.16 nm pixel
<sup>−1</sup>
. Both provide a resolution of 1300. In total, AAOmega offers 400 fibres per observation; however, a significant number of these were at times used for other projects (e.g.
<xref ref-type="bibr" rid="b44">Ross et al. 2008</xref>
) and were locked to guide stars, sky targets or simply malfunctioning, and so our target numbers range from ∼50 to 230 per observation. We targeted four 2dF with multiple exposures of 1200 s each. The observations are summarized in
<xref ref-type="table" rid="t2">Table 2</xref>
. The four observed fields are targeted towards the Cosmic Evolution Survey (COSMOS;
<xref ref-type="bibr" rid="b49">Scoville et al. 2007</xref>
) field, the d05 and e04 fields from the 2dF-SDSS LRG and QSO (
<xref ref-type="bibr" rid="b14">Croom et al. 2004</xref>
) survey and the S11 field from COMBO-17.</p>
<table-wrap id="t2">
<label>Table 2</label>
<caption>
<p>Coordinates of the four fields targeted with the number of
<italic>gri</italic>
selected ELG candidates in each 2dF.</p>
</caption>
<table frame="hsides" rules="groups">
<thead>
<tr>
<th align="left">Field</th>
<th align="left">COSMOS</th>
<th align="left">d05</th>
<th align="left">e04</th>
<th align="left">S11</th>
</tr>
</thead>
<tbody>
<tr>
<td align="left">Date</td>
<td align="left">06/03/06</td>
<td align="left">04/03/06</td>
<td align="left">04/03/06</td>
<td align="left">06/03/06</td>
</tr>
<tr>
<td align="left">RA</td>
<td align="left">
<inline-formula>
<inline-graphic xlink:href="mnras0403-1261-mu28.gif"></inline-graphic>
</inline-formula>
118</td>
<td align="left">
<inline-formula>
<inline-graphic xlink:href="mnras0403-1261-mu29.gif"></inline-graphic>
</inline-formula>
399</td>
<td align="left">
<inline-formula>
<inline-graphic xlink:href="mnras0403-1261-mu30.gif"></inline-graphic>
</inline-formula>
899</td>
<td align="left">
<inline-formula>
<inline-graphic xlink:href="mnras0403-1261-mu31.gif"></inline-graphic>
</inline-formula>
741</td>
</tr>
<tr>
<td align="left">Declination</td>
<td align="left">+
<inline-formula>
<inline-graphic xlink:href="mnras0403-1261-mu32.gif"></inline-graphic>
</inline-formula>
2052</td>
<td align="left">
<inline-formula>
<inline-graphic xlink:href="mnras0403-1261-mu33.gif"></inline-graphic>
</inline-formula>
2124</td>
<td align="left">
<inline-formula>
<inline-graphic xlink:href="mnras0403-1261-mu34.gif"></inline-graphic>
</inline-formula>
2141</td>
<td align="left">
<inline-formula>
<inline-graphic xlink:href="mnras0403-1261-mu35.gif"></inline-graphic>
</inline-formula>
7159</td>
</tr>
<tr>
<td align="left">Exposure time</td>
<td align="left">3 × 1200 s</td>
<td align="left">3 × 1200 s</td>
<td align="left">4 × 1200 s</td>
<td align="left">3 × 1200 s</td>
</tr>
<tr>
<td align="left">Seeing</td>
<td align="left">≈ 3.0 arcsec</td>
<td align="left">≈ 2.0 arcsec</td>
<td align="left">≈ 2.5 arcsec</td>
<td align="left">≈ 1.6 arcsec</td>
</tr>
<tr>
<td align="left">Candidates</td>
<td align="left">378</td>
<td align="left">329</td>
<td align="left">343</td>
<td align="left">391</td>
</tr>
<tr>
<td align="left">Targeted</td>
<td align="left">217</td>
<td align="left">45</td>
<td align="left">225</td>
<td align="left">219</td>
</tr>
<tr>
<td align="left">ELG redshifts</td>
<td align="left">44</td>
<td align="left">10</td>
<td align="left">84</td>
<td align="left">142</td>
</tr>
</tbody>
</table>
</table-wrap>
<p>Target objects were selected using our selection criteria applied to the SDSS data available for each of the fields. Over the course of five nights, seeing ranged from ∼1.5 to 3.0 arcsec, with a mean of ∼2.0 arcsec. All observations were flat fielded, arc calibrated and combined using the AAO's
<sc>2dfdr</sc>
tool. Approximately 20 per cent of fibres were affected by an early instrumentation problem known as fringing, which led to an almost sinusoidal signal in the output. In the S11 field, this affected 27 of the fibres targeted on ELG candidates. A further problem is encountered due to the strong sky emission lines above 8250 Å. These limit the identification of Hβ and [O
<sc>iii</sc>
] above
<italic>z</italic>
≈ 0.65– 0.7; however, they do not interrupt identification of [O
<sc>ii</sc>
] and so the impact of the sky lines is limited.</p>
</sec>
<sec id="ss2-3">
<title>2.3 Galaxy redshifts</title>
<p>We use the 2dF Galaxy Redshift Survey (2dFGRS) software
<sc>autoz</sc>
(
<xref ref-type="bibr" rid="b13">Croom et al. 2001</xref>
) and
<sc>runz</sc>
(
<xref ref-type="bibr" rid="b10">Colless et al. 2001</xref>
) to search for emission features with which to identify galaxies in our observed sample and determine redshifts.
<sc>autoz</sc>
performs an initial identification of each spectrum, fitting absorption and emission features. Each fibre spectrum was then evaluated by eye to assign a redshift and quality rating,
<italic>q
<sub>op</sub>
</italic>
(which ranges from 0 to 5 depending on the confidence of the identification). Only objects with
<italic>q
<sub>op</sub>
</italic>
≥ 3 were accepted as positive identifications.</p>
<p>Examples of the spectra obtained with the AAOmega instrument are provided in
<xref ref-type="fig" rid="f3">Fig. 3</xref>
. The spectra are all binned to a bin width of ≈10 Å, and key emission and absorption features are marked. We also show the unbinned data for the [O
<sc>ii</sc>
] feature (insets), where it is evident that the doublet nature of the feature is marginally detectable at the observed resolution. Although data were obtained on both the blue and red arms, only spectra from the red arm are plotted here as there are few features useful for identification in the blue wavelength range given the signal-to-noise ratio of our data. The key emission features that facilitate the identification of these galaxies with short exposure times, i.e. [O
<sc>ii</sc>
], Hβ and the [O
<sc>iii</sc>
] doublet, are all evident in these spectra.</p>
<fig position="float" id="f3">
<label>Figure 3</label>
<caption>
<p>Example spectra taken on the AAOmega spectrograph with the 385R grism, binned to 10 Å bins. Wavelengths of galaxy emission and absorption features are marked; however, the features of key use in identification were the [O
<sc>ii</sc>
], Hβ and [O
<sc>iii</sc>
] doublet emission lines. The insets each show the [O
<sc>ii</sc>
] feature in closeup and unbinned, showing the doublet nature of the [O
<sc>ii</sc>
] feature to be marginally discernible given the resolution of the spectrograph. The red dashed lines show the expected positions of the doublet peaks at rest wavelengths of 3726 and 3729 Å. Objects 1, 3, 5 and 6 are all marked in
<xref ref-type="fig" rid="f6">Fig. 6</xref>
as showing discrepancy between spectroscopic and photometric redshifts.</p>
</caption>
<graphic xlink:href="mnras0403-1261-f3.gif"></graphic>
</fig>
<p>There were no positive identifications of galaxies with just absorption-line features and no emission lines in the spectroscopic observations. It is likely however that any absorption-line galaxies targeted remained unidentified given the relatively short exposure times, which make it difficult to confidently identify absorption-line features in the spectra.</p>
<p>A summary of the numbers of ELGs identified in our four fields is provided in
<xref ref-type="table" rid="t2">Table 2</xref>
. Our most successful field was the COMBO-17 S11 field in which we were able to target 219 ELG candidates in seeing conditions of ≈1.6 arcsec. In this field we identified 121 of the 219 candidates as being ELGs from their emission lines with a confidence of
<italic>q
<sub>op</sub>
</italic>
≥ 3. In total, we were able to identify 311 ELGs over a combined area of 12.4 deg
<sup>2</sup>
, giving an average sky density of 25 deg
<sup>−2</sup>
. However, three of the observed fields suffered poor seeing conditions of ≥2.0 arcsec, limiting our ability to successfully identify objects in these fields. At worst, completeness was reduced to <25 per cent in the COSMOS field due to the seeing of ≈3.0 arcsec. However, in the more reasonable observing conditions encountered with the observations in the S11 field (where the seeing was 1.6 arcsec), we find that the identification rate is a more promising ∼65 per cent, with a sky density of ≈40 deg
<sup>−2</sup>
.</p>
<p>
<xref ref-type="fig" rid="f4">Fig. 4</xref>
gives the redshift distribution of the spectroscopically confirmed galaxies in the S11 field. The plot incorporates all galaxies identified in the S11 field and the original photometric redshift distribution from COMBO-17 data (black dashed line) also from the S11 field. Our spectroscopic sample follows the expected distribution closely, with
<inline-formula>
<inline-graphic xlink:href="mnras0403-1261-mu7.gif"></inline-graphic>
</inline-formula>
(compared to
<inline-formula>
<inline-graphic xlink:href="mnras0403-1261-mu8.gif"></inline-graphic>
</inline-formula>
). There is some contamination from lower redshift (i.e.
<italic>z</italic>
< 0.5) galaxies, and in the spectroscopic sample this is at a level of ≈18 per cent (compared to a level of ≈23 per cent obtained with the COMBO-17 photometric redshift sample).</p>
<fig position="float" id="f4">
<label>Figure 4</label>
<caption>
<p>The redshift distribution of all successfully identified ELGs from the four fields targeted using AAOmega is shown (red histogram). A total of 280 galaxies were successfully identified. The original photo-
<italic>z</italic>
redshift distribution incorporating all the galaxies selected using our
<italic>z</italic>
≈ 0.7 colour cuts in the COMBO-17 S11 field is also shown (black dashed line). Both distributions are normalized to give an area under the histogram equal to unity.</p>
</caption>
<graphic xlink:href="mnras0403-1261-f4.gif"></graphic>
</fig>
<p>
<xref ref-type="fig" rid="f5">Fig. 5</xref>
shows identifications as a function of source magnitude in the S11 field. The lower panel shows number counts of spectroscopically confirmed galaxies exhibiting emission lines (
<italic>N</italic>
<sub>em</sub>
, dark bars) and of all objects targeted with AAOmega fibres (
<italic>N</italic>
<sub>T</sub>
, pale bars), whilst the upper panel shows the fraction
<italic>N</italic>
<sub>em</sub>
/
<italic>N</italic>
<sub>T</sub>
. The consistency of the 65 per cent identification rate across our magnitude range is evident and we are clearly reaching the
<italic>i</italic>
= 20.5 mag limit successfully. A small falloff in the fraction of ELGs identified is observed in the fainter magnitude bins; however, numbers still remain high.</p>
<fig position="float" id="f5">
<label>Figure 5</label>
<caption>
<p>Number counts of objects observed as a function of SDSS
<italic>i</italic>
-band magnitude. The dark histogram shows counts of objects identified with emission lines (
<italic>N</italic>
<sub>em</sub>
), whilst the pale histogram shows the total number of objects (
<italic>N</italic>
<sub>T</sub>
) observed in each magnitude bin. The top panel shows the fraction
<italic>N</italic>
<sub>em</sub>
/
<italic>N</italic>
<sub>T</sub>
as a function of
<italic>i</italic>
-band magnitude. Data are only shown from the S11 field as all other fields were limited by adverse seeing.</p>
</caption>
<graphic xlink:href="mnras0403-1261-f5.gif"></graphic>
</fig>
<p>In
<xref ref-type="fig" rid="f6">Fig. 6</xref>
, we compare our spectroscopically determined redshifts against the COMBO-17 photometric redshifts for those galaxies lying in the central
<inline-formula>
<inline-graphic xlink:href="mnras0403-1261-mu9.gif"></inline-graphic>
</inline-formula>
region covered by the COMBO-17 data. The vertical error bars represent the σ
<sub>
<italic>z</italic>
</sub>
∼ 0.03 error quoted by the COMBO-17 team for the photometric redshifts. We find a total of 24 objects that have both COMBO-17 photometric redshifts and spectroscopic redshifts from this work. Overall there appears to be good agreement between the data with just four outliers (taken here as a difference between the photometric and spectroscopic results of 3σ
<sub>
<italic>z</italic>
</sub>
) having significantly different redshifts. The spectra for all four of these objects are given in
<xref ref-type="fig" rid="f3">Fig. 3</xref>
and each of the outliers are marked in
<xref ref-type="fig" rid="f6">Fig. 6</xref>
by the spectrum number (1, 3, 5 and 6) from
<xref ref-type="fig" rid="f3">Fig. 3</xref>
. We find a mean offset between the spectroscopic and photometric redshifts of Δ
<italic>z</italic>
= 0.01 ± 0.04 (after excluding points 1 and 5).</p>
<fig position="float" id="f6">
<label>Figure 6</label>
<caption>
<p>Comparison of the spectroscopic redshifts of 24 galaxies in the central
<inline-formula>
<inline-graphic xlink:href="mnras0403-1261-mu25.gif"></inline-graphic>
</inline-formula>
of the S11 field with photometric redshifts from the COMBO-17 survey. The error bars show the σ
<sub>
<italic>z</italic>
</sub>
∼ 0.03 error quoted by the COMBO-17 team for their photometric redshifts. The four numbered points (1, 3, 5 and 6) are objects in which the photometric and spectroscopic redshifts disagree by more than 3σ
<sub>
<italic>z</italic>
</sub>
(the numbers refer to the spectrum numbers from
<xref ref-type="fig" rid="f3">Fig. 3</xref>
).</p>
</caption>
<graphic xlink:href="mnras0403-1261-f6.gif"></graphic>
</fig>
<p>We show in
<xref ref-type="fig" rid="f7">Fig. 7</xref>
the distribution of spectroscopically confirmed
<italic>z</italic>
> 0.5 ELGs (filled blue circles),
<italic>z</italic>
< 0.5 ELGs (green triangles) and unidentified objects (red crosses) in the
<italic>g</italic>
<italic>r</italic>
versus
<italic>r</italic>
<italic>i</italic>
colour plane. It is evident that the
<italic>z</italic>
> 0.5 ELGs are reasonably evenly spread in the
<italic>g</italic>
<italic>r</italic>
versus
<italic>r</italic>
<italic>i</italic>
colour plane as are the objects without any discernible emission, although there is some bias in these to be towards the redder end of the selection in both
<italic>r</italic>
<italic>i</italic>
and
<italic>g</italic>
<italic>r</italic>
. The
<italic>z</italic>
< 0.5 ELGs appear to be biased towards the upper left limits of the selection region, towards the low-redshift main sequence. These may be further reduced by altering our constraints; however, this would also remove a significant number of
<italic>z</italic>
> 0.5 objects at the same time. The model evolution track from
<xref ref-type="fig" rid="f1">Fig. 1</xref>
is again plotted for reference.</p>
<fig position="float" id="f7">
<label>Figure 7</label>
<caption>
<p>Spectroscopic results from the S11 and e04 fields. We show objects identified as
<italic>z</italic>
≥ 0.5 ELGs (filled blue circles),
<italic>z</italic>
≤ 0.5 ELGs (green triangles) and objects with no identified redshift (red crosses). The same evolution track as plotted in
<xref ref-type="fig" rid="f1">Fig. 1</xref>
is also shown.</p>
</caption>
<graphic xlink:href="mnras0403-1261-f7.gif"></graphic>
</fig>
<p>Now looking at the properties of the galaxy spectra, we measure the equivalent widths of the nebular emission lines by fitting Gaussian curves to the [O
<sc>ii</sc>
] 3727 Å, Hβ and [O
<sc>iii</sc>
] 5007 Å lines. We were able to measure equivalent widths with confidence for [O
<sc>ii</sc>
] 3727 Å, Hβ and [O
<sc>iii</sc>
] 5007 Å in 109, 53 and 51 of the galaxies in our sample, respectively. From these, we determined mean equivalent widths of 23.0, 8.12 and 8.98 Å for [O
<sc>ii</sc>
] 3727 Å, Hβ and [O
<sc>iii</sc>
] 5007 Å, respectively. These mean equivalent widths are broadly consistent with other measurements of emission lines in late-type galaxies (e.g.
<xref ref-type="bibr" rid="b31">Kennicutt 1992</xref>
;
<xref ref-type="bibr" rid="b52">Shi, Gu & Peng 2006</xref>
). In 27 of these galaxies, we were able to measure all three of the above nebular emission lines with confidence and have attempted to evaluate the presence of active galactic nuclei (AGN) in our sample using the ‘blue diagnostic’ constraints of
<xref ref-type="bibr" rid="b32">Lamareille et al. (2004)</xref>
, which are based on the [O
<sc>ii</sc>
]λ3727/Hβ and [O
<sc>iii</sc>
]λ5007/Hβ line ratios. This is shown in
<xref ref-type="fig" rid="f8">Fig. 8</xref>
, where the solid line marks the estimated division between AGN (above) and star-forming galaxies (below). The dashed lines mark the region of uncertainty between the two populations. In all, 22 of this subsample fall within the star-forming galaxy region, whilst the remaining five (two of which have large uncertainties) fall within the uncertain region and none lie in the AGN region. Within the reliability of the blue diagnostic diagram, we can say that our sample is dominated by star-forming galaxies and this method shows no positive evidence for any AGN contamination of our sample although there are a small number of borderline cases.</p>
<fig position="float" id="f8">
<label>Figure 8</label>
<caption>
<p>‘Blue diagnostic’ diagram based on
<xref ref-type="bibr" rid="b32">Lamareille et al. (2004)</xref>
. Line ratios are plotted for the subsample of our spectroscopically observed sample for which we have equivalent widths for the [O
<sc>ii</sc>
]λ3727, Hβ and [O
<sc>iii</sc>
]λ5007 nebular emission lines. The solid line marks the limit estimated by
<xref ref-type="bibr" rid="b32">Lamareille et al. (2004)</xref>
between star-forming galaxies and AGN and the dashed lines show the region of uncertainty. In total, 22 objects lie within the star-forming region of the diagnostic plot and are marked by filled blue circles. A further five lie within the overlap region (cyan stars) and none of the objects lies within the AGN region.</p>
</caption>
<graphic xlink:href="mnras0403-1261-f8.gif"></graphic>
</fig>
<p>
<xref ref-type="fig" rid="f9">Fig. 9</xref>
shows a composite spectrum of all of the confirmed ELGs over all redshifts, with significant emission and absorption features labelled. The key emission lines used in our spectral identification (i.e. [O
<sc>ii</sc>
], Hβ and [O
<sc>iii</sc>
]) are clearly evident. We also see the Balmer absorption features redwards of the [O
<sc>ii</sc>
] emission, whilst the weak ELG 4000-Å break is also apparent in this composite.</p>
<fig position="float" id="f9">
<label>Figure 9</label>
<caption>
<p>Composite spectrum of the 280 successfully identified ELGs. The key emission-line features used for identification are clearly visible: [O
<sc>ii</sc>
], Hβ and [O
<sc>iii</sc>
], whilst absorption features which are difficult to observe in individual spectra are now evident.</p>
</caption>
<graphic xlink:href="mnras0403-1261-f9.gif"></graphic>
</fig>
</sec>
</sec>
<sec id="ss3">
<title>3 CLUSTERING</title>
<sec id="ss3-1">
<title>3.1 Angular correlation function</title>
<p>We now evaluate the angular correlation function for a sample of galaxies selected based on our three photometric selections. The data sets taken from SDSS DR6, as described in the previous section, are used for this purpose. We calculate the angular correlation function of the samples using the Landy–Szalay estimator:
<disp-formula id="m1">
<label>1</label>
<graphic xlink:href="mnras0403-1261-m1.gif"></graphic>
</disp-formula>
where
<italic>DD</italic>
and
<italic>n
<sub>D</sub>
</italic>
are the numbers of galaxy–galaxy pairs and the total number of galaxies, respectively. For these calculations, we use a random catalogue which exactly matches the sky coverage of our SDSS galaxy samples and with a factor of 20 more random points than galaxies in each of our galaxy samples. The total number of random points is given by
<italic>n
<sub>R</sub>
</italic>
and
<italic>DR</italic>
is simply the number of galaxy random pairs. Statistical errors are estimated using field-to-field errors, using 16 separate fields within our complete field. Our results for the three photometric samples are shown in
<xref ref-type="fig" rid="f10">Fig. 10</xref>
where the blue triangles, green squares and red crosses show the low-, mid- and high-redshift samples, respectively.</p>
<fig position="float" id="f10">
<label>Figure 10</label>
<caption>
<p>The angular correlation functions,
<italic>w</italic>
(θ), for our three photometric redshift selections. Blue crosses, green diamonds and red squares represent the low- (
<italic>z</italic>
< 0.4), mid- (0.4 <
<italic>z</italic>
< 0.6) and high-redshift (
<italic>z</italic>
> 0.6) samples, respectively. The best-fitting power-law models are plotted through each set of data.</p>
</caption>
<graphic xlink:href="mnras0403-1261-f10.gif"></graphic>
</fig>
<p>From these measurements of the angular correlation function, we now estimate the two-point correlation function [2PCF, ξ(
<italic>r</italic>
)] using Limber's formula. We make an estimate of ξ(
<italic>r</italic>
) for each of the samples using a double power law with a central break, i.e.
<inline-formula>
<inline-graphic xlink:href="mnras0403-1261-mu10.gif"></inline-graphic>
</inline-formula>
and
<inline-formula>
<inline-graphic xlink:href="mnras0403-1261-mu11.gif"></inline-graphic>
</inline-formula>
. This is then combined with our best estimate of the redshift distribution (based on the COMBO-17 photometric redshift data for the low- and mid-redshift samples and the spectroscopic redshift data for the high-redshift sample) to calculate the resultant
<italic>w</italic>
(θ) with Limber's formula. A full treatment of this calculation is given by
<xref ref-type="bibr" rid="b41">Phillipps et al. (1978)</xref>
. We then perform a χ
<sup>2</sup>
fitting, in the range 2 arcmin < θ < 20 arcmin to our data. The best-fitting models are plotted with the data in
<xref ref-type="fig" rid="f10">Fig. 10</xref>
, whilst the associated parameters are listed in
<xref ref-type="table" rid="t3">Table 3</xref>
. We find reasonable fits to both the low- and mid-redshift samples, the low-redshift sample being well fitted by a double power law with a break at 0.5
<italic>h</italic>
<sup>−1</sup>
Mpc and the mid-redshift sample by just a single power law. We note, however, that we struggle to fit to the high-redshift sample with either a double or single power law. This is largely due to strong deviations from a simple power law trend at separations of <2 arcmin. This results in large χ
<sup>2</sup>
values for our attempts to fit the correlation function in this range. The angular correlation function does however return to a simple power law at separations of 2 arcmin < θ < 20 arcmin where we are able to provide a reasonable power-law fit using the Limber method.</p>
<table-wrap id="t3">
<label>Table 3</label>
<caption>
<p>Comoving correlation lengths,
<italic>r</italic>
<sub>0</sub>
and power-law slopes, γ, for the double power-law model used to provide fits to the angular correlation functions for each redshift selection.</p>
</caption>
<table frame="hsides" rules="groups">
<thead>
<tr>
<th align="left">
<italic>z</italic>
</th>
<th align="left">
<italic>r
<sub>b</sub>
</italic>
(
<italic>h</italic>
<sup>−1</sup>
Mpc)</th>
<th align="left">
<italic>r</italic>
<sub>0</sub>
(<
<italic>r
<sub>b</sub>
</italic>
) (
<italic>h</italic>
<sup>−1</sup>
Mpc)</th>
<th align="left">γ(<
<italic>r
<sub>b</sub>
</italic>
)</th>
<th align="left">
<italic>r</italic>
<sub>0</sub>
(>
<italic>r
<sub>b</sub>
</italic>
) (
<italic>h</italic>
<sup>−1</sup>
Mpc)</th>
<th align="left">γ(>
<italic>r
<sub>b</sub>
</italic>
)</th>
<th align="left">
<italic>b</italic>
</th>
</tr>
</thead>
<tbody>
<tr>
<td align="left">0.29 ± 0.05</td>
<td align="left">0.5</td>
<td align="left">1.30 ± 0.03</td>
<td align="left">2.21 ± 0.03</td>
<td align="left">2.78 ± 0.08</td>
<td align="left">1.55 ± 0.03</td>
<td align="left">0.72 ± 0.02</td>
</tr>
<tr>
<td align="left">0.44 ± 0.08</td>
<td align="left">n/a</td>
<td align="left">n/a</td>
<td align="left">n/a</td>
<td align="left">3.71 ± 0.11</td>
<td align="left">1.65 ± 0.03</td>
<td align="left">0.92 ± 0.03</td>
</tr>
<tr>
<td align="left">0.65 ± 0.21</td>
<td align="left">0.5</td>
<td align="left">3.40 ± 0.3</td>
<td align="left">2.30 ± 0.05</td>
<td align="left">5.50 ± 0.13</td>
<td align="left">1.67 ± 0.03</td>
<td align="left">1.43 ± 0.03</td>
</tr>
</tbody>
</table>
</table-wrap>
<p>From our estimates of ξ(
<italic>r</italic>
), we now go on to estimate the bias of each sample. The biasing parameter,
<italic>b</italic>
, quantifies the relative clustering of a given galaxy population compared to the underlying dark matter (DM) distribution (
<xref ref-type="bibr" rid="b56">Tegmark & Peebles 1998</xref>
). This can be expressed as the following:
<disp-formula id="m2">
<label>2</label>
<graphic xlink:href="mnras0403-1261-m2.gif"></graphic>
</disp-formula>
</p>
<p>Here, ξ
<sub>gal</sub>
(
<italic>r</italic>
) is the 2PCF of the galaxy sample and ξ
<sub>DM</sub>
(
<italic>r</italic>
) is the 2PCF of DM at the same epoch. We determine the DM correlation function by first using the Code for Anisotropies in the Microwave Background (
<sc>camb</sc>
;
<xref ref-type="bibr" rid="b34">Lewis, Challinor & Lasenby 2000</xref>
) software to estimate the DM power spectrum at the mean redshifts of each of our galaxy samples. The power spectrum is calculated using the
<sc>halofit</sc>
model (
<xref ref-type="bibr" rid="b54">Smith et al. 2003</xref>
) to fit non-linear features, at each of the mean redshifts of our samples. With the DM power spectra calculated at each redshift, we then simply calculate the corresponding 2PCFs via the Fourier transform:
<disp-formula id="m3">
<label>3</label>
<graphic xlink:href="mnras0403-1261-m3.gif"></graphic>
</disp-formula>
</p>
<p>We now estimate the bias by evaluating the DM and the galaxy 2PCFs to a maximum separation of 20 Mpc (
<xref ref-type="bibr" rid="b15">Croom et al. 2005</xref>
). This limit restricts the calculations to the linear regime at which our fits to the correlation function are still valid. Thus, the biasing parameter can be estimated using
<disp-formula id="m4">
<label>4</label>
<graphic xlink:href="mnras0403-1261-m4.gif"></graphic>
</disp-formula>
where
<inline-formula>
<inline-graphic xlink:href="mnras0403-1261-mu12.gif"></inline-graphic>
</inline-formula>
is given by
<disp-formula id="m5">
<label>5</label>
<graphic xlink:href="mnras0403-1261-m5.gif"></graphic>
</disp-formula>
</p>
<p>We show
<inline-formula>
<inline-graphic xlink:href="mnras0403-1261-mu13.gif"></inline-graphic>
</inline-formula>
for each of our three redshift samples in
<xref ref-type="fig" rid="f11">Fig. 11</xref>
(denoted by the stars). For comparison, we also plot
<inline-formula>
<inline-graphic xlink:href="mnras0403-1261-mu14.gif"></inline-graphic>
</inline-formula>
for the 2dFGRS late-type galaxy samples of
<xref ref-type="bibr" rid="b37">Norberg et al. (2002)</xref>
. These are split into absolute magnitude bins of −18 <
<italic>M
<sub>bj</sub>
</italic>
− 5 log
<sub>10</sub>
(
<italic>h</italic>
) < −19, −19 <
<italic>M
<sub>bj</sub>
</italic>
− 5 log
<sub>10</sub>
(
<italic>h</italic>
) < −20, −20 <
<italic>M
<sub>bj</sub>
</italic>
− 5 log
<sub>10</sub>
(
<italic>h</italic>
) < −21 and −20.5 <
<italic>M
<sub>bj</sub>
</italic>
− 5 log
<sub>10</sub>
(
<italic>h</italic>
) < −21.5 and are calculated based on the correlation parameters given in their
<xref ref-type="table" rid="t3">Table 3</xref>
. Based on the redshift and apparent magnitude distributions of our three samples, we estimate absolute magnitude ranges of
<inline-formula>
<inline-graphic xlink:href="mnras0403-1261-mu15.gif"></inline-graphic>
</inline-formula>
and −20.9 ± 0.4 for the low-, mid- and high-redshift samples, respectively. These estimates include
<italic>K</italic>
+
<italic>e</italic>
corrections based on the τ= 9Gyr SFR model given in
<xref ref-type="sec" rid="ss2">Section 2</xref>
.</p>
<fig position="float" id="f11">
<label>Figure 11</label>
<caption>
<p>Estimated
<inline-formula>
<inline-graphic xlink:href="mnras0403-1261-mu26.gif"></inline-graphic>
</inline-formula>
plotted versus redshift for each of our three photometric samples (stars). Also plotted is the
<inline-formula>
<inline-graphic xlink:href="mnras0403-1261-mu27.gif"></inline-graphic>
</inline-formula>
for late-type galaxies from the 2dFGRS from
<xref ref-type="bibr" rid="b37">Norberg et al. (2002)</xref>
, split by absolute magnitude (triangles). The dashed lines show the long-lived model normalized to the ELG data points, whilst the dash–dotted lines show the stable clustering model also normalized to the ELG data. The dotted lines project the clustering of each population with no evolution in comoving coordinates.</p>
</caption>
<graphic xlink:href="mnras0403-1261-f11.gif"></graphic>
</fig>
<p>Also plotted in
<xref ref-type="fig" rid="f11">Fig. 11</xref>
are three simple clustering evolution models: the long-lived model (dashed lines), stable clustering (dot–dashed lines) and no evolution of the comoving space clustering (solid lines). All three models have been normalized to each of the ELG clustering amplitudes.</p>
<p>The long-lived model is equivalent to assuming that the galaxies have ages of the order of the Hubble time. The clustering evolution is then governed by their motion within the gravitational potential (
<xref ref-type="bibr" rid="b20">Fry 1996</xref>
;
<xref ref-type="bibr" rid="b15">Croom et al. 2005</xref>
). The bias evolution is thus governed by
<disp-formula id="m6">
<label>6</label>
<graphic xlink:href="mnras0403-1261-m6.gif"></graphic>
</disp-formula>
where
<italic>D</italic>
(
<italic>z</italic>
) is the linear growth rate and is determined using the fitting formulae of
<xref ref-type="bibr" rid="b8">Carroll, Press & Turner (1992)</xref>
. For the bias,
<italic>b</italic>
, we use the values given in
<xref ref-type="table" rid="t3">Table 3</xref>
: 0.72, 0.92 and 1.43 for the low-, mid- and high-redshift samples, respectively. The stable clustering model represents the evolution of virialized structures and is characterized by (
<xref ref-type="bibr" rid="b40">Peacock 1999</xref>
):
<disp-formula id="m7">
<label>7</label>
<graphic xlink:href="mnras0403-1261-m7.gif"></graphic>
</disp-formula>
where
<italic>r</italic>
is the comoving distance and γ is the slope of the clustering correlation function. Finally, the no-evolution model simply assumes that there is no-evolution of the clustering in comoving coordinates.</p>
<p>It is important to note that the various samples have not been refined to be precisely equivalent in that neither the number densities nor absolute magnitudes have been ideally matched between any of the samples. Further to this, the clustering strengths of the
<italic>z</italic>
≈ 0.3 and 0.45 are based on the photometric redshift distributions from the COMBO-17 S11 field, which as yet have not been fully calibrated. We note that the low-redshift sample shows a relatively low clustering strength in
<xref ref-type="fig" rid="f11">Fig. 11</xref>
and a low bias compared with the mid-redshift sample, which we predict to have a relatively similar absolute luminosity range. This may be the result of an underestimate of the mean redshift of the low-
<italic>z</italic>
sample from the number of photometric redshifts available.</p>
<p>Looking at the low- and mid-redshift ranges we find that the clustering measurements suggest an increase in the clustering amplitudes of the ELGs from redshifts of
<italic>z</italic>
= 0.3–0.5 to more recent epochs if they are to evolve to have equivalent clustering properties to star-forming populations of comparable absolute magnitude ranges (i.e. the −19.5 >
<italic>M
<sub>b</sub>
</italic>
> −20.5 2dF sample) in the nearby Universe.</p>
<p>The high-redshift sample appears more consistent with a no-evolution model if it is to evolve to have similar clustering properties to the most comparable 2dF samples (i.e. −20.5 >
<italic>M
<sub>b</sub>
</italic>
> −21.5) in the nearby Universe. However, the stable and long-lived clustering evolution models are still only 1– 1.5σ above the brightest 2dF ξ(20) value and therefore cannot be ruled out by the present accuracy of the 2dF late-type data.</p>
</sec>
<sec id="ss3-2">
<title>3.2 Redshift-space correlation function</title>
<p>We now estimate the redshift-space correlation function, ξ(
<italic>s</italic>
), using
<italic>z</italic>
≥ 0.5 galaxies identified with
<italic>q
<sub>op</sub>
</italic>
≥ 3 from the four fields observed with AAOmega. The redshift distribution from
<xref ref-type="fig" rid="f4">Fig. 4</xref>
was used to create random catalogues with which to perform the autocorrelation analysis. In each field, we use a catalogue of 20× the number of random points as galaxies in that field. In total, this calculation encompasses 276 galaxies across 12.6 deg
<sup>2</sup>
.</p>
<p>We use the correlation estimator given in
<xref ref-type="disp-formula" rid="m1">equation (1)</xref>
to determine ξ(
<italic>s</italic>
), whilst errors are estimated using Poisson errors. The result is shown in
<xref ref-type="fig" rid="f12">Fig. 12</xref>
(filled square points). We fit the ξ(
<italic>s</italic>
) measurement with a single power law [noting that the break used in the double power laws previously lies below the range of our ξ(
<italic>s</italic>
) result] and find a best fit (using a fixed slope of γ= 1.8) given by a clustering length of
<italic>s
<sub>o</sub>
</italic>
= 6.4 ± 0.8
<italic>h</italic>
<sup>−1</sup>
Mpc (solid line).</p>
<fig position="float" id="f12">
<label>Figure 12</label>
<caption>
<p>The redshift-space correlation function (ξ(
<italic>s</italic>
)) for the full sample of spectroscopically identified objects. The data points show the correlation function of the spectroscopic sample of galaxies incorporating the S11, COSMOS, e04 and d05 fields. The solid line shows a best fit to the data points (with a fixed slope of γ= 1.8), which is characterized by a correlation length of
<italic>s
<sub>o</sub>
</italic>
= 6.4 ± 0.8
<italic>h</italic>
<sup>−1</sup>
Mpc. The dashed line is the ξ(
<italic>s</italic>
) determined from the angular correlation function estimate of the real-space correlation function (
<italic>r
<sub>o</sub>
</italic>
= 5.88
<italic>h</italic>
<sup>−1</sup>
Mpc, γ= 1.83 at
<italic>r</italic>
> 1
<italic>h</italic>
<sup>−1</sup>
Mpc). This incorporates the coherent infall (β= 0.54) and random pairwise velocity (
<italic>a</italic>
= 500 km s
<sup>−1</sup>
) effects.</p>
</caption>
<graphic xlink:href="mnras0403-1261-f12.gif"></graphic>
</fig>
<p>We also show the expected ξ(
<italic>s</italic>
) determined from the power-law form of ξ(
<italic>r</italic>
) given by our estimate of
<italic>w</italic>
(θ) (dashed line). To do this, we take the power-law form and apply both coherent infall and random pairwise velocity effects. The coherent infall imprint on the correlation function is characterized by the infall parameter, β, which is given by
<disp-formula id="m8">
<label>8</label>
<graphic xlink:href="mnras0403-1261-m8.gif"></graphic>
</disp-formula>
where Ω
<sub>m</sub>
(
<italic>z</italic>
) is the mass density at the required redshift and
<italic>b</italic>
is again the sample bias (
<xref ref-type="bibr" rid="b29">Kaiser 1987</xref>
). Using the value of
<italic>b</italic>
= 1.43 from
<xref ref-type="table" rid="t3">Table 3</xref>
, this gives a value of the infall parameter of β= 0.54. For the random pairwise velocities, we use a value of
<italic>a</italic>
= 500 km s
<sup>−1</sup>
as a reasonable estimate of the random motions based on the 2dFGRS data (
<xref ref-type="bibr" rid="b24">Hawkins et al. 2003</xref>
). The expected ξ(
<italic>s</italic>
) was then calculated using the relations given in
<xref ref-type="bibr" rid="b24">Hawkins et al. (2003)</xref>
. Based on this calculation, we see from
<xref ref-type="fig" rid="f12">Fig. 12</xref>
that we find good agreement between the ξ(
<italic>s</italic>
) of our observed spectroscopic sample and that determined from the photometric data, within the associated errors.</p>
</sec>
</sec>
<sec id="ss4">
<title>4 INTEGRATED SACHS–WOLFE EFFECT</title>
<sec id="ss4-1">
<title>4.1 Overview</title>
<p>As described in the introduction the ISW effect is characterized by the energy boost that CMB photons experience as they cross temporally evolving gravitational potential wells in an accelerating Universe. The effect is therefore a potential tool for placing constraints on the acceleration of the Universe as characterized by the cosmological constant, Λ. Given the effect's large scale, the production of all-sky CMB maps from the
<italic>WMAP</italic>
experiment has made it possible to attempt measures of the effect through the cross-correlation of galaxies (as tracers of the large gravitational potentials) with the CMB. Further to this, the large-scale nature of the effect lends itself well to the use of photometrically selected galaxy populations as detailed redshift information is unnecessary. In this vein, several authors (e.g.
<xref ref-type="bibr" rid="b19">Fosalba et al. 2003</xref>
;
<xref ref-type="bibr" rid="b50">Scranton et al. 2003</xref>
;
<xref ref-type="bibr" rid="b7">Cabré et al. 2006</xref>
;
<xref ref-type="bibr" rid="b42">Rassat et al. 2007</xref>
) have used a number of galaxy samples to attempt measurements of the ISW signal in the
<italic>WMAP</italic>
first- and third-year data. The samples used have mostly been photometrically selected LRGs at redshifts of
<italic>z</italic>
< 0.6 and simple magnitude selected samples.</p>
<p>We now use our ELG sample to attempt to measure the ISW effect in
<italic>WMAP</italic>
5-yr data at our sample redshifts of
<italic>z</italic>
≈ 0.3, 0.5 and 0.7. As stated, much of the ISW work done thus far has been with LRGs and magnitude cut samples at
<italic>z</italic>
< 0.6. Our use of the ELG samples provides the benefit of extending to greater redshifts, whilst also using an alternative galaxy population. This in itself has benefits and drawbacks. First, the measured signal will be heavily dependant on the bias of the sample (i.e. how well the sample traces the DM structure and hence the gravitational potential). Given that the ELGs are less clustered than the LRG samples used thus far, we therefore expect to measure a weaker signal, making the measurement potentially more difficult. The potential gain in the low clustering strengths of the ELG samples however, is that they are less likely to reside in rich clusters and so we may expect the ISW signal to be less affected by the Sunyaev–Zel'dovich (SZ) effect produced as CMB photons pass through hot intracluster gas. This potentially provides an interesting alternative to the highly clustered LRG samples used in a number of previous studies.</p>
</sec>
<sec id="ss4-2">
<title>4.2 Data</title>
<p>For this ISW analysis, we use the three galaxy samples described thus far in this paper. The redshift distributions that we use for each of the samples are given in
<xref ref-type="fig" rid="f2">Fig. 2</xref>
in the case of the low- and mid-redshift samples (estimated from photometric redshifts for a subset of the whole sample) and in
<xref ref-type="fig" rid="f4">Fig. 4</xref>
in the case of the high-redshift sample (estimated from spectroscopic redshifts for a subset of the whole sample). The number densities of each of the samples are 103 deg
<sup>−2</sup>
, 71.9 deg
<sup>−2</sup>
and 85.1 deg
<sup>−2</sup>
for the low-, mid- and high-redshift samples.</p>
<p>For this cross-correlation, we have used the
<italic>W-, V-, Q-</italic>
and
<italic>K</italic>
-band temperature maps from the
<italic>WMAP</italic>
5-yr DR (
<xref ref-type="bibr" rid="b25">Hinshaw et al. 2009</xref>
). We use the full-resolution maps in all cases. Before performing the cross-correlation we apply two masks to the data. The first is the
<italic>WMAP</italic>
KP0 mask (
<xref ref-type="bibr" rid="b2">Bennett et al. 2003</xref>
) which removes the majority of the galactic (Milky Way) foreground and is the most rigorous mask provided by the
<italic>WMAP</italic>
team. Secondly we mask the data to match the coverage of our SDSS DR6 galaxy samples, which is described further below.</p>
<p>Pixelized sky-density maps are constructed from each of the three galaxy samples using the
<sc>healpix</sc>
software. These are constructed with a resolution identical to the
<italic>WMAP</italic>
temperature maps characterized by the
<sc>healpix</sc>
parameter
<italic>NSIDE</italic>
= 512 (pixel width ≈7 arcmin). We then limit our galaxy sample to incorporate only the contiguous north galactic pole region of the SDSS. Thus, our sample is limited to 100° < RA < 270°, and stripes 39, 42 and 43 are also excluded.</p>
</sec>
<sec id="ss4-3">
<title>4.3 Method</title>
<p>Following the work of
<xref ref-type="bibr" rid="b19">Fosalba et al. (2003)</xref>
and
<xref ref-type="bibr" rid="b7">Cabré et al. (2006)</xref>
, we use the cross-correlation of the galaxy and
<italic>WMAP</italic>
data as the expectation value of the product of the galaxy overdensity,
<inline-formula>
<inline-graphic xlink:href="mnras0403-1261-mu16.gif"></inline-graphic>
</inline-formula>
and the normalized CMB anisotropy temperature,
<inline-formula>
<inline-graphic xlink:href="mnras0403-1261-mu17.gif"></inline-graphic>
</inline-formula>
as a function of the angular separation, θ. This is given by
<disp-formula id="m9">
<label>9</label>
<graphic xlink:href="mnras0403-1261-m9.gif"></graphic>
</disp-formula>
</p>
<p>Again following
<xref ref-type="bibr" rid="b19">Fosalba et al. (2003)</xref>
and
<xref ref-type="bibr" rid="b7">Cabré et al. (2006)</xref>
, the form of the ISW as probed by a given galaxy population can be expressed by the following Legendre polynomial expansion:
<disp-formula id="m10">
<label>10</label>
<graphic xlink:href="mnras0403-1261-m10.gif"></graphic>
</disp-formula>
<italic>C</italic>
<sup>ISW</sup>
<sub>
<italic>GT</italic>
</sub>
(
<italic>l</italic>
) is simply the ISW/galaxy population power spectrum as given by
<disp-formula id="m11">
<label>11</label>
<graphic xlink:href="mnras0403-1261-m11.gif"></graphic>
</disp-formula>
where
<italic>P</italic>
(
<italic>k</italic>
) is the mass power spectrum and
<italic>W</italic>
<sub>ISW</sub>
(
<italic>z</italic>
) and
<italic>W
<sub>G</sub>
</italic>
(
<italic>z</italic>
) are given by
<disp-formula id="m12">
<label>12</label>
<graphic xlink:href="mnras0403-1261-m12.gif"></graphic>
</disp-formula>
<disp-formula id="m13">
<label>13</label>
<graphic xlink:href="mnras0403-1261-m13.gif"></graphic>
</disp-formula>
where
<italic>D</italic>
(
<italic>z</italic>
) is the linear growth rate and
<italic>b</italic>
(
<italic>z</italic>
) is the bias of the galaxy population (taken from
<xref ref-type="sec" rid="ss3">Section 3</xref>
). φ(
<italic>z</italic>
) is the galaxy selection function, set from the
<italic>n</italic>
(
<italic>z</italic>
) distribution of each of the galaxy samples.</p>
</sec>
<sec id="ss4-4">
<title>4.4 Results and error analysis</title>
<p>We perform the cross-correlation using the
<sc>npt</sc>
(N-point spatial statistic) software (
<xref ref-type="bibr" rid="b23">Gray et al. 2004</xref>
) with the weighting for each pixel given by the galaxy density, δ
<sub>g</sub>
, and the CMB anisotropy temperature, Δ
<italic>T</italic>
. The results are shown in
<xref ref-type="fig" rid="f13">Figs 13</xref>
to
<xref ref-type="fig" rid="f15">15</xref>
for four
<italic>WMAP</italic>
bands:
<italic>W, V, Q</italic>
and
<italic>K</italic>
. We also plot the predicted result using predictions based on equation (6) of
<xref ref-type="bibr" rid="b7">Cabré et al. (2006)</xref>
.</p>
<fig position="float" id="f13">
<label>Figure 13</label>
<caption>
<p>Cross-correlation between the low-redshift galaxy sample and the
<italic>WMAP V</italic>
-band data. The solid line shows the predicted model. Errors are field to field based on splitting the data sample into 16 distinct segments.</p>
</caption>
<graphic xlink:href="mnras0403-1261-f13.gif"></graphic>
</fig>
<fig position="float" id="f14">
<label>Figure 14</label>
<caption>
<p>As in
<xref ref-type="fig" rid="f13">Fig. 13</xref>
but with our mid-redshift sample of ELGs.</p>
</caption>
<graphic xlink:href="mnras0403-1261-f14.gif"></graphic>
</fig>
<fig position="float" id="f15">
<label>Figure 15</label>
<caption>
<p>As in
<xref ref-type="fig" rid="f13">Fig. 13</xref>
but with our high-redshift sample of ELGs.</p>
</caption>
<graphic xlink:href="mnras0403-1261-f15.gif"></graphic>
</fig>
<p>We estimate the errors on the cross-correlation analysis using field-to-field errors. For this purpose, we split the studied region into 16 approximately equal area subfields and recalculate the cross-correlation within each subfield. The error in each angular bin is thus estimated as
<inline-formula>
<inline-graphic xlink:href="mnras0403-1261-mu18.gif"></inline-graphic>
</inline-formula>
, where σ is the standard deviation across the subfields and
<italic>n</italic>
is the number of subfields.</p>
<p>Overall, the results for the
<italic>Q, V</italic>
and
<italic>W</italic>
bands show reasonable agreement with the standard model predictions although the errors are large and correlated. Otherwise, we only note that for the low- and mid-redshift samples there also appears a spike at around 300 arcmin. Although this does not appear in
<xref ref-type="fig" rid="f15">Fig. 15</xref>
for the high-redshift sample, similar features are seen in ISW analyses of SDSS 18 <
<italic>r</italic>
< 19 and 19 <
<italic>r</italic>
< 20 mag-limited galaxy samples (see figs 12a,b of
<xref ref-type="bibr" rid="b48">Sawangwit et al. 2009</xref>
). We believe that this feature is caused by some unknown artefact in either the
<italic>WMAP</italic>
or SDSS data.</p>
<p>Summing over all bins at θ < 100 arcmin, we find amplitudes for
<italic>w</italic>
<sub>Tg</sub>
(<100 arcmin) in the
<italic>WMAP W</italic>
band of 0.25 ± 0.27, 0.17 ± 0.20 and 0.17 ± 0.16 μK for the low-, mid- and high-redshift samples, respectively. Similar results are obtained with the
<italic>V</italic>
and
<italic>Q</italic>
bands, whilst the
<italic>K</italic>
band (which has a greater level of galactic contamination and a lower resolution) is less consistent, giving signals of
<italic>w</italic>
<sub>Tg</sub>
(<100 arcmin) = 0.13 ± 0.36, −0.16 ± 0.29 and 0.38 ± 0.18 μK for the low-, mid- and high-redshift samples, respectively.</p>
<p>We also evaluate the significance of the observed correlation by repeating the cross-correlation with rotated realizations of the
<italic>WMAP</italic>
data. This method uses the data itself in place of random realizations by rotating the masked
<italic>WMAP</italic>
data in 30° steps in galactic longitude. We note at this point that rotating in RA would lead to the galactic plane entering the field of view and although the galactic plane region is masked, it would reduce the number pixels in the analysis significantly. For consistency, we also rotate the
<italic>WMAP</italic>
Kp0 mask before applying it to the galaxy density map. The result of this treatment, using the high-redshift sample, is given in
<xref ref-type="fig" rid="f16">Fig. 16</xref>
. Here, the
<italic>w</italic>
<sub>Tg</sub>
(<100 arcmin) signal is plotted as a function of rotation of the
<italic>WMAP</italic>
data through a full 360° in galactic longitude. The dotted line shows the non-rotated signal. Again we see that the positive signal that we see in the data does not appear statistically significant, with the rotated results showing a large amount of scatter around
<italic>w</italic>
<sub>Tg</sub>
(<100 arcmin) = 0 μK and two of the results (at 30° and 90°) showing more significant positive correlation than the non-rotated result.</p>
<fig position="float" id="f16">
<label>Figure 16</label>
<caption>
<p>Cross-correlation signal,
<italic>w</italic>
<sub>Tg</sub>
(<100 arcmin), for the high-redshift galaxy sample as a function of rotation of the
<italic>WMAP</italic>
5-yr data in galactic longitude. The plotted errors are field-to-field errors based on the segmentation of the data into 16 distinct regions, and the dotted line shows the measurement from the non-rotated data.</p>
</caption>
<graphic xlink:href="mnras0403-1261-f16.gif"></graphic>
</fig>
<p>We now attempt to improve our statistics by combining the low-, mid- and high-redshift results.
<xref ref-type="fig" rid="f17">Fig. 17</xref>
shows the mean of the 3 × 16 separate cross-correlation results. The errors are again given by the field-to-field errors, this time across the whole 48 sample set. Again we see a positive signal that appears to show some agreement with the model. In the
<italic>W, V, Q</italic>
and
<italic>K WMAP</italic>
bands, we derive signals of
<italic>w</italic>
<sub>Tg</sub>
(<100 arcmin) = (0.20 ± 0.12), (0.20 ± 0.12), (0.18 ± 0.12) and (0.11 ± 0.16) μK respectively. Repeating the rotation analysis (
<xref ref-type="fig" rid="f18">Fig. 18</xref>
), but with the combined sample, we again find significant scatter about
<italic>w</italic>
<sub>Tg</sub>
(<100 arcmin) = 0. Indeed, a stronger signal is again found at some rotation angles than at the zero position.</p>
<fig position="float" id="f17">
<label>Figure 17</label>
<caption>
<p>Cross-correlation result averaged across the 3 × 16 redshift/segment samples.</p>
</caption>
<graphic xlink:href="mnras0403-1261-f17.gif"></graphic>
</fig>
<fig position="float" id="f18">
<label>Figure 18</label>
<caption>
<p>Cross-correlation signal,
<italic>w</italic>
<sub>Tg</sub>
(<100 arcmin), for the combined low-, mid- and high-redshift galaxy sample as a function of rotation of the
<italic>WMAP</italic>
5-yr data in galactic longitude. The plotted errors are field-to-field errors based on the segmentation of the data into 3 × 16 distinct regions. Again the result from the non-rotated data is shown by the dotted line.</p>
</caption>
<graphic xlink:href="mnras0403-1261-f18.gif"></graphic>
</fig>
<p>Comparing this analysis to previous results,
<xref ref-type="bibr" rid="b7">Cabré et al. (2006)</xref>
obtained a signal at 100 arcmin of
<italic>w</italic>
<sub>Tg</sub>
= 0.6 ± 0.3 μK using a sample of
<inline-formula>
<inline-graphic xlink:href="mnras0403-1261-mu19.gif"></inline-graphic>
</inline-formula>
LRGs and a signal of
<italic>w</italic>
<sub>Tg</sub>
=≈0.65 ± 0.2 μK with a 20 <
<italic>r</italic>
< 21 mag selected sample with a median redshift of
<inline-formula>
<inline-graphic xlink:href="mnras0403-1261-mu20.gif"></inline-graphic>
</inline-formula>
. In addition,
<xref ref-type="bibr" rid="b18">Fosalba & Gaztañaga (2004)</xref>
claimed a detection of 0.35 ± 0.14 μK at angular scales of θ= 4°–10° using APM galaxies, but found their signal was dominated by the SZ component at scales of θ < 4°. Our observed signal is consistent with the weaker signal expected of the ELG samples, based on both the model predictions and comparison with correlations based on more strongly clustered populations. However, we note that the measurement of the ISW is susceptible to a number of systematic effects, full details of which can be found in
<xref ref-type="bibr" rid="b26">Ho et al. (2008)</xref>
and
<xref ref-type="bibr" rid="b22">Giannantonio et al. (2008)</xref>
. These effects include systematic signal from incorrect correction for dust extinction, contamination from galactic foregrounds, contamination from cluster SZ signals and contamination from point sources. Ultimately, given the combination of these systematic errors and our estimated statistical errors, no detection of the ISW effect can be claimed at this point with this analysis.</p>
</sec>
</sec>
<sec id="ss5">
<title>5 CONCLUSIONS</title>
<p>Colour selected samples are an extremely useful tool in modern astronomy and cosmology. They offer a cheap route to large galaxy redshift surveys, facilitating investigations in several key areas of interest, including the study of dark energy via both the BAOs and the ISW. With this in mind, we have developed photometric selections with which to identify galaxies in three broad redshift ranges characterized by
<inline-formula>
<inline-graphic xlink:href="mnras0403-1261-mu21.gif"></inline-graphic>
</inline-formula>
and 0.65 ± 0.21. Applying these to SDSS data, we are able to select galaxy samples covering the given redshift ranges down to magnitudes of
<italic>i</italic>
≈ 20.5.</p>
<p>The calibration of the high-redshift sample has been performed, using the AAOmega spectrograph at the AAT to provide spectroscopic redshifts for this sample. From these observations, we have shown that it is possible to target and spectroscopically identify
<italic>z</italic>
> 0.5 star-forming galaxies with integration times of just 1 h on the 4-m AAT. The results of this have shown our high-redshift selection to work well, giving a close match to the expected redshift distribution, with
<inline-formula>
<inline-graphic xlink:href="mnras0403-1261-mu22.gif"></inline-graphic>
</inline-formula>
. Further, this has proven that our selection can be a firm basis on which to conduct large-scale spectroscopic surveys of
<italic>z</italic>
> 0.5 ELGs.</p>
<p>We have investigated the clustering properties of our three photometric samples using the angular correlation function. By fitting the angular correlation function using Limber's formula, we estimate the real-space clustering properties of the samples and find that both the low- and high-redshift populations are best fitted by double power laws, whilst the mid-redshift population seems best fitted by a single power law. From these calculations, we estimate clustering lengths (at
<italic>r</italic>
> 0.5
<italic>h</italic>
<sup>−1</sup>
Mpc) of 2.78 ± 0.08, 3.71 ± 0.11 and 5.50 ± 0.13
<italic>h</italic>
<sup>−1</sup>
Mpc for the low-, mid- and high-redshift samples, respectively. Further to this, from our spectroscopic observations we measure a clustering length for the high-redshift sample of 6.4 ± 0.8
<italic>h</italic>
<sup>−1</sup>
Mpc in agreement with the measurement based on the angular clustering measurement. Comparing these clustering measurements with comparable populations of late-type galaxies from 2dF data, we note that the high-redshift sample appears to have an unexpectedly high clustering strength.</p>
<p>The development of photometric redshift selections has a number of scientific applications, not least the evaluation of the ISW effect. We have used our photometric selection to evaluate the ISW effect in the region of the SDSS by cross-correlating the density fluctuations in our galaxy distributions with the CMB anisotropies from the
<italic>WMAP</italic>
5-yr data. The results obtained using all three data sets show a positive correlation in accordance with the predicted model. However, none of these three prove to be significant, with signals in the
<italic>WMAP W</italic>
band of (0.25 ± 0.27), (0.17 ± 0.20) and (0.17 ± 0.16) μK for the low-, mid- and high-redshift samples, respectively. We attempt to improve the statistics by combining the three redshift samples, which results in a signal of (0.20 ± 0.12) μK when cross-correlated with the
<italic>WMAP W</italic>
band, still only marginal (1.67σ). Also in tests of contamination by systematics, we found similar results at arbitrary angles of rotation between the CMB data and the ELG samples which means that no detection of the ISW can be claimed above the random and systematic noise in this analysis.</p>
</sec>
</body>
<back>
<ack>
<p>We thank C. Wolf for supplying the COMBO-17 photometric redshift catalogue data and the staff of the AAO for their work in operating the AAOmega facility during our observations. Specific thanks also goes to Rob Sharp for assistance during the AAT observations. We would also like to thank Shirley Ho for comment and input to this work. This paper has used data from both the SDSS and
<italic>WMAP</italic>
projects. Funding for the SDSS and SDSS-II has been provided by the Alfred P. Sloan Foundation, the Participating Institutions, the National Science Foundation, the US Department of Energy, the National Aeronautics and Space Administration, the Japanese Monbukagakusho, the Max Planck Society and the Higher Education Funding Council for England. The SDSS Web Site is
<ext-link ext-link-type="uri" xlink:href="http://www.sdss.org/">http://www.sdss.org/</ext-link>
.
<italic>WMAP</italic>
is the result of a partnership between Princeton University and NASA's Goddard Space Flight Center. Scientific guidance is provided by the
<italic>WMAP</italic>
Science Team. RMB and NPR acknowledge the support of a STFC PhD Studentships. SMC acknowledges the support of an Australian Research Council QEII Fellowship and a J. G. Russell Award from the Australian Academy of Science.</p>
</ack>
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<affiliation>Department of Physics, Durham University, South Road, Durham DH1 3LE</affiliation>
<affiliation>Institut d'Astrophysique de Paris, UMR 7095 CNRS, Université Pierre et Marie Curie, 98bis boulevard Arago, 75014 Paris, France</affiliation>
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<affiliation>Department of Astronomy and Astrophysics, Pennsylvania State University, 525 Davey Laboratory, University Park, PA 16802, USA</affiliation>
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<abstract>We investigate the use of simple colour cuts applied to the Sloan Digital Sky Survey (SDSS) optical imaging to perform photometric selections of emission-line galaxies (ELGs) out to z < 1. Our selection is aimed at discerning three separate redshift ranges: 0.2 ≲z≲ 0.4, 0.4 ≲z≲ 0.6 and 0.6 ≲z≲ 1.0, which we calibrate using data taken by the COMBO-17 survey in a single field (S11). We thus perform colour cuts using the SDSS g, r and i bands and obtain mean photometric redshifts of and . We further calibrate our high-redshift selection using spectroscopic observations with the AAOmega spectrograph on the 4-m Anglo-Australian Telescope, observing ≈50–200 galaxy candidates in four separate fields. With just 1 h of integration time and seeing of ≈ 1.6 arcsec, we successfully determined redshifts for ≈65 per cent of the targeted candidates. We compare our spectroscopic redshifts to the photometric redshifts from the COMBO-17 survey and find reasonable agreement between the two. We calculate the angular correlation functions of these samples and find correlation lengths of r0= 2.78 ± 0.08, 3.71 ± 0.11 and 5.50 ± 0.13 h−1 Mpc for the low-, mid- and high-redshift samples, respectively. Comparing these results with predicted dark matter clustering, we estimate the bias parameter for each sample to be b= 0.72 ± 0.02, b= 0.93 ± 0.03 and b= 1.43 ± 0.03. We calculate the two-point redshift-space autocorrelation function at z≈ 0.6 and find a clustering amplitude of so= 6.4 ± 0.8 h−1 Mpc. Finally, we use our photometric sample to search for the integrated Sachs–Wolfe signal in the Wilkinson Microwave Anisotropy Probe (WMAP) 5-yr data. We cross-correlate our three redshift samples with the WMAP W, V, Q and K bands and find an overall trend for a positive signal similar to that expected from models. However, the signal in each is relatively weak, with the results in the WMAP W band being wTg(<100 arcmin) = 0.25 ± 0.27, 0.17 ± 0.20 and 0.17 ± 0.16 μK for the low-, mid- and high-redshift samples, respectively. Combining all three galaxy samples, we find a signal of wTg(<100 arcmin) = 0.20 ± 0.12 μK in the WMAP W band, a significance of 1.7σ. However, in testing for systematics where the WMAP data are rotated with respect to the ELG sample, we found similar results at several different rotation angles, implying the apparent signal may be produced by systematic effects.</abstract>
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