The 2dF Galaxy Redshift Survey: Spectra and redshifts

TL;DR: The 2dF Galaxy Redshift Survey (2dFGRS) as discussed by the authors uses the 2DF multi-fibre spectrograph on the Anglo-Australian Telescope, which is capable of observing 400 objects simultaneously over a 2-degree diameter field.

Abstract: The 2dF Galaxy Redshift Survey (2dFGRS) is designed to measure redshifts for approximately 250000 galaxies. This paper describes the survey design, the spectroscopic observations, the redshift measurements and the survey database. The 2dFGRS uses the 2dF multi-fibre spectrograph on the Anglo-Australian Telescope, which is capable of observing 400 objects simultaneously over a 2-degree diameter field. The source catalogue for the survey is a revised and extended version of the APM galaxy catalogue, and the targets are galaxies with extinction-corrected magnitudes brighter than b_J=19.45. The main survey regions are two declination strips, one in the southern Galactic hemisphere spanning 80deg x 15deg around the SGP, and the other in the northern Galactic hemisphere spanning 75deg x 10deg along the celestial equator; in addition, there are 99 fields spread over the southern Galactic cap. The survey covers 2000 sq.deg and has a median depth of z=0.11. Adaptive tiling is used to give a highly uniform sampling rate of 93% over the whole survey region. Redshifts are measured from spectra covering 3600A-8000A at a two-pixel resolution of 9.0A and a median S/N of 13 per pixel. All redshift identifications are visually checked and assigned a quality parameter Q in the range 1-5; Q>=3 redshifts are 98.4% reliable and have an rms uncertainty of 85 km/s. The overall redshift completeness for Q>=3 redshifts is 91.8%, but this varies with magnitude from 99% for the brightest galaxies to 90% for objects at the survey limit. The 2dFGRS database is available on the WWW at this http URL

Summary

1. Introduction

• In commutative information geometry the Fisher–Rao metric can be characterised in (at least) three ways: (i) it is the unique statistically monotone metric (Chentsov theorem); (ii) it is the Hessian of the Kullback–Leibler relative entropy; (iii) it is obtained by division of square root of densities.
• In a previous paper3 the authors considered a scalar product on density matrices derived by the pull-back of the map ρ → √ρ.

2. Pull-Back of Riemannian Metrics

• Let M be a differentiable manifold and (N, g) a Riemannian manifold (see Ref. 1 for differential geometric concepts).
• Suppose ϕ: M → N is an immersion, that is a differentiable map such that its differential Dρϕ: TρM → Tϕ(ρ)N is injective, for any ρ ∈M.
• On M there exists a unique Riemannian scalar product gϕ := ϕ∗g compatible with the differential structure of M such that ϕ: (M, gϕ) → (N, g) is an isometry.
• Under the above hypothesis g is said the pull-back metric induced by ϕ. Remark 2.3.

4. The Wigner–Yanase Skew Information

• Dn be a density matrix and let A be a self-adjoint matrix.
• Let f be a symmetric operator monotone function and cf (x, y) := 1 yf(x/y) the associated Chentsov–Morotsova function.
• Petz classification theorem states that each statistically monotone metric on TDn has the form M f ρ (A,B) := Tr(Acf (Lρ, Rρ)(B)), where Lρ(A) := ρA and Rρ(A) := Aρ. Each statistically monotone metric has a unique expression (up to a constant) given by Tr(ρ−1A2), for A ∈ (TρDn)c, because of the Chentsov uniqueness theorem.

5. The Main Result

• Let us consider the unit sphere ofMn, denoted by Sn, as a real Riemannian submanifold of Mn.
• The natural metric on Sn is the one induced by the Hilbert–Schmidt scalar product of Mn. Let Dn ⊂.
• Mn be the manifold of strictly positive definite matrices.
• Sn is differentiable so the authors can apply the results of Sec. 2.

Figures

Figure 2. The survey fields in the NGP (left) and SGP (right) on maps of the extinction AbJ derived from Schlegel et al. (1998).

Figure 12. The magnitude distributions of the 2dFGRS sample, the repeat observations in the 2dFGRS sample, and the five samples of objects in common with other redshift catalogues: CfA2, SAPM, PSCz, LCRS and ZCAT.

Figure 17. The redshift distribution of the 2dFGRS (histogram) and a simple smooth analytic approximation (curve).

Figure 5. The distribution of the unallocated objects within the stacked 2dF fields.

Figure 19. Redshift slices for different spectral types: type 1 corresponds to E/S0, type 2 to Sa/Sb, type 3 to Sc/Sd and type 4 to Irr.

Table 1. Summary statistics by quality class and method.

Figure 9. The distribution of redshift differences between repeat measurements with Q $ 3 is shown in the top panel, along with the Gaussian having the same median and rms. The dependence of the redshift differences on redshift, apparent magnitude, S/N ratio and quality class for the best observation, is shown in the lower panels (note that the quality classes have small random offsets added to make the distribution of redshift differences clear). The lines in the lower panels are the running median and the ^2s ranges.

Table 4. FITS keywords for the spectra (extensions 1…spectra).

Figure 16. Redshift completeness as a function of apparent magnitude. The different panels are for fields of different overall field completeness: top left, fields with completeness in the range 95 per cent , cF # 100 per cent; top right, fields with 90 per cent , cF # 95 per cent; bottom left, fields with 85 per cent , cF # 90 per cent, and bottom right, fields with 80 per cent , cF # 85 per cent: Note that over 76 per cent of the observed fields fall in the first two bins, with cF . 90 per cent: The dashed curves are one-parameter model fits (see text).

Figure 8. Example 2dFGRS spectra, showing objects with quality classes Q ¼ 3, Q ¼ 4 and Q ¼ 5, and both absorption (ABS) and emission (EMI) redshifts. The most common spectral features are marked at the wavelengths corresponding to the measured redshift of each object.

Figure 3. The distribution of extinction corrections AbJ with Galactic latitude b (dots and left axis), and the fraction of corrections larger than a given value (line and right axis).

Figure 14. The fraction of the sky in the NGP and SGP survey strips where the survey limit is fainter than a given bJ magnitude.

Full text

The 2dF Galaxy Redshift Survey: spectra and redshifts
Matthew Colless,
1P
Gavin Dalton,
2
Steve Maddox,
3
Will Sutherland,
4
Peder Norberg,
5
Shaun Cole,
5
Joss Bland-Hawthorn,
6
Terry Bridges,
6
Russell Cannon,
6
Chris Collins,
7
WarrickCouch,
8
NicholasCross,
4
KathrynDeeley,
8
RobertoDePropris,
8
SimonP.Driver,
4
George Efstathiou,
9
Richard S. Ellis,
10
Carlos S. Frenk,
5
Karl Glazebrook,
11
Carole Jackson,
1
Ofer Lahav,
9
Ian Lewis,
6
Stuart Lumsden,
12
Darren Madgwick,
9
John A. Peacock,
13
Bruce A. Peterson,
1
Ian Price,
1
Mark Seaborne
2
and Keith Taylor
6,10
(the 2dFGRS team)
1
Research School of Astronomy and Astrophysics, The Australian National University, Weston Creek, ACT 2611, Australia
2
Department of Physics, University of Oxford, Keble Road, Oxford OX1 3RH
3
School of Physics and Astronomy, University of Nottingham, Nottingham NG7 2RD
4
School of Physics and Astronomy, University of St Andrews, North Haugh, St Andrews, Fife, KY6 9SS
5
Department of Physics, University of Durham, South Road, Durham DH1 3LE
6
Anglo-Australian Observatory, PO Box 296, Epping, NSW 2121, Australia
7
Astrophysics Research Institute, Liverpool John Moores University, Twelve Quays House, Birkenhead L14 1LD
8
Department of Astrophysics, University of New South Wales, Sydney, NSW 2052, Australia
9
Institute of Astronomy, University of Cambridge, Madingley Road, Cambridge CB3 0HA
10
Department of Astronomy, California Institute of Technology, Pasadena, CA 91125, USA
11
Department of Physics and Astronomy, Johns Hopkins University, Baltimore, MD 21218-2686, USA
12
Department of Physics, University of Leeds, Woodhouse Lane, Leeds LS2 9JT
13
Institute for Astronomy, University of Edinburgh, Royal Observatory, Blackford Hill, Edinburgh EH9 3HJ
Accepted 2001 August 9. Received 2001 July 30
ABSTRACT
The 2dF Galaxy Redshift Survey (2dFGRS) is designed to measure redshifts for
approximately 250000 galaxies. This paper describes the survey design, the spectroscopic
observations, the redshift measurements and the survey data base. The 2dFGRS uses the 2dF
multifibre spectrograph on the Anglo-Australian Telescope, which is capable of observing
400 objects simultaneously over a 28 diameter field. The source catalogue for the survey is a
revised and extended version of the APM galaxy catalogue, and the targets are galaxies with
extinction-corrected magnitudes brighter than b
J
¼ 19:45. The main survey regions are two
declination strips, one in the southern Galactic hemisphere spanning 808 158 around the
SGP, and the other in thenorthern Galactic hemisphere spanning 758  108 along the celestial
equator; in addition, there are 99 fields spread over the southern Galactic cap. The survey
covers 2000deg
2
and has a median depth of

z ¼ 0:11. Adaptive tiling is used to give a highly
uniform sampling rate of 93 per cent over the whole survey region. Redshifts are measured
from spectra covering 3600–8000

A at a two-pixel resolution of 9.0A
˚
and a median S/N of
13pixel
21
. All redshift identifications are visually checked and assigned a quality parameter
Q in the range 1–5; Q $ 3 redshifts are 98.4 per cent reliable and have an rms uncertainty of
85kms
21
. The overall redshift completeness for Q $ 3 redshifts is 91.8 per cent, but this
varies with magnitude from 99 per cent for the brightest galaxies to 90 per cent for objects at
the survey limit. The 2dFGRS data base is available on the World Wide Web at http://www.
mso.anu.edu.au/2dFGRS.
Key words: surveys – galaxies: clusters: general – galaxies: distances and redshifts –
cosmology: observations – large-scale structure of Universe.
P
E-mail: colless@mso.anu.edu.au
Mon. Not. R. Astron. Soc. 328, 1039–1063 (2001)
q 2001 RAS
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1 INTRODUCTION
The 2dF GalaxyRedshift Survey(2dFGRS) isdesigned tomeasure
redshifts for approximately 250000 galaxies in order to achieve an
order-of-magnitudeimprovementon previous redshiftsurveys,and
provide a detailed and representative picture of the galaxy
population and its large-scale structure in the nearby Universe
(Colless 1999). The main goals of the 2dFGRS are as follows.
(1) To measurethe galaxy power spectrumP(k) on scales up toa
few hundred Mpc, filling the gap between the small scales where
P(k)is known frompreviousgalaxy redshiftsurveysand thelargest
scales whereP(k) iswell determined by observationsof thecosmic
microwave background(CMB) anisotropies. Particular goals are to
determine the scale of the turnover in the power spectrum and to
observein thegalaxy distribution theacoustic peaksdetected inthe
CMB power spectrum (Percival et al. 2001).
(2) To measure the redshift-space distortion of the large-scale
clustering that results from the peculiar velocity field produced by
the mass distribution(Peacock etal. 2001).This distortiondepends
on both the mass density parameter V and the bias factor b of the
galaxy distribution with respect to the mass distribution,
constraining the combination
b
¼ V
0:6
=b.
(3) To measure higher order clustering statistics of the galaxy
distribution in order to (a) determine the bias parameter b,
revealing the relationship between the distributions of mass and
light and yielding a direct measure of V; (b) establish whether the
galaxy distribution on large scales is a Gaussian random field, as
predicted by most inflationary models of the early Universe, and
(c) investigate the non-linear growth of clustering in the small-
scale galaxy distribution.
(4) To fully and precisely characterize the galaxy population in
terms of the distributions of fundamental properties such as
luminosity, surface brightness,spectral typeand star formationrate
(Folkes et al. 1999; Cole et al. 2001; Cross et al. 2001; Madgwick
et al. 2001a).
(5) To quantify the relationships between the internal properties
of galaxies (such as luminosity, spectral type and star formation
rate) and their external environment (the local density of galaxies
and the surrounding large-scale structure) in order to constrain
models of galaxy formation and evolution (Norberg et al. 2001).
(6) To investigate the properties of galaxy groups and clusters,
not just from existing cluster catalogues (De Propris et al. 2001),
but by defining a large, homogeneous sample of groups and
clusters in redshift space, avoiding the problems of cluster
catalogues defined in projection and allowing detailed study of the
mass distributions and dynamical evolution in the most massive
bound structures in the Universe.
(7) To provide a massive spectroscopic data base for use in
conjunction with other surveys, for finding rare and interesting
types of object, and as a source for a wide variety of follow-up
observations (Cole et al. 2001; Magliocchetti et al. 2001; Sadler
et al. 2001).
This paper provides an overview of the survey and detailed
description of thesurveyobservations.The layoutof the paperis as
follows. Section 2 summarizes the main capabilities of the 2dF
multifibre spectrograph; Section 3 describes the input source
catalogue for the survey; Section 4 discusses the survey design,
including the areas of sky covered by the survey and the tiling of
the survey fields; Section 5 outlines the algorithm used to assign
fibres to targets, and its uniformity and completeness; Section 6
describes the spectroscopic data obtained for the survey and the
data reduction methods; Section 7 deals with the estimation of the
redshifts and various internal and external checks on their
reliability and precision; Section 8 describes the survey masks,
which encapsulate the coverage, magnitude limits and redshift
completeness of the survey; Section 9 outlines the main
components and features of the survey data base; Section 10
summarizes some of the main results emerging from the survey,
and Section 11 provides conclusions.
2 THE 2DF SPECTROGRAPH
The survey is designed around the Two-degree Field (2dF)
multifibre spectrograph on the Anglo-Australian Telescope, which
is capable of observing up to 400 objects simultaneously over a 28
diameter field of view. Here we summarize the aspects of the
instrument relevant to the 2dFGRS; a full description is provided
by Lewis et al. (2001) and the 2dF User Manual (http://www.
aao.gov.au/2df). The four main components of 2dF are the
corrector optics, the fibre positioner, the fibres and the
spectrographs.
The2dF correctoroptics are afour-elementlens assemblywhich
gives 1-arcsec images over a 28: 1 diameter flat field of view at the
prime focus of the AAT. The corrector incorporates an atmospheric
dispersion compensator (ADC), which corrects for atmospheric
dispersion at zenith distances less than about 708. The most
significant remaining image degradationis a chromatic variation in
distortion, which has the effect of dispersing images in the radial
direction. This effect is largest halfway out from the field centre,
wherethe wavelengthrange 0:35–1:0mmis dispersed over 2arcsec
radially. The radial distortion introduced by the corrector gives an
image scale that varies over the field of view, from
15.5arcsecmm
21
at the centre to 14.2arcsecmm
21
at the edge;
the corresponding change in focal ratio is from f=3:4tof=3:7.
The 2dF fibre positioner X–Y robot takes about 6–7s on average
to position onefibre. Sinceapproximately 550–580fibre moves are
required to reconfigure a typical 400-fibre field, this means that a
full reconfiguration takes about 60–65min. The actual configur-
ation time varies, depending on the number of fibres used and the
complexity of the field. To avoid dead-time there are two field
plates, each with 400 fibres. While one field plate is placed at the
focal plane for observing, the other is being reconfigured by the
fibre positioner. The positions of the field plates are reversed by
tumbling them about their horizontal axis.
The fibres are have 140-mm diameter cores, corresponding to
2.16arcsec at the field centre and 1.99arcsec at the field edge.
There are400 fibreson eachfield plate. The internal precisionwith
which the fibres are positioned is 11mm (0.16arcsec) on average,
with no fibres outside 20mm (0.3arcsec). The fibres terminate in
magnetic ‘buttons’ that attach to the steel field plates. Each button
has a right-angle prism which directs the light from the focal plane
into the fibre. To prevent fibre buttons coming into direct contact
and to protect the fragile prisms, the fibres cannot be placed too
close together. The absolute minimum fibre separation is 800mm
(approximately 12arcsec), and the required separation is generally
larger (approximately 30arcsec), as it depends on the detailed
geometry of the buttons and their relative orientations.
Half the fibres on each field plate go to one of the two identical
spectrographs. Each spectrograph has an f=3:15 off-axis Maksutov
collimator feeding a 150-mm collimated beam to the grating and
then, at anangle of408,toanf=1:2 wide-field Schmidtcamera. The
detectors are Tektronix CCDswith 1024  1024 24-mmpixels. The
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200-fibre spectra imaged on to each CCD are separated by
approximately 5pixels. The 2dFGRS used the 300B gratings,
which are blazed at 4200A
˚
and give a dispersion of 178.8A
˚
mm
21
(4.3A
˚
pixel
21
). For a typical spectrograph focus of 2.1pixels
(FWHM), this corresponds to a FWHM spectral resolution of
9.0A
˚
. The2dFGRS observations used a central wavelength around
5800A
˚
, and covered the approximate range 3600–8000

A. Flexure
is less than 0.2pixelhr
21
(i.e., less than 40kms
21
over a typical
integration time).
The overall system efficiency (source to detector) of 2dF with
the300B gratingsused inthe 2dFGRS is2.8per centat 4400A
˚
,4.3
per cent at 5500A
˚
and 4.7 per cent at 7000A
˚
. These figures
were obtained from measurements of photometric standard stars,
corrected to nominal 1-arcsec seeing.
3 SOURCE CATALOGUE
The sourcecatalogue for thesurvey (Maddoxet al., in preparation)
is a revised and extended version of the APM galaxy catalogue
(Maddox et al. 1990a,b,c; Maddox, Efstathiou & Suntherland
1996). This catalogue is based on Automated Plate Measuring
machine (APM) scans of 390 plates from the UK Schmidt
Telescope (UKST) Southern Sky Survey. The extended version of
the APM catalogue includes over 5 million galaxies down to b
J
¼
20:5 in both north and south Galactic hemispheres over a region of
almost 10
4
deg
2
(bounded approximately by declination
d
#138
and Galactic latitude b $ 308Þ. Small regions around bright stars,
satellite trails and plate flaws are excluded;these are accounted for
by the survey mask (see Section 8.1).
The b
J
magnitude system for the Southern SkySurvey is defined
by the response of Kodak IIIaJ emulsion in combination with a
GG395filter. It iszero-pointed toVega – i.e., b
J
isequal to Johnson
B for an object with zero colour in the Johnson–Cousins system.
The colour equation is normally taken to be
b
J
¼ B 2 0:28ðB 2 VÞ; ð1Þ
followingBlair &Gilmore (1982).Alarger coefficient (20.35)has
been suggested by Metcalfe, Fong & Shanks (1995), but we
measure 20:27 ^ 0:02 in comparison with the ESO Imaging
Survey (Arnouts et al. 2001), and we therefore retain the usual
valueof 20.28. The photometry ofthe catalogue is calibrated with
numerous CCD sequences and, for galaxies with b
J
¼ 17–19:45,
hasa 68 percent spreadof approximately0.15mag, butwith anon-
Gaussian tail to the error distribution. We emphasize that the
calibration is to total CCD photometry, which absorbs any
remaining correction to the thresholded APM magnitudes.
The star–galaxy separation is as described in Maddox et al.
(1990b), and the locus dividing stars and galaxies was chosen to
exclude as few compact galaxies as possible, while keeping the
contamination of the galaxy sample by stars to about 5 per cent.
Spectroscopic identifications of the survey objects (see Section 7),
show that the stellar contamination is in fact 6 per cent.
The source catalogue is incomplete at all magnitudes due to
various effects, including the explicit exclusion of objects
classified by the APM as merged images, the misclassification of
some galaxies as stars, and the non-detection (or misclassification
as noise) of some low surface brightness objects. This
incompleteness has been studied in comparisons with deeper
wide-area CCD photometry by Pimbblet et al. (2001) and Cross &
Driver (in preparation). The overall level of incompleteness is
10–15 per cent and varies slightly with apparent magnitude, being
largest for the brightest and faintest objects. The main classes of
objects that are excluded are (i) merged galaxy images that are
explicitly excluded from the 2dFGRS source catalogue (about 60
per cent of themissing objects);(ii) largegalaxies that are resolved
into components that are classified as stellar, merged or noise
objects (20 per cent); (iii) compact normal galaxies that are
detected but classified as stars (15 per cent), and (iv) low surface
brightnessgalaxies thatareeither notdetected orclassified as noise
objects (5 per cent). Thus the main cause of incompleteness is
misclassification of objects rather than their non-detection.
The target galaxies for the 2dFGRS were selected to have
extinction-corrected magnitudes brighter than b
J
¼ 19:45. Since
the targets were selected, improvements to the photometric
calibrations and revised extinction corrections have resulted in
slight variations to the magnitude limit over the survey regions –
this is precisely quantified by the magnitude limit mask for the
survey (see Section 8.1). The b
J
extinction is taken to be
A
b
J
¼ 4:035EðB 2 VÞ, where the coefficient, and the reddening
EðB 2 VÞ as a function of position, come from Schlegel,
Finkbeiner & Davis (1998). The limit of b
J
¼ 19:45 was chosen
because (i) the surface density of galaxies at b
J
¼ 19:45
(approximately 165deg
22
) is sufficiently larger than the surface
density of 2dF fibres on the sky (127deg
22
) to allow efficient
use of all fibres – few fibres are unused even in low-density
fields, and (ii) the time taken to configure a typical field
ð60–65minÞ allows, with overheads, a sufficiently long exposure
time to reach the desired signal-to-noise level of S=N . 10pixel
21
for galaxies with b
J
¼ 19:45 even in rather poor conditions. This
limiting magnitude correspondsto a median redshift for the survey
of about

z ¼ 0:1, so that the 2dFGRS is essentially a survey of the
local Universe.
4SURVEYDESIGN
4.1 Survey areas
The areas of the sky covered by the survey were chosen so as to
satisfy a number of different requirements. The first goal was to
cover as large a volume as possible, in order to closely approach
a statistically representative sample of the Universe on the
largest possible scales. The second was to obtain near-complete
sampling down to the survey limit in order to have the finest
possible resolution of structure on small scales. The third require-
ment was to match the sample to the observational capabilities
of the 2dF instrument in order to achieve high efficiency. The
adopted geometry is an effective compromise between these
requirements.
The survey consists of two separate declination strips of
overlapping28 fieldsplus 99 scattered ‘random’ 28 fields. Onestrip
(the SGP strip) is in the southern Galactic hemisphere and covers
approximately 808 158 centred close to the South Galactic Pole
ð21
h
40
m
,
a
, 03
h
40
m
, 2378: 5 ,
d
,2228: 5Þ. The other strip
(the NGP strip) is in the northern Galactic hemisphere and covers
758  108 ð09
h
50
m
,
a
, 14
h
50
m
, 278: 5 ,
d
,128: 5Þ. The 99
‘random’ fields are chosen from the low-extinction region of the
APM catalogue in the southern Galactic hemisphere outside the
survey strip (the mean extinction over each field is required to be
less than 0.2mag – see fig. 2 of Efstathiou & Moody 2001). The
fields are chosen pseudo-randomly within this region, except that
the field centres are at least 38 apart. A map of the survey fields on
the sky is shown in Fig. 1; the locations of the fields with respect
to the extinctionmap derivedfrom Schlegelet al.(1998) areshown
in Fig. 2. All the survey fields lie at Galactic latitudes greater than
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jbj¼308, and the whole of the SGP strip, and most of the NGP
strip and the random fields, lie at Galactic latitudes greater than
jbj¼458.
The distribution of extinction corrections as a function of
Galactic latitude,and the fraction of correctionslarger thana given
value, are shown in Fig. 3. Overall, the median correction is
0.07mag, 90 per cent are less than 0.16mag, and 99 per cent are
less than 0.26mag; the corresponding quantiles in the NGP are
(0.12,0.19,0.28)mag, in the SGP (0.05,0.07,0.11)mag, and in the
random fields (0.07,0.13,0.30)mag.
The 2dFGRS target sample of galaxies contains 193550
galaxies in the SGP strip, 139144 galaxies in the NGP strip, and
57019 galaxies in the random fields. This gives a total of 389713
possible targets,significantly more than the survey goal of 250000
galaxies. Survey observations of the NGP and SGP strips are
proceeding outwards in declination from the centre of each strip
towards this goal. Note that the total number of galaxies listed in
the survey source catalogue (and the survey data base) is 467214,
which is larger than the number of possible survey targets because
the source catalogues for the NGP and SGP strips conservatively
include galaxies fainter than the spectroscopic survey magnitude
limit, down to b
J
¼ 19:6.
At the median redshift of the survey ð

z ¼ 0:11Þ the SGP strip
extends over 400h
21
Mpc 75h
21
Mpc, and the NGP strip over
375h
21
Mpc 50h
21
Mpc. Out tothe effectivelimit ofthe survey
at z < 0:3, the strips contain a volume of 1:2  10
8
h
23
Mpc
3
(for
V
m
¼ 0:3, V
L
¼ 0:7Þ; the volume sparsely sampled including the
random fields is between 2 and 3 times larger.
Figure 1. The 2dFGRS regions shown in an Aitoff projection of RA and Dec., with individual 2dF fields marked as small circles. Also shown are the lines of
Galactic latitude jbj¼08,308 and 458. Thenumbers of surveygalaxies in these regions are 193550 in the 643fields of the 808  158 SGP strip, 139144 in the
450 fields of the 758 108 NGP strip, and 57019 in the 99 fields scattered around the SGP strip.
Figure 2. The survey fields in the NGP (left) and SGP (right) on maps of the extinction A
b
J
derived from Schlegel et al. (1998).
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4.2 Tiling the survey
The survey limit of b
J
¼ 19:45 was chosen, in part, because it
gives a good match between the surface density of galaxies and
the surface density of 2dF fibres. Due to clustering, however, the
number of galaxies in a given field varies considerably. The rms
variation in the number of galaxies per randomly placed 28 field
is 140 at b
J
¼ 19:5, and is largely independent of the choice of
magnitude limit over the range considered here. To make
efficient use of 2dF, we therefore require an algorithm for tiling
the sky with 28 fields that allows us to cover the survey area at a
high, and nearly uniform, sampling rate with the minimum
number of 2dF fields.
So long as the sampling of the source catalogue is not biased in
any way that depends on the photometric or spectroscopic
properties of the galaxies, we can always use the source catalogue
to accurately determine the sampling rate as a function of position
(see Section 8). The sampling can then be accounted for in any
analysis. However, to keep such corrections to a minimum,
considerable effort has been invested in making the sampling as
complete and uniform as possible.
There are a number of possible approaches to laying down target
field centres. The simplest is to adopt a uniform grid of equally
spacedcentres, and theneitherrandomly sampleeach field withthe
number of available fibres or observe each field several times until
all the galaxies have been observed. The second of these options is
clearly inefficient, as it will give rise to a large number of fields
being observed with significantly less than the full complement of
fibres, while the first is undesirable as it gives a different sampling
factor for each field. A more efficient solution is to use an adaptive
tiling strategy, where we allow each field centre to drift from the
regular grid so that we maximize the number of targets that are
assigned to each field, subject to the constraint that the number of
targets assigned to any one field should not exceed the number of
available fibres, N
f
.
We begin with a uniform grid with field centres equally spaced
by s ¼
ffiffiffi
3
p
8 in right ascension along rows 18: 5 apart in declination.
Foreach galaxyin thesurveywe thendetermine howmany fieldsit
lies within, and assign each field a weight w
i
, where
w
i
¼ 0ifN
i
$ N
f
¼ 1 2
N
i
N
f
if N
i
, N
f
ð2Þ
and N
i
is the number of galaxies in this field. These weights are
normalized such that
P
N
t
1
w
i
¼ 1, where N
t
is the number of fields
that this galaxycould beassigned to. Thegalaxy in questionis then
randomly assigned to one of the fields using these weights, unless
all the fields are already filled, in which case it is assigned to the
firstfield inwhich itwas found.Once all thefieldoccupancies have
been determined in this way, we move each field in right ascension
by an amount
da
i
¼ D
a
1 0:05s
N
i
N
f
if ðN
i
$ N
f
Þ
¼ D
a
2 s
0
1 2
N
i
N
f

if ðN
i
, N
f
Þ;
ð3Þ
where s is the maximum allowed separation between adjacent
fields,s
0
is the currentdistance tothe neighbouringfield centre,and
D
a
is the cumulative shift that has currently been applied to this
row. New fields are added at the end of each row if the total length
of the row has contracted enough to exclude any galaxies at the
trailing edge. We found that using a fixed separation of 18: 5in
declination, and adjusting the tile positions in right ascension only,
provided sufficient flexibility to achieve uniform high complete-
ness without a large increase in the total number of fields and
without leaving gaps in the sky coverage.
In practice, it is found that the above prescription requires a
further modification to account for the position of each object
within the field. This additional constraint arises because of the
physical restrictions on the positioning of individual fibres, both in
terms of their deviation from the radial angle and their extension
from the parked position at the edge of the field. We apply this
constraint by dividing each field into 36 subfields and restricting
the number of targets that can be assigned to each subfield to 16.
This is larger than the number of fibres whose park positions fall
within the arc of the sector, but allows for the fact that the area of
the field that can be reached by each fibre is increasing with the
fibre extension. Withoutthis extra constraint the algorithmtends to
place large clusters in the overlapping areas of neighbouring fields
where, although there are more available fibres because of the
overlap, it rapidly becomes impossible to use these fibres because
of the high density of targets close to the edge of each field.
Limiting the number of targets within each sector effectively
removesthis problem,andso increases theuniformity ofthe survey
completeness.
The adaptive tiling algorithm also needed to cope with the
requirement that the galaxy redshift survey be merged with the
concurrent survey of QSO candidates (the 2dF QSO Redshift
Survey: Boyle et al. 2000; Croom et al. 2001). This results in a
higher surface density of targets in the region of overlap, forwhich
we compensate by reducing the separation in declination of the
tiling strips in the QSO surveyregions to 75 per cent of the original
value (i.e., to 18: 125). As the QSO survey occupies the central
declination strip of our SGP survey region this results in a 3–4–3
arrangement of tiling strips over the three rows of UKST fields
usedin theSGP survey. Asimilarconsideration appliedto theNGP
surveyregion gives a 3–4 arrangement if we consider the full areas
of the two rows of UKST fields used.
With these additional modifications, our tiling algorithm was
Figure 3. The distribution of extinction corrections A
b
J
with Galactic
latitude b (dots and left axis), and the fraction of corrections larger than a
given value (line and right axis).
2dFGRS: spectra and redshifts 1043
q 2001 RAS, MNRAS 328, 1039–1063
Downloaded from https://academic.oup.com/mnras/article-abstract/328/4/1039/1082731 by California Institute of Technology user on 20 May 2020

Frequently asked questions

Q1. What contributions have the authors mentioned in the paper "The 2df galaxy redshift survey: spectra and redshifts" ?

This paper describes the survey design, the spectroscopic observations, the redshift measurements and the survey data base. 8 per cent, but this varies with magnitude from 99 per cent for the brightest galaxies to 90 per cent for objects at the survey limit. 

Q2. What is the effect of the close packing of the fibres on the detector?

The close packing of the fibres on the detector means that their spatial profiles overlap, producing cross-talk between neighbouring spectra. 

Q3. What is the spectra that is not a fluxcalibrated?

The spectra, which are not fluxcalibrated, are finally multiplied by a simple quadratic approximation to the mean flux calibration correction in order to give appropriate weighting across the whole spectral range. 

Q4. How many unallocated fibres can be assigned?

If no unallocated fibres can be assigned the authors repeat this process recursively until one of the following conditions have been satisfied: either (i) a previously unallocated fibre is allocated (implying that u has been allocated and that all previously allocated targets remain allocated), or (ii) the search exceeds a depth of 10 iterations. 

Q5. What is the average rms residual for the spectral range?

The final fits usually include 21–22 lines over the 4400-Å spectral range, and have typical rms residuals of 0.3 Å (0.07 pixels). 

Q6. What is the smallest and homogeneous set of radio-source spectra?

Using 20 per cent of the full 2dFGRS area, Sadler et al. find 757 optical counterparts for NVSS sources – the largest and most homogeneous set of radio-source spectra to date. 

Q7. Why is the slit block not precisely reproducible?

This is necessary because the positioning of the slit block is not precisely reproducible, so that the locations of the fibres on the CCD can change by a few pixels, and occasionally the first or last fibre may fall off the edge of the detector. 

Q8. How many unallocated fibres are allocated to blank sky positions?

After this correction to the configuration, a number of unallocated fibres (at least 10 for each spectrograph) are allocated to blank sky positions. 

Q9. How does the algorithm compensate for the higher surface density of targets in the region of overlap?

This results in a higher surface density of targets in the region of overlap, for which the authors compensate by reducing the separation in declination of the tiling strips in the QSO survey regions to 75 per cent of the original value (i.e., to 18: 125). 

Q10. What is the rms precision of single measurements?

Table 1 gives the rms precision of single measurements as a function of redshift quality class or measurement method (ABS¼ cross-correlation of absorption features; EMI¼ automatic fit to emission lines; MAN¼manual fit to features).