The VIMOS Public Extragalactic Redshift Survey (VIPERS)

14 Pages·2017·4.45 MB·English

A&A609,A84(2018) Astronomy
DOI:10.1051/0004-6361/201630114
&
(cid:13)c ESO2018 Astrophysics
The VIMOS Public Extragalactic Redshift Survey (VIPERS)
Full spectroscopic data and auxiliary information release (PDR-2)(cid:63)
M.Scodeggio1,L.Guzzo2,3,B.Garilli1,B.R.Granett2,3,M.Bolzonella4,S.delaTorre5,U.Abbas6,C.Adami5,
S.Arnouts5,D.Bottini1,A.Cappi4,7,J.Coupon8,O.Cucciati4,9,I.Davidzon4,5,P.Franzetti1,A.Fritz1,A.Iovino2,
J.Krywult10,V.LeBrun5,O.LeFèvre5,D.Maccagni1,K.Małek11,A.Marchetti1,F.Marulli4,9,12,M.Polletta1,13,14,
A.Pollo11,15,L.A.M.Tasca5,R.Tojeiro16,D.Vergani17,A.Zanichelli18,J.Bel19,E.Branchini20,21,22,G.DeLucia23,
O.Ilbert5,H.J.McCracken24,T.Moutard5,25,J.A.Peacock26,G.Zamorani4,A.Burden27,M.Fumana1,E.Jullo5,
C.Marinoni19,28,Y.Mellier24,L.Moscardini9,12,24,andW.J.Percival27
(Affiliationscanbefoundafterthereferences)
Received22November2016/Accepted28April2017
ABSTRACT
Wepresentthefullpublicdatarelease(PDR-2)oftheVIMOSPublicExtragalacticRedshiftSurvey(VIPERS),performedattheESOVLT.We
releaseredshifts,spectra,CFHTLSmagnitudesandancillaryinformation(asmasksandweights)foracompletesampleof86775galaxies(plus
4732otherobjects,includingstarsandserendipitousgalaxies);wealsoincludetheirfullphotometrically-selectedparentcatalogue.Thesampleis
magnitudelimitedtoi ≤22.5,withanadditionalcolour-colourpre-selectiondevisedastoexcludegalaxiesatz<0.5.Thispracticallydoubles
AB
theeffectivesamplingoftheVIMOSspectrographovertherange0.5<z<1.2(reaching47%onaverage),yieldingafinalmedianlocalgalaxy
densitycloseto5×10−3h3Mpc−3.Thetotalareaspannedbythefinaldatasetis(cid:39)23.5deg2,correspondingto288VIMOSfieldswithmarginal
overlaps, split over two regions within the CFHTLS-Wide W1 and W4 equatorial fields (at RA (cid:39) 2 and (cid:39) 22 h, respectively). Spectra were
observedataresolutionR=220,coveringawavelengthrange5500−9500Å.Datareductionandredshiftmeasurementswereperformedthrough
afullyautomatedpipeline;allredshiftdeterminationswerethenvisuallyvalidatedandassignedaqualityflag.Measurementswithaqualityflag
≥2areshowntohaveaconfidencelevelof96%orlargerandmakeup88%ofallmeasuredgalaxyredshifts(76552outof86775),constituting
theVIPERSprimecatalogueforstatisticalinvestigations.Forthissamplethermsredshifterror,estimatedusingrepeatedmeasurementsofabout
3000galaxies,isfoundtobeσ =0.00054(1+z).Alldataareavailableathttp://vipers.inaf.itandontheESOArchive.
z
Keywords. cosmology:observations–large-scalestructureofUniverse–galaxies:distancesandredshifts–galaxies:statistics–surveys
1. Introduction volumes of the Universe in a highly effective way, notwith-
standing a rather dilute sampling of the total galaxy population
Largephotometricandspectroscopicgalaxysurveyshaveplayed (SDSS-IIIBOSS;Alametal.2015).[Amorecompleteaccount
a key role in building our current understanding of the Uni- ofthedevelopmentofgalaxyredshiftsurveysoverthepasttwo
verse. At z ≤ 0.2, the 2dFGRS (Collessetal. 2003) and SDSS decadeswasgiveninGuzzoetal.2014].
(Yorketal. 2000; Abazajianetal. 2009) redshift surveys have TheVIMOSPublicExtragalacticRedshiftSurvey(VIPERS)
assembled samples of over a million objects, precisely charac- adopted the original broad approach of SDSS-I, transposed to
terisinglarge-scalestructureandgalaxypropertiesinthenearby the redshift range 0.5 < z < 1.2, essentially extending to a
Universeonscalesrangingfrom0.1to100h−1 Mpc.TheSDSS much larger volume of the Universe the exploration initiated
has then extended its reach, first by using luminous red galax- withsmaller-areaVIMOSprecursors,i.e.VVDS(LeFèvreetal.
ies(LRG)topushtoz (cid:39) 0.35(SDSS-II;Eisensteinetal.2011; 2013a; Garillietal. 2008) and zCOSMOS (Lillyetal. 2009).
Ahnetal. 2012), and more recently (to z (cid:39) 0.5) by using a In practice, VIPERS was conceived to obtain a large-volume,
moreheterogeneoussetofcolour-selectedobjectstotracelarge densesampleofthegeneralgalaxypopulation,characterisedby
asimple,broadselectionfunction,completetoagivenfluxlimit
(cid:63) Based on observations collected at the European Southern Ob-
within a well-defined redshift range and complemented by ex-
servatory, Cerro Paranal, Chile, using the Very Large Telescope un-
tendedphotometricinformation.
der programmes 182.A-0886 and partly 070.A-9007. Also based on
observations obtained with MegaPrime/MegaCam, a joint project of ThispaperaccompaniesthePublicDataRelease2(PDR-2)
CFHT and CEA/DAPNIA, at the Canada-France-Hawaii Telescope of the complete VIPERS data set and is organised as follows:
(CFHT), which is operated by the National Research Council (NRC)
in Sect. 2.1 we summarise the survey design and scope, which
of Canada, the Institut National des Sciences de l’Univers of the
we discussed in detail in the papers by Guzzoetal. (2014)
Centre National de la Recherche Scientifique (CNRS) of France, and
and Garillietal. (2014), which accompanied the first data re-
the University of Hawaii. This work is based in part on data prod-
lease (PDR-1); in Sect. 3 we present the final survey mask and
uctsproducedatTERAPIXandtheCanadianAstronomyDataCentre
as part of the Canada-France-Hawaii Telescope Legacy Survey, a completeness estimates, while redshift measurements are sum-
collaborative project of NRC and CNRS. The VIPERS web site is marisedinSect.4,andtheoverallpropertiesofthePDR-2sam-
http://www.vipers.inaf.it/ plearepresentedinSect.5.
ArticlepublishedbyEDPSciences A84,page1of14
A&A609,A84(2018)
2. Summaryofsurveydesignandexecution photometric catalogue (approximately 0.05 mag). As a result,
thetransitionregionfromfullrejectionoflowredshiftgalaxies
2.1. Surveydesign
to full inclusion of high redshift ones spans the redshift range
VIPERSwasdesignedtosample,atamedianredshiftz(cid:39)0.7,a 0.4<z<0.6(seeSect.3.3).
volumecomparabletotheonecoveredbyredshiftsurveysmap- Finally,stellarobjectswereremovedusingacombinationof
ping the local Universe (2dFGRS and SDSS), with a similarly two methods: for objects brighter than iAB = 21.0, stars were
highsamplingdensityofthegalaxypopulation.Toachieveuse- identified on the basis of their half-flux radius, as measured on
fulspectralqualityinalimitedexposuretimeusingtheVIMOS thei-bandCFHTLSimages;forfainterobjects,acombinationof
spectrograph(LeFèvreetal.2003b),arelativelybrightlimitof image size and SED fitting of the 5-band CFHTLS photometry
i ≤ 22.5wasadopted,andthisgeneratedtwomainissuesfor wasused(seeAppendixAofGuzzoetal.2014;andSect.2.1of
AB
efficient sample selection. At this depth, many galaxies will lie Garillietal.2014).
belowtheredshiftrangeofinterest,i.e.0.5<z<1.2(seeforex- Overall,some21%oftheobjectsinthetotalphotometriccat-
ampleLeFèvreetal.2005,2013a;Lillyetal.2009);also,itwas aloguehavebeenremovedbecausetheywereclassifiedasstars,
known from previous similar studies such as the VVDS-Wide 32%wereremovedbecausetheywereclassifiedaslowredshift
(Garillietal. 2008) that such a purely magnitude-limited sam- galaxies, and the remaining 47% became the VIPERS parent
plewouldsufferfromapproximately30%stellarcontamination. photometricsample,whichwasthensupplementedwithasmall
Here we give a brief summary of the steps taken to overcome additionalsampleofAGNcandidates,chosenfromobjectsthat
these difficulties (see Guzzoetal. 2014; and Garillietal. 2014; wereinitiallyclassifiedasstarsonthebasisofacolour−colour
forfullerdetails). criterion (see Sect. 2.2 of Garillietal. 2014). This sample con-
TheVIPERStargetselectionwasderivedfromthe‘T0005’ tributes on average 2−5 objects per VIMOS quadrant (against
release of the CFHTLS Wide photometric survey, completed about 90 galaxy targets) with negligible impact on the galaxy
and improved using the subsequent T0006 release. A prelimi- selection function. In the PDR-2 catalogue these additional ob-
narymulti-bandcatalogue,includingallobjectswithextinction- jectscanbeeasilyidentifiedandseparatedfromthemaingalaxy
correctedapparentmagnitudei ≤22.5,wasbuiltstartingfrom samplethroughanappropriatekeyword,asdescribedinSect.5.
AB
theindividualCFHTLS1-deg2tiles.Particularcarewastakento
verify the homogeneity of these original single-tile catalogues:
2.2. ImprovementsinCFHTLSphotometryduring
by analyzing the colour-colour stellar locus within each such
theconstructionofVIPERS
catalogue,wewereabletoidentifysignificanttile-to-tileoffsets
in the photometric zero-points for different photometric bands. The tile-to-tile colour shifts in the T0005 data discussed in the
To ensure that the final VIPERS parent photometric catalogue previous section were a clear evidence that the initial global
was as spatially homogeneous as possible, a tile-to-tile offset photometric calibration could be significantly improved. Such
correction to the observed colours was estimated and applied. a step forward was provided by the CFHTLS T0007 revision
AsdiscussedextensivelybyGuzzoetal.(2014),thisoffsetwas (Hudelotetal. 2012). For VIPERS, the most important fea-
obtainedbycomparingthepositionincolourspaceofthe(well- ture of T0007 compared to previous releases is that each tile
defined)stellarlocuswiththatofareferencetile(theoneover- in the CFHTLS was rescaled to an absolute calibration pro-
lappingtheVVDSF02surveyfield,LeFèvreetal.2013a). vided by a new dedicated survey of calibrators carried out at
Thehomogenisationofgalaxycoloursoverthefullareawas the CFHT. In addition, in order to ensure that seeing variations
particularly crucial for the subsequent removal of low-redshift between tiles and filters were correctly accounted for, aper-
galaxies (nominally z < 0.5), which was implemented via a ture fluxes were rescaled to allow for the seeing of each in-
colour-colourselectioninthe(r−i)vs.(u−g)plane:onlygalax- dividual tile. These aperture fluxes have then become the ba-
ieswhosecoloursobeythefollowingrelation: sis of the new photometric catalogue for VIPERS, since it has
been shown that Kron (mag auto) flux estimates provide less
(r−i)>0.5×(u−g) OR (r−i)>0.7 (1) accurate colour estimates, which lead, among other things, to
worsephoto-z’s(Moutardetal.2016b;Hildebrandtetal.2012).
areincludedintheVIPERSparentsample.Thisrelativelysim- A new photometric catalogue was therefore created, based on
plecriterion,whichwaspreferredtoamorecomplexonebased Terapix T0007 isophotal aperture magnitudes, with the addi-
onphotometricredshiftsbecauseitcouldbeeasilyimplemented tion of UV photometry from GALEX (Martinetal. 2005), and
for comparisons using other data sets, either real or simulated NIR K -band photometry from WIRCam (Pugetetal. 2004)
s
ones,wastunedusingtheVVDScompleteredshiftdata(details or from VISTA (Emersonetal. 2004), obtained as part of the
canbefoundinGuzzoetal.2014).Theeffectivenessofthecri- VIPERS Multi-Lambda Survey (VIPERS-MLS; Moutardetal.
terion is due to the fact that galaxy spectral type, as measured 2016b)ortheVISTADeepExtragalacticObservations(VIDEO;
bythestrengthoftheD4000spectralbreak,stronglycorrelates Jarvisetal.2013),respectively.Theisophotalmagnitudeswere
withthe(u−g)colour,whereasthe(r−i)onedependsstrongly thencorrectedtopseudo-totalonesusinganaperturecorrection
on galaxy redshift. Therefore when moving from blue to red for each individual object, obtained as the average of the aper-
(u−g) colour along the selection boundary one finds galaxies turecorrectionsobtainedfortheg,r,i,andK bands.Detailscan
s
of all spectral types, from the star-forming (low D4000) to the befoundinMoutardetal.(2016b).
passively evolving (high D4000) ones. On the contrary, when This new photometric catalogue became available after
moving from blue to red (r − i) colour away from the selec- VIPERS was well under way, and it was therefore decided not
tion boundary, one finds galaxies of progressively larger red- to replace the original parent VIPERS catalogue, because such
shift.However,thenaturalspreadingalaxypropertiesissome- asubstitutionwouldhaveturnedtheoriginalwell-definedmag-
whatlimitingtheeffectivenessofthecolourcriterion:galaxiesin nitudelimitintoasomewhatfuzzylimit,resultingfromtheap-
any redshift interval ∆(z) = 0.1 occupy a region approximately proximately 0.05 mag scatter in the magnitude comparison be-
0.2 mag wide in (r − i) colour, significantly broader than the tween the T0005 and T0007 photometry (at the 22.5 mag limit
intrinsic uncertainty with which this colour is measured in the ofthecatalogue).Achoicewasthereforemadetomatchthetwo
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catalogues,andtoprovideT0007photometryforalltheobjects
in the original T0005-based catalogue. The matching was car-
riedoutusingamatchcircleof0.6arcsec,whichensuresa97%
matching success rate, with an almost null incidence of mul-
tiple object matches. Although the original VIPERS catalogue
is limited to i ≤ 22.5, the matching was carried out limit-
AB
ing both the old and the new catalogue to i ≤ 23.0, to avoid
AB
the scatter at the catalogue limit to affect the resulting match.
For the small fraction of objects that could not be satisfacto-
rily matched (mostly due to small differences in the source de-
blending procedure), we computed pseudo-T0007 magnitudes:
we estimated the median offset between the T0005 and T0007
cataloguesforeachphotometricbandandeachCFHTLSparent
tile using objects with i ≤ 21.0, and added this offset to the
AB
originalT0005magnitudes(themagnitudeuncertaintywaskept
equal to the T0005 value). Areas in the photometric catalogue
withpoorquality,corruptedsourceextraction,orbrightstarsare
describedbyabinarymask,asdiscussedinSect.3.
Thesmallmagnitudedifferencesbetweenthetwocatalogues
arenotexpectedtohaveanysignificantimpactontheVIPERS
parentsampleselection.AsalreadydiscussedinSect.2.1,galax- Fig.1.TheeffectiveseeingdistributionfortheVIPERSobservations.
iesofanyspectraltypearepresentclosetotheselectionlinein TheseeingvalueisobtainedfromthemeasurementoftheFWHMsize
the colour-colour plane, and the colour span for galaxies in a ofthespectraltracesforbrightobjectsinthespectroscopicexposures.
small redshift range of ∆(z) = 0.1 is of approximately 0.2 mag
in (r −i) colour, significantly broader than the intrinsic uncer-
wavelengthrange.Thisupgradesignificantlyimprovedtheaver-
taintywithwhichthiscolourismeasuredinthephotometriccat-
agequalityofVIPERSspectra,resultinginasignificantlyhigher
alogue.Asaconsequence,weobserveasmoothtransitionfrom
redshiftmeasurementsuccessrate.
fullrejectiontocompleteinclusionintheVIPERSparentsample
ThecompleteVIPERSsurveyconsistsof288VIMOSpoint-
acrossallgalaxytypes.
ings, 192 over the W1 area, and 96 over the W4 area of the
CFHTLS,overlappingatotalskyareaofabout23.5squarede-
grees.DuetothespecificfootprintofVIMOS,failedquadrants
2.3. Spectroscopicobservations
and masked regions, this corresponds to an effectively covered
AllVIPERSobservationswerecarriedoutusingVIMOS(VIs- areaof16.3squaredegrees.Thenumberofslitsinthespectro-
ible Multi-Object Spectrograph), on “Melipal”, Unit 3 of the scopicmasksrangedfrom60to121perVIMOSquadrant,with
ESOVeryLargeTelescope(VLT)–seeLeFèvreetal.(2003b). a median value of 87, for a total of 96929 slits over the whole
VIMOS is a 4-channel imaging spectrograph; each channel (a survey. For nine pointings, observations were repeated because
‘quadrant’) covers ∼7 × 8 arcmin2 for a total field of view (a theoriginalobservationwascarriedoutundersub-optimalsee-
“pointing”)of∼224arcmin2.Eachchannelisacompletespec- ingand/oratmosphericconditions,whilefourpointingsalready
trographwiththepossibilityofinserting30 × 30cm2slitmasks observedbeforetheVIMOS2010upgradewerere-observedas
at the entrance focal plane, as well as broad-band filters or partoftherelatedre-commissioning.Overall,observationswere
grisms. The precise sizes of the quadrants are in principle all carried out starting in November 2008, and were completed by
slightlydifferentfromeachother:thefourchannelsofVIMOS December 2014. For 23 pointings (6 in the W1 area, and 17 in
all differ slightly, and they also changed with time during the theW4one)somemaskinsertionproblempreventedtheacqui-
surveydevelopment,whentheVIMOSCCDswererefurbished sition of useful spectroscopic data in one of the four VIMOS
(seebelow).Thereisalsovariationfromonepointingtoanother, quadrants, leaving some small “holes” in the survey sky cover-
e.g.duetovignettingbytheguidestarprobe.Allthesepiecesof age (see Fig. 2). These are termed “failed” quadrants. Airmass
information are quantified accurately by the mask files associ- duringtheobservationsrangedfrom1.06to1.44,withamedian
atedwiththePDR-2release,whichwediscussinthefollowing valueof1.14,whiletheeffectiveseeing(measureddirectlyfrom
section. the observed size of the reference objects used to align the VI-
The pixel scale on the CCD detectors is 0.205 arcsec/pixel, MOS masks) ranged from 0.41 to 1.21 arcsec, with a median
value of 0.78 arcsec. Figure 1 shows the distribution of these
providing excellent sampling of the Paranal mean image qual-
effectiveseeingvalues.
ity and Nyquist sampling for a slit 0.5 arcsec in width. For
VIPERS,weusedaslitwidthof1arcsec,togetherwiththe“low-
resolutionred”(LR-Red)grism,resultinginaspectralresolution
3. Skycoverage,angularselectionfunctions
R (cid:39) 220 at the centre of the wavelength range covered by this
andcompleteness
grism (i.e. ∼5500−9500 Å). In summer 2010, VIMOS was up-
graded with new red-sensitive CCDs in each of the four chan- TheVIPERSangularselectionfunctionistheresultofthecom-
nels,aswellaswithanewactiveflexurecompensationsystem. bination of several different angular completeness functions.
Thereliabilityofthemaskexchangesystemwasalsoimproved Two of these are binary masks (i.e. describing areas that are
(Hammersleyetal. 2010). The original thinned E2V detectors fully used or fully lost). The first mask (that we call the pho-
werereplacedbytwice-thickerE2Vdevices,considerablylow- tometric mask) is related to defects in the parent photomet-
eringthefringingandincreasingtheglobalinstrumentefficiency ric sample (mostly areas masked by bright stars) and the other
by up to a factor 2.5 (one magnitude) in the redder part of the (thatwecallthespectroscopicmask)tothespecificfootprintof
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Fig.2.LayoutontheskyofallpointingsthatcontributetothePDR-2finalrelease,forthetwofieldsW1andW4,superimposedonthephotometric
surveymask.ThecontoursofeachofthefourquadrantsthatcompriseallVIMOSpointingsareshowninred.Theblue(grey)areasintheback-
groundcorrespondtoareaswheretheparentphotometryiscorruptedorobservationsarenotpossibleduetothepresenceofforegroundobjects,
particularly bright stars and their diffraction spikes. Note that in this plot failed quadrants and other features introduced by the “spectroscopic
mask”arenotindicated(seeSect.3.2andFigs.3and5).
providedinsteadonaper-galaxybasis:1)withineachofthefour
VIMOSquadrantsonaverageonly47%oftheavailabletargets
satisfying the selection criteria are actually placed behind a slit
and observed, defining what we call the target sampling rate;
2) since the set of available targets is defined based on the ob-
servedcolour,asdiscussedinSect.2.1,acoloursamplingrateis
neededtokeepthisselectioneffectintoconsideration;3)varying
observingconditionsandtechnicalissuesdetermineavariation
fromquadranttoquadrantoftheactualnumberofredshiftsmea-
suredwithrespecttothenumberoftargetedgalaxies,whileour
capabilitytomeasuretheredshiftdependsonintrinsicgalaxypa-
rameters, as we shall discuss in Sect. 3.5 when introducing the
spectroscopicsuccessrate.
Detailedknowledgeofallthesecontributionsisacrucialin-
gredient for computing any quantitative statistics of the galaxy
distribution, as e.g. its first and second moments (i.e. luminos-
ity/stellar mass functions and two-point correlation functions,
respectively).
3.1. CFHTLS-VIPERSphotometricmask
Fig. 3. A 1 deg2 detail of the masks developed for VIPERS. The re-
The photometric quality across the CFHTLS images is tracked
visedphotometricmaskbuiltforVIPERScorrespondstothemagenta
withasetofmasksthataccountforimagingartefactsandnon-
circlesandcrosspatterns;forcomparison,theoriginal,moreconserva-
uniformcoverage.Weusethemaskstoexcluderegionsfromthe
tivemaskdistributedbyTerapixisshowningreen.Thequadrantsthat
survey area with corrupted source extraction or degraded pho-
makeuptheVIPERSpointingsareplottedinred.Inthebackgroundis
theCFHTLST0006χ2imageofthefield020631−050800producedby tometricquality.Themasksconsistprimarilyofpatchesaround
Terapix.Notethesignificantgaininusableskyobtainedwiththenew bright stars (BVega < 17.5) owing to the broad diffraction pat-
VIPERS-specificmask. tern and internal reflections in the telescope optics. At the core
of a saturated stellar halo there are no reliable detections, leav-
ingaholeinthesourcecatalogue,whileinthehaloanddiffrac-
VIMOSandhowthedifferentpointingsaretailoredtogetherto tionspikesspurioussourcesmayappearinthecataloguedueto
mosaictheVIPERSarea.Theothercompletenessfunctionsare falsedetections.Wealsoaddtothemaskextendedextragalactic
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sourcesthatmaybefragmentedintomultipledetectionsorthat
may obscure potential VIPERS sources. The details of the re-
visedphotometricmaskconstructionweregiveninGuzzoetal.
(2014) and a visual rendition of the two W1 and W4 masks is
given in Fig. 2, while Fig. 3 provides a zoom into a smaller
area, in particular showing the details of the custom-developed
VIPERS photometric mask, compared to the original CFHTLS
mask.
Itisimportanttostressherethatasmallfractionofspectro-
scopicallyobservedgalaxiesactuallyfallwithinregionsforbid-
denbythephotometricmask.Theseareobjectsforwhich,typ-
ically,oneofthephotometricbandshadtoolargeanerrortobe
acceptable,butwereneverthelessobservedasfillers.Assuch,in
anycomputationofspatialstatisticsthephotometricandspectro-
scopicmasksmustbeappliednotonlytoanyauxiliaryrandom
sample (as typically needed for two-point clustering measure-
ments), but also re-applied to the observed spectroscopic cata-
logue itself. This is required in order to trim these little “leak-
ages”withinafewspecificareas.
Fig. 4. Estimate of the colour sampling rate (CSR) of VIPERS The
3.2. VIPERSspectroscopicmasks plot shows the fraction of galaxies that are selected by the VIPERS
colour-colour criteria as a function of redshift, when applied to a
The general layout of VIMOS is well known, but the precise sample of galaxies from the VVDS-Deep and VVDS-Wide surveys
geometryofeachquadranthastobespecifiedcarefullyforeach (LeFèvreetal.2013a).Thisisahighlysignificanttest,giventhatthe
observation,inordertoperformpreciseclusteringmeasurements originalcolour-colourboundariestoselectVIPERStargetswerecali-
withtheVIPERSdata.Forexample,althoughitrarelyhappens, bratedonthesameVVDSdata.BothW1andW4fieldsprovidecon-
aquadrantmaybepartlyvignettedbytheVLTguideprobearm; sistent selection functions, yielding a colour selection function that is
in addition, the size and geometry of each quadrant changed essentiallyunityabovez=0.6andcanbeconsistentlymodelledinthe
transitionregion0.4<z<0.6.
slightlybetweenthepre-andpost-refurbishmentdata(i.e.from
mid-2010on),duetothedismountingoftheinstrumentandthe
technical features of the new CCDs. We therefore had to build
reproducehereforcompleteness:fromthisfigureitisquiteclear
our own extra mask for the spectroscopic data, accounting for
how the VIPERS catalogue is virtually 100% complete above
all these aspects at any given point on the sky covered by the
z = 0.6, when compared to a corresponding purely magnitude-
survey.
limitedsample.
The masks for the W1 and W4 data were constructed from
thepre-imagingobservationsbyrunninganimageanalysisrou-
tine that identifies “good” regions within those images. First, a
3.4. Targetsamplingrate
polygonisdefinedthattracestheedgesoftheimage.Themean
and variance ofthe pixels are computedin small patches at the A Multi-Object Spectrograph (MOS) survey inevitably has to
verticesofthepolygon,andthesemeasurementsarecomparedto deal with the limitation of MOS slits creating a shadow effect
thestatisticsatthecentreoftheimage.Theverticesofthepoly- in the targeting of potential sources that is strongly density-
gon are then iteratively moved inward toward the centre until dependent. In practice the high-density peaks of the projected
thestatisticsalongtheboundaryarewithinanacceptablerange galaxy density field are under-sampled with respect to the
ofthosemeasuredatthecentre.Theboundarythatresultsfrom low-density regions, because the MOS slit length imposes a
this algorithm is used as the basis for the field geometry. The minimumangularpairseparationinthespectroscopictargetse-
polygonisnextsimplifiedtoreducethevertexcount:shortseg- lection. In VIPERS, this was performed using the SPOC al-
ments that are nearly co-linear are replaced by long segments. gorithm (Bottinietal. 2005, within the VMMPS software dis-
The World Coordinate System information in the fits header is tributedbyESO),whichmaximisesthenumberofslitsobserved
usedtoconvertfrompixelcoordinatestoskycoordinates.Each in each quadrant. As a result, (a) very close pairs below a cer-
maskwasthenexaminedbyeye.Featuresduetostarsattheedge tainscalearepracticallyunobservable;(b)theangulardistribu-
ofanimagewereremoved,wigglysegments werestraightened tion of slits is more uniform than the underlying galaxy distri-
and artefacts due to moon reflections were corrected. The red bution.InVIPERS,thefirsteffectsuppressesangularclustering
lines in Fig. 3 show the detailed borders of the VIMOS quad- below a scale of 5 arcsec, producing a scale-dependent damp-
rants,describingthespectroscopicmask. ing of the observed clustering below (cid:39)1h−1 Mpc; the second
is instead responsible for a nearly scale-independent reduction
ofthetwo-pointcorrelationfunctionamplitudeabovethisscale.
3.3. Coloursamplingrate These effects and their correction are discussed in detail in the
parallelpaperbyPezzottaetal.(2017).Themethodbuildsupon
The completeness of the colour-colour pre-selection applied to
theoriginalapproachofdelaTorreetal.(2013,byup-weighting
ideally isolate z > 0.5 galaxies using the CFHTLS corrected
galaxiesonthebasisofthetargetsamplingrate(TSR),namely
photometry, has been quantified and discussed in Guzzoetal.
(2014).UsingthedatafromtheVVDSsurvey,thecoloursam-
pling rate (CSR) was estimated as a function of redshift. This 1
w = · (2)
isshowninFig.4(originallyfromGuzzoetal.2014),whichwe i
TSR
i
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Fig.5.Angulardistributionoverthesurveyareasofthetargetsamplingrate(TSR,colourscale),estimatedlocallyforeachgalaxyasdescribed
inthetext.Inthisplot,eachvaluehasbeensmoothedonascaleof2arcmintoenhancethe(inverse)relationshipoftheTSRwiththeprojected
large-scalestructureinthegalaxydistribution.
IndelaTorreetal.(2013),however,theTSRwasevaluatedonly was about 23% (Garillietal. 2008), i.e. half of what we have
onaquadranttoquadrantbasissothatallthetargetedgalaxies achieved here. We remark how the TSR essentially mirrors the
fallinginthesamequadrantareup-weightedbythesamefactor. intrinsicfluctuationsinthenumberdensityofgalaxiesasafunc-
This procedure does not recover the total missing power, since tionofpositiononthesky,andhowsinglequadrantssometimes
itdoesnotaccountfortheaboveeffectsonsub-quadrantscales. have a strong internal inhomogeneity in the sampling of galax-
Thenewcorrectiveapproachissimilar,butusesalocalTSRthat ies.
accounts much more effectively for the angular inhomogeneity
oftheselectionfunction.Thisisestimatedforeachgalaxyasthe
3.5. Spectroscopicsuccessrate
ratio of the local surface densities of target and parent galaxies
(i.e.beforeandafterapplyingthetargetselection),properlyesti- We quantify the VIPERS redshift measurement success via the
matedandthenaveragedwithinanapertureofappropriateshape spectroscopic success rate (SSR), which is defined as the ratio
and size. If we call these quantities δis and δip, then the TSRi is between the number of objects for which we have successfully
definedas measured a redshift N and the number of objects targeted
success
δs bythespectroscopicobservations Ntarget.Wedefinethesuccess
TSR = i · (3) ofaredshiftmeasurementonthebasisoftheredshiftqualityflag
i δip discussedindetailinSect.4.1;generallyweadoptthe95%mea-
surementconfidencethreshold(seeSect.4.2)andacceptflags2,
A continuous δ field is obtained, starting from the discrete sur-
3, 4 and 9 as markers of a successful measurement. Targeted
facedistribution,byfirstusingaclassicalDelaunaytessellation
objects for which the spectral extraction completely failed (of-
to get the density at the position of each galaxy, and then lin-
tenthesearespuriousobjectsinthephotometriccatalogue)are
earlyinterpolating.Thisisfinallyintegratedaroundtheposition
not counted among the targets. Additionally, we correct for the
ofeachobservedgalaxywithinarectangularaperturewithsize
stellarcontaminationbysubtractingthenumberofspectroscopi-
60×100arcsec2 to obtain the local values of δs and δp. It can
beshown(Pezzottaetal.2017)thatarectangulairapertuiremore callyconfirmedstarsNstar fromthenumeratoranddenominator.
TheSSRestimatoristherefore:
efficientlyaccountsfortheangularanisotropyinthedistribution
oftargetswithinaquadrantintroducedbytheshadowingeffect N −N
SSR= success star· (4)
oftheMOSslits. N −N
target star
TheresultingdistributionoftheTSRvaluesoverthesurvey
regions is shown in Fig. 5. Thanks to the adopted strategy (i.e. The ability to measure a redshift with confidence depends on a
havingdiscardedthroughthecolourselectionalmosthalfofthe number of factors, starting from the observing conditions for a
magnitude-limitedsamplelyingatz < 0.5),theaverageTSRof given survey pointing, and the apparent flux of a given galaxy,
VIPERS is (cid:39)47%, a high value that represents one of the spe- but also including intrinsic galaxy properties, such as its spec-
cificimportantfeaturesofVIPERS.Foracomparison,withthe tral type and redshift. The top part of Fig. 6 shows that, if we
VVDS-Wide sample, selected to the same magnitude limit, but usejustthegalaxyapparenti-bandmagnitudetoparametrizethe
withoutcolourpre-selectionandstarrejection,thesamplingrate SSR,wecannotsuccessfullyreproducetheSSRdependenceon
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Trends: i
1.2
1.0
e
at0.8
ss r0.6 CWoemigphlteetdeness
e
c Distribution
c0.4
u
S
0.2
0.0
20 22 0.8 1.6 21 18 0.8 1.6 2 4 0 1 0.6 0.8 1.0
i Photometric redshift MB MU−MV MNUV−Mr Mr−MK Q
1.2Trends: i, MB, MU−MV, Q
1.0
e
at0.8
ss r0.6 CWoemigphlteetdeness
e
c Distribution
c0.4
u
S
0.2
0.0
20 22 0.8 1.6 21 18 0.8 1.6 2 4 0 1 0.6 0.8 1.0
i Photometric redshift MB MU−MV MNUV−Mr Mr−MK Q
Fig.6.Spectroscopicsuccessrate(SSR)asafunctionofdifferentobservedphotometricproperties(bluesolidcurve),comparedtotheresultof
applyingtheweighttocorrectincompleteness(redsolidcurve).Thetworowsofplotsshowhowthecompletenesscorrectionchangeswhenone
onlyconsidersasimpleSSRdependenceontheselectioni-bandmagnitude(top),orratherincludesthemoresubtledependenciesonobserved
coloursand,inparticular,qualityofthespecificVIMOSquadrant(“Q”parameter,quantifiedviathemeanSSRforallgalaxiesinthatquadrant).
Thedifferentialdistributionofeachparameterisalsoplottedineachpanel(dashedcurve).
other parameters, such as the galaxy rest-frame colour. When figure’smiddlepanel,butallpanelsquiteclearlyshowhowthe
insteadweusemultipleparameters,includingtheapparentmag- lowestSSRvaluesarecharacteristicofgalaxieswithintermedi-
nitude,therest-framecolour,thegalaxyB-bandluminosity,and ate rest-frame colour. These are objects whose spectra contain
the overall quality of the specific VIMOS quadrant (quantified neitherstrongemissionlines(aswouldbeseeninthebluestpart
via the mean SSR for all galaxies in that quadrant), we obtain of the sample) nor a strong 4000Å break (as would be seen in
a significant improvement on the SSR capability of describing thereddestpartofthesample).Thisgeneralfeaturewasalready
the VIPERS sample, as shown in the bottom part of Fig. 6. In observed for the zCOMOS bright survey (Lillyetal. 2009, see
bothrowsofplotsinthatfigureweshowtheSSRasafunction theirFig.2).
of different observed photometric properties (blue solid curve),
compared to the result of applying the SSR weight to correct
for incompleteness (red solid curve) the total VIPERS sample. 4. Redshiftmeasurements,confidenceflags
Rest-frameproperties(galaxyluminosityandcolour)inthiscase andstatisticaluncertainties
are computed on the basis of the galaxy photometric redshift,
inordertoenabletheircomputationalsoforgalaxieswithouta Figure8showsarepresentativesetofspectraofdifferentquality,
spectroscopicredshiftmeasurement(thatenterintothedenomi- as available at the end of the automatic data reduction pipeline
natorofEq.(3)).Photometricredshiftestimatesaretakenfrom of VIPERS. This, together with the procedure for redshift val-
Moutardetal.(2016b),andhaveatypicalaccuracyofσ ≤0.04, idation,havebeenextensivelydescribedinGarillietal.(2010),
z
withafractionofcatastrophicfailuressmallerthan2%. Garillietal.(2012),Guzzoetal.(2014)andGarillietal.(2014).
Herewebrieflysummarizethelastpartofthisprocess,i.e.how
The SSR is computed adaptively using a nearest-neighbour
redshiftsaremeasuredandtheirqualityevaluated.
algorithm. Depending on which parameters we want to use to
As the final step of the VIPERS automated data-reduction
parametrize the SSR, we build an N-dimensional dataset (with
pipeline developed at INAF–IASF Milano (Garillietal. 2014),
N = 1 when we use only the apparent magnitude, and N = 4
redshiftswereestimatedusingtheEZcode(Garillietal.2010).
whenweaddalsotherest-framecolour,theluminosity,andthe
First, a set of potential emission lines is identified in the
quadrant quality); then, for each object in this N-dimensional
1-dimensionalspectrum,andalistofpotentialredshiftestimates
space, we determine the distance R to its Kth nearest neigh-
K is associated to each such line, based on a pre-defined list of
bour (we use K = 100). We then count the number of sources
typical lines observed in galaxy spectra. If two or more strong
in the successfully measured sample that are contained within
emission lines (i.e. lines detected with a signal-to-noise ratio
the radius R : N (≤R ). The SSR at the specified point is
K success K S/N > 5) give a matching redshift value, this value is kept
givenbythefractionSSR = N (≤R )/K.Distancesinthis
success K as the final measurement. Otherwise full cross-correlations be-
N-dimensionalspacearecomputedusingtherankdistancemea-
tween the 1-dimensional spectrum and a set of galaxy spectra
sure(i.e.theranksofeachparameterinthesampleareusedwhen
templates are carried out, and the 5 strongest correlation peaks
computingseparations).
are kept as potential redshift estimates. In this case the final
Figure 7 shows the bivariate distribution of SSR values as redshift measurement is associated to the galaxy template and
a function of rest-frame colour and redshift, apparent i-band redshift estimate combination that provides the best overall fit
magnitude,andrest-frame B-bandluminosity,respectively.The to the observed 1-dimensional spectrum. Finally, an estimate
mean SSR is about 83%, but it is clear from this figure that of the redshift measurement reliability is obtained by repeating
complexSSRvariationsexistasafunctionofgalaxyproperties. thecross-correlationoftheobservedspectrumwiththebestfit-
An obvious apparent magnitude trend is clearly visible in the tingtemplate,limitedtoapre-definedsetofwavelengthranges
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A&A609,A84(2018)
Fig. 7. 2D plots of the SSR in the photometric parameter space. We show the dependence on the rest-frame U −V colour jointly with three
photometric parameters: photometric redshift (left), apparent i-band magnitude (center), and rest-frame B-band magnitude (right). The solid
contourscontain10,50,90and99%ofthesample.
Fig.8.ExamplesofVIPERSspectra:onelate-typeandoneearly-typegalaxyspectrumisshownforthedifferentredshiftmeasurementquality
flags.Themeasuredredshiftforallobjectsisclosetoz=0.7,thepeakoftheVIPERSredshiftdistribution.
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M.Scodeggioetal.:TheVIMOSPublicExtragalacticRedshiftSurvey(VIPERS)
where,dependingonthetemplateandtheredshiftmeasurement,
wecanexpecttoobservethestrongestspectralfeatures(Balmer-
seriesHydrogenlinesandOxygenlinesforlate-typetemplates,
D4000,CaH+K,G-bandforearly-typetemplates).
These measurements are then reviewed by two team mem-
bersindependently,usingEZininteractivemodethroughauser-
friendly dedicated interface. If the automated measurement is
obviously correct, nothing is modified, and the measurement is
stored in the final VIPERS database. Otherwise, the full mea-
surementprocedureisre-runbythereviewer,untilasatisfactory
redshiftestimateisachieved.Theresultsofthetworeviewsare
eventually matched, and in case of disagreement the full set of
spectroscopicinformationavailable(includingtheoneandtwo-
dimensional spectra, the sky background spectrum, and all the
cross-correlationresults)isvisuallyexaminedbythetworeview-
erstogether,untilagreementisreachedonamostlikelyredshift
estimateanditsassociatedqualityflag.
AllredshiftmeasurementspresentedinthePDR-2catalogue
are as observed and have not been corrected to a heliocentric
or Local-Group reference frame. Information to perform these
corrections is nevertheless contained in the FITS header of the
spectra.
Fig.9.QualityoftheVIPERSredshiftmeasurementsfordifferentred-
4.1. Redshiftqualityflags shifts.Specifically,theplotshowshowthefractionofmeasurementsfor
differentqualityflagschangesasafunctionofredshift.Notehowthe
ThequalityflagsystemadoptedbytheVIPERSsurveyhasbeen “reliablesample”,i.e.thatwithqualityflag≥2,tobeusedforstatistical
inspired by and is in fact very close to those of other precur- analyses,showsastablemeasuredfractionouttothelimitofthesurvey.
sor surveys (e.g. LeFèvreetal. 2005; Lillyetal. 2009). The
meaning of the various flags has been described in detail in
Garillietal.(2014)andGuzzoetal.(2014);herewerepeatthe 4.2. Updatedestimateofredshiftreliability
meaningoftheflagsforthoseobjectsreleasedwithPDR-2:
AswasdoneforPDR-1,weestimateredshifterrorsbycompar-
ing independent redshift measurements that are available for a
– Flags 4.X and 3.X: highly secure redshift, with confidence subset of galaxies. Some VIPERS targets were observed more
>99%. than once within the survey, or are in common with other sur-
– Flag2.X:stillfairlysecure,>95%confidencelevel. veys.Thisalsogivesusawaytoquantifytheconfidencelevelof
– Flag1.X:tentativeredshiftmeasurement,with∼50%chance ourqualityflags.
tobewrong. Attheendofthesurvey,thetotalnumberoftargetswithre-
– Flag 9.X: redshift based a single emission feature, usually peatedobservationsis3556,comparedto1941thatwereavail-
[OII]3727Å.WiththePDR-1dataweshowedthatthecon- ableatthetimeofPDR-1.For3114ofthese,tworedshiftmea-
fidencelevelofthisclassis∼90%. surementsareavailable,includinganyvalueforthequalityflag
(seeTable1).
After the human validation procedure has produced the integer Considering the distribution of the differences between the
part of the redshift quality flag, a decimal fraction is added to tworedshiftmeasurements∆z,wedefinematchingpairsasthose
it,withpossiblevalues0.2,0.4,0.5,toindicaterespectivelyno, that satisfy the condition |∆z| < 0.005. This threshold has been
marginal or good agreement of the spectroscopic measurement set on the basis of the first visible gap in the ∆z distribution.
with the object photometric redshift (see Guzzoetal. 2014, for This identifies 2626 matching pairs (i.e. a matching fraction of
the specific criteria defining this agreement). If no photometric 84%).Thissamplestillincludessomeredshiftswithqualityflag
redshiftexistsforthatobject,thedecimalpartissetto0.1. 1,i.e.redshiftswithconfidencelevel∼50−60%(seeGuzzoetal.
A“1”infrontoftheaboveflagsindicatesabroadlinesAGN 2014), which are in general not reliable for statistical analyses
spectrum,whilea“2”indicatesasecondobjectserendipitously and have been excluded from all VIPERS investigations so far.
observedwithintheslitofaVIPERStarget. Restrictingconsiderationtopairswithbothflag2.Xorabove(i.e
In all VIPERS papers, objects with a redshift flag between thereliablemeasurements),thematchingfractionrisesto92.3%
2.X and 9.X are referred to as reliable (or secure) redshifts (2275outof2466).Evenfurther,ifweconsideronlyflagseither
and are the only ones normally used in the science analyses. 3.Xor4.X,i.e.thehighestqualityspectra,thematchingreaches
In Garillietal. (2014) we discussed in detail the reliability of 99.1%(1238outof1249).UsingEq.(7)inGarillietal.(2014),
flag9.Xobjects.InFig.9thefractionofredshiftmeasurements wecanemploythesefigurestoestimatetheaverageconfidence
withagivenqualityflagisshownasafunctionofredshift,lim- levelofsinglemeasurementsinthereliableredshiftsample
itedtothemainredshiftrangecoveredbytheVIPERSsample. √
Noticehowthehighestqualitysubsetofredshiftmeasurements Cflag≥2 = 0.923=96.1%, (5)
is always the largest one in the survey, up to z (cid:39) 1.2 and also
how, very importantly, the fraction of measured redshifts with andtheoneofthehigh-qualityredshifts
flag2.Xorlarger(i.e.thereliablesampletobeusedforscience √
investigations)isessentiallyconstantouttoatleastz=1.2. C = 0.991=99.54%, (6)
flag3,4
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A&A609,A84(2018)
Table1.Statisticsofdoubleredshiftmeasurements,bothinternaltotheVIPERSsampleandagainstexternaldata.
√
Sample N N Matching σ (∆z/(1+z)) σ =σ / 2 σ =cσ Mean∆v
gal agree 2 z 2 v z
(%) (kms−1) (kms−1)
InternalComparison
Allmeasurements 3114 2626 84.3% 0.00079 0.00056 166 –
Bothflags≥2 2466 2275 92.3% 0.00077 0.00054 163 –
Bothflags3,4 1249 1238 99.1% 0.00075 0.00053 159 –
Bothflags≥2;faint – 1099 – 0.00077 0.00055 164 –
Bothflags≥2;bright – 336 – 0.00071 0.00050 150 –
Bothflags≥2;weakEL – 1153 – 0.00079 0.00056 167 –
Bothflags≥2;strongEL – 508 – 0.00066 0.00046 139 –
ExternalComparisonwithVVDS
Allmeasurements 737 629 85.3% 0.00093 0.00066 198 26
Bothflags3,4 358 350 97.8% 0.00083 0.00059 177 40
ExternalComparisonwithBOSS
Allmeasurements 747 736 98.5% 0.00064 0.00045* 136* −108
VIPERSflags3,4 690 684 99.1% 0.00061 0.00043* 130* −113
Notes. ThisisprobablyanunderestimateoftheuncertaintyontheVIPERSside,becausetheassumptionofuncertaintyequipartitiondoesnot
fullyapplyintheBOSScomparison.
which agrees very well with the value obtained in Guzzoetal. the redshift measurement uncertainty. For PDR-1 we adopted
(2014)andGarillietal.(2014)usingthePDR-1data. thecommonassumptionthatredshiftuncertaintiesscalewiththe
Comparable results are obtained when comparing the redshiftitselfas(1+z).Thisassumptionwouldapplyinthesim-
VIPERS measurements to external data. The VIPERS sky ar- ple case of a spectrograph that yields spectra with a resolution
eas have a non negligible overlap with the VVDS Wide F22 andsensitivitythatareconstantandindependentofwavelength,
sampleGarillietal.(2008,844galaxies)andtheBOSSsample butneitherofthesecriteriaaresatisfiedbyVIMOSspectra.The
(Dawsonetal.2013;751galaxies).Theresultsofthesecompar- spectrum signal-to-noise ratio is influenced by the observing
isonsareshowninTable1.Notethesignificantlyhighermatch- conditions, but is nevertheless mostly driven by the galaxy ap-
ingfractioninthecaseofBOSS.Thisiseasilyunderstoodwhen parentmagnitude.Thisinturndepends(albeitwithasignificant
consideringthatBOSSCMASSgalaxieshaveamagnitudelimit scatter)onthegalaxyredshift,andthereforemustinducesome
brighterthani(cid:39)20andsoallmatchesmustcorrespondtobright increase of the redshift measurement error with redshift. Also,
VIPERS galaxies. Not surprisingly, then, the matching fraction whenredshiftsaremeasuredthroughcross-correlationwithtem-
inthiscaseiscomparabletothatofthehighestqualityVIPERS plates,asinthecaseofVIPERS,somescalingoftheuncertainty
class. withredshiftcouldbeexpectedbecauseofthe(1+z)shrinking
oftheavailablerest-framewavelengthrange(althoughwhenthe
redshiftmeasurementisdominatedbyafewkeyfeaturesinthe
4.3. Updatedestimateofredshifterrors spectrum,whichremainobservableovermostofthesurveyred-
shiftrange–e.g.the[OII]λ3727lineand4000Åbreakregion–
An accurate knowledge of the typical redshift measurement thiseffectshouldbenegligible).Inshort,aredshiftdependence
uncertainty is clearly important for the scientific analysis of of the measurement error can be expected, but not necessarily
the VIPERS sample, in particular when modelling the ob- withalineardependenceon(1+z).
served shape of the power spectrum or the effect of Red- The observed distribution of ∆z values as a function of
shift Space Distortions (see the parallel papers by Rotaetal. galaxyredshiftisshowninFig.10,limitedtothematchingpairs
2017;delaTorreetal.2017;Pezzottaetal.2017;Wilsonetal., of measurements. Using these data points, we have determined
in prep.). It is also important to probe the possible redshift de- thescatterinboththe∆zandthe∆z/(1+z)valueswithinsepa-
pendence of this uncertainty. We have used the repeated red- rateredshiftbins,stillusingtheMADestimatorasforthewhole
shift measurements discussed in the previous section to up- sample.TheresultsofthisestimateareshowninFig.11,where
datetheestimateoriginallypresentedinGuzzoetal.(2014)and itisclearlyseenthattheobservedscatterofthe∆z/(1+z)dif-
Garillietal.(2014).Toobtainarobustestimateofthemeasure- ferences is substantially constant, whereas the scatter of the ∆z
menterrorweusedthematchingpairsofmeasurements(asde- differences increases with the median redshift of the bin, with
finedintheprevioussection),computedthemedianabsolutede- a scaling that is roughly proportional to (1 + z). We therefore
viation (MAD) of the ∆z values, and scaled it to the standard conclude that this simple scaling does after all provide an ad-
deviationequivalent,whichforaGaussiandistributionisgiven equate description of the effective uncertainty of the VIPERS
byσ=1.4826×MAD.Theresultingscatter,whenweconsider redshift measurements. We do not extend this exercise to red-
onlyreliableredshiftmeasurements(qualityflag2.Xandabove, shiftsabove1.1,becauseofthelimitednumberofrepeatedmea-
2275 pairs), is σ∆z = 0.0013. A very similar result is obtained surementsavailableatthoseredshifts.Thefinalestimateweob-
byfittingaGaussiantothedistributionof∆zvalues. tainforthesingleredshiftmeasurementuncertaintyistherefore
With the current large set of duplicate measurements, we σ = 0.00054×(1+z),whichwecancomparewiththefigure
z
can also re-consider the overall approach used to characterise ofσ =0.00047×(1+z)giveninthePDR-1paper(onthebasis
z
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