Photo-z Performance for Precision Cosmology II : Empirical Verification

0.21 MB·English

by  R. Bordoloi

Mon.Not.R.Astron.Soc.000,1–??(—-) Printed6January2012 (MNLATEXstylefilev2.2)
z
Photo- Performance for Precision Cosmology II :
⋆
Empirical Verification
2
1 R. Bordoloi,1† S. J. Lilly,1 A. Amara,1 P. A. Oesch,1,2 S. Bardelli,3 E. Zucca,3
0
2 D. Vergani,4,3 T. Nagao,5,7 T. Murayama,6 Y. Shioya5 & Y. Taniguchi5

n 1Institute for Astronomy, ETH Zu¨rich, Wolfgang-Pauli-Strasse 27, CH-8093, Zu¨rich
a 2UCO/Lick Observatory, Department of Astronomy and Astrophysics, Universityof California, Santa Cruz, CA 95064
J 3INAF Osservatorio Astronomico di Bologna, Bologna, Italy
4 4IstitutoNazionale diAstrofisica -Istitutodi Astrosica, Spaziale eFisica Cosmica Bologna, viaP.Gobetti 101, I-40129 Bologna, Italy
5Research Centerfor Space and Cosmic Evolution,Ehime University,Bunkyo-cho, Matsuyama 790-8577, Japan

] 6Astronomical Institute, Graduate School of Science, Tohoku University,Aramaki, Aoba, Sendai 980-8578, Japan
O 7The Hakubi Project, Kyoto University,Yoshida-Ushinomiya-cho, Sakyo-ku, Kyoto606-8302, Japan
C
.
h
p Accepted —-.Received—-;inoriginalform—-
-
o
r
t ABSTRACT
s
The success of future large scale weak lensing surveys will critically depend on the
a
[ accurateestimationof photometric redshifts of verylargesamples of galaxies.This in
turndependsonboththequalityofthephotometricdataandthephoto-z estimators.
1
In a previous study, (Bordoloi et al. 2010) we focussed primarily on the impact of
v
photometricqualityonphoto-z estimatesandonthe developmentofnoveltechniques
5
to construct the N(z) of tomographic bins at the high level of precision required for
9
precision cosmology, as well as the correction of issues such as imprecise corrections
9
0 for Galactic reddening. We used the same set of templates to generate the simulated
. photometry as were then used in the photo-z code, thereby removing any effects of
1
“template error”.In this work we now include the effects of “template error”by gen-
0
eratingsimulatedphotometricdatasetfromactualCOSMOSphotometry.Weusethe
2
trick of simulating redder photometry of galaxies at higher redshifts by using a bluer
1
: setofpassbandsonlowz galaxieswithknownredshifts.Wefindthat“templateerror”
v isarathersmallfactorinphoto-z performance,atthephotometricprecisionandfilter
i
X complementexpectedforall-skysurveys.Withonlyasmallsub-setoftraininggalaxies
with spectroscopic redshifts, it is in principle possible to construct tomographic red-
r
a shiftbins whosemeanredshiftis known,fromphoto-z alone,to the requiredaccuracy
of |∆<z>|60.002(1+z).
Key words: galaxies: distances and redshifts- cosmology: observations- methods:
Statistical
1 INTRODUCTION havea depthof IAB 624.5, and contain multi-band photo-
metricmeasurementsoftheorderof∼109galaxiesovera2π
In the coming years, the next generation of all sky surveys
srsurveyarea.Theuseofthesesurveysforprecisioncosmol-
plan to map the whole extragalactic sky in visible & near
ogyandformanyothertypesofsciencewillrequiretheuse
infra-redphotometricbands.Inordertoachievetheperfor-
of photometrically-estimated redshifts (hereafter photo-z).
mance required for precision cosmology, such surveys will
The use of photo-z for precision cosmology, e.g. in weak-
lensing tomography (Hu 1999), will require an impressive
performance from the photo-z, not only in statistical accu-
⋆ Based on observations undertaken at the European Southern racy per object, but especially in the control of systematic
Observatory(ESO)VeryLargeTelescope(VLT)underLargePro- biases in themean redshifts of sets of galaxies used for cos-
gram 175.A-0839. Also based on data collected at Subaru Tele- mologicalanalysis.Itiseasytoderivethataprecisionof1%
scope,whichisoperated bytheNational AstronomicalObserva- inthedarkenergyequationofstateparameter(w),requires
toryofJapan.
† E-mail:[email protected]
2 R. Bordoloi et al.
knowledge of the redshifts of the probes with a systematic 1
accuracy of 0.002(1+z).
In a previous paper (Bordoloi et al. 2010) (hereafter
BLA-10), we simulated the photometric redshift perfor- 0.8 g r i z Y J H
mance for a numberof different photometric depths. These
were defined as a combination of a Euclid-like infrared sur-
n
vey (Refregier et al. 2010), complemented with additional o0.6
si
ground-basedphotometryinthevisiblewaveband.Artificial s
mi
photometriccataloguesweregeneratedfromthemockCOS- s
n
MOS light-cone catalogues of Kitzbichler & White (2007) a0.4
Tr
andphoto-z ofgalaxies wereproducedusingatemplatefit-
ting code ZEBRA (Feldmann et al. 2006). We deliberately
usedexactlythesamesetoftemplatestoconstructthesim- 0.2
ulatedphotometryaswerethenusedinZEBRAtoestimate
thephoto-z.Thischoiceeliminatedtheeffectsof“template-
error” onthephoto-z,byconstruction,allowing ustofocus 0
on other issues. We argued in BLA-10 that the exceptional 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8
performanceofphoto-zinCOSMOS(seeIlbert et al.2009), λ (Å) x 104
wheredeepphotometryisavailableinalargenumberoffil-
ters,suggestedthattemplateerrorwasunlikelytobeadom- Figure1.ActualCOSMOSfilterresponsecurves,aftertransfor-
mationbyafactorof1.38inwavelength(asdescribedinSection
inant factor with the poorer and more limited photometric
2.3), compared with the nominal top-hat filters used in BLA-10
datathatcanrealisticallybeanticipatedoverthewholesky.
tosimulateanall-skysurveycombiningground-andspace-based
However, that analysis nevertheless represents an idealized
data.Thereisareasonablematchinspacingandwidth.Sincethe
situation, and a certain “circularity” of the argument. In current photo-z analysis used these transformed filter response
thispaperweaim torectify thisshortcoming bybasing the curves,thedifferencesshouldnotbeimportant.
simulated photometry on actual photometric data.
Clearly, the ideal approach would be to take already
availablephotometrythatwascomparabletothatwhichwill photo-zareestimatedandfinallyinSection4howtheyper-
be available for the all-sky surveys, estimate the photo-z, form. Much of the performance analysis follow closely the
andcomparetheperformancewithacompletesetofreliable approachofBLA-10towhichthereaderisreferredformore
spectroscopically-determinedredshifts.However,atpresent, details.
thereisnophotometricsurveythatgivesnear-infraredpho-
tometryatthedepthenvisagedfore.g.Euclid(Y,J,H =24
at5σ(Refregier et al.2010)),noristhereasufficientlycom-
pletespectroscopicsamplethatextendsdowntoIAB 624.5, 2 CREATING THE MOCK CATALOGUE
where the redshift distribution extends well into the “red-
Our goal is to simulate a realistic photometric survey con-
shift desert” at z>1.2.
sistingofvisiblephotometryofthedepthandfiltercoverage
Wecanhoweverperformthefollowingtrick.Tofirstor-
of planned surveys. In BLA-10, we defined three nominal
der, the photo-z performance that we are interested in, i.e.
surveys that were defined by increasing photometric depth
on galaxies at some redshift using some given set of filters
in thevisible, combined with NIRphotometry of thedepth
atsomephotometricdepth,canbesimulatedusingphotom-
expected from the proposed Euclid survey. The second of
etry on a set of brighter galaxies at slightly lower redshifts
these, Survey B, which we argued had just sufficient per-
using a bluer set of filters. These photo-z can also then be
formance, was intended to simulate the depth of the Pan-
tested on a brighter spectroscopic sample at more benign STARRS-21 or DES2 surveys. For precise comparison with
(lower) redshifts. We argue below that degraded uBVrizJ
theresults ofBLA-10, weusethissame intermediatedepth
photometricdatafromCOSMOS,plushighqualityredshifts
SurveyB for the present analysis.
fromthezCOSMOS-brightredshiftsurvey(Lilly et al.2007,
2009) at V 622.5 and 0.2 < z <1.0 are well-matched (in-
cludingin intrinsic luminosity) to asurvey at 0.7<z<1.8
2.1 Input photometric data
with IAB 6 24.5, i.e. with a change in (1+z) of a factor
∼1.4.Ofcourse,theprocessisnotperfect:itmightbethat WeusetheCOSMOSphotometriccataloguewhichcontains
templates (even at similar luminosities) become pathologi- fluxes measured in 30 bands from Subaru, HST, CHFT,
cal between 0.2<z <1.0 and 0.7<z <1.8 but there is in UKIRT,SpitzerandGALEXtelescopes(Ilbert et al.2009).
our view not much evidence to support this. Perhaps more We refer the reader to Capak et al. (2008) for a complete
seriously, the number density of galaxies will be artificially description of observations, data reductions and the pho-
low, by a factor of about four, so the problem of overlap- tometrycatalogue. Forourpresentpurposeweuseonlythe
ping objects that we discussed in BLA-10 will not be fully uBVrizJ broad-band filter data from this catalogue as de-
accounted for. scribed in detail in section 2.3 .
The paper is organized as follows: in Section 2 we de-
scribethephotometricandspectroscopiccataloguesthatare
usedandtheconstructionofthesimulatedphotometriccat- 1 http://pan-starrs.ifa.hawaii.edu
alogue. Then we proceed to describe in Section 3 how the 2 http://www.darkenergysurvey.org
Photo-z Performance for Precision Cosmology II 3
2.2 Input spectroscopic data 3.5
Transformed Sample
We use the spectroscopic data from the zCOSMOS sur- Initial Sample
vey (Lilly et al. 2007). We use the so-called “20k-bright” 3 Predicted Euclid N(z)
sample of 20,000 galaxies selected at IAB 6 22.5 (Lilly et
al., in preparation). These galaxies were observed with the 2.5
VIMOS/VLT spectrograph covering a wavelength range of z)
5500˚A 6 λ 6 9000˚A at a resolution of 600. The average d N( 2
accuracy of individual redshifts is 110 km s−1, irrespective ze
of redshift. mali1.5
Unfortunately, the spectroscopic sample is not 100% or
N
complete. As described in Lilly et al. 2009, each redshift in
1
zCOSMOS is assigned to a confidence class that is based
on both a subjective assessment of the reliability of the
0.5
spectroscopic measurement and whether there is a broad
consistencybetweenthespectroscopicandphotometricred-
shifts, i.e. whether |∆z| < 0.08(1+z). The photo-z come 0
0 0.5 1 1.5 2
from from the full COSMOS photometric data set, as de-
Redshift
scribed in Ilbert et al. 2009. The actual reliability of the
redshiftsacrosstheconfidenceclassschemeisestimatedus- Figure2.Theredshiftdistributionsofthesamplesunderstudy.
ing the repeatability of the redshifts from duplicated spec- Thesolidlinegivesthenormalizeddistributionoftheoriginalset
troscopic observations. In the current work we only make of zCOSMOS galaxies within 0.2 6 z 6 1.0 and V 6 22.5, as
described in the text. The shaded histogram gives the normal-
use of the redshift measurements having confidence classes
izeddistributionofthesamesetofgalaxiesaftertransformingto
( 4.x, 3.x, 9.5 + 9.4 + 9.3 + 2.5 + 2.4 + 1.5) which are
higher redshift using equation 1, spanning 0.65 < z < 1.8. For
demonstrated from therepeat observations tobe 99 % reli- comparison,thedashedlinegivesthenormalizedpredictedN(z)
able(Lilly et al.2009).Thedecimalplacesintheconfidence forIAB 624.5adoptedfromAmara&R´efr´egier2007
classsaywhetherthereisbroadagreementbetweenthespec-
troscopic and photometric redshifts, e.g. a decimal place of
.5 signifies agreement between the spectroscopic and pho- securespectroscopicredshiftsthatareinconsistentwiththe
tometric redshift estimates for that object, otherwise they photo-z, are in fact wrong spectroscopic identifications. If
donotagree.Theconfidenceclassesmarked4.xand3.xare thefraction of real “catastrophic failures” in the photo-z is
objects with verysecurespectroscopic redshifts irrespective notcorrelatedwiththesuccessinmeasuringaspectroscopic
of their photometric redshifts. redshift, then the number of such failures would be under-
As detailed below, we restrict the redshift range of the estimated in the current sample by 20%, i.e. of order 0.2%
sampleto0.2<z <1.0andselectgalaxiestohaveV 622.5. in the overall sample, which we believe is unimportant for
We exclude stars and broad line AGN from their spectro- thecurrent purposes.
scopic flags (as they are point sources, they can be photo- This point does however emphasize the need to have
metrically identified and will not be used in a weak lensing large spectroscopic samples in the future with very high
analysis). Reliableredshifts(asdefinedabove)areavailable completeness in securing highly reliable redshifts if photo-z
for83.5%oftheremaininggalaxies.Ofthese,80%havevery schemes are to be adequately tested and characterized at
secureredshifts(99.5% reliable)basedonthespectraalone. the levels of precision required. With this caveat in mind,
The remainder haveless secure spectroscopic redshifts that the present purposes are nevertheless served by the avail-
aretrustedonlybecausetheyareconsistentwiththephoto- able spectroscopic sample.
z. Clearly, any of these galaxies which have a pathological
spectral energy distribution yielding a wrong photo-z will
2.3 Generating the mock photometric catalogues
have been excluded from our sample. However, any such
pathological objectsforwhich wesecuredareliableredshift As outlined above, we assume that bluer photometry of
from the spectrum alone would be included and would be lower redshift galaxies (at 0.2 < z < 1.0) can be used as
a “catastrophic failure” in the photo-z. It should be noted asubstituteforredderphotometryof higherredshift galax-
that the most secure spectro-z have a catastrophic failure ies. Specifically, we take actual broad band uBVrizJ pho-
rate in photo-z of about 1%. tometry from COSMOS to mimic the grizYJH bands for
It should be recognized that this procedure, which we thesimulated data. Asshown in Figure-1,thisbroadly cor-
cannotavoid,meansthatthecurrentanalysismayunderes- responds to a multiplicative transformation in wavelength
timatethenumberof“catastrophicfailures”inthephoto-z, given by λ′ = δλ, with δ ∼ 1.38. The match is naturally
and thus the photo-z quality, in the overall sample if the not perfect, but this should not matter since we will use
incidence of failure, or the photo-z error, are in some way the transformed COSMOS filter passbands in the photo-z
correlated with the difficulty of measuring a purely spec- code and it is unlikely that the precise location of photo-
troscopicredshift (Hildebrandt et al.2008).Asdiscussedin metric bands affects the photo-z performance. In Figure-1
Lilly et al. (2007) there is in fact a very good correspon- the vertical shaded regions give the wavelength ranges of
dence between the spectroscopic repeatability of the red- thefiltersofSurveyB,whilethecurvesrepresentthebroad
shifts and the fraction of objects with consistent photo-z, band COSMOS filters after the above wavelength transfor-
indicating that the vast majority of the objects with less mation. Given that the match is not perfect, the photo-z
4 R. Bordoloi et al.
performance obtained in this paper should therefore not be 0.15
regarded as exact “predictions”, but rather are intended to
enable us to examine the general issue of “template error” )ot
in template fittingphoto-z codes. zph 0.1
+
shiftTtrhaisnswfoarvmelaetnigotnhotfrgaanlsafxoriemsaatsiofnollioswesq:uivalent to a red- σ (z)/(1z0.05
′
z =δ(1+z)−1 (1)
0
We first isolate all the galaxies in zCOSMOS-bright
with secure redshifts 0.2 < zspec < 1.0 which do not lie 0.05
in photometrically masked areas of Ilbert et al. (2009) and )ot
h
which have complete photometric information in the se- zp 0
+
lected bands. Since essentially all IAB 622.5 galaxies have z)/(1 −0.05
(V −I)AB >0wecanassumethatthissamplewillbecom- ∆ (z
plete down to V 6 22.5 and we retain only these galaxies. −0.1
Thisgivesusasampleofapproximately8500galaxiesdown
to V 622.5. 0.6 0.8 1 1.2 1.4 1.6
z
To convert theavailable COSMOS photometry to sim- phot
ulateSurveyBwerenamethefiltersuBVrizJ togrizYJH
Figure 3.Theoverallphoto-z performanceforSurveyBdepth,
and add 2.0 magnitudes to all the photometric measure-
basedonasingle“maximumlikelihood”photo-z foreachgalaxy.
mentsofeachgalaxy.Thiscreatesafainterphotometriccat-
Thebluelinegivestheinitialperformancewithoutanycleaning,
aloguethatshouldbecompleteinthe“transformedI-band”
the green line after “a priori”cleaning, which eliminates almost
to Itr,AB 624.5. The filter response curves are carried over 20% of galaxies, and the red line gives the performance after
by shifting thewavelengths bya factor 1.38. cleaning and after generating the probability distribution func-
Finally we apply the above redshift transformation to tionsfromthelikelihoodsasinBordoloietal.(2010).ThisFigure
allthespectroscopicredshifts.Thisproducesanewredshift shouldbecomparedwithFigure-2inBordoloietal.(2010).
distribution between 0.65<z<1.8 thatis well matched to
that expected,at z>0.65, for an IAB 624.5 sample in the
sky.ThisisshowninFigure-2wherethedashedlinegivesthe shifts since the dimming corresponds quite closely to the
normalized predicted redshift distribution for an I 6 24.5 change in distance modulus. Changes in metallicity and in
sample, with a median redshift zmedian =0.9,adopted from theoverallspecificstar-formationratesarecertainlypresent
Amara & R´efr´egier 2007, compared with the redshift dis- between these redshifts (Lilly et al. 1996; Elbaz et al. 2007;
tribution of the original V 6 22.5 zCOSMOS sample and Daddiet al. 2007) but are not dramatic. Mannucci et al.
the “transformed” IAB 6 24.5 sample. The redshift range (2010)haveshownthatgalaxiesuptoz∼2.5followafunda-
at z > 0.8 is where the performance of photo-z generally mentalmetallicityrelation(FMR)witharesidualdispersion
is less proven. Furthermore, it should be noted that the in- of∼0.05dexinmetallicity(12%)andwithnoindicationof
creased distance modulus (2.2 between z =0.2 and z =0.7 evolution with redshift. Other more practical shortcomings
and 1.6 between z = 1 and z = 1.8, allowing for a band- are that problems associated with over-lappingobjects (see
width stretching term) is well-matched to the 2.0 magni- BLA-10foradiscussion)willbelesssevere,sincetheparent
tude increase in depth between V = 22.5 and IAB = 24.5. photometriccatalogueiseffectivelybasedonbrightergalax-
Thismeansthatthetransformedsimulatedgalaxiesarewell- ies,witharoughlyfourfoldlowersurfacedensityonthesky.
matched in absolute magnitude to the lower redshift input Furthermore,thedominantuncertaintiesinthephotometry
sample. come from our added “artificial” Gaussian term.
The catalogue thus created therefore contains actual
photometric data from the COSMOS survey. As a result,
Iteffectively eliminates thecircularity problem of usingthe
3 ESTIMATING THE PHOTO-Z
same SEDs to create a mock photometric catalogue and to
estimatethephoto-z ofthegalaxies. Inviewofthe+2mag The estimation of photo-z is done in the same way as was
transformationofthemagnitudes,thenoiseintheCOSMOS done in BLA-10, using the template-fitting photo-z code
fluxdensitiesisartificially low.Wethereforeaddadditional ZEBRA(Feldmann et al.2006)tocalculatephoto-z forthe
Gaussian noise to the transformed flux densities in each galaxiesinthefinalsimulatedcatalogue.ZEBRAgivesboth
pass-band. We use the adopted survey parameters as given asinglebestfit“maximumlikelihood”redshiftandtemplate
in Table 1 of BLA-10 to define the required noise on each type, together with confidence limits based on the χ2 sur-
galaxy in each band, and add random noise in quadrature faces,andnormalizedlikelihood functionsL(z)fortheindi-
to the (known) uncertainties in the transformed COSMOS vidual galaxies. The filter response curves used in ZEBRA
photometry so as to match this required final uncertainty. for this analysis are generated from the actual COSMOS
Although it eliminates the obvious circularity of us- filter curves, shifted in wavelength by a factor of 1.38 as
ing templates to construct the catalogue, this procedure is described above.
clearlynotperfect.Itfirstassumesthatanyproblemsassoci- We stress that the templates used in this work
atedwiththetemplatesarenomoresevereat1.0<z<1.8 are purely synthetic stellar populations generated from
than they are at 0.2 < z < 1.0. As noted above, the lu- Bruzual & Charlot (2003) evolutionary models and the pa-
minosities of the galaxies are rather similar at the two red- rameters varied to compute the whole set of templates are
Photo-z Performance for Precision Cosmology II 5
4 theirrespectivepdfs.Somesetofgalaxieswithknown(spec-
troscopic)redshiftsisthereforeusedtoconstructamapping
3.5 between L(z) and L(z) which is assumed to be the same,
incumulativeprobabilityspace, forall galaxies. Thereader
3 is referred to BLA-10 for details of this algorithm, and the
mapping of L(z) to L(z) is given by the equation 12 and
z)2.5 shown in Figure 3 of BLA-10. In the current simulation,
N(
d thistransformation isconstructedusingarandomsubsetof
alize 2 ∼10%ofthetotalsample,(i.e.oftheorderof103 galaxies),
m theremaining 90% then serving as a test.
Nor1.5 In weak lensing tomography using photo-z, there are
two principal requirements. First, the photo-z of individ-
1
ual galaxies must be known to a precision of about σz <
0.05(1+z) in order that tomographic bins can be defined
0.5
without significant overlap, thereby reducing the effects of
“intrinsic alignments”. Second, and more demanding, the
0
N(z)ofeachofthesebinsmustbeknownaccuratelyforthe
0.6 0.8 1 1.2 1.4 1.6 1.8 2 2.2 2.4
z correct quantitative interpretation of the lensing signal. It
isfoundthat themean oftheN(z) isthemost relevant pa-
Figure 4. Examples of reconstructed N(z) for maximum like- rameter (Amara & R´efr´egier 2007). Hence we quantify our
lihood redshifts (blue) after “a priori” cleaning of outliers, sum
results in terms of this quantity. As noted above, to attain
of the uncorrected likelihood functions (green) and sum of pdfs
aprecisionoforder1%onthedarkenergyequationofstate
obtainedbyapplyingastatisticalcorrection(red).Thefilledhis-
togram represents the true N(z) of the tomographic bin. The parameter, w, the mean of the N(z) for each redshift bin
mustbeknown toan accuracy of 0.002(1+z),and wetake
verticallinesshowthemeanredshiftforeachreconstruction.The
sum of pdfs (red) represent the best reconstruction of the true thisas ournominal requirement.
N(z). As in BLA-10, we first look at the use of a single
“maximum-likelihood” photo-z for each galaxy. In Figure-
3 we plot the r.m.s. dispersion σz(z) and the mean bias
age, star formation history (continuousunderlyingSFR su- ∆z(z) derived from individual galaxies by comparing the
perimposed with single or multiple bursts), dust obscura- maximumlikelihoodredshiftswiththeactualredshifts.The
tion in the galaxy and stellar metallicity. These templates blue line gives the initial performance of the photo-z code,
include a range of internal reddening, which ranges from withoutanyremovalofoutliers.Thegreenlinegivestheper-
0 < Av < 2 magnitudes. Intergalactic absorption in each formance after the “a priori” identification of outliers (rec-
template is compensated for using the Madau law (Madau ognized purely from their likelihood curves, see BLA-10 for
1995). A final set of 10,000 templates are produced which details) and the red line gives the performance after modi-
are used to estimate photo-z for the simulated survey. The fyingthelikelihood functionstoproducethefinalpdfs,and
standard small adjustment of photometric zero-points was using the peaks of the pdf. It can be seen that the photo-z
undertaken (Ilbert et al. 2009), but we emphasize that the performance improves after each of these steps, although it
templates were not optimized using the COSMOS photome- should be noted that almost 20% of galaxies are lost in the
try. cleaning process - most of which would have had a quite
usable photo-z. As in BLA-10, the required σz(z) can be
achieved relatively easily.
Turningtothemoredemandingproblemoftheerroron
4 PHOTO-Z PERFORMANCE
theN(z),theuse of maximum likelihood redshifts will not,
Inthissectionweassesstheperformanceofthephotometric by definition, include the wings of the N(z) or deal with
redshiftestimatorasappliedtoourmorerealisticsimulated any catastrophic failures in the photo-z. Figure-4 shows a
photometryandquantifytheresultsincomparisonwiththe reconstructed tomographic bin for different methods. The
results of BLA-10. We follow closely theprocedures of that true N(z) (shaded histogram) is best represented by the
first paper and refer the reader to it for further technical summing of pdfs obtained by applying the L(z) to L(z)
details. transformation (red line). The mean of each reconstruction
Galaxiesarefirstbinnedinredshiftonthebasisoftheir isshown bytheverticallines and fortheabovemethod the
observed maximum-likelihood photo-z.The bias ∆z(z) and we obtain theminimum bias in the reconstruction.
dispersion σz(z), as defined in Bordoloi et al. (2010), are In Figure-5 the blue diamonds show the bias in the
computedasafunctionoftheobservedphoto-z.AsinBLA- mean of the N(z) using just the maximum likelihood red-
10,thesamplesarecleanedbyapplyingan“apriori”clean- shifts after “a priori” cleaning. The error bars are simply
ingalgorithmthatisbasedsolelyontheshapeoftheoutput calculated as the expected uncertainty in the average red-
L(z)function.Theredshiftprobabilitydistributionfunction shiftbasedonPoissonstatistics,knowingσz(z),i.e.wecould
(pdf)ofeachgalaxy,L(z),isconstructedfromitsindividual notdetectsystematicbiasesbelowthislevel.Thebiasesus-
likelihood function L(z) using the procedure described by ingthesemaximumlikelihoodredshiftsfallwellshortofthe
BLA-10.Thisisbasedontheprinciplethattherealredshifts requirement of 0.002(1+z) (shown by the shaded region)
(for those galaxies with known redshifts) should, within a and are much larger than the Poisson uncertainties in our
large enough sample, be uniformly distributed throughout simulation.
6 R. Bordoloi et al.
0.06
0.04
0.02
0
〉z
∆〈
−0.02
−0.04
−0.06 After Cleaning +Σ Maximum Likelihood photo−z
After Cleaning + Σ L(z)
After Cleaning + Modification of PDF

0.6 0.8 1 1.2 1.4 1.6 1.8
z
spec
Figure 5. The error in the mean of the N(z) for tomographic redshift bins for the simulated Survey B. The blue diamond symbols
are obtained using only the maximum likelihood redshifts, the open squares are obtained from the sum of the uncorrected likelihood
functions,andthefilledcirclesbysummingthepdfsobtainedbyapplyingastatisticalcorrection.Allthreecasesareafterthe“apriori”
removalofabout20%ofgalaxies.Theshadedregiongivesthenominalrequirementof|∆<z>|60.002(1+z).
As in BLA-10, some improvement is obtained by sum- transformation is effectively an empirical determination of
ming the individual L(z) curves to define the N(z), shown the errors on the redshifts. It is not surprising that, to go
astheredsquares,buttherequiredperformance isonly re- fromaσz ∼0.05toabiasthatis30timessmaller,requiresof
alized when we sum the individual pdfs that are obtained order302 knownredshifts,c.f.equation(2)inBLA-10.This
foreachgalaxyusingtheprocedureoutlinedabove,andde- suggests that the number of spectroscopic redshifts would
scribedinmoredetailinBLA-10.Theseareshownasblack notincreasedramaticallyasthetotalsampleofphoto-z ob-
filled circles. In this case, the error bars come from taking jects goes up.
different subsets of the spectroscopic sample to define the On the other hand, the discussion in Section 2.2 high-
L(z) to L(z) transformation. With this procedure, an un- lightsthedangersofusingaspectroscopicsamplethatisnot
certainty of 0.002(1+z) is met for each of thebins. demonstrably complete, because of lingering concerns that
Comparing Figure-3 with Figure-2 in BLA-10, it can the “catastrophic failure” rate of the photo-z, or even the
be seen that there is a degradation of performance in this statistical error σz, may be correlated with the success of
more realistic simulation compared with that of our earlier measuring a spectroscopic redshift, and therefore that the
paper.This is clearly thesignature of “template error” and set of galaxies used to set up thescheme may not be repre-
oftheotherrealisticobservationalproblemsthatarepresent sentative.Establishingthatthecalibratingsampleisinfact
in the current study through the use of actual photometric completely representative, i.e. demonstrating to a possibly
data. However, the degradation is relatively small: in order skeptical audience that the photo-z performance has been
to achieve the same performance, about 7% more galaxies met, will likely require a very muchlarger sample.
are lost due to “a priori” cleaning as compared to BLA-
10.Thismodestdegradationjustifiesourearlierassumption
thattemplateerrorwasunlikelytobeadominantfactor,at
5 SUMMARY
least with the typical S/N and number of filters expected
for foreseeable all-sky photometric surveys. This paper is the second to focus on the problem of photo-
As described above, the required performance is met z performance for weak-lensing cosmology from anticipated
withoforder1000objectstomapthistransformation. This all-skysurveys.Inapreviousstudy(Bordoloi et al.2010)we
number makes sense: In BLA-10 we pointed out the po- usedasimulated photometriccatalogue that was generated
tential reduction in the number of spectroscopic redshifts usingthesamesetoftemplatesaswerethenusedtoestimate
neededifthesewereusedtocharacterizethephoto-zscheme thephoto-z,therebyremovinganyissuesassociatedwiththe
rather than to estimate the N(z) directly. Our use of spec- choice of templates from the analysis.
troscopic redshifts to construct the L(z) to L(z) mapping To avoid this potential circularity, we have used in
Photo-z Performance for Precision Cosmology II 7
the current study a more realistic photometric catalogue Capak, P., et al. 2008, VizieR Online Data Catalog, 2284,
that has been generated by degrading actual photometry 0
of galaxies in the COSMOS field for which secure spectro- Daddi, E., et al. 2007, ApJ, 670, 156
scopic redshifts are available from zCOSMOS. In order to Elbaz, D., et al. 2007, Astronomy and Astrophysics, 468,
generateasimulatedphotometriccataloguethatextendsto 33
the required depth in the near-infrared, and to overcome Feldmann, R.,et al. 2006, MNRAS,372, 565
the paucity of spectroscopic redshifts at z > 1, we employ Hildebrandt,H.,Wolf, C., &Ben´ıtez, N.2008, Astronomy
the trick of basing the catalogue on bluer photometry of and Astrophysics, 480, 703
somewhat brighter objects at lower redshifts, in particular Hu,W. 1999, ApJL,522, L21
simulating an IAB 6 24.5 sample at 0.65 < z < 1.8 from a Ilbert, O., et al. 2009, ApJ,690, 1236
V 6 22.5 sample at 0.2 < z < 1.0. Such galaxies are well Kitzbichler, M.G. &White, S.D.M. 2007, MNRAS,376,
matched in luminosity. 2
The photo-z are estimated using synthetic templates Lilly, S. J., Le Fevre, O., Hammer, F., & Crampton, D.
with no attempt at optimization, so in this sense no spec- 1996, ApJL, 460, L1+
troscopic redshifts are formally used for calibration of the Lilly, S.J., et al. 2007, ApJS,172, 70
photo-z.About10%ofthesample(∼103redshifts)areused Lilly, S.J., et al. 2009, ApJS,184, 218
insettingupthealgorithmthatisusedtoconvertthelikeli- Madau, P.1995, ApJ,441, 18
hood functions to probability distribution functions, which Mannucci, F., Cresci, G., Maiolino, R., Marconi, A., &
is essential for the accurate estimate of the mean redshifts. Gnerucci, A.2010, MNRAS,408, 2115
Wesuspectthatitisthetotalnumberandnotthepercent- Refregier, A., Amara, A., Kitching, T. D., Rassat, A.,
agewhichwillberelevantifthisapproachisappliedtomuch Scaramella,R.,Weller,J.,&EuclidImagingConsortium,
larger samples. f. t. 2010, ArXiv e-prints:-1001.0061
Wefindthat,althoughtheperformanceofthenewsim-
ulation is slightly worse than the previous, more idealized
simulation,thedegradationisquitesmall.Ineffect,7%more
galaxies must be eliminated through an “a priori” cleaning
in order to attain the required performance. This supports
ourearlierassertionthat“templateerror”wouldbeunlikely
to dominate the photo-z performance of surveys with the
modestS/Nandlimitednumbersoffiltersthatarelikelyto
beavailable in all-sky surveys.
The new analysis therefore supports our earlier con-
clusion that photo-z performance at the level required for
precisioncosmologyareinprincipleachievablewithforesee-
ablephotometricsurveys.Whileitindicatesthatasatisfac-
tory photo-z scheme can be set up, it highlights however
that large spectroscopic samples of very high completeness
andwithveryreliablespectroscopicredshiftdeterminations
may be required in order to actually demonstrate that the
required performance has been achieved, because of linger-
ingconcernsthatredshiftincompletenessmaybecorrelated
with photo-z accuracy.This mayultimately bethelimiting
factor.
6 ACKNOWLEDGEMENTS
This work has been supported by the Swiss National Sci-
enceFoundationandisbasedonobservationsundertakenat
theEuropeanSouthernObservatory(ESO)VeryLargeTele-
scope (VLT) under Large Program 175.A-0839. Also based
ondatacollectedatSubaruTelescope,whichisoperatedby
theNational Astronomical Observatory of Japan.
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