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A&A650,A81(2021)
/0004-6361/202140463Astronomy
cP.-é&
Astrophysics
ImprovingtheastrometricsolutionoftheHyperSuprime-Camwith
anisotropicGaussianprocesses
P.-éget1,2,,,,,,5,,7,,1
1LPNHE,CNRS/IN2P3,SorbonneUniversité,LaboratoiredePhysiqueNucléaireetdeHautesÉnergies,75005Paris,France
e-mail:pierrefrancois.******@
2KavliInstituteforParticleAstrophysicsandCosmology,DepartmentofPhysics,StanfordUniversity,Stanford,CA94305,USA
3DepartmentofPhysicsandAstronomy,UniversityofPennsylvania,Philadelphia,PA19104,USA
4DepartmentofAstrophysicalSciences,PrincetonUniversity,4IvyLane,Princeton,NJ08544,USA
5SLACNationalAcceleratorLaboratory,MenloPark,CA94025,USA
6DepartmentofPhysicsandAstronomy,UniversityofHawai’iatManoa,Honolulu,Hawai’i96822,USA
,1CyclotronRd.,Berkeley,CA94720,USA
Received1February2021/Accepted17March2021
ABSTRACT
-Camimages.
sources.
(kernel)measuredfromthedatatosmoothandcorrect
theobservedastrometricresidualfleld.
ármánkernelallowsustoreducethecovariancesofastrometric
residualsfornearbysourcesbyaboutoneorderofmagnitude,from30mas2to3mas2atangularscalesof
-Camsensors
e ,particularly
inthecontextofcosmicshearanalysesattheRubinObservatoryLegacySurveyofSpaceandTime.
:observations–gravitationallensing:weak–techniques:imageprocessing–atmospherice ects–
astrometry
)abiasdependentonsignal-to-noiseleveltranslatesintoa
redshift-dependentbias,whichispotentiallydisastrousfor
Astrometryreferstothedeterminationofthepositionofastro-evaluatingcosmologicalconstraints,particularlyregardingthe
,acrucialstepinevolutionasafunctionofredshiftofstructureformation
astrometryisthedeterminationofthemappingofcoordinates,().Inthesamevein,abiasa ectingsuper-
measuredinpixelspaceonthesensors,toacelestialcoordinatenovafluxesinaredshift-dependentfashioncompromisesthe
-redshiftrelation
andthedeterminationofthemappingarebotha ectedbyuncer-().
taintiesthatmayholdconsequencesfordown-streammeasure-Forrepeatedimagingofthesameskyarea,theissueofposi-
mentsperformedontheimages,especiallywhenseveralimagestionuncertaintiesinducingmeasurementbiasescanbemitigated
ofthesameastronomicalscenearecombinedinordertoper-byusingasourcepositioncommontoallimages:thiscommon
ectedbynoisethanpositionsmeasuredinde-
ofSpaceandTime(LSST),particularlyinthecontextof
(LSSTScienceCollaboration2009),weconsidertwocosmolog-RubinObservatory,wheretwoback-to-back15sexposuresare
icalprobes:themeasurementofdistantTypeIaSupernova(SN)thecurrentbaselineobservingplan().How-´
lightcurves(seeAstier2012forareview),andthemeasurementever,averagingpositionsoverimagesrequiresaccuratemap-
ofgalaxyshapes(ormorepreciselyquantitiesderivedfromsec-pingsbetweenimagecoordinatesystemsor,equivalently,map-
ondmoments)forevaluatingcosmicshear(seeMandelbaumpingsfromimagecoordinatesystemstosomecommonframe.
2018forareview).TheinferredvaluesforthefluxandshapeInthecaseofgalaxyshapemeasurements,itispossibletorely
dependonthedeterminationoftheposition(;again,this
).Inbothcases,therequiresaccuratecoordinatemappings.
noiseinthepositionestimationgenerallybiasestheestima-Above,wementionthebiasinthefluxorshapeestimate
(.,
functionofredshift;,thisinduces
A81,page1of14
OpenAccessarticle,publishedbyEDPSciences,underthetermsoftheCreativeCommonsAttributionLicense(),
whichpermitsunrestricteduse,distribution,andreproductioninanymedium,:.
A&A650,A81(2021)
,weaverage
correlatedbiasesinshapeareclearlyaconcernbecausethecor-theaposterioriresidualsininstrumentcoordinatesinorderto
relationfunctionofshearistheprimeobservableofcosmicdetectthesmallpositiondistortionspresumablyduetosensors.
,weevaluatetheexpectedsizeofturbulence-induced
Forground-basedwide-fleldimaging,atmosphericturbu-positiono setsforRubinObservatoryandestimatethespurious
lencecontributestotheastrometricuncertaintybudget,partic-shearcorrelationsthiscausesifnotcorrectedundersomereduc-
ularlyforRubinObservatoryobservingmode,.
oftwoback-to-back15sexposures:distortionsinducedbytheInthetimewhenwewerecompletingworkonthispaper,
atmosphereappeartoscaleempiricallyasT1=2(.(2020,hereafterF20)producedapaperonthe
exp
2012;,hereafterB17),whereTexpisthesamesubjectusingsomewhatdi erenttechniquesandusingthe
(DES)
correlatesmeasuredpositionsinananisotropicfashion(asweanastrometricsolverdescribedinB17,whichareverysimi-
willshowlater), erencesbetweenthetwoworkscome
erentsites(),tele-
Ifshapemeasurementsareperformedonco-addedimages,scopesizes(),telescopemounts(-
theastrometricresidualswilla ectthemeasuredshapesoftheaz),andinstruments(inparticular,ourinstrumentisequipped
galaxiesinacorrelatedwayandthepointspreadfunction(PSF)withanatmosphericdispersioncorrector).Wemakecompar-
oftheco-.
istoproperlyaccountforthecomplexcorrelationpatternfor
PSFshapeparametersthatisinducedbythecombinationof
-addedimagehastwocomponents:oneHyperSuprime-Cam
thatisattributedtotheactualPSFoftheindividualexposuresHyperSuprime-Cam(HSC)isaprime-focusimaginginstrument
andoneduetomisregistrationthatisduetoturbulence--4kdeep-
-depletedCharge-CoupledDevice(CCD)sensorscoverabout
tributeequallyovertheco-addedimagearea,itiscommonto1:
transformallinputimagestothesamePSFpriortoco-adding,canbefoundinMiyazakietal.(2018).Thepublicdata1usedin
sothatmaskedareasandgapsbetweensensorsdonotcausePSFthisstudycorrespondtoobservationsacquiredfortheDeepand
-UltraDeeplayersoftheSubaruStrategicProgram2(SSP).The
tionisnotequippedtocopewithmisregistration,subsequentlydataconsistofaseriesofexposuresof180sto300s,ineachof
leadingtothecontribututionofsmallPSFdiscontinuitiesonthetheflveopticalbandsofthecamera(grizy).Onagivennight,
co-,withaflxed
onindividualexposures,
estimate,
correlationsintroducedbycorrelatedpositionresiduals,butthisthispapercorrespondto2294exposures,imagedintwoseasons
wouldlikelyrequireasigniflcante orttoattaintherequiredofsearchesfortransientobjectsusingHSC():
-fromNovember2016toMay2017intheCOSMOSfleld,and
novae,wecanreadilyevaluatethesizeofsystematicpositionfromMarch2014toNovember2016intheSXDSfleld.
residualsforagivenexposureandcorrectthefluxestimatorfor
theinducedbias.
shortexposures,reducingtheatmosphericcontributiontoastro-
metricresidualswillimprovetheusabilityofshapemeasure-WereducedtheHSCdatausingclassicalprocedures:simple
ments,mostlybecauseofthecomplexcorrelationpatternofoverscanandbiassubtraction,implementationofaflat-fleld
-domescreen,
laterinthispaper,reducingtheseastrometricresidualswillbedetectionofsourcesusingSExtractor(Bertin&Arnouts1996),
astrometricsystematicsbiaseswillalsobenefltotherscienceflttothedetectedsources,andaninitialsolutionfortheworld
goalsofRubinObservatory,forinstance,inthecontextoftrans-coordinatesystem(WCS)determinedbymatchingtheimage
Neptunianobjectsearches((USNO-B),withtypicalresiduals
.
example)orthemeasurementofpropermotionsofstarstoofaint
tobemeasuredbyGaia().´Wethenperformedasimultaneousastrometricflttothe
Inthispaper,weinvestigatebulktrendsofastrometricresid-catalogsfortheimagesforeachnightandeachbandsepa-
ualsthatarepresumablydominatedbyatmosphericturbulencerately–5to15imagesofthesamefleld,withdithersofthe
’sfortheinputimages
,weusedatafromtheareusedtoassociatethedetectionsofthesameastronomi-
SubarutelescopeequippedwiththeHyperSuprime-Camwide-calsourcesindi -
-Cam,themetricaltransformationsfrompixelspacetoskycoordinates,
dataset,.
probableatmosphericoriginoftheobservedpositionresiduals1Publicdatacanbefoundat/
(atleastforbrightsources,whereshotnoisedoesnotdominate).ssp/data-release/,andtherawimagescanbedownloadedfrom
,themodelingofthespatialdistribu-
,we2DetailsoftheSSPsurveydesignandimplementationcanbefound
presentourresults,inparticular,thereductioninvariancesandat/
A81,page2of14:.
P.-égetetal.:AstrometryandGaussianprocesses
Thefltispossiblebecauseweconstrainasmallfractionofandiscurlfree(Helmholtz’stheorem).Thedecompositionintoa
thedetectedsourcepositionstotheirGaia(DataRelease2,curl-freeE-modeandadivergence-freeB-modeofvectorflelds
GaiaCollaboration2018)positionsonthedateofobservation;ontheplaneB17allowsustotesttheabovehypothesis.
werefertothesesourcesas“anchors”.Thegeometrictransfor-FollowingB17(seeAppendixA,inparticular),weevaluate
mationsaremodeledasaper-CCDmappingofpixelcoordinatesthetwo-pointcorrelationfunctions+,,andfortheastr
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