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Astronomy&Astrophysicsmanuscriptno.15664 (cid:13)c ESO2011 January17,2011 Solar velocity references from 3D HD photospheric models J.delaCruzRodr´ıguez1,2,D.Kiselman1,andM.Carlsson3,4 1 InstituteforSolarPhysics,RoyalSwedishAcademyofSciences,AlbaNovaUniversitycenter,SE-10691Stockholm,Sweden 2 DepartmentofAstronomy,StockholmUniversity,AlbaNovaUniversitycenter,SE-10691Stockholm,Sweden 3 InstituteofTheoreticalAstrophysics,UniversityofOslo,P.O.Box1029Blindern,N-0315Oslo,Norway 4 CenterofMathematicsforApplications,UniversityofOslo,P.O.Box1053Blindern,N-0316Oslo,Norway Preprintonlineversion:January17,2011 1 ABSTRACT 1 0 Context.ThemeasurementofDopplervelocitiesinspectroscopicsolarobservationsrequiresareferenceforthelocalframeofrest. 2 TherotationalandradialvelocitiesoftheEarthandtherotationoftheSunintroducevelocityoffsetsintheobservations.Normally, goodreferencesforvelocitiesaremissing(e.g.telluriclines),especiallyinfilter-basedspectropolarimetricobservations. n Aims.Wedetermineanabsolutereferenceforline-of-sightvelocitiesmeasuredfromsolarobservations foranyheliocentricangle, a J calibratingtheconvectivelineshiftofspatially-averagedprofilesonquietsunfroma3Dhydrodynamical simulation.Thismethod workswheneverthereisquietsuninthefield-of-view,andithastheadvantageofbeingrelativelyinsensitivetouncertaintiesinthe 3 atomicdata. 1 Methods.We carry out radiative transfer computations in LTE for selected Ci and Fei lines, whereas the Caii infrared lines are synthesized innon-LTE. Radiative transfer calculations are done witha modified version of Multi, using the snapshots of anon- ] R magnetic3Dhydrodynamicalsimulationofthephotosphere. Results.TheresultingsyntheticprofilesshowtheexpectedC-shapedbisectoratdiskcenter.Thedegreeofasymmetryandtheline S shifts,however,showacleardependenceontheheliocentricangleandthepropertiesofthelines.Theprofilesatµ=1arecompared h. withobservedprofilestoprovetheirreliability,andtheyaretestedagainsterrorsinducedbytheLTEcalculations,inaccuraciesinthe p atomicdataandthe3Dsimulation. - Conclusions.Theoretical quiet-sunprofilesoflinescommonlyused bysolar observersareprovided tothecommunity. Thosecan o beusedasabsolutereferencesforline-of-sightvelocities.Thelimbeffectisproducedbytheprojectionofthe3Datmospherealong r thelineofsight.Non-LTEeffectsonFeilinesarefoundtohaveasmallimpactontheconvectiveshiftsofthelines,reinforcingthe t s usabilityoftheLTEapproximationinthiscase.Weestimatetheprecisionofthedisk-centerlineshiftstobeapproximately50ms−1, a buttheoff-centerprofilesremaintobetestedagainstobservations. [ Keywords. Convection–Sun:photosphere–Line:fomation–Radiativetransfer–Sun:granulation–Hydrodynamics 1 v 1 1. Introduction Below,wediscusssomemethodsthathavebeenusedtode- 7 6 fineavelocityreferenceforsolarobservations. Theneedforhighspatialandspectralresolutioninsolarobser- 2 vations stimulates new advances in telescope and instrumenta- – Sunspotumbraearecommonstandards(e.g.,Beckers1977; . 1 tiontechnology,adaptiveopticsandimagereconstructiontech- Scharmeretal.2008;Ortizetal.2010),butthisonlyworks 0 niques.However,theaccuracyofthemeasurementsisoftenlim- when a suitable sunspot is in the field-of-view and relies 1 ited by calibration issues. This is evident when using Doppler on the assumption that the umbra is at rest because of the 1 shifts of spectral lines to acquire line-of-sight velocities in the convectivemotionsbeingsuppressedbythestrongmagnetic v: solarplasma,wherethetaskoffindingalocalstandardofrestis fields.Furthermore,thelinemustbemeasurableintheum- i oftenproblematic. braandwavelengthshiftswhichareinducedbyblendsfrom X The current work is partly motivated by the installation of lines uniquely formed in the umbra (e.g. molecules), must r the CRisp ImagingSpectropolarimeter(CRISP, Scharmeretal. beaccountedfor.Finally,observationsofumbraearealways a 2008)attheSwedish1-mSolarTelescope(SST,Scharmeretal. plagued by stray light from the much brighter quiet photo- 2003).Instrumentslike thisusuallylacklaboratorywavelength sphere. references,whiletheuseoftelluriclineshaslimitationsasdis- – Telluric lines can be used to define a laboratory-frame cussedbelow.Theobvious(andcommonlyused)solutionoflet- reference, which can then be converted to the Sun. tingthespectrallineofinterest–averagedoveralargeenough MartinezPilletetal. (1997) and BellotRubioetal. (2008) areaandlongenoughtime–definealocalframeofrestiscon- used telluric lines to derive the wavelength scale for their foundedbythefactthatconvectivemotionsleavestrongfinger- observations,thenconvertedtoanabsolutewavelengthscale printsonanyspectrallineformedinthesolarphotosphere.The ontheSungiventheephemerisconstants,timeoftheobser- statisticalaverageofbrightblueshiftedanddarkredshiftedpro- vations,solarrotationandthelaboratorywavelengthsforall filesformedingranulesandintergranularlanesrespectively,pro- observedspectrallines. ducestheblueshiftedC-shapedbisectorsofphotosphericlinesas – A spectral atlas, most commonly the atlas acquired reviewedbyDravins(1982). with the Fourier Transform Spectrometer at the McMath- Pierce Telescope (hereafter called the FTS atlas) of Sendoffprintrequeststo:J.d.l.C.R.:e-mail:[email protected] Brault&Neckel (1987), can be used to calibrate observa- 1 J.delaCruzRodr´ıguezetal.:Solarvelocityreferencesfrom3DHDphotosphericmodels tions. Thiswas doneby Langangenetal. (2007), who used Table 1. Atomic data, sorted by element in increasing wave- the laboratory wavelength to define the reference for ve- length. locities, assuming an absence of systematic errors in the FTS atlas itself and correctingfor the gravitationalredshift λ (Å) E loggf σ(1) α(2) logǫ(3) 0 c (633 m s−1). This method only works at disk center where Ci5380.3370 7.6850 -1.824 1238 0.229 8.53 theatlaswasrecorded. Fei5250.2089 0.1210 -4.938 207 0.253 7.44 – Numerical models can be used to predict convective line Fei5250.6460 2.1980 -2.181 344 0.268 7.71 shifts and thus provide a velocity reference. A two- Fei5576.0888 3.4300 -1.000 854 0.232 7.69 component model of the solar photosphere has been de- Fei6082.7106 2.2230 -3.573 306 0.271 7.45 Fei6301.5012 3.6540 -0.718 834 0.243 7.55 rived by Borrero&BellotRubio (2002) from the inversion of Fei spectral lines. Since it does not contain any hori- Fei6302.4940 3.6860 -1.203 850 0.239 7.50 Fei7090.3835 4.2300 -1.210 934 0.248 7.63 zontal velocities, it then is in principle limited to calibrat- Caii8498.0134 1.6920 -0.6391 291 0.275 6.31 ing disk-centerobservations,for which it has been used by Caii8542.0532 1.7000 -0.4629 291 0.275 6.31 Tritschleretal. (2004) andFranz&Schlichenmaier(2009). Caii8662.1605 1.6920 -0.7231 291 0.275 6.31 However,BellotRubioetal.(2004)useditwiththeempiri- calresultsofBalthasar(1988)toalsoestimatelineshiftsoff Notes.(1)thecross-sectioninunitsoftheBohrradius,(2)dimension- solar center. Langangenetal. (2007) employ a 3D numeri- lessparameterusedwith(1)inthecomputationofcollisionalbroaden- calgranulationmodeltocomputetheconvectiveblueshiftof ing(Barklemetal.1998).(3)thefittedvalueoftheabundanceforeach theCi5380Ålineandcalibratetheirobservations.Thisap- line. proachwasnecessarybecausethelaboratorywavelengthof the Ci line is not known with enough precision to use the tionsnapshots.TheFei andCi lineswerecalculatedassuming atlascalibrationthatismentionedabove. local thermodynamical equilibrium (LTE), which is a reason- able assumption for the wings of most photospheric Fei lines We note that telluric lines cannot always be observed with (Gadunetal. 1999; Asplundetal. 2000). Fabbianetal. (2006) the solar diagnostic lines and that when this is the case, ob- foundthatnon-LTEeffectsforCilinesareexpectedtobesmall serving them can be expensive. Observations with tunable fil- withtheeffectonderivedabundancebeing<0.05dex.Possible ters require high cadence because of seeing variability and so- errorsproducedbynon-LTEeffectswillbefurtherdiscussedin lar evolution. Any time spent recording telluric lines thus de- Section4.3.1. creasesthe spatialresolutionand thesignal-to-noiseof thesci- TheCaiilineswerecomputedin1.5Dnon-LTE–wherethe encedata.Thiswouldalsoapplytoanylaboratoryspectral-line non-LTEproblemissolvedin1D–usingthesamemodelatom source used for calibration.Furthermore,approachesusing tel- asLeenaartsetal.(2009),whichconsistsof5boundlevelsplus luriclines(orothercalibrationlines)andspectralatlasesallre- acontinuum. quireveryaccurateatomicdatatodefinethezerovelocitypoint Atomic data were obtained from the VALD-2 database andthusconvertthe wavelengthscale intovelocityscale. Such (Kupkaetal.2000).ThetreatmentofvanderWaalsbroadening data are unfortunately not available for many of the lines that followsthatofBarklemetal.(1998)andtherequiredcrosssec- areextensivelyusedin solarphysicsasis apparentin the work tions were taken from Barklemetal. (2000), except for the Ci of Langangenetal. (2007) described above. Their approach is line providedby Paul Barklem (private comunication).The ef- proposedinthisstudy:usingrealistic3Dnumericalsimulations fectivequantumnumbersn∗forthistransitionare1.95→3.27. ofthesolarphotospheretocomputespatially-averagedlinepro- Thetreatmentbecomeslessreliablewhenn∗>3.0butitismore files. As the radiativetransfercomputationis carriedoutin the accuratethanthecommonlyusedUnsold(1955)formulation. local frame of rest of the Sun and the adopted atomic data is To achieve the best possible fit between the synthetic line known, the velocity shifts of the spatially-averagedprofile can profile at µ = 1 and the FTS atlas, the elemental abundance becomputedaccuratelyfordifferentheliocentricangles,relative is individually adjusted for each line. The resulting abundance totheassumedcenteroftheline.Thismethodreliesonthede- values(lastcolumninTable1)shouldnotberegardedassuch. greeofrealismofthe3Dsimulationandrequiresalargestatisti- Instead, they act as free parameters that compensate for errors calsampleofspectratocomputethespatially-averagedprofile. fromatomicdata,theLTEapproximation,andthemodelsthem- The aim of this work is to provide the community with a set selves.Thehopeisthatbyfittingtheprofilethecorrectlayerof oftheoreticalspatially-averagedquiet-Sunprofilesoflinescom- the modelwith the appropriatevelocity field is being sampled. monly used in solar physics, that are computed for a range of Since non-LTE effects could be expected to affect the cores of heliocentricangles. stronglines,onlythewingsofeachlinewereusedforthefitof In Sect. 2 the atomic data and radiative transfer details are theabundance;however,theresultschangemarginallywhenthe discussed. The 3D HD simulation is described in Sect. 3. In fullprofileisusedtofit. Sect. 4 the results are presented together with an error analy- The results for the Caii infrared triplet lines must be ap- sisandarealfilter-basedobservationiscalibratedusingthenew proachedwith extracautionsince the lines are verystrong and data.Section5describestheelectronicdatamadeavailableand the 3D simulation does not extend all the way up to the chro- Sect.6summarizesthemainconclusionsofthiswork. mosphere. Therefore the calculated core of the line cannot be comparedtorealobservations,butthephotosphericoriginofthe wings suggests the usability of the models with these lines, as 2. Linelistandradiativetransfer discussedbyShine&Linsky(1974). The calculations were carried out with a selection of lines We have included blends affecting the Fei and Ci lines. (Table 1) that are extensively used in solar physics, including The atomic parametersfor these were taken from the VALD-2 lines that can currently be observedwith CRISP at the SST. A database (Kupkaetal. 2000). The blends are weak, but have a modifiedversionoftheradiativetransfercodeMulti(Carlsson smalleffectontheupperpartofsomebisectors.TheCaiilines 1986) was used to compute synthetic spectra from the simula- have some strong blends in the wings which greatly affect the 2 J.delaCruzRodr´ıguezetal.:Solarvelocityreferencesfrom3DHDphotosphericmodels highandthesurfaceoftheintergranularlanesbecomessmaller. Theblueshiftdecreasesmonotonouslytowardsthelimb. A variety of bisector shapes and µ dependences are found in the Fei lines. At µ = 1, the lines have the expected blueshiftedconvectiveC-shapedbisectors.Whengoingoffcen- ter, the blueshift for many lines increases, while the blueshift decreases again at even higher heliocentric angles, sometimes turningintoaredshift,andthebisectorsbecomemore\-shaped. Each line shows its own individual behavior – function of its strength, excitation potential, and other properties. The line coreshave beenexcludedfromthe bisectorsfor the Caii lines. These wing bisectors show a progression from a C-shape to a \-shapefromcentertolimb. Table2listsnumericalvaluesfortheconvectiveshiftscom- puted as the mean of the bisector – excluding the part closest Fig.1. Mean bisector velocity as a function of the number of to the continuum– for each line and µ value, and Table 3 lists snapshotsusedtocomputethespatially-averagedspectrum. thelinecorevelocitiesfoundwhenconvolvingthesyntheticline profileswiththeappropriateCRISPinstrumentalprofile. bisectors, so these blends were not present in the present Caii 4.1.Effectofspectralresolution calculations. Theasymmetryofthelineswilldecreasewithdecreasedspectral resolution.Whencomparingwithobservations,orusingthethe- 3. 3Dhydrodynamicalphotosphericmodels oreticalprofilesforvelocitycalibration,theprofilesmustbecon- volvedtothe properspectralresolution.Figure3illustratesthe The3Dhydrodynamicalsimulationconsistsof90snapshotsand dependence of the mean bisector, the center-of-gravity (COG) covers around 45 minutes of solar time (Trampedach et al., in velocity, and the line-core velocity on spectral resolution. The prep.;Pereiraetal.2009).Thesimulationdoesnotincludemag- corevelocityisnaturallytheonemostsensitivetospectralreso- netic fields. The radiative energy transportwas computed with lution.COGisleastsensitiveinthisspecificcase,butthedevia- animprovedmulti-groupopacitybinningof12bins,whencom- tionsinallcasesstartatsuchspectralresolutionsthatwearecon- paredwiththe3DmodelsofAsplundetal.(2000).Theoriginal tenttousethemeanbisectorvelocityinallourillustrationshere. simulationof240×240×240grid-pointscoveringaregionof Wedothinkthatanypracticaluseofourlineprofilesshoulduse 6×6×4 Mm was interpolatedto a finer verticaldepthgrid in thedetailedprofilewiththeapplicationoftheappropriateinstru- theradiativezoneandsampledtoacoarsergridinthehorizon- mentalsmearingandweighting. tal planefor radiativetransfercalculations.The resulting snap- shotshadasizeof50×50×82gridpointsrepresentinga6Mm square.Ourtestsshowthattheeffectofsucharesamplinginthe 4.2.Thelimbeffect horizontalplanehasanegligibleeffectonthespatially-averaged profilesofthelines. The bisectors change with heliocentric angle, and close to the The presence of oscillations in the simulation broadensthe limb the blueshift usually gets small and is sometimes turned time-averagedprofilecomparedtotheindividualsnapshots.The into a redshift for the line cores. This limb effect (Adametal. oscillationshaveaquasi-periodicbehavior,soatleastoneperiod 1976; Beckers&Nelson 1978; Balthasar 1985) was subject shouldbeincludedinthetimeaverageinordertoavoidsystem- to much speculation before granulation was understood (see atic shifts of the average profiles. Figure 1 shows the average Dravins1982).Itseemsthatacomprehensiveexplanationisstill velocity(integratedalongthebisector)ofthetimeaveragedpro- lacking, which could be because the complicated nature of the file as a function of the number of snapshots used in the time situation precludessimple explanations.Nevertheless,we want series. The limited sample of granules and intergranular lanes todiscussithereinthelightofourresults. enclosed in a 6 Mm box reinforces the need to use more than The convectiveblueshiftand line asymmetry at disk center one period in order to convergeto a stable average for the line arecausedbytheasymmetryoflargebrightgranuleswitharel- shift. Therefore,the whole time series was used for computing atively slow upward flow producing blueshifted lines and nar- theaveragelineprofiles. rowdarkintergranularlaneswith fastdownwardflowsproduc- Toproduceprofilesoffdiskcenter,thepropertiesofthe3D ing redshifted lines. As we leave the disk center, a number of effects will changethe shifts and the line profiles. Towardsthe snapshots are slanted assuming periodic boundary conditions, limb,higherphotosphericlayersaresampledthathavedifferent and the velocity vector is projected into the new line-of-sight. velocitypatternsanddifferentstatisticalrelationsbetweeninten- Theheightscaleisalsomodifiedtomatchthenewgeometryof sityandline-of-sightvelocities.Ofparticularinterestisthepat- the3Dmodel. tern of inverse granulation (e.g., Cheungetal. 2007) that char- acterizesthephotosphericstructureaboveacertainheight.Also, 4. Results horizontalvelocitiesbecomemoreimportantastheviewingan- gledecreasesandwillsoondominatethecontributionfromver- In Fig. 2 the resulting line profiles for all heliocentric angles tical convective motions. There are also 3D effects due to the are plottedtogether,alongwith their bisectors. TheCi 5380Å corrugatednatureoftheopticaldepthsurface.We canconsider lineshowsthestrongestconvectiveblueshift,anexpectedresult the following mechanisms that can decrease the blueshift and giventhatthelineisformedverydeepduetothehightexcitation ultimatelyleadtoaredshiftintheaveragelineprofiles: potentialofthetransition.Indeeplayers,verticalvelocitiesare 3 J.delaCruzRodr´ıguezetal.:Solarvelocityreferencesfrom3DHDphotosphericmodels Fig.2.Syntheticprofilesandthecorrespondingbisectorsresultingfromthecalculationsof Ci,FeiandCaiilines.Thegrayscale indicatesthevariationintheheliocentricanglefromµ = 1.0toµ = 0.3.ThebisectorsfortheCaiilinesarenotshowninthecore part. 1. The intensity-velocity correlation changes as higher and terofagranule(x∼4000km),seeminglyblockingaredshifted higher levels in the photosphere are sampled by the line sideofagranule.Onecanthusarguethatsomeofthementioned (e.g.Janssen&Cauzzi2006;Cheungetal.2007).Thisisthe mechanismsandotherscanproduceablueshiftwithdecreasing sameeffectthatcausestheC-shapeindisk-centerbisectors. µ.Decidingwhichmechanismswilldominaterequiresaquanti- 2. The redshiftedpartof thegranuleis seen againsta brighter tativeanalysis.Wemadeafirsteffortinthatdirection. background than the blueshifted part (Beckers&Nelson Effects2,3,and4aretrue3Deffectsthatbreakthesymme- 1978;Asplundetal.2000). try between redshifted limbside granular parts and blueshifted 3. Near the limb, surface corrugation causes redshifted parts centerside parts. They shouldgo away in a multi-1D treatment of granules to show larger areas to the observer (Balthasar whereeachcolumninthesimulationistreatedasaplane-parallel 1985). atmosphere.Theresultsofsuchanumericalexperimentsfortwo 4. Reversed granulation“hills” overintergranularlanes shield of our lines can be seen in Fig. 5. It is clear that for each line, blueshiftedpartsofgranuleswhenobservedoffdiskcenter. thevariationofbisectorswithµissmallerthanin3D.Itisalso Figure4showsacrosssectionthroughasimulationsnapshot monotonousandalwaysinthesensethataprofilebecomesred- illustratingline formationat µ = 0.3.Inspectionof thesimula- deratthecoreofthelinewithdecreasingµ.Theclosefollowing tionsnapshotsinthiswaycangivesupporttoallthelistedmech- of the successive bisectors to that of µ = 1 is an illustration anismsandalsoinspireinventionofnewones.Theeffectofthe of the Eddington-Barbierrelations: the µ dependenceis equiv- hotwalloveranintergranularlane(at x ∼ 2200km)is,forex- alentto the depthdependence.We takethis to meanthatmuch ample,obvious.Itblockstheviewtowardsthe blueshiftedside ofthecenter-to-limbvariationofspectrallineshiftsisdueto3D ofagranule.Butasimilarstructureisalsopresentoverthecen- effects. The latter either shifts the bisectors to redder or bluer 4 J.delaCruzRodr´ıguezetal.:Solarvelocityreferencesfrom3DHDphotosphericmodels Fig.3. Left: Bisectors of the synthetic Fei 6301.5 Å line as a functionofthespectralresolution.Right:Velocitiesmeasuredin differentways fromthe profilesonthe left panel,as a function ofspectralresolution. wavelengths,relativetothe1Dcase.Forexample,theblueshift relative to disk center that is seen in many lines for moderate heliocentricanglesmustbeduetoa3Dmechanism.Wehypoth- esise that this comes from the screening of narrow downdrafts fromviewasthelineofsightdepartsfromthevertical. 4.3.Erroranalysis 4.3.1. Non-LTEeffectsinFeilines Our radiative transfer calculations assume LTE. The errors in- troducedby this approximationwill to some extentbe reduced by fitting the line profiles using an individualabundance value for each line as a free parameter. Shchukina&TrujilloBueno (2001) studied the impact of non-LTE effects on Fei and Feii linesusinga3Dsimulation(buta1Dtreatmentofthenon-LTE problem,thus1.5D)andreportedlargerdeparturesfromLTEin granulesthaninintergranularlanes.Basedonthiswork,wecan Fig.4.Propertiesofthemodelalongasliceofoneofthesnap- expectthefollowingtwonon-LTEmechanismstodominate shotsatµ = 0.3:temperature,absorptioncoefficientatthecore 1. Overionization: A line from a neutral species typically has of Fei6301.5Å, andlineofsightvelocityfromtoptobottom. lowerlineopacitythanitsLTEvaluebecauseofoverioniza- Thesolidlinethatisoverplottedoverthethreepanelsrepresents tion thatis caused by the UV radiationfield beingstronger the layer where τ = 1 along the line of sight. Four rays are LC than the local Planck function. This causes the line to be shownassolidlinesaboveτ =1anddashedbelowthisheight. LC formed deeper in the atmosphere and thus be weaker than Thebottompanelshowstheline-of-sightvelocitiesalongthedi- inLTE. rectionshownbytherays.Thehorizontaldashedlinerepresents 2. The non-LTE line source function Sl can be expressed in thelayerwhereτ equals1atµ=0.3. ν 500 terms of the departure coefficients of the populations from theupper(b )andlower(b)levels(seeRutten2003)ifstim- j i ulatedemissionisneglected, thesensitivityoftheresultinglineshifttosuchdifferentialdepar- turesfromLTE.Oneofthe3Dsnapshotswasdividedingranules b Sl ∼ jB (T) (1) and intergranularlanes based on the sign of the verticalveloc- ν bi ν ities at τ500 = 1 and synthetic spectra were computed for dif- whereB (T)isthePlanckfunction.Photonlossesintheline ferent values of the iron abundance. The aim was to find the ν itself leadto a decreasein b andincrease onb, producing combinations of abundances in granules and intergranules that j i alinesourcefunctionthatislowerthanthePlanckfunction. reproduce a spatially-averaged spectrum with the same equiv- ThisleadstoastrongerlinethaninLTE. alent width as the observed profile. We used a nonlinear least- squaresfit,describedinMarkwardt(2009),inordertoinferthese Thefirsteffecttendstobethemostimportantforweaklines, pairsof values.Figure6 illustratesthe averageshiftof the line whilethesecondisfoundforstronglinesbecausethelineopac- asafunctionofabundancedifferencebetweenthegranulesand ity dominates the backgroundopacity. In some cases, the non- the intergranularlanes. The reference was set where the abun- LTE and LTE profiles are very similar because the two effects dance derived from the granulesand intergranulesis the same. cancel out. However, the presence of larger LTE departures in Shchukina&TrujilloBueno(2001)findanaveragenon-LTEef- thegranulesthanintheintergranularlanesnotonlychangesthe fectonderivedFeabundancesof0.1dex.Ifthisnumberistaken strengthoftheline,butalsotheconvectivelineshift.Wetested asalsotypicalofthe differencebetweengranuleandintergran- 5 J.delaCruzRodr´ıguezetal.:Solarvelocityreferencesfrom3DHDphotosphericmodels Table2. Convectiveshiftsinms−1ofthestudiedlinesfromµ=1.0toµ=0.3. Element λ (Å) µ=1.0 µ=0.9 µ=0.8 µ=0.7 µ=0.6 µ=0.5 µ=0.4 µ=0.3 0 Ci 5380.34 -948 -936 -922 -910 -897 -888 -880 -844 Fei 5250.21 -294 -372 -410 -426 -420 -394 -346 -259 Fei 5250.65 -304 -354 -370 -369 -348 -308 -245 -140 Fei 5576.09 -334 -378 -388 -383 -360 -317 -249 -140 Fei 6082.71 -441 -495 -522 -536 -531 -511 -473 -397 Fei 6301.50 -307 -349 -358 -351 -325 -279 -211 -101 Fei 6302.49 -335 -387 -404 -403 -381 -342 -280 -176 Fei 7090.38 -352 -396 -409 -407 -389 -354 -302 -210 Caii 8498.01 -265 -288 -289 -275 -248 -206 -148 -70 Caii 8542.05 -335 -364 -374 -372 -359 -337 -307 -269 Caii 8662.16 -272 -294 -293 -279 -251 -208 -149 -68 Notes. Thebisector of each linewasintegrated from95% of thecontinuum intensity tothecore of the line. Inthecase of theCaii lines, the non-LTEcorewasexcluded.ForCitheupperthresholdwashigher(97%)becausethelineisweak. Table3. Linecorevelocitiesofthesyntheticspectrallines(excludingCaii) convolvedwiththeappropriatetheoreticalprofileof CRISPforeachwavelength. Element λ (Å) µ=1.0 µ=0.9 µ=0.8 µ=0.7 µ=0.6 µ=0.5 µ=0.4 µ=0.3 0 CI 5380.34 -928 -895 -867 -840 -820 -810 -795 -764 FeI 5250.21 -178 -306 -358 -370 -354 -315 -246 -134 FeI 5250.65 -115 -196 -221 -213 -177 -115 -26 108 FeI 5576.09 -163 -222 -231 -209 -164 -96 -3 126 FeI 6082.71 -403 -470 -499 -508 -500 -480 -433 -341 FeI 6301.50 -188 -238 -241 -217 -173 -109 -17 108 FeI 6302.49 -255 -326 -347 -338 -306 -255 -178 -57 FeI 7090.38 -315 -378 -396 -388 -362 -321 -255 -148 Fig.6. Differential Doppler shift of the Fei 6082.7Å line pro- duced by changes in the relative abundance between granules and inter-granules. The combinations of granular/intergranular abundanceswerefittedtoreproducetheequivalenthwidthofthe FTSatlas. Fig.5. Bisectors for two lines computed in the plane-parallel dancesinferredbyAsplundetal.(2005)normallyleadtodiffer- treatment,“1D”,comparedtothefull“3D”result. entresultsforthedifferentlines,somepresentingmoredamped wingsthantheatlasandothersnarrowerones.Theabundanceis usedasafreeparameterinordertomatchthewingsofthesyn- uleabundanceinFig.6,theerrorsinthecomputedlineshiftdue theticprofilesforµ=1withtheFTSatlas.Theinnercoreisnot tonon-LTEeffectsshouldbesmallerthan±30ms−1. includedinthefittingprocedurebecausegenerallynon-LTEef- fectsareexpectedtobelargerthere(seeRutten&Kostik1982), andthemodelsnapshotsbecomelessreliableclosetotheupper 4.3.2. Profilefitting boundary(seeAsplundetal.2000). DuetotheeffectsdescribedinSection4.3.1andbecuasethe3D Asanindicatoroftheerrorsduetothisfittingprocedure,we modelsareonlyrealisticuptoacertainheight,theresultingpro- performedtestcalculationstogetthesensitivityofthebisectors filesshowdifferencescomparedtotheFTSatlas.Thesolarabun- tochangesintheassumedabundance.Theresultsareshownin 6 J.delaCruzRodr´ıguezetal.:Solarvelocityreferencesfrom3DHDphotosphericmodels Fig.8.Feisyntheticbisectors(fulldrawn)comparedwithbisectorsmeasuredfromtheFTSatlas(dashed). sultsbymorethanthisamount.Theestimatedoesnot,however, includetheintrinsicerrorsofthesimulation. To check the realism of the simulations, we compared the synthetic line profiles at µ = 1.0 with the FTS atlas after ap- plying a gravitational redshift on the former. The average syn- thetic Ci bisector lies 530 m s−1 redwards of that measured from the FTS atlas, something that we deem mostly to be due to errorin thelaboratorywavelengthofthe line.Atface value, our simulations implies a wavelength of 5380.3275 Å on the FTS-atlaswavelengthscale.Thisiswithintheciteduncertainty (0.02Å)ofthelaboratoryvalueof5380.3370ÅfromJohansson (1966),whichwasusedhere.Itisalsocomfortinglyclosetothe 5380.3262ÅfoundinasimilarwaybyLangangenetal.(2007) from their observations and simulations of magnetic regions. ThebisectorsfortheFeilinesaredisplayedinFig.8.Thesyn- thetic bisector shapes show an acceptablecorrespondencewith those measured from the FTS atlas. The standard deviation of thedifferencesinmeanvelocityis56ms−1 whichcorresponds toapproximately1mÅ.Thisiscomparabletoourestimateofthe Fig.7. Bisectors calculated for at µ = 1.0,0.6,0.3 for a range internalerrorsfromnon-LTEeffectsandfittingprocedures,but of abundances. The results are only from five snapshots which onceagainthereisstrongreasontobelievethatasignificantpart means that they cannot be directly compared with, e.g., Fig2. of these deviations are due to errors in the adopted laboratory Left:abundancetestforFei6301ÅwithvaluesoftheFeabun- wavelengths. dancewithin[7.25-7.65].Right:testforCi5380Å,thevalues Finally we note that AllendePrieto&GarciaLopez (1998) oftheabundancespananunrealisticrangecomparedtothenom- estimate the precision in FTS wavelengths to be on the order inalvalue[8.19-8.69]. of 50 m s−1. It seems likely that several of the error estimates discussed aboveare too conservative,but the synthetic profiles seemtopassthetestandtheyshouldbecorrectwithin50ms−1. Observationalchecksoftheoff-centerprofilesaremoredifficult Fig.7.TheleftpanelscorrespondtotheFei6301Åline,calcu- but would be welcome. Since photosphericmodelingoftenbe- lated on three different heliocentric angles, for different values comes more uncertainfor low µ values, it is naturalto suspect ofthe Fe abundance.Thepanelsonthe rightcorrespondto the that the accuracyof our convectiveline shifts will decrease to- Ci5380Å,wheretheabundancecoversanunrealisticrangeof wardsthelimb. values[8.19,8.69].Thisweak line, whichis formedveryclose tothecontinuum,ismoresensitivetochangesintheabundance The hydrodynamic granulation simulations do not include thanthestrongerFeiline.Thelowerpanelsshowtherelativeve- magnetic fields. This is potentially the most important source locityshiftintegratedoverthewholebisector.We estimatethat oferrorsinthepracticalapplicationofthesesyntheticlinepro- the uncertainties from the fitting procedure are within 0.1 dex files for velocity calibrations. For example, Langangenetal. inabundancewhichthencorrespondsto±10ms−1 fortheinte- (2007) estimated a difference of 200 m s−1 in convective shift gratedbisector. for the Ci 5380 Å line between non-magneticand active gran- ulation.(Thiswasmostlycausedbythechangingintensityand velocity pattern and not by Zeeman splitting.) Any calibration 4.3.3. Discussion work must use the least magnetic photospheric region avail- Fromthetestsabove,theestimatederrorintheshiftofthelines able. However, how strong the quiet Sun magnetic fields are islessthan50ms−1.Thismeansthatafullnon-LTEtreatment is still an ongoing debate (e.g. Mart´ınezGonza´lezetal. 2008; combinedwiththeexactatomicdatashouldnotchangethesere- PietarilaGrahametal.2009;deWijnetal.2009). 7 J.delaCruzRodr´ıguezetal.:Solarvelocityreferencesfrom3DHDphotosphericmodels 4.4.CalibrationofSST/CRISPobservations A quiet Sun dataset acquired with SST/CRISP at µ = 1.0 was calibrated using the current results. The Fei 6302 Å line was sampled with eight wavelength points, evenly distributed with a separation of dλ = 48 mÅ and processed using the image restorationcode MOMFBD (vanNoortetal. 2005). The telecentric optical design of CRISP (Scharmer 2006) is opti- mumforhighimagequality,butitintroducesinstrumentalfield- dependent wavelength shifts produced by irregularities on the surfaceoftheetalons,whicharecommonlyknownascavityer- rors. The latter complicate the task of obtaining the spatially- averaged spectrum, as the profile is effectively broadened by these random pixel-to-pixel shifts. The average spectrum was computedwithaleast-squares-fitofallthedatapointstoaspline whichwascharacterizedwithtenparameters.Forthispurpose, all the individual spectra were corrected for cavity errors and then arranged in a large array, which was sorted in increasing wavelength. Tocarryoutthevelocitycalibration,thesyntheticspectrum obtained from the 3D simulation was convolved with the the- oretical instrumental profile of CRISP, which included the ef- fects of the beam converging at f/165. The velocity calibra- tion was determined by finding the constant wavelength shift to the observed bisector that minimized the difference to the synthetic one. Figure 9 illustrates the results of the calibration, wheretheDopplermapatthecoreofthelineisscaledbetween ±1500 m s−1. The bottom-leftpanelcontains a density map of the spatially resolved spectra, corrected for cavity errors. The dispersionofpointsaroundthe sevennominalwavelengthsap- pears after correctingfor the cavity errorsin combinationwith the granulation contrast. The bisector of our calibrated data is overplotted to the bisector of the synthetic spectrum that was convolvedwiththeinstrumentalprofileofCRISP.Thereisatel- luricblendonthe redwing ofthe observedprofile,notpresent inthesyntheticspectrum,thatpollutestheupperpartofthebi- sector. Fig.9.Top:Dopplermapofquietsungranulationobservedwith SST/CRISP at Fei 6302Å. The image gray scale is clipped to 5. Usageofelectronicdata ±1500m s−1. Bottom-left:Spatially-averagedprofilecomputed along the image shown in the top panel. The density map rep- Thesyntheticprofilesthathavebeenpresentedinthisstudycan resentsthespatially-resolvedprofilescorrectedforinstrumental be accessed electronically.The spectralresponse ofany instru- cavity errors. The average profile was computed using a least mentproducesbroadeningandcanintroduceasymmetriesinthe squaresfit ofall thepointsto a spline,consistingof 10param- observed profiles. Thus it is imperative that the profiles be de- eters.Bottom-right:Bisectoroftheobservedspatially-averaged graded with the proper instrumental response before they are profile. The velocity calibrationwas carried outusing our syn- usedtocalibrateobservations. theticprofileconvolvedwiththeCRISPinstrumentalprofile. The quiet Sun’s average spectrum can be computed from quiet regions in the observations. However, the presence of p- modes(oscillations)willproducean unrealisticshiftin the ob- servedaverageprofile.Thus,it shouldbeaveragedintime and spectraproducedbyconvectivemotionsatdifferentheliocentric space, or at least from a sufficiently large sample of quiet Sun angles for Ci, Fei, and Caii lines as commonly used for solar spectra. physicsdiagnostics. We proposeto use the profilesas absolute Wehavebeencautiousinthetreatmentoflinecores,butthe localreferencesforline-of-sightvelocitiestoallowaccurateve- comparison with the FTS atlas suggests that the errors in the locitymeasurements. cores are small. Except for the Caii IR triplet, we do not dis- A realistic 3D hydrodynamical simulation of the non- courage including the cores in velocity calibrations. We think, magnetic solar photosphere was used to synthesize the spec- however,thatavelocitymeasurethatweighinmoreofthepro- tra. The computations were done in LTE for Ci and Fei lines filewillgiveamorereliableresult. whereasnon-LTEcomputationswerecarriedoutintheCaiiin- fraredlines.Astheconversionfromwavelengthtovelocityscale isdoneusingthesame laboratorywavelengthasusedforcom- 6. Conclusions putingthe profiles,the measuredline shifts are relativelyunaf- We made use of the approach described by (Langangenetal. fected by errors in the central wavelength. Uncertaintiesin the 2007)toobtainanabsolutereferenceforvelocitiesinsolarob- rest of atomic parameters are partially compensated when the servations.Forthispurpose,wecalibratedtheshiftinsynthetic profilesarefittedtoreproducethestrengthoftheFTSatlas. 8 J.delaCruzRodr´ıguezetal.:Solarvelocityreferencesfrom3DHDphotosphericmodels Ourresultsshowasystematiccenter-to-limbvariationofthe Johansson,L.1966,Ark.Fys.,31,201 bisectors,whichisdeterminedtoalargeextentbythe3Dstruc- Kupka,F.G.,Ryabchikova, T.A.,Piskunov,N.E.,Stempels,H.C.,&Weiss, ture of the atmosphere, which is projected along the line-of- W.W.2000,BalticAstronomy,9,590 Langangen, Ø.,Carlsson, M.,RouppevanderVoort,L.,&Stein,R.F.2007, sight. However, there is a small amount of redshift (relative to ApJ,655,615 µ = 1.0) producedby the change in the formation height with Leenaarts,J.,Carlsson,M.,Hansteen,V.,&RouppevanderVoort,L.2009,ApJ, the heliocentric angle (non-3D effects), which is not related to 694,L128 projectioneffects.Acarefulanalysisofthemodelssuggeststhat Markwardt, C. B. 2009, in Astronomical Society of the Pacific Conference Series,Vol.411,AstronomicalSocietyofthePacificConferenceSeries,ed. alargenumberof3Dsnapshotsmustbeusedinstudiesofline D.A.Bohlender,D.Durand,&P.Dowler,251–+ shiftssothe oscillationsareproperlysampledandthestatistics Mart´ınezGonza´lez,M.J.,Collados,M.,RuizCobo,B.,&Beck,C.2008,A&A, ofgranulesandintergranulesarecomplete,whereasnon-LTEef- 477,953 fectsseemtohaveaminorinfluenceontheshiftofourFeilines. MartinezPillet,V.,Lites,B.W.,&Skumanich,A.1997,ApJ,474,810 Thelargestuncertaintyisrelatedtothenon-magneticnatureof Ortiz,A.,BellotRubio,L.R.,&RouppevanderVoort,L.2010,ApJ,713,1282 Pereira,T.M.D.,Kiselman,D.,&Asplund,M.2009,A&A,507,417 thesimulation.Nevertheless,weestimateourcalibrationstobe PietarilaGraham,J.,Danilovic,S.,&Schu¨ssler,M.2009,ApJ,693,1728 accurateupto∼ 50ms−1 atµ = 1,remaininguntestedtowards Rutten, R. J. 2003, Radiative transfer in stellar atmospheres, ed. Utrecht thesolarlimb. Universitylecturenotes,8thedition Wewouldliketoemphasizethesomewhatlimitedusability Rutten,R.J.&Kostik,R.I.1982,A&A,115,104 of the Caii calibration, as observations are polluted by a sig- Scharmer,G.B.2006,A&A,447,1111 Scharmer, G. B., Bjelksjo, K., Korhonen, T. K., Lindberg, B., & Petterson, nificantnumberof blends,whichshouldbe maskedin orderto B. 2003, in Society of Photo-Optical Instrumentation Engineers (SPIE) comparewiththecalibrationdata. Conference Series, Vol. 4853, Society of Photo-Optical Instrumentation Oursyntheticprofilesreproducespatially-averagedsolarob- Engineers(SPIE)ConferenceSeries,ed.S.L.Keil&S.V.Avakyan,341– servationsaccurately, but it would be interesting to test for the 350 Scharmer,G.B.,Narayan,G.,Hillberg,T.,etal.2008,ApJ,689,L69 impactofmagneticfieldsontheconvectiveshiftofthelines,and Shchukina,N.&TrujilloBueno,J.2001,ApJ,550,970 confirmthereliabilityofourcalculationsnearthelimb. Shine,R.A.&Linsky,J.L.1974,Sol.Phys.,37,145 Tritschler,A.,Schlichenmaier,R.,BellotRubio,L.R.,etal.2004,A&A,415, Acknowledgements. WethankTiagoPereiraforprovidingthe3Dsnapshotsof 717 theHDsimulationandRoaldSchnerrandMichielvanNoortforprovidingre- Unsold, A. 1955, Physik der Sternatmospharen, MIT besonderer duced data from the SST/CRISP. We are most grateful to Paul Barklem for BerucksichtigungderSonne.,ed.Unsold,A. providingunpublished cross-sections forcollisional broadening. Thisresearch vanNoort,M.,RouppevanderVoort,L.,&Lo¨fdahl,M.G.2005,Sol.Phys., project has been supported by a Marie Curie Early Stage Research Training 228,191 FellowshipoftheEuropeanCommunity’sSixthFrameworkProgramundercon- tract number MEST-CT-2005-020395: The USO-SP International School for SolarPhysics. TheSwedish1-mSolar Telescope is operated ontheisland of La Palma by the Institute for Solar Physics of the Royal Swedish Academy of Sciences in the Spanish Observatorio del Roque de los Muchachos of the InstitutodeAstrof´ısicadeCanarias. References Adam,M.G.,Ibbetson,P.A.,&Petford,A.D.1976,MNRAS,177,687 AllendePrieto,C.&GarciaLopez,R.J.1998,A&AS,131,431 Asplund,M.,Grevesse, N.,&Sauval, A.J.2005,inAstronomicalSociety of thePacificConferenceSeries,Vol.336,CosmicAbundancesasRecordsof Stellar Evolution andNucleosynthesis, ed. T.G. Barnes III& F.N.Bash, 25–+ Asplund,M.,Nordlund,Å.,Trampedach,R.,AllendePrieto,C.,&Stein,R.F. 2000,A&A,359,729 Balthasar,H.1985,Sol.Phys.,99,31 Balthasar,H.1988,A&AS,72,473 Barklem, P. S., Anstee, S. D., & O’Mara, B. J. 1998, Publications of the AstronomicalSocietyofAustralia,15,336 Barklem,P.S.,Piskunov,N.,&O’Mara,B.J.2000,VizieROnlineDataCatalog, 414,20467 Beckers,J.M.1977,ApJ,213,900 Beckers,J.M.&Nelson,G.D.1978,Sol.Phys.,58,243 BellotRubio,L.R.,Balthasar,H.,&Collados,M.2004,A&A,427,319 BellotRubio,L.R.,Tritschler,A.,&Mart´ınezPillet,V.2008,ApJ,676,698 Borrero,J.M.&BellotRubio,L.R.2002,A&A,385,1056 Brault, J. W. & Neckel, H. 1987, Spectral Atlas of Solar Absolute Disk- averagedandDisk-CenterIntensityfrom3290to12510Å,ftp://ftp.hs.uni- hamburg.de/pub/outgolng/FTS-Atlas Carlsson,M.1986,UppsalaAstronomicalObservatoryReports,33 Cheung,M.C.M.,Schu¨ssler,M.,&Moreno-Insertis,F.2007,A&A,461,1163 deWijn,A.G.,Stenflo,J.O.,Solanki,S.K.,&Tsuneta,S.2009,SpaceSci.Rev., 144,275 Dravins,D.1982,ARA&A,20,61 Fabbian,D.,Asplund,M.,Carlsson,M.,&Kiselman,D.2006,A&A,458,899 Franz,M.&Schlichenmaier,R.2009,A&A,508,1453 Gadun,A.S.,Solanki,S.K.,&Johannesson,A.1999,A&A,350,1018 Janssen, K. & Cauzzi, G. 2006, in Astronomical Society of the Pacific ConferenceSeries,Vol.354,SolarMHDTheoryandObservations:AHigh SpatialResolutionPerspective,ed.J.Leibacher,R.F.Stein,&H.Uitenbroek, 49–+ 9

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Preview Solar velocity references from 3D HD photospheric models

Astronomy&Astrophysicsmanuscriptno.15664 (cid:13)c ESO2011 January17,2011 Solar velocity references from 3D HD photospheric models J.delaCruzRodr´ıguez1,2,D.Kiselman1,andM.Carlsson3,4 1 InstituteforSolarPhysics,RoyalSwedishAcademyofSciences,AlbaNovaUniversitycenter,SE-10691Stockholm,Sweden 2 DepartmentofAstronomy,StockholmUniversity,AlbaNovaUniversitycenter,SE-10691Stockholm,Sweden 3 InstituteofTheoreticalAstrophysics,UniversityofOslo,P.O.Box1029Blindern,N-0315Oslo,Norway 4 CenterofMathematicsforApplications,UniversityofOslo,P.O.Box1053Blindern,N-0316Oslo,Norway Preprintonlineversion:January17,2011 1 ABSTRACT 1 0 Context.ThemeasurementofDopplervelocitiesinspectroscopicsolarobservationsrequiresareferenceforthelocalframeofrest. 2 TherotationalandradialvelocitiesoftheEarthandtherotationoftheSunintroducevelocityoffsetsintheobservations.Normally, goodreferencesforvelocitiesaremissing(e.g.telluriclines),especiallyinfilter-basedspectropolarimetricobservations. n Aims.Wedetermineanabsolutereferenceforline-of-sightvelocitiesmeasuredfromsolarobservations foranyheliocentricangle, a J calibratingtheconvectivelineshiftofspatially-averagedprofilesonquietsunfroma3Dhydrodynamical simulation.Thismethod workswheneverthereisquietsuninthefield-of-view,andithastheadvantageofbeingrelativelyinsensitivetouncertaintiesinthe 3 atomicdata. 1 Methods.We carry out radiative transfer computations in LTE for selected Ci and Fei lines, whereas the Caii infrared lines are synthesized innon-LTE. Radiative transfer calculations are done witha modified version of Multi, using the snapshots of anon- ] R magnetic3Dhydrodynamicalsimulationofthephotosphere. Results.TheresultingsyntheticprofilesshowtheexpectedC-shapedbisectoratdiskcenter.Thedegreeofasymmetryandtheline S shifts,however,showacleardependenceontheheliocentricangleandthepropertiesofthelines.Theprofilesatµ=1arecompared h. withobservedprofilestoprovetheirreliability,andtheyaretestedagainsterrorsinducedbytheLTEcalculations,inaccuraciesinthe p atomicdataandthe3Dsimulation. - Conclusions.Theoretical quiet-sunprofilesoflinescommonlyused bysolar observersareprovided tothecommunity. Thosecan o beusedasabsolutereferencesforline-of-sightvelocities.Thelimbeffectisproducedbytheprojectionofthe3Datmospherealong r thelineofsight.Non-LTEeffectsonFeilinesarefoundtohaveasmallimpactontheconvectiveshiftsofthelines,reinforcingthe t s usabilityoftheLTEapproximationinthiscase.Weestimatetheprecisionofthedisk-centerlineshiftstobeapproximately50ms−1, a buttheoff-centerprofilesremaintobetestedagainstobservations. [ Keywords. Convection–Sun:photosphere–Line:fomation–Radiativetransfer–Sun:granulation–Hydrodynamics 1 v 1 1. Introduction Below,wediscusssomemethodsthathavebeenusedtode- 7 6 fineavelocityreferenceforsolarobservations. Theneedforhighspatialandspectralresolutioninsolarobser- 2 vations stimulates new advances in telescope and instrumenta- – Sunspotumbraearecommonstandards(e.g.,Beckers1977; . 1 tiontechnology,adaptiveopticsandimagereconstructiontech- Scharmeretal.2008;Ortizetal.2010),butthisonlyworks 0 niques.However,theaccuracyofthemeasurementsisoftenlim- when a suitable sunspot is in the field-of-view and relies 1 ited by calibration issues. This is evident when using Doppler on the assumption that the umbra is at rest because of the 1 shifts of spectral lines to acquire line-of-sight velocities in the convectivemotionsbeingsuppressedbythestrongmagnetic v: solarplasma,wherethetaskoffindingalocalstandardofrestis fields.Furthermore,thelinemustbemeasurableintheum- i oftenproblematic. braandwavelengthshiftswhichareinducedbyblendsfrom X The current work is partly motivated by the installation of lines uniquely formed in the umbra (e.g. molecules), must r the CRisp ImagingSpectropolarimeter(CRISP, Scharmeretal. beaccountedfor.Finally,observationsofumbraearealways a 2008)attheSwedish1-mSolarTelescope(SST,Scharmeretal. plagued by stray light from the much brighter quiet photo- 2003).Instrumentslike thisusuallylacklaboratorywavelength sphere. references,whiletheuseoftelluriclineshaslimitationsasdis- – Telluric lines can be used to define a laboratory-frame cussedbelow.Theobvious(andcommonlyused)solutionoflet- reference, which can then be converted to the Sun. tingthespectrallineofinterest–averagedoveralargeenough MartinezPilletetal. (1997) and BellotRubioetal. (2008) areaandlongenoughtime–definealocalframeofrestiscon- used telluric lines to derive the wavelength scale for their foundedbythefactthatconvectivemotionsleavestrongfinger- observations,thenconvertedtoanabsolutewavelengthscale printsonanyspectrallineformedinthesolarphotosphere.The ontheSungiventheephemerisconstants,timeoftheobser- statisticalaverageofbrightblueshiftedanddarkredshiftedpro- vations,solarrotationandthelaboratorywavelengthsforall filesformedingranulesandintergranularlanesrespectively,pro- observedspectrallines. ducestheblueshiftedC-shapedbisectorsofphotosphericlinesas – A spectral atlas, most commonly the atlas acquired reviewedbyDravins(1982). with the Fourier Transform Spectrometer at the McMath- Pierce Telescope (hereafter called the FTS atlas) of Sendoffprintrequeststo:J.d.l.C.R.:e-mail:[email protected] Brault&Neckel (1987), can be used to calibrate observa- 1 J.delaCruzRodr´ıguezetal.:Solarvelocityreferencesfrom3DHDphotosphericmodels tions. Thiswas doneby Langangenetal. (2007), who used Table 1. Atomic data, sorted by element in increasing wave- the laboratory wavelength to define the reference for ve- length. locities, assuming an absence of systematic errors in the FTS atlas itself and correctingfor the gravitationalredshift λ (Å) E loggf σ(1) α(2) logǫ(3) 0 c (633 m s−1). This method only works at disk center where Ci5380.3370 7.6850 -1.824 1238 0.229 8.53 theatlaswasrecorded. Fei5250.2089 0.1210 -4.938 207 0.253 7.44 – Numerical models can be used to predict convective line Fei5250.6460 2.1980 -2.181 344 0.268 7.71 shifts and thus provide a velocity reference. A two- Fei5576.0888 3.4300 -1.000 854 0.232 7.69 component model of the solar photosphere has been de- Fei6082.7106 2.2230 -3.573 306 0.271 7.45 Fei6301.5012 3.6540 -0.718 834 0.243 7.55 rived by Borrero&BellotRubio (2002) from the inversion of Fei spectral lines. Since it does not contain any hori- Fei6302.4940 3.6860 -1.203 850 0.239 7.50 Fei7090.3835 4.2300 -1.210 934 0.248 7.63 zontal velocities, it then is in principle limited to calibrat- Caii8498.0134 1.6920 -0.6391 291 0.275 6.31 ing disk-centerobservations,for which it has been used by Caii8542.0532 1.7000 -0.4629 291 0.275 6.31 Tritschleretal. (2004) andFranz&Schlichenmaier(2009). Caii8662.1605 1.6920 -0.7231 291 0.275 6.31 However,BellotRubioetal.(2004)useditwiththeempiri- calresultsofBalthasar(1988)toalsoestimatelineshiftsoff Notes.(1)thecross-sectioninunitsoftheBohrradius,(2)dimension- solar center. Langangenetal. (2007) employ a 3D numeri- lessparameterusedwith(1)inthecomputationofcollisionalbroaden- calgranulationmodeltocomputetheconvectiveblueshiftof ing(Barklemetal.1998).(3)thefittedvalueoftheabundanceforeach theCi5380Ålineandcalibratetheirobservations.Thisap- line. proachwasnecessarybecausethelaboratorywavelengthof the Ci line is not known with enough precision to use the tionsnapshots.TheFei andCi lineswerecalculatedassuming atlascalibrationthatismentionedabove. local thermodynamical equilibrium (LTE), which is a reason- able assumption for the wings of most photospheric Fei lines We note that telluric lines cannot always be observed with (Gadunetal. 1999; Asplundetal. 2000). Fabbianetal. (2006) the solar diagnostic lines and that when this is the case, ob- foundthatnon-LTEeffectsforCilinesareexpectedtobesmall serving them can be expensive. Observations with tunable fil- withtheeffectonderivedabundancebeing<0.05dex.Possible ters require high cadence because of seeing variability and so- errorsproducedbynon-LTEeffectswillbefurtherdiscussedin lar evolution. Any time spent recording telluric lines thus de- Section4.3.1. creasesthe spatialresolutionand thesignal-to-noiseof thesci- TheCaiilineswerecomputedin1.5Dnon-LTE–wherethe encedata.Thiswouldalsoapplytoanylaboratoryspectral-line non-LTEproblemissolvedin1D–usingthesamemodelatom source used for calibration.Furthermore,approachesusing tel- asLeenaartsetal.(2009),whichconsistsof5boundlevelsplus luriclines(orothercalibrationlines)andspectralatlasesallre- acontinuum. quireveryaccurateatomicdatatodefinethezerovelocitypoint Atomic data were obtained from the VALD-2 database andthusconvertthe wavelengthscale intovelocityscale. Such (Kupkaetal.2000).ThetreatmentofvanderWaalsbroadening data are unfortunately not available for many of the lines that followsthatofBarklemetal.(1998)andtherequiredcrosssec- areextensivelyusedin solarphysicsasis apparentin the work tions were taken from Barklemetal. (2000), except for the Ci of Langangenetal. (2007) described above. Their approach is line providedby Paul Barklem (private comunication).The ef- proposedinthisstudy:usingrealistic3Dnumericalsimulations fectivequantumnumbersn∗forthistransitionare1.95→3.27. ofthesolarphotospheretocomputespatially-averagedlinepro- Thetreatmentbecomeslessreliablewhenn∗>3.0butitismore files. As the radiativetransfercomputationis carriedoutin the accuratethanthecommonlyusedUnsold(1955)formulation. local frame of rest of the Sun and the adopted atomic data is To achieve the best possible fit between the synthetic line known, the velocity shifts of the spatially-averagedprofile can profile at µ = 1 and the FTS atlas, the elemental abundance becomputedaccuratelyfordifferentheliocentricangles,relative is individually adjusted for each line. The resulting abundance totheassumedcenteroftheline.Thismethodreliesonthede- values(lastcolumninTable1)shouldnotberegardedassuch. greeofrealismofthe3Dsimulationandrequiresalargestatisti- Instead, they act as free parameters that compensate for errors calsampleofspectratocomputethespatially-averagedprofile. fromatomicdata,theLTEapproximation,andthemodelsthem- The aim of this work is to provide the community with a set selves.Thehopeisthatbyfittingtheprofilethecorrectlayerof oftheoreticalspatially-averagedquiet-Sunprofilesoflinescom- the modelwith the appropriatevelocity field is being sampled. monly used in solar physics, that are computed for a range of Since non-LTE effects could be expected to affect the cores of heliocentricangles. stronglines,onlythewingsofeachlinewereusedforthefitof In Sect. 2 the atomic data and radiative transfer details are theabundance;however,theresultschangemarginallywhenthe discussed. The 3D HD simulation is described in Sect. 3. In fullprofileisusedtofit. Sect. 4 the results are presented together with an error analy- The results for the Caii infrared triplet lines must be ap- sisandarealfilter-basedobservationiscalibratedusingthenew proachedwith extracautionsince the lines are verystrong and data.Section5describestheelectronicdatamadeavailableand the 3D simulation does not extend all the way up to the chro- Sect.6summarizesthemainconclusionsofthiswork. mosphere. Therefore the calculated core of the line cannot be comparedtorealobservations,butthephotosphericoriginofthe wings suggests the usability of the models with these lines, as 2. Linelistandradiativetransfer discussedbyShine&Linsky(1974). The calculations were carried out with a selection of lines We have included blends affecting the Fei and Ci lines. (Table 1) that are extensively used in solar physics, including The atomic parametersfor these were taken from the VALD-2 lines that can currently be observedwith CRISP at the SST. A database (Kupkaetal. 2000). The blends are weak, but have a modifiedversionoftheradiativetransfercodeMulti(Carlsson smalleffectontheupperpartofsomebisectors.TheCaiilines 1986) was used to compute synthetic spectra from the simula- have some strong blends in the wings which greatly affect the 2 J.delaCruzRodr´ıguezetal.:Solarvelocityreferencesfrom3DHDphotosphericmodels highandthesurfaceoftheintergranularlanesbecomessmaller. Theblueshiftdecreasesmonotonouslytowardsthelimb. A variety of bisector shapes and µ dependences are found in the Fei lines. At µ = 1, the lines have the expected blueshiftedconvectiveC-shapedbisectors.Whengoingoffcen- ter, the blueshift for many lines increases, while the blueshift decreases again at even higher heliocentric angles, sometimes turningintoaredshift,andthebisectorsbecomemore\-shaped. Each line shows its own individual behavior – function of its strength, excitation potential, and other properties. The line coreshave beenexcludedfromthe bisectorsfor the Caii lines. These wing bisectors show a progression from a C-shape to a \-shapefromcentertolimb. Table2listsnumericalvaluesfortheconvectiveshiftscom- puted as the mean of the bisector – excluding the part closest Fig.1. Mean bisector velocity as a function of the number of to the continuum– for each line and µ value, and Table 3 lists snapshotsusedtocomputethespatially-averagedspectrum. thelinecorevelocitiesfoundwhenconvolvingthesyntheticline profileswiththeappropriateCRISPinstrumentalprofile. bisectors, so these blends were not present in the present Caii 4.1.Effectofspectralresolution calculations. Theasymmetryofthelineswilldecreasewithdecreasedspectral resolution.Whencomparingwithobservations,orusingthethe- 3. 3Dhydrodynamicalphotosphericmodels oreticalprofilesforvelocitycalibration,theprofilesmustbecon- volvedtothe properspectralresolution.Figure3illustratesthe The3Dhydrodynamicalsimulationconsistsof90snapshotsand dependence of the mean bisector, the center-of-gravity (COG) covers around 45 minutes of solar time (Trampedach et al., in velocity, and the line-core velocity on spectral resolution. The prep.;Pereiraetal.2009).Thesimulationdoesnotincludemag- corevelocityisnaturallytheonemostsensitivetospectralreso- netic fields. The radiative energy transportwas computed with lution.COGisleastsensitiveinthisspecificcase,butthedevia- animprovedmulti-groupopacitybinningof12bins,whencom- tionsinallcasesstartatsuchspectralresolutionsthatwearecon- paredwiththe3DmodelsofAsplundetal.(2000).Theoriginal tenttousethemeanbisectorvelocityinallourillustrationshere. simulationof240×240×240grid-pointscoveringaregionof Wedothinkthatanypracticaluseofourlineprofilesshoulduse 6×6×4 Mm was interpolatedto a finer verticaldepthgrid in thedetailedprofilewiththeapplicationoftheappropriateinstru- theradiativezoneandsampledtoacoarsergridinthehorizon- mentalsmearingandweighting. tal planefor radiativetransfercalculations.The resulting snap- shotshadasizeof50×50×82gridpointsrepresentinga6Mm square.Ourtestsshowthattheeffectofsucharesamplinginthe 4.2.Thelimbeffect horizontalplanehasanegligibleeffectonthespatially-averaged profilesofthelines. The bisectors change with heliocentric angle, and close to the The presence of oscillations in the simulation broadensthe limb the blueshift usually gets small and is sometimes turned time-averagedprofilecomparedtotheindividualsnapshots.The into a redshift for the line cores. This limb effect (Adametal. oscillationshaveaquasi-periodicbehavior,soatleastoneperiod 1976; Beckers&Nelson 1978; Balthasar 1985) was subject shouldbeincludedinthetimeaverageinordertoavoidsystem- to much speculation before granulation was understood (see atic shifts of the average profiles. Figure 1 shows the average Dravins1982).Itseemsthatacomprehensiveexplanationisstill velocity(integratedalongthebisector)ofthetimeaveragedpro- lacking, which could be because the complicated nature of the file as a function of the number of snapshots used in the time situation precludessimple explanations.Nevertheless,we want series. The limited sample of granules and intergranular lanes todiscussithereinthelightofourresults. enclosed in a 6 Mm box reinforces the need to use more than The convectiveblueshiftand line asymmetry at disk center one period in order to convergeto a stable average for the line arecausedbytheasymmetryoflargebrightgranuleswitharel- shift. Therefore,the whole time series was used for computing atively slow upward flow producing blueshifted lines and nar- theaveragelineprofiles. rowdarkintergranularlaneswith fastdownwardflowsproduc- Toproduceprofilesoffdiskcenter,thepropertiesofthe3D ing redshifted lines. As we leave the disk center, a number of effects will changethe shifts and the line profiles. Towardsthe snapshots are slanted assuming periodic boundary conditions, limb,higherphotosphericlayersaresampledthathavedifferent and the velocity vector is projected into the new line-of-sight. velocitypatternsanddifferentstatisticalrelationsbetweeninten- Theheightscaleisalsomodifiedtomatchthenewgeometryof sityandline-of-sightvelocities.Ofparticularinterestisthepat- the3Dmodel. tern of inverse granulation (e.g., Cheungetal. 2007) that char- acterizesthephotosphericstructureaboveacertainheight.Also, 4. Results horizontalvelocitiesbecomemoreimportantastheviewingan- gledecreasesandwillsoondominatethecontributionfromver- In Fig. 2 the resulting line profiles for all heliocentric angles tical convective motions. There are also 3D effects due to the are plottedtogether,alongwith their bisectors. TheCi 5380Å corrugatednatureoftheopticaldepthsurface.We canconsider lineshowsthestrongestconvectiveblueshift,anexpectedresult the following mechanisms that can decrease the blueshift and giventhatthelineisformedverydeepduetothehightexcitation ultimatelyleadtoaredshiftintheaveragelineprofiles: potentialofthetransition.Indeeplayers,verticalvelocitiesare 3 J.delaCruzRodr´ıguezetal.:Solarvelocityreferencesfrom3DHDphotosphericmodels Fig.2.Syntheticprofilesandthecorrespondingbisectorsresultingfromthecalculationsof Ci,FeiandCaiilines.Thegrayscale indicatesthevariationintheheliocentricanglefromµ = 1.0toµ = 0.3.ThebisectorsfortheCaiilinesarenotshowninthecore part. 1. The intensity-velocity correlation changes as higher and terofagranule(x∼4000km),seeminglyblockingaredshifted higher levels in the photosphere are sampled by the line sideofagranule.Onecanthusarguethatsomeofthementioned (e.g.Janssen&Cauzzi2006;Cheungetal.2007).Thisisthe mechanismsandotherscanproduceablueshiftwithdecreasing sameeffectthatcausestheC-shapeindisk-centerbisectors. µ.Decidingwhichmechanismswilldominaterequiresaquanti- 2. The redshiftedpartof thegranuleis seen againsta brighter tativeanalysis.Wemadeafirsteffortinthatdirection. background than the blueshifted part (Beckers&Nelson Effects2,3,and4aretrue3Deffectsthatbreakthesymme- 1978;Asplundetal.2000). try between redshifted limbside granular parts and blueshifted 3. Near the limb, surface corrugation causes redshifted parts centerside parts. They shouldgo away in a multi-1D treatment of granules to show larger areas to the observer (Balthasar whereeachcolumninthesimulationistreatedasaplane-parallel 1985). atmosphere.Theresultsofsuchanumericalexperimentsfortwo 4. Reversed granulation“hills” overintergranularlanes shield of our lines can be seen in Fig. 5. It is clear that for each line, blueshiftedpartsofgranuleswhenobservedoffdiskcenter. thevariationofbisectorswithµissmallerthanin3D.Itisalso Figure4showsacrosssectionthroughasimulationsnapshot monotonousandalwaysinthesensethataprofilebecomesred- illustratingline formationat µ = 0.3.Inspectionof thesimula- deratthecoreofthelinewithdecreasingµ.Theclosefollowing tionsnapshotsinthiswaycangivesupporttoallthelistedmech- of the successive bisectors to that of µ = 1 is an illustration anismsandalsoinspireinventionofnewones.Theeffectofthe of the Eddington-Barbierrelations: the µ dependenceis equiv- hotwalloveranintergranularlane(at x ∼ 2200km)is,forex- alentto the depthdependence.We takethis to meanthatmuch ample,obvious.Itblockstheviewtowardsthe blueshiftedside ofthecenter-to-limbvariationofspectrallineshiftsisdueto3D ofagranule.Butasimilarstructureisalsopresentoverthecen- effects. The latter either shifts the bisectors to redder or bluer 4 J.delaCruzRodr´ıguezetal.:Solarvelocityreferencesfrom3DHDphotosphericmodels Fig.3. Left: Bisectors of the synthetic Fei 6301.5 Å line as a functionofthespectralresolution.Right:Velocitiesmeasuredin differentways fromthe profilesonthe left panel,as a function ofspectralresolution. wavelengths,relativetothe1Dcase.Forexample,theblueshift relative to disk center that is seen in many lines for moderate heliocentricanglesmustbeduetoa3Dmechanism.Wehypoth- esise that this comes from the screening of narrow downdrafts fromviewasthelineofsightdepartsfromthevertical. 4.3.Erroranalysis 4.3.1. Non-LTEeffectsinFeilines Our radiative transfer calculations assume LTE. The errors in- troducedby this approximationwill to some extentbe reduced by fitting the line profiles using an individualabundance value for each line as a free parameter. Shchukina&TrujilloBueno (2001) studied the impact of non-LTE effects on Fei and Feii linesusinga3Dsimulation(buta1Dtreatmentofthenon-LTE problem,thus1.5D)andreportedlargerdeparturesfromLTEin granulesthaninintergranularlanes.Basedonthiswork,wecan Fig.4.Propertiesofthemodelalongasliceofoneofthesnap- expectthefollowingtwonon-LTEmechanismstodominate shotsatµ = 0.3:temperature,absorptioncoefficientatthecore 1. Overionization: A line from a neutral species typically has of Fei6301.5Å, andlineofsightvelocityfromtoptobottom. lowerlineopacitythanitsLTEvaluebecauseofoverioniza- Thesolidlinethatisoverplottedoverthethreepanelsrepresents tion thatis caused by the UV radiationfield beingstronger the layer where τ = 1 along the line of sight. Four rays are LC than the local Planck function. This causes the line to be shownassolidlinesaboveτ =1anddashedbelowthisheight. LC formed deeper in the atmosphere and thus be weaker than Thebottompanelshowstheline-of-sightvelocitiesalongthedi- inLTE. rectionshownbytherays.Thehorizontaldashedlinerepresents 2. The non-LTE line source function Sl can be expressed in thelayerwhereτ equals1atµ=0.3. ν 500 terms of the departure coefficients of the populations from theupper(b )andlower(b)levels(seeRutten2003)ifstim- j i ulatedemissionisneglected, thesensitivityoftheresultinglineshifttosuchdifferentialdepar- turesfromLTE.Oneofthe3Dsnapshotswasdividedingranules b Sl ∼ jB (T) (1) and intergranularlanes based on the sign of the verticalveloc- ν bi ν ities at τ500 = 1 and synthetic spectra were computed for dif- whereB (T)isthePlanckfunction.Photonlossesintheline ferent values of the iron abundance. The aim was to find the ν itself leadto a decreasein b andincrease onb, producing combinations of abundances in granules and intergranules that j i alinesourcefunctionthatislowerthanthePlanckfunction. reproduce a spatially-averaged spectrum with the same equiv- ThisleadstoastrongerlinethaninLTE. alent width as the observed profile. We used a nonlinear least- squaresfit,describedinMarkwardt(2009),inordertoinferthese Thefirsteffecttendstobethemostimportantforweaklines, pairsof values.Figure6 illustratesthe averageshiftof the line whilethesecondisfoundforstronglinesbecausethelineopac- asafunctionofabundancedifferencebetweenthegranulesand ity dominates the backgroundopacity. In some cases, the non- the intergranularlanes. The reference was set where the abun- LTE and LTE profiles are very similar because the two effects dance derived from the granulesand intergranulesis the same. cancel out. However, the presence of larger LTE departures in Shchukina&TrujilloBueno(2001)findanaveragenon-LTEef- thegranulesthanintheintergranularlanesnotonlychangesthe fectonderivedFeabundancesof0.1dex.Ifthisnumberistaken strengthoftheline,butalsotheconvectivelineshift.Wetested asalsotypicalofthe differencebetweengranuleandintergran- 5 J.delaCruzRodr´ıguezetal.:Solarvelocityreferencesfrom3DHDphotosphericmodels Table2. Convectiveshiftsinms−1ofthestudiedlinesfromµ=1.0toµ=0.3. Element λ (Å) µ=1.0 µ=0.9 µ=0.8 µ=0.7 µ=0.6 µ=0.5 µ=0.4 µ=0.3 0 Ci 5380.34 -948 -936 -922 -910 -897 -888 -880 -844 Fei 5250.21 -294 -372 -410 -426 -420 -394 -346 -259 Fei 5250.65 -304 -354 -370 -369 -348 -308 -245 -140 Fei 5576.09 -334 -378 -388 -383 -360 -317 -249 -140 Fei 6082.71 -441 -495 -522 -536 -531 -511 -473 -397 Fei 6301.50 -307 -349 -358 -351 -325 -279 -211 -101 Fei 6302.49 -335 -387 -404 -403 -381 -342 -280 -176 Fei 7090.38 -352 -396 -409 -407 -389 -354 -302 -210 Caii 8498.01 -265 -288 -289 -275 -248 -206 -148 -70 Caii 8542.05 -335 -364 -374 -372 -359 -337 -307 -269 Caii 8662.16 -272 -294 -293 -279 -251 -208 -149 -68 Notes. Thebisector of each linewasintegrated from95% of thecontinuum intensity tothecore of the line. Inthecase of theCaii lines, the non-LTEcorewasexcluded.ForCitheupperthresholdwashigher(97%)becausethelineisweak. Table3. Linecorevelocitiesofthesyntheticspectrallines(excludingCaii) convolvedwiththeappropriatetheoreticalprofileof CRISPforeachwavelength. Element λ (Å) µ=1.0 µ=0.9 µ=0.8 µ=0.7 µ=0.6 µ=0.5 µ=0.4 µ=0.3 0 CI 5380.34 -928 -895 -867 -840 -820 -810 -795 -764 FeI 5250.21 -178 -306 -358 -370 -354 -315 -246 -134 FeI 5250.65 -115 -196 -221 -213 -177 -115 -26 108 FeI 5576.09 -163 -222 -231 -209 -164 -96 -3 126 FeI 6082.71 -403 -470 -499 -508 -500 -480 -433 -341 FeI 6301.50 -188 -238 -241 -217 -173 -109 -17 108 FeI 6302.49 -255 -326 -347 -338 -306 -255 -178 -57 FeI 7090.38 -315 -378 -396 -388 -362 -321 -255 -148 Fig.6. Differential Doppler shift of the Fei 6082.7Å line pro- duced by changes in the relative abundance between granules and inter-granules. The combinations of granular/intergranular abundanceswerefittedtoreproducetheequivalenthwidthofthe FTSatlas. Fig.5. Bisectors for two lines computed in the plane-parallel dancesinferredbyAsplundetal.(2005)normallyleadtodiffer- treatment,“1D”,comparedtothefull“3D”result. entresultsforthedifferentlines,somepresentingmoredamped wingsthantheatlasandothersnarrowerones.Theabundanceis usedasafreeparameterinordertomatchthewingsofthesyn- uleabundanceinFig.6,theerrorsinthecomputedlineshiftdue theticprofilesforµ=1withtheFTSatlas.Theinnercoreisnot tonon-LTEeffectsshouldbesmallerthan±30ms−1. includedinthefittingprocedurebecausegenerallynon-LTEef- fectsareexpectedtobelargerthere(seeRutten&Kostik1982), andthemodelsnapshotsbecomelessreliableclosetotheupper 4.3.2. Profilefitting boundary(seeAsplundetal.2000). DuetotheeffectsdescribedinSection4.3.1andbecuasethe3D Asanindicatoroftheerrorsduetothisfittingprocedure,we modelsareonlyrealisticuptoacertainheight,theresultingpro- performedtestcalculationstogetthesensitivityofthebisectors filesshowdifferencescomparedtotheFTSatlas.Thesolarabun- tochangesintheassumedabundance.Theresultsareshownin 6 J.delaCruzRodr´ıguezetal.:Solarvelocityreferencesfrom3DHDphotosphericmodels Fig.8.Feisyntheticbisectors(fulldrawn)comparedwithbisectorsmeasuredfromtheFTSatlas(dashed). sultsbymorethanthisamount.Theestimatedoesnot,however, includetheintrinsicerrorsofthesimulation. To check the realism of the simulations, we compared the synthetic line profiles at µ = 1.0 with the FTS atlas after ap- plying a gravitational redshift on the former. The average syn- thetic Ci bisector lies 530 m s−1 redwards of that measured from the FTS atlas, something that we deem mostly to be due to errorin thelaboratorywavelengthofthe line.Atface value, our simulations implies a wavelength of 5380.3275 Å on the FTS-atlaswavelengthscale.Thisiswithintheciteduncertainty (0.02Å)ofthelaboratoryvalueof5380.3370ÅfromJohansson (1966),whichwasusedhere.Itisalsocomfortinglyclosetothe 5380.3262ÅfoundinasimilarwaybyLangangenetal.(2007) from their observations and simulations of magnetic regions. ThebisectorsfortheFeilinesaredisplayedinFig.8.Thesyn- thetic bisector shapes show an acceptablecorrespondencewith those measured from the FTS atlas. The standard deviation of thedifferencesinmeanvelocityis56ms−1 whichcorresponds toapproximately1mÅ.Thisiscomparabletoourestimateofthe Fig.7. Bisectors calculated for at µ = 1.0,0.6,0.3 for a range internalerrorsfromnon-LTEeffectsandfittingprocedures,but of abundances. The results are only from five snapshots which onceagainthereisstrongreasontobelievethatasignificantpart means that they cannot be directly compared with, e.g., Fig2. of these deviations are due to errors in the adopted laboratory Left:abundancetestforFei6301ÅwithvaluesoftheFeabun- wavelengths. dancewithin[7.25-7.65].Right:testforCi5380Å,thevalues Finally we note that AllendePrieto&GarciaLopez (1998) oftheabundancespananunrealisticrangecomparedtothenom- estimate the precision in FTS wavelengths to be on the order inalvalue[8.19-8.69]. of 50 m s−1. It seems likely that several of the error estimates discussed aboveare too conservative,but the synthetic profiles seemtopassthetestandtheyshouldbecorrectwithin50ms−1. Observationalchecksoftheoff-centerprofilesaremoredifficult Fig.7.TheleftpanelscorrespondtotheFei6301Åline,calcu- but would be welcome. Since photosphericmodelingoftenbe- lated on three different heliocentric angles, for different values comes more uncertainfor low µ values, it is naturalto suspect ofthe Fe abundance.Thepanelsonthe rightcorrespondto the that the accuracyof our convectiveline shifts will decrease to- Ci5380Å,wheretheabundancecoversanunrealisticrangeof wardsthelimb. values[8.19,8.69].Thisweak line, whichis formedveryclose tothecontinuum,ismoresensitivetochangesintheabundance The hydrodynamic granulation simulations do not include thanthestrongerFeiline.Thelowerpanelsshowtherelativeve- magnetic fields. This is potentially the most important source locityshiftintegratedoverthewholebisector.We estimatethat oferrorsinthepracticalapplicationofthesesyntheticlinepro- the uncertainties from the fitting procedure are within 0.1 dex files for velocity calibrations. For example, Langangenetal. inabundancewhichthencorrespondsto±10ms−1 fortheinte- (2007) estimated a difference of 200 m s−1 in convective shift gratedbisector. for the Ci 5380 Å line between non-magneticand active gran- ulation.(Thiswasmostlycausedbythechangingintensityand velocity pattern and not by Zeeman splitting.) Any calibration 4.3.3. Discussion work must use the least magnetic photospheric region avail- Fromthetestsabove,theestimatederrorintheshiftofthelines able. However, how strong the quiet Sun magnetic fields are islessthan50ms−1.Thismeansthatafullnon-LTEtreatment is still an ongoing debate (e.g. Mart´ınezGonza´lezetal. 2008; combinedwiththeexactatomicdatashouldnotchangethesere- PietarilaGrahametal.2009;deWijnetal.2009). 7 J.delaCruzRodr´ıguezetal.:Solarvelocityreferencesfrom3DHDphotosphericmodels 4.4.CalibrationofSST/CRISPobservations A quiet Sun dataset acquired with SST/CRISP at µ = 1.0 was calibrated using the current results. The Fei 6302 Å line was sampled with eight wavelength points, evenly distributed with a separation of dλ = 48 mÅ and processed using the image restorationcode MOMFBD (vanNoortetal. 2005). The telecentric optical design of CRISP (Scharmer 2006) is opti- mumforhighimagequality,butitintroducesinstrumentalfield- dependent wavelength shifts produced by irregularities on the surfaceoftheetalons,whicharecommonlyknownascavityer- rors. The latter complicate the task of obtaining the spatially- averaged spectrum, as the profile is effectively broadened by these random pixel-to-pixel shifts. The average spectrum was computedwithaleast-squares-fitofallthedatapointstoaspline whichwascharacterizedwithtenparameters.Forthispurpose, all the individual spectra were corrected for cavity errors and then arranged in a large array, which was sorted in increasing wavelength. Tocarryoutthevelocitycalibration,thesyntheticspectrum obtained from the 3D simulation was convolved with the the- oretical instrumental profile of CRISP, which included the ef- fects of the beam converging at f/165. The velocity calibra- tion was determined by finding the constant wavelength shift to the observed bisector that minimized the difference to the synthetic one. Figure 9 illustrates the results of the calibration, wheretheDopplermapatthecoreofthelineisscaledbetween ±1500 m s−1. The bottom-leftpanelcontains a density map of the spatially resolved spectra, corrected for cavity errors. The dispersionofpointsaroundthe sevennominalwavelengthsap- pears after correctingfor the cavity errorsin combinationwith the granulation contrast. The bisector of our calibrated data is overplotted to the bisector of the synthetic spectrum that was convolvedwiththeinstrumentalprofileofCRISP.Thereisatel- luricblendonthe redwing ofthe observedprofile,notpresent inthesyntheticspectrum,thatpollutestheupperpartofthebi- sector. Fig.9.Top:Dopplermapofquietsungranulationobservedwith SST/CRISP at Fei 6302Å. The image gray scale is clipped to 5. Usageofelectronicdata ±1500m s−1. Bottom-left:Spatially-averagedprofilecomputed along the image shown in the top panel. The density map rep- Thesyntheticprofilesthathavebeenpresentedinthisstudycan resentsthespatially-resolvedprofilescorrectedforinstrumental be accessed electronically.The spectralresponse ofany instru- cavity errors. The average profile was computed using a least mentproducesbroadeningandcanintroduceasymmetriesinthe squaresfit ofall thepointsto a spline,consistingof 10param- observed profiles. Thus it is imperative that the profiles be de- eters.Bottom-right:Bisectoroftheobservedspatially-averaged graded with the proper instrumental response before they are profile. The velocity calibrationwas carried outusing our syn- usedtocalibrateobservations. theticprofileconvolvedwiththeCRISPinstrumentalprofile. The quiet Sun’s average spectrum can be computed from quiet regions in the observations. However, the presence of p- modes(oscillations)willproducean unrealisticshiftin the ob- servedaverageprofile.Thus,it shouldbeaveragedintime and spectraproducedbyconvectivemotionsatdifferentheliocentric space, or at least from a sufficiently large sample of quiet Sun angles for Ci, Fei, and Caii lines as commonly used for solar spectra. physicsdiagnostics. We proposeto use the profilesas absolute Wehavebeencautiousinthetreatmentoflinecores,butthe localreferencesforline-of-sightvelocitiestoallowaccurateve- comparison with the FTS atlas suggests that the errors in the locitymeasurements. cores are small. Except for the Caii IR triplet, we do not dis- A realistic 3D hydrodynamical simulation of the non- courage including the cores in velocity calibrations. We think, magnetic solar photosphere was used to synthesize the spec- however,thatavelocitymeasurethatweighinmoreofthepro- tra. The computations were done in LTE for Ci and Fei lines filewillgiveamorereliableresult. whereasnon-LTEcomputationswerecarriedoutintheCaiiin- fraredlines.Astheconversionfromwavelengthtovelocityscale isdoneusingthesame laboratorywavelengthasusedforcom- 6. Conclusions putingthe profiles,the measuredline shifts are relativelyunaf- We made use of the approach described by (Langangenetal. fected by errors in the central wavelength. Uncertaintiesin the 2007)toobtainanabsolutereferenceforvelocitiesinsolarob- rest of atomic parameters are partially compensated when the servations.Forthispurpose,wecalibratedtheshiftinsynthetic profilesarefittedtoreproducethestrengthoftheFTSatlas. 8 J.delaCruzRodr´ıguezetal.:Solarvelocityreferencesfrom3DHDphotosphericmodels Ourresultsshowasystematiccenter-to-limbvariationofthe Johansson,L.1966,Ark.Fys.,31,201 bisectors,whichisdeterminedtoalargeextentbythe3Dstruc- Kupka,F.G.,Ryabchikova, T.A.,Piskunov,N.E.,Stempels,H.C.,&Weiss, ture of the atmosphere, which is projected along the line-of- W.W.2000,BalticAstronomy,9,590 Langangen, Ø.,Carlsson, M.,RouppevanderVoort,L.,&Stein,R.F.2007, sight. However, there is a small amount of redshift (relative to ApJ,655,615 µ = 1.0) producedby the change in the formation height with Leenaarts,J.,Carlsson,M.,Hansteen,V.,&RouppevanderVoort,L.2009,ApJ, the heliocentric angle (non-3D effects), which is not related to 694,L128 projectioneffects.Acarefulanalysisofthemodelssuggeststhat Markwardt, C. B. 2009, in Astronomical Society of the Pacific Conference Series,Vol.411,AstronomicalSocietyofthePacificConferenceSeries,ed. alargenumberof3Dsnapshotsmustbeusedinstudiesofline D.A.Bohlender,D.Durand,&P.Dowler,251–+ shiftssothe oscillationsareproperlysampledandthestatistics Mart´ınezGonza´lez,M.J.,Collados,M.,RuizCobo,B.,&Beck,C.2008,A&A, ofgranulesandintergranulesarecomplete,whereasnon-LTEef- 477,953 fectsseemtohaveaminorinfluenceontheshiftofourFeilines. MartinezPillet,V.,Lites,B.W.,&Skumanich,A.1997,ApJ,474,810 Thelargestuncertaintyisrelatedtothenon-magneticnatureof Ortiz,A.,BellotRubio,L.R.,&RouppevanderVoort,L.2010,ApJ,713,1282 Pereira,T.M.D.,Kiselman,D.,&Asplund,M.2009,A&A,507,417 thesimulation.Nevertheless,weestimateourcalibrationstobe PietarilaGraham,J.,Danilovic,S.,&Schu¨ssler,M.2009,ApJ,693,1728 accurateupto∼ 50ms−1 atµ = 1,remaininguntestedtowards Rutten, R. J. 2003, Radiative transfer in stellar atmospheres, ed. Utrecht thesolarlimb. Universitylecturenotes,8thedition Wewouldliketoemphasizethesomewhatlimitedusability Rutten,R.J.&Kostik,R.I.1982,A&A,115,104 of the Caii calibration, as observations are polluted by a sig- Scharmer,G.B.2006,A&A,447,1111 Scharmer, G. B., Bjelksjo, K., Korhonen, T. K., Lindberg, B., & Petterson, nificantnumberof blends,whichshouldbe maskedin orderto B. 2003, in Society of Photo-Optical Instrumentation Engineers (SPIE) comparewiththecalibrationdata. Conference Series, Vol. 4853, Society of Photo-Optical Instrumentation Oursyntheticprofilesreproducespatially-averagedsolarob- Engineers(SPIE)ConferenceSeries,ed.S.L.Keil&S.V.Avakyan,341– servationsaccurately, but it would be interesting to test for the 350 Scharmer,G.B.,Narayan,G.,Hillberg,T.,etal.2008,ApJ,689,L69 impactofmagneticfieldsontheconvectiveshiftofthelines,and Shchukina,N.&TrujilloBueno,J.2001,ApJ,550,970 confirmthereliabilityofourcalculationsnearthelimb. Shine,R.A.&Linsky,J.L.1974,Sol.Phys.,37,145 Tritschler,A.,Schlichenmaier,R.,BellotRubio,L.R.,etal.2004,A&A,415, Acknowledgements. WethankTiagoPereiraforprovidingthe3Dsnapshotsof 717 theHDsimulationandRoaldSchnerrandMichielvanNoortforprovidingre- Unsold, A. 1955, Physik der Sternatmospharen, MIT besonderer duced data from the SST/CRISP. We are most grateful to Paul Barklem for BerucksichtigungderSonne.,ed.Unsold,A. providingunpublished cross-sections forcollisional broadening. 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