Solar velocity references from 3D HD photospheric models

2 MB·English

by  Jaime de la Cruz Rodríguez

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–+
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