Molecfit: A general tool for telluric absorption correction II. Quantitative evaluation on ESO-VLT X-Shooter spectra

1.7 MB·English

by  W. Kausch

Astronomy&Astrophysicsmanuscriptno.molecfit_paper_2 (cid:13)cESO2015
January29,2015
Molecfit: A general tool for telluric absorption correction∗
II. Quantitative evaluation on ESO-VLT/X-Shooter spectra
W.Kausch1,2,S.Noll1,A.Smette3,S.Kimeswenger4,1,M.Barden5,C.Szyszka1,A.M.Jones1,H.Sana6,2,H.Horst7,
andF.Kerber8
1 InstituteforAstro-andParticlePhysics,UniversityofInnsbruck,Technikerstr.25/8,A-6020Innsbruck,Austria
e-mail:[email protected]
5 2 UniversityofVienna,DepartmentofAstrophysics,Türkenschanzstr.17(Sternwarte),A-1170Vienna,Austria
1 3 EuropeanSouthernObservatory,AlonsodeCórdova3107,19001Casilla,Santiago19,Chile
0 4 InstitutodeAstronomía,UniversidadCatólicadelNorte,AvenidaAngamos0610,Antofagasta,Chile
2 5 InternationalGraduateSchoolofScienceandEngineering,TechnischeUniversitätMünchen, Boltzmannstr.17,85748 Garching
beiMünchen,Germany
n
6 SpaceTelescopeScienceInstitute,3700SanMartinDr,Baltimore,MD21218,UnitedStates
a
7 Josef-Führer-Straße33,80997München,Germany
J
8 EuropeanSouthernObservatory,Karl-Schwarzschild-Str.2,85748GarchingbeiMünchen,Germany
8
2 Received;accepted

]
M ABSTRACT
I Context.AbsorptionbymoleculesintheEarth’satmospherestronglyaffectsground-basedastronomicalobservations.Theresulting
.
h absorption line strength and shape depend on the highly variable physical state of the atmosphere, i.e. pressure, temperature, and
p mixingratioofthedifferentmoleculesinvolved.Usually,supplementaryobservationsofso-calledtelluricstandardstars(TSS)are
- neededtocorrectforthiseffect,whichisexpensiveintermsoftelescopetime.Wehavedevelopedthesoftwarepackagemolecfit
o
toprovidesynthetictransmissionspectrabasedonparametersobtainedbyfittingnarrowrangesoftheobservedspectraofscientific
r
objects.ThesespectraarecalculatedbymeansoftheradiativetransfercodeLBLRTMandanatmosphericmodel.Inthisway,the
t
s telluricabsorptioncorrectionforsuitableobjectscanbeperformedwithoutanyadditionalcalibrationobservationsofTSS.
a Aims.WeevaluatethequalityofthetelluricabsorptioncorrectionusingmolecfitwithasetofarchivalESO-VLT/X-Shootervisible
[
andnear-infraredspectra.
1 Methods.Thankstothewavelength coveragefromtheU tothe K band, X-Shooter iswellsuitedtoinvestigatethequalityofthe
v telluric absorption correction with respect to the observing conditions, the instrumental set-up, input parameters of the code, the
5 signal-to-noiseoftheinputspectrum,andtheatmosphericprofiles.Theseinvestigationsarebasedontwofiguresofmerit, Ioff and
6 Ires,thatdescribethesystematicoffsetsandtheremainingsmall-scaleresidualsofthecorrections.Wealsocomparethequalityofthe
2 telluricabsorptioncorrectionachievedwithmolecfittotheclassicalmethodbasedonatelluricstandardstar.
7 Results.Theevaluation ofthetelluriccorrectionwithmolecfitshows aconvincing removal ofatmospheric absorptionfeatures.
0 The comparison with the classical method reveals that molecfit performs better because it is not prone to the bad continuum
. reconstruction,noise,andintrinsicspectralfeaturesintroducedbythetelluricstandardstar.
1 Conclusions.Fitted synthetic transmission spectra are an excellent alternative to the correction based on telluric standard stars.
0 Moreover,molecfitofferswideflexibilityforadaptiontovariousinstrumentsandobservingsites.
5
1 Keywords. Radiativetransfer–Atmosphericeffects–Instrumentation:spectrographs–Methods:dataanalysis–Methods:numer-
: ical–Techniques:spectroscopic
v
i
X
r1. Introduction This applies particularly to the correction arising from
a molecular absorption in the Earth’s atmosphere. The required
Ground-based observations are naturally affected by various supplementary calibration frames are observations of telluric
physicalprocessesintheEarth’satmosphere,inparticularscat- standard stars (hereafter TSS). The TSS are usually bright hot
teringandabsorption.Thedynamicsoftheweatherconditions, stars (e.g. B-type), that show only a few, well known intrinsic
seasonal effects, or climate change lead to variabilities in tem- spectralfeatures.The TSShavetobe observedata similar air-
perature,pressure,andthechemicalcompositionontimescales mass, time, and line of sight as the science target to probe the
fromsecondstodecades,makingtheabsorptioncorrectionade- sameatmospherecolumn.
manding matter. Thus, any data calibration usually needs sup- Within the framework of the in-kind contribution of Aus-
plementary calibration frames. However, this approach is very tria’s accession to the European Southern Observatory (ESO),
expensiveintermsoftelescopetime,becausethesedatashould we developed a comprehensive sky model1 covering a wave-
betakendirectlybeforeorafterthesciencetarget. lengthrangefrom0.3to30µm (Nolletal.2012).Itwasorigi-
1http://www.eso.org/observing/etc/skycalc/skycalc.
∗ http://www.eso.org/sci/software/pipelines/skytools/ htm
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nally designedfor the ESO ExposureTime Calculator2 and in- Table1.Tableofobjectsusedfordetailedtests.
corporatesseveralcomponents,suchasairglow,scatteredmoon-
light(Jonesetal.2013),zodiacallight(Leinertetal.1998),scat- #a object mediancounts slit Prog.-ID
tered starlight, and the telescope emission modelled as a grey type [ADU] [′′×′′]
body.ItalsocontainsaspectralmodeloftheEarth’sloweratmo-
1 Seyfert2 462 1.5x11 087.B-0614
sphere in local thermalequilibriumcalculated by means of the
radiative transfer code LNFL/LBLRTM3 (Clough et al. 2005). 2 GRB 241 0.9x11b 091.C-0934
Thiscodeisusedwiththespectrallineparameterdatabaseaer,
3 B[e]star 7684 0.4x11 084.C-0952
which is based on HITRAN4 (Rothman et al. 2009)and deliv-
4 E0galaxy 5236 0.9x11 384.B-1029
ered together with the code. Averagedatmospheric profiles for
5 Carbonstar 50587 0.9x11 084.D-0117
Cerro Paranal describing the chemical composition as a func-
6 PN 6214 0.4x11 385.C-0720
tionofheight(combinationoftheESOMeteoMonitor5,astan-
dardatmosphere6 andthe3DGlobalDataAssimilationSystem
Notes.
(GDAS)model7)arealsousedasinput.TheGDASmodelispro- (a)Objects#1and#2aredatawithlowS/N usedfortestsontherelia-
videdbytheNationalOceanicandAtmosphericAdministration bilityofmolecfitwhenappliedtosuchdata.#3through#6areused
(NOAA)7 andcontainstime-dependentprofilesofthetempera- foradetailedcomparisonwiththeclassicalmethod.
ture,pressure,andhumidity. (b)observedwiththeKbandblockingfilter(Vernetetal.2011)
TheESOIn-Kindsoftwarealsoincludestoolsforremoving
theatmosphericsignatureinspectra8,9.Thepackagemolecfit
observations,forwhichbothmethodsareoptimised.Inthisway,
is an alternative approach for performing the telluric absorp-
individually optimised results can be compared for both meth-
tion correction by means of theoretically calculated transmis-
ods.Theresultsofthiscomparisonaredemonstratedbyfocusing
sion spectra based on the atmospheric model. We use the pre-
onthescientificallyrelevantspectraldetails.Section6provides
viously mentioned radiative transfer code and line database to
asummaryofourfindings.
derivesynthetic transmissioncurves.The requiredatmospheric
input profile is created in the same way as for the sky model,
but for the time and location of the observations and not aver- 2. Telluriccorrectionwithmolecfit
aged. The algorithm and package functionalities are described
in moredetailin Smette etal. (2014)(hereafterPaperI). Here, Thecorrectionwiththemolecfitpackageisperformedintwo
weevaluatethequalityofmolecfitasatelluricabsorptioncor- steps:
rection tool for ESO Very Large Telescope (VLT) instruments.
– Determination of the best-fit atmospheric and instrumental
ThefocusliesonobservationstakenwiththeX-Shooterinstru-
parameters:theyarerelatedto thetotalcolumndensitiesof
ment (Vernetet al. 2011), an echelle spectrograph coveringsi-
the input atmospheric profile and the instrumental param-
multaneouslythewavelengthregimefromthe U to the K band
eters (spectral line profile, wavelength calibration, contin-
atmediumresolution.Weusetwomethods:(a)astatisticalstudy uum position) are optimised by means of a χ2-Levenberg-
ofthequalityofthecorrectionbymeansoffiguresofmerit,and
Marquardt minimisation algorithm (see Paper I for a com-
(b) a comparison of the molecfit correction with that obtained
prehensivedescriptionoftheunderlyingalgorithms)tobest
usingthetraditionalmethodbasedonobservationsofTSS.
reproduce the observed telluric spectrum in selected wave-
Wefirstbrieflydescribethemethodofthetelluricabsorption
length regions. By varying the scaling factor of the molec-
correctionincorporatedinmolecfit(Sect.2).Adescriptionof
ularprofilesoftheinitialinputatmosphericprofile,thepro-
thetestdatasetisgiveninSect.3.Inthefollowing,weperform
grammeiterativelycalculatestransmissioncurves,whichare
twodifferenttests:InSect.4,weinvestigatethedependenceof
fitted to theinputsciencespectrum.To minimisethe calcu-
thetelluricabsorptioncorrectionqualityonseveralparameters,
lation time, to optimise the continuum fit, and/or to avoid
i.e.theinfluenceofthelinetransmission,observingconditions,
regionsaffectedbystellarspectralfeaturesorinstrumentde-
spectral resolution, fitting ranges, input parameters, the atmo-
fects,thefittingisrestrictedtouser-definedspectralranges.
sphericprofiles,andthesignal-to-noiseratioS/N.Forthispur-
– Correctionofthe telluricspectrum:thebest-fitatmospheric
pose,weintroducetwofiguresofmerittoestimatethequalityof
andinstrumentalparametersareusedtocalculatetheatmo-
thetelluriccorrectionI andI ,describingthesystematicoff-
off res spheric transmission spectrum over the entire wavelength
sets and the remaining small-scale residuals of the corrections,
rangeof the scientific observation.The science spectrumis
respectively.Thesequantitiesaredeterminedforalargedataset
then divided by this transmission curve to produce telluric
of X-Shooter spectra, to which molecfit is applied with de-
correcteddata.
faultparametersoptimisedforthisinstrument.Theresultsofthis
analysisallowtheusertoestimatetheachievablequalityforthe
telluricabsorptioncorrectionincaseanindividualparameterset
3. Thedataset
optimisationisnotpossible,e.g.duetothelargenumberofspec-
tra.InSect.5,wecomparetheclassicalmethodbasedonaTSS Inordertoevaluatetheperformanceofmolecfit,wehaveused
with molecfit as another test. We have selected four science archival data obtained with the X-Shooter instrument mounted
at the ESO VLT (Vernet et al. 2011). This instrument covers
2http://www.eso.org/observing/etc/
the entire wavelength range from 0.3 to 2.5µm in three spec-
3http://rtweb.aer.com/lblrtm_frame.html
tralarms(UVBarmfromtheultraviolettotheBband;VISarm
4http://www.cfa.harvard.edu/hitran/
5http://archive.eso.org/asm/ambient-server in the visual regime; NIR arm in the near-infrared regime), at
6http://www.atm.ox.ac.uk/RFM/atm/ medium resolution (R ∼ 3300 to 18200, depending on the slit
7http://www.ready.noaa.gov/gdas1.php width)simultaneously.Thisbroadwavelengthregimegivesthe
8http://www.eso.org/pipelines/skytools/ opportunityto study the correctionof severalabsorptionbands
9http://www.uibk.ac.at/eso/software/ ofdifferentspeciessimultaneously(e.g.H O,O ,CO ).
2 2 2
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W.Kauschetal.:Molecfit: Ageneraltoolfortelluricabsorptioncorrection
WehavereducedtheentirepublicallyavailableESOarchive Table 4. Wavelength ranges (vacuum) for fitting NIR- and VIS-arm
X-ShooterTSSspectra
data from October 2009 to March 2013, leading to a compre-
hensivedatasettakenundervariousobservingconditions,since
X-Shooterisfrequentlyused.WeusedtheESOstandardpipeline
Arm No. λ [µm] λ [µm] Mainmolecule
inversionV2.0.0underReflexV2.3onourcluster10. min max
NIR 1 1.120 1.130 H O
2
Forstudyingtheinfluenceoftheatmosphericconditionsand NIR 2 1.470 1.480 H O
2
instrumentalset-upsonthequalityoftelluricabsorptioncorrec- NIR 3 1.800 1.810 H O
2
tion(seeSect.4),wehavetakenall1DspectraofTSSwithout NIR 4 2.060 2.070 CO
2
fluxcalibrationuntilMarch2013.Intotal,thereare4218NIR- NIR 5 2.350 2.360 CH
4
armand3823VIS-armspectra.UVB-armspectrawerenotcon-
sidereddueto thelack ofmolecularabsorptionfeatures11. Due VIS 1 0.686 0.694 O2
VIS 2 0.759 0.770 O
to occasional failures of the automatic X-Shooter pipeline, the 2
VIS 3 0.930 0.945 H O
number of obtained spectra is lower than the number of expo- 2
suresinthearchive.Sincetheobtainedsetofreduceddatawas
large enoughfor our purpose, we did not attempt to re-run the
pipeline manually (possibly using tuned reduction parameters)
forthecasesforwhichtheautomaticapproachfailed.
Twoobservationsofaγ-rayburstandaSeyfert2galaxy(#1
and2inTables1 and2)wereusedtoinvestigatethe qualityof
thetelluricabsorptioncorrectionobtainedwithmolecfitwhen
appliedtodatawithlowS/N.Bothobservationsshowlowcount
numbers(462and241ADU,respectively)andwerealso taken
atsignificantairmass,whichincreasestheeffectofatmospheric
absorption.
For the comparison with the classical method described in
Sect. 5, we have selected science observations of four differ-
ent astrophysical objects (#3 through 6 in Tables 1 and 2) in
conjunction with their corresponding TSS observations manu-
allyfromourX-Shootertestdatasetinordertoperformacom- Fig. 1. Reference X-Shooter NIR-arm model transmission spectrum
parisonbetweenthetelluricabsorptioncorrectionachievedwith binned in 1nm stepsfor a mean amount of precipitable water vapour
molecfitandtheclassicalmethodrelatedtoTSS.Thescience (PWV)of3.1mmandanairmassof1. Thebinsmarked byredsym-
test data sets were selected to cover different astrophysicalob- bolsareclassifiedascontinuum.Thetransmissionofthesebinsranges
from0.95to1.00.Themeanvalueis0.99.Theselectedbinsareused
jectsandS/N tracedbythecountsinADU(seeTable1)toalso
toderivethesystematicoffsets(residuals)inthetelluricabsorptioncor-
estimatethelimitsoftheapplicationofbothmethods.TheTSS
rectedspectra.Binsthatbelongtofourspecifictransmissionrangescor-
spectra were selected to coincidebest with the airmass and the respondingtoT =0.9(blue),0.8(cyan),0.5(magenta),and0.2(green)
dateofthecorrespondingscienceobservation(seeTable2)and areindicatedaswell.Thefigurealsoshowsthefittingranges(yellow
wereusuallyreducedwiththesameflatfield.Asthemajorityof bars)thatwereusedbymolecfit(seealsoTable4).
the telluric absorptionfeatures arise in the infrared regime, we
restrictthisinvestigationtoNIR-armdata.
4.1.Testset-upandfiguresofmerit
Theperformanceofmolecfitwastestedwithafixedinputpa-
rameterset.Thisapproachisappropriatetoestimatestatistically
thequalityofthecorrectiononalargesetofdata.Nevertheless,
furtherqualityimprovementscouldbeobtainedbyadjustingthe
fittingparametersforeachindividualspectrum.
4. Qualityoftelluricabsorptioncorrection
FortheNIRarm,theappliedset-upisshowninTable3(see
also Paper I). For the wavelength range from 1 to 2.5µm, the
In the following, we evaluate the quality of telluric absorp- model-relevantmoleculesareO2,CO2,H2O,CH4,andCO.For
tion correction with molecfit by means of a large sample of the VIS arm, it is sufficientto consider O2 and H2O. Only wa-
X-Shooter TSS spectra (see Sect. 3). We mainly focus on the tervapourisfittedinspectraofbotharms,sincetheconcentra-
NIRarm,wherethetelluricabsorptioncorrectionismostcrucial. tionvariationsandtheimpactontheX-Shooterdataoftheother
We also complement the discussion with results from the VIS speciesareexpectedtobesmall.Theequatorialstandardatmo-
arm. The molecfittest set-up for the data set and the quality spheric profile that we use is already more than a decade old
indicatorsusedarediscussedinSect.4.1.Theresultsareshown (preparedby J. J. Remedios2001;see Seifahrtet al. 2010).As
inSects.4.2to4.4.Theeffectofchangingthefittingrangesand theglobalCO2concentrationincreaseswithtime(WorldMeteo-
molecfit input parameters is discussed for an example spec-
truminSects.4.5and4.6,respectively.Theinfluenceofdiffer- [email protected]/12GBRAMpernode
encesintheinputwatervapourprofileisdescribedinSect.4.7. 11NotethattheozoneabsorptionbytheHugginsandChappuisbands
Finally,we investigatethe effectof low S/N data on the fitting (seePaperI)isusuallytakenintoaccountbytheextinctioncorrection
qualityinSect.4.8. (seee.g.Patatetal.2011).
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Table2.X-ShooterNIR-armdatasetusedforthedetailedtests(seealsoTable1).
Scienceobservations Telluricstandardstars
#a object airmass obs.datet star airmass obs.datet ∆t b[min]
SCI TSS obs
1 PKS1934-63 1.69 2011-07-01T01:57:23 – – – –
2 GRB130606A 1.715 2013-06-07T04:09:16 – – – –
3 V921-Sco 1.109 2010-03-10T09:01:02 Hip084409 1.058 2010-03-10T09:42:39 42
4 NGC5812 1.06 2010-03-13T08:57:03 Hip073345 1.128 2010-03-13T08:48:11 9
5 HE1331-0247 1.075 2010-03-24T06:10:55 Hip085195 1.152 2010-03-24T07:54:29 104
6 IC1266 1.222 2010-07-05T05:54:38 Hip085885 1.248 2010-07-05T06:07:41 13
Notes.
(a)Objects#1and#2aredatawithlowS/Nusedfortestsonthereliabilityofmolecfitwhenappliedtosuchdata.#3through#6areusedfora
detailedcomparisonwiththeclassicalmethod.
(b)approximatetimebetweenTSSandsciencetargetobservations(∆t =|t −t |)
obs SCI TSS
Table3.Molecfitparameterset-upforthetelluricabsorptioncorrectionevaluationofNIR-armX-ShooterTSSspectra
Parametera Value Shortdescription
wlgtomicron 10−3 factortoconverttheinputwavelengthunitsintoµm
vac_air air wavelengthsinvacuumorair
ftol 10−2 relativeχ2convergencecriterion
xtol 10−2 relativeparameterconvergencecriterion
list_molec O CO H OCH CO listofmoleculestobeincludedinthemodel
2 2 2 4
fit_molec 00100 flagsforifeachmoleculeistobefit(1=yes,0=no)
relcol 1.1.051.1.1. relativemolecularcolumndensities(1=inputprofile)
fit_cont 1 flagforpolynomialfitofthecontinuum(1=yes,0=no)
cont_n 1 degreeofpolynomialforthecontinuumfit
cont_const 104 initialconstanttermforthecontinuumfit
fit_wlc 1 flagforrefinementofwavelengthsolution(1=yes,0=no)
wlc_n 0 degreeofChebyshevpolynomialforrefinedwavelength
solution
wlc_const 0. initialconstanttermoftheChebyshevpolynomial
fit_res_box 1 flagforresolutionfitusingaboxcarfilter(1=yes,0=no)
relres_box 0.75 initialvalueforFWHMofboxcarrelativetoslitwidth
(≥0and≤2)
kernmode 0 kernelmode(0=independentGaussianandLorentzian,
1=Voigtprofile)
fit_res_gauss 1 flagforresolutionfitusingaGaussianfilter(1=yes,0=no)
res_gauss 1. initialvalueforFWHMofGaussian(inpixels)
fit_res_lorentz 0 flagforresolutionfitusingaLorentzianfilter(1=yes,0=no)
res_lorentz 0. initialvalueforFWHMofLorentzian(inpixels)
kernfac 3. kernelsizeinunitsofFWHM
varkern 1 flagforselectingaconstant(=0)oravariablekernel(=1)
pixsc 0.20 pixelscaleinarcsec
Notes.
(a)OnlyparametersrequiredforthefittingprocedureandspecifictotheX-Shooterdataarelisted(seethemolecfitUserManualformoredetails
rologicalOrganization2012),theinputCO columnwasmulti- profile, a combination of a boxcar and Gaussian was assumed.
2
pliedby1.05toberepresentativeoftheX-Shooterarchivaldata. A possible Lorentzianwas notconsidered,since a study of the
shape of the line profiles did not reveal significant Lorentzian
A linearfit (cont_n= 1)was performedto correctthe con- wings. The width of the initial boxcar was chosen to be 75%
tinuaofthespectraineachofthefittingranges(seebelow).The oftheslitwidth(relres_box),whichshouldbeclosetothereal
initial continuumfactor cont_const was set to 104 to be in the valueforthedifferentslits(asconfirmedbytests).Anexception
orderofthetypicalcountlevelinADUofX-Shooterdatawith- isthe5”slit,whichis,however,rarelyusedforobservationsof
out flux calibration. For the wavelength grid correction, which sciencetargets.FortheGaussian,areasonableinitialFWHMof
isrequiredtohandlecalibrationuncertaintiesandaninaccurate 1pixel(res_gauss)andakernelsizeof3FWHM(kernfac)were
centringofthetargetintheslit,onlyaconstantshiftwasallowed given.Sinceechellespectraarefitted,thekernelFWHMwasse-
(wlc_n=0)(seeSect.4.6foradiscussion).Fortheinstrumental
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W.Kauschetal.:Molecfit: Ageneraltoolfortelluricabsorptioncorrection
Fig. 3. Indicators I for systematic offsets (upper panel) and I for
off res
small-scale residuals (lower panel) of the telluric absorption correc-
tion for single 1nm bins of the X-Shooter NIR-arm spectrum shown
inFig.2.Bothquantitiesaregivenasafunctionoftransmission.Bins
belongingtothedifferenttransmissionrangesusedinthediscussionare
markedbydifferentcolours(seelegendandFig.1).Smallredsymbols
identifybinswhichareexcludedfromfurtheranalysisduetoeithervery
lowtransmissionorveryweaklinestrength.
thefullwavelengthrange(seealsoSects.4.5and4.6).Moreover,
ouroptimisedsetoffittingrangesavoidsabsorptionfeaturesof
typicalTSS.
TheVISarmismuchlessaffectedbymolecularabsorption.
The only prominent bands are the A and B molecular oxygen
Fig. 2. Quality of telluric absorption correction for an example TSS
bandsand the water vapourband at 0.94µm. Therefore,fitting
spectrumtakenwiththeNIRarmoftheX-Shooterspectrograph. The
star was observed with a 1.2” slit at an airmass of 1.32. The seeing ranges were only defined in these three bands as indicated by
was0.76”andthePWV(asderivedfromthefitting)was1.46mm.Up- Table 4. The H2O-related range avoids the wavelengths of po-
perpanel:Thetelluricabsorptioncorrectedspectrum(red)isshownin tentially strong Paschen lines, which are present in spectra of
comparisonwiththeoriginalspectrum(black).Middleandlowerpan- hotTSS.
els:MeancountsandstandarddeviationinADUforagridof1nmbins RunningmolecfitfortheinputparameterslistedinTable3
forthetelluricabsorptioncorrectedexamplespectrum.Thetwosubfig- andthefittingrangesshowninTable4resultsinthebest-fitpa-
uresalsohighlightthepixelsforthecontinuuminterpolation(red)and
rametersforeachsampleexposure(seeSect.3).Thesearethen
thedifferenttransmissionrangesforthequalityanalysisofthetelluric
usedto providea telluricabsorptioncorrectedspectrumforthe
absorptioncorrection.Formoredetails,seeFig.1.
full wavelength range (see Fig. 2). The quality of the fit in the
pre-defined fitting ranges can be evaluated by considering the
lected to beproportionalto the wavelength(varkern = 1).The RMSoftheresiduals,whichisprovidedbymolecfit.However,
thequalityofthetelluricabsorptioncorrectionmustbestudied
profile-relatedinputparametersrefertothecentralwavelengths
overthe wholespectralrange with respectto the qualityof the
of1.74µmand0.78µm fortheNIRandVISarm,respectively.
correctedobjectspectrumandthereforerequiresadifferentanal-
For the 214 spectra (5.1%) taken with a K-blocking filter (see
ysis. For this purpose,we have defined the figures of merit I
Vernetetal.2011),thecorrespondingwavelengthis1.55µm. off
andI .Theformermeasuresthecontinuum-normaliseddiffer-
AsshownbyTable4andFig.1,thefittingoftheatmospheric res
encebetweentheoriginalandtelluricabsorptioncorrectedspec-
transmission model in the NIR arm was restricted to five nar-
trum,relativeto a locally-averagedtelluricabsorptionstrength.
row10nmwidefittingranges(orinclusionregions;cf.PaperI).
Thelattertracesthecontinuum-normalisedstandarddeviationof
Theycoveronlyabout3%oftheentirewavelengthrange,which
theresidualsofthecorrection,relativetoalocally-averagedtel-
ensuresthatthe fitting time is reasonable(typically1 to 2min)
luric absorption strength. Therefore, I and I are indicators
and the continuum fit with a low order polynomial is accurate off res
of large-scale systematic offsets in the telluric absorption cor-
enough.Moreover,only a relatively small fraction of the NIR-
rectedspectraandsmall-scale(orhigh-frequency)variationsof
armwavelengthrangeissuitableforthefits,sinceagoodfitre-
theresiduals,respectively.Thesequalityindicatorswere calcu-
quiresawiderangeoftransmissionvalues.Thewindowsaresuf-
latedinthefollowingway:
ficient to derivethe amountof atmosphericwater vapour(CO
2
andCH arenotfitted),thewavelengthshift,andtheinstrumen- – First, each telluric absorption corrected NIR- and VIS-arm
4
talprofile.Sincethelasttwopropertieshavetobedeterminedfor spectrum was divided into 1nm and 0.5nm wide bins, re-
theentirespectrum,Ranges4and5,whichdonotshowsignif- spectively (corresponding to about 17 and 25 pixels, i.e. a
icantH Oabsorption,arealsoimportantforagoodcoverageof fewresolutionelements;cf.Sect.4.4).
2
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– The mean and the standard deviation were calculated for
eachofthesebins(seeFig.2).
– ThebinsforwhichtheaveragetransmissionmodelinFig.1
showsnooronlyminorabsorptionwereselectedascontin-
uumnodes.Eventhoughthisselectionincludesweakouter
wingsofsomebands,thisisnotcritical.Lineswithadepth
of about 1% can be well corrected (see Fig. 2), especially
withrespecttothemuchstrongerlinesforwhichthequality
ofthecorrectionisevaluated.
– Thecontinuumbinswereusedtointerpolatetheobjectcon-
tinuumatthepositionsofbinswithsignificantabsorption.
– The interpolatedcontinuumintensity for each bin was then
subtractedfromthecorrespondingmeasuredmean.Thisre-
sults in an estimate of systematic offsets in the telluric ab-
sorptioncorrectedspectra.
– Tobeindependentoftheabsoluteflux,theoffsetsandstan-
darddeviationsofeachbinweredividedbytheinterpolated
continuummeanvalues.
– Tomaketheresultingvaluesindependentofthewavelength-
and time-dependenttransmission T, the relative offsets and Fig.4.Small-scaleresidualindicatorIresfor1nmbinsversusthemean
model continuum counts in ADU for the five fitting ranges. The red
standard deviationswere divided by 1−T, i.e. the average
dashed lineshows the selection criterion for sufficiently high S/N for
amountofabsorptionforeachbin(seeFig.3).
thedetailedanalysis.
– Fivetransmissionrangesweredefinedforadetailedanalysis
ofthetelluricabsorptioncorrection.Apartfromawiderange
from0.1to0.95,rangescentredaround0.9,0.8,0.5,and0.2 systematiccontinuumoffsetsonaverage.Foradiscussionofthe
weredefined(seeFigs.1to3).WedidnotconsiderT close qualityofthetelluricabsorptioncorrectionforlow-S/Nspectra,
to 1 and 0, since the related resultsare mainlynoise driven seeSect.4.8.
andarethereforenotsuitedtoevaluatemolecfit(seealso
TheoutputfilesoftheX-Shooterpipelineprovidebadpixel
Sects.4.2and4.3). masks,whichcanbeusedbymolecfittoexcludecriticalpix-
– The bins that belong to each of the five ranges were deter-
els from the fitting procedure. Sometimes in the NIR arm, it
minedbyusingthebest-fittransmissionspectraoftheindi-
seems that more pixels were rejected by the pipeline than re-
vidualsamplespectra.Thus,thebinassignmentdependson
quired. In the case of a very small number of available pixels,
theairmass,amountofatmosphericwatervapour,andspec-
the fit becomes unreliable. While the standard deviation might
tralresolution.
evendecrease, systematic offsets are expectedto become more
– Finally, to obtain the figures of merit and to reduce the ef-
significant.Inaddition,crucialcontinuumpixelsfortheinterpo-
fectofoutliers,wetookthemedianoftherelativeoffsetand
lationofrangeswithstrongabsorptionbandscouldbemissing,
standarddeviationofthebinsforeachtransmissionrangeas
whichmakesthederivationof I lessreliable.Forthisreason,
showninFig.3. off
weexcluded247NIR-armspectra(5.9%)withlessthanhalfthe
TheresultingqualityindicatorsI andI areusedinthesubse- maximumnumberofpixelsinthefittingranges.
off res
quentanalysis.Ifthetransmissionrangeisnotspecifiedexplic- Sofar,wehavemainlyrejectedspectrawhereapropercal-
itly, the results for the wide range are given. Note that Ioff and culationofthequalityindicatorsIoffandIrescouldnotbeguaran-
I havetobemultipliedby1−T toprovidethesystematicoff- teed.However,forevaluatingthequalityofthetelluric absorp-
res
setsofthecorrectionandtheintra-binstandarddeviationsofthe tioncorrection,itisimportanttoknowthefractionofobviously
residuals relative to the object continuum. More details on the failed fits. For this purpose, we studied the best-fit FWHM of
interpretationofourfiguresofmeritcanbefoundinSect.4.3. theinstrumentalprofile(combinedboxcarandGaussian)andthe
best-fit shift of the wavelength grid. Interestingly,only a small
number of NIR-arm spectra (no VIS-arm spectra) showed val-
4.2.Outliers
ueswhichwereclearly separatedfromthe generaldistribution.
28best-fitmodelspectrawithaFWHMabove10pixels(orbe-
The indicator I measures variationsin the count level within
res
low1.5pixels)orwavelengthshiftsofmorethan2.5pixelsrel-
each of the narrowbinsof a telluricabsorptioncorrectedspec-
ativetothesamplemeancouldbeidentifiedasclearoutliers.14
trum.Primarily,thistracesthesmall-scalequalityofthetelluric
ofthese28spectrawerealreadyrejectedbythecriteradescribed
absorption correction. However, random noise, defects in the
above.Molecfitappearstoshowaveryrobustperformance,at
spectra, sky subtraction residuals, and spectral features of the
leastforX-ShooterTSSspectra.
observedobjectcanalsocauseanincreaseofI .Thisisdemon-
res
stratedforrandomnoiseinFig.4,whichshowsaclearincrease For further analysis, we excluded all the discussed spectra
of the scatter for lower mean counts (calculated for the fitted withsuspiciousfits.Thisresultsinsubsamplesof3837NIR-arm
pixels),i.e.decreasingS/N.Inordertoavoiddifficultiesininter- (91%ofthefullsample)and3787VIS-armspectra(99%).
preting the I sample statistics, spectra with mean counts less
res
than104ADUareexcludedfromfurtheranalysis.Thisthreshold
4.3.Influenceoflinetransmissionandobservingconditions
concerns120 spectra of the NIR arm (i.e. 2.8%of the sample)
and36spectraoftheVISarm(0.9%).Excludingthesedatadoes For the filtered NIR-arm sample (see Sect. 4.2),Table 5 shows
notmeanthattheircorrectedspectrahaveabadquality.Forex- the mean values and standard deviationsof I and I for the
off res
ample,themean I forNIR-armspectrawithmeancountsbe- five transmission ranges listed. In addition, the individual val-
off
tween 103 and104ADU is 0.000(σ = 0.053),i.e. thereare no uesforthewidetransmissionrangefrom0.1to0.95areplotted
Articlenumber,page6of17
W.Kauschetal.:Molecfit: Ageneraltoolfortelluricabsorptioncorrection
Table5.Sampleaveragesandstandarddeviationsforthetransmission-
dependentindicatorsI andI ofthequalityofthetelluricabsorption
off res
correctionofNIR-armX-Shooterspectra
Ref.T T range I I
off res
mean σ mean σ
— 0.10−0.95 −0.009 0.032 0.196 0.063
0.9 0.88−0.92 −0.008 0.044 0.209 0.071
0.8 0.75−0.85 −0.024 0.046 0.184 0.068
0.5 0.45−0.55 −0.004 0.038 0.150 0.059
0.2 0.15−0.25 +0.035 0.063 0.237 0.136
Fig.7.Best-fitPWVobtainedbymolecfitinmmasfunctionofthe
observingdateinyears.
inFig.5.Thelatterdoesnotindicatesignificantfeaturesinthe
distributionof the data points. I clustersarounda value of0,
off
whichmeansthatthetelluricabsorptioncorrectiondoesnotap-
peartobeaffectedbysystematicoffsets.Thescatterisonlyabout
3%ofthelinestrengths.ThemeanI isabout0.20withascat-
res
ter of 0.06, i.e. the relative standard deviation of the residuals
ofthecorrectedtelluricabsorptionisabout20%.Thistranslates
intotypicalerrorsof2%and10%relativetothecontinuumfor
spectralrangeswithT =0.9and0.5,respectively.ThemeanI
off
and I valuesfor the X-ShooterVISarm −0.002(σ = 0.048)
res
and0.184(σ = 0.059)areverysimilarto theNIR-armresults.
This implies that the telluric absorption correction is of good
qualityinbothX-Shooterarms.Theresultsareconsistentwitha
typicalcorrectionaccuracyof2%ofthecontinuumorbetterfor
wavelengthrangeswithunsaturatedtelluriclinesasreportedin
Fig.5.IndicatorsI forsystematicoffsetsandI forsmall-scaleresid-
off res PaperIbasedondatafromdifferentinstruments.Notethatindi-
ualsofthetelluricabsorptioncorrectionfor1nmbins.Onlydatapoints
vidualmolecularlinesarenotresolvedintheX-Shooterspectra,
ofthefilteredsubsampleareshown.
whichlowersandsmoothesthemeasuredtelluricabsorption.
Table5listsI andI dependingonthefournarrowtrans-
off res
missionrangescentredatT =0.9,0.8,0.5,and0.2.Thedistribu-
tionsagreequitewellwiththeresultsforthewidetransmission
range.Consequently,themixingof transmissionsis notcrucial
for the resulting quality indicators,at least if T very close to 1
and0 arenotconsidered(asforourwide T range).In the case
of very high T, the figuresof merit are no longer reliable with
respecttothequalityofthetelluricabsorptioncorrection,since
randomnoise,systematicerrorsinthereducedspectra,andfea-
turesof the observedobjectcan have a strong effectdue to the
normalisation by 1 − T (see Fig. 3). The correction quality is
probablycomparablewiththeresultsforintermediateT,which
arecrucialforthemodelfitforallT.InthecaseofverylowT,
therelativelylowS/N,possiblezeropointerrors,andthestrong
variationinT overnarrowwavelengthrangescancausehighI
off
and I . The correction of spectral ranges with T close to 0 is
res
difficult(seeFig.2).However,thisisusuallynotanissue,since
theinformationfromthesciencetargetalsotendstobeverylim-
ited. The I values in Table 5 illustrate the described effects.
res
Fig.6.FractionofNIR-armbinswithstandarddeviationsoftheresid- Theminimumof0.15isobtainedforintermediatetransmissions
ualsofthetelluricabsorptioncorrectiongreaterthanorequalto5%of (T =0.5),whereasthevaluesforT =0.9and0.2areabove0.2.
theobjectcontinuum asfunctionof thebest-fitPWVinmm.Thered
The rough proportionalityof the telluric absorption correc-
regressionlinehasaslopeof0.15perdex.
tionerrorsrelativetothecontinuumand1−T forawiderange
of T implies that the overall correction quality of a spectrum
Articlenumber,page7of17
A&Aproofs:manuscriptno.molecfit_paper_2
is correlated with propertieswhich affect T, i.e. the airmass of Table6.Slit-dependentqualityofthetelluricabsorptioncorrectionof
NIR-armX-Shooterspectra
theobservationandthecolumndensityofthemolecularspecies
concerned.Thiscanbeunderstoodbyconsideringthatthetrans-
missionT isrelatedtotheopticaldepthalongthelineofsightτ
Slit N FWHMa I I
foreachwavelengthλby off res
[”] [pixels]
mean σ mean σ mean σ
T(λ)=e−τ(λ), (1)
0.4 437 2.49 0.20 +0.008 0.059 0.239 0.069
whereτcanbeapproximatedbytheproductoftheopticaldepth 0.6 711 3.07 0.31 −0.002 0.020 0.199 0.047
atzenithτ andtheairmassX: 0.9 1927 3.95 0.74 −0.012 0.027 0.193 0.064
0
1.2 566 4.44 1.01 −0.015 0.024 0.179 0.056
1.5 148 5.03 1.62 −0.020 0.020 0.158 0.059
τ(λ)≈τ (λ)X. (2)
0 5.0 48 5.41 1.57 −0.057 0.025 0.156 0.066
This works best if the geometrical distributions of the given
Notes.
molecule and air are similar. Finally, the optical depth τ for
0 (a)SincetheFWHMinpixelsdependsonthewavelengthforanearly
molecular absorption by a single species at wavelength λ can
constant spectral resolution, theFWHMisgiven for thecentre of the
becalculatedby
full NIR-arm wavelength range, i.e. 1.74µm (see also Sect. 4.1). For
spectratakenwithaK-blockingfilter,whichonlyextendupto2.1µm,
∞ theFWHMwascorrectedtobealsorepresentativeof1.74µm.
τ (λ)=σ (λ) n(h)dh, (3)
0 abs Z
h0
where σ is the wavelength-dependent absorption cross sec-
abs
tion and the integral corresponds to the column density of the
molecule,whichisderivedfromthedensitynatheightshabove
the observerat h . Consequently,telluric absorptioncorrection
0
ismostdifficultifatargetisobservedatalargezenithdistance
andwithahighatmosphericwatervapourcontent.Theamount
of water vapour is critical, since most prominent bands in the
X-Shooter wavelength range are caused by this molecule and
theconcentrationanddistributionishighlyvariableintimeand
space.
Theeffectof water vapouron the qualityofthe telluric ab-
sorptioncorrectionis shownin Fig. 6, which displaysthe frac-
tion of 1nm NIR-arm binswith residuals greater than or equal
to 5% of the corrected object continuum as function of the
amountofprecipitablewatervapour(PWV)inmmasderivedby
molecfit.For our X-Shooter NIR-arm TSS sample, the fitted
PWVrangefrom0.2to18.2mmwithameanvalueof3.1mm.
Themedianis2.2mm.Thesevaluesareingoodagreementwith Fig. 8. Small-scale residual indicator I for 1nm bins versus the
res
othermeasurementsofthePWV,whichisroutinelymonitoredat FWHM of the line profile in pixels. As indicated by the legend, the
CerroParanalbyastand-alonemicrowaveradiometerinsupport differentcolourscorrespondtodifferentslitwidths.
of science observations(see Kerber et al. 2014,and Sect. 4.7).
Thereisaclear,nearlylinearincreaseofthenumberofbinswith
4.4.Influenceofresolution
significantresidualswith increasingPWV in logarithmicunits.
A regression analysis indicates that the fraction fσ≥0.05 grows Since the echelle gratings of the X-Shooter spectrographs are
fromabout0.20at1mmto about0.35at10mm.Forcompari- fixed, the slit width is the only instrumental parameter that af-
son,thefractionofbinswitha transmissionlowerthan0.95of fects the line-spread functions of the resulting spectra. For the
the mean spectrum plotted in Fig. 1 is about0.5. The effect of NIR and VIS arms, seven different widths from 0.4” to 5.0”
theairmasson fσ≥0.05 issmallerthanforthePWV,sincetheair- can be selected as displayed in Table 612. Apart from the slit
massonlyvariesbyafactorofabout2.IntheVIS-armrange,the selection,thepositioningaccuracyofthetargetintheslitandits
regressionlineexhibitsanincreaseof fσ≥0.05 fromabout0.04at changewithtimecontributetotheresultingline-spreadfunction.
1mmto0.07at10mm.Sincestrong(watervapour)linesarerare Finally, the FWHM of a line is influenced by the seeing at the
in this wavelength regime, the fractions are distinctly smaller timeoftheobservationofthepoint-likestandardstar,especially
thanintheNIR-armrange. iftheslitislargerthanthelightprofileofthetarget.Forthisrea-
The quality of the correction of water vapour bands may son,Table6 showsanincrease ofthe FWHM (asderivedfrom
roughly depend on the time of the year. Figure 7 indicates a thecombinedbest-fitboxcarandGaussiankernels,seeSect.4.1)
strong seasonal dependence of the atmospheric water vapour aswellasitsscatterwithincreasingslitwidthfortheNIRarm.
abundance. In winter, the PWV is relatively low (mean of The slit-dependentresultsfor the qualityindicators I and
off
1.9mmformeteorologicalwinter),whereasthehighestamounts I for the wide transmission range are also provided by Ta-
res
andalargescatterarefoundinsummer(meanof5.2mm).The ble 6. The systematic offsets appear to indicate a weak trend
strengthof molecularoxygenandcarbondioxidebandscan be from slight overcorrection for the 0.4” slit to moderate under-
consideredasnearlystableexceptforthelong-termincreaseof
theCO2 concentration(seeSect.4.1). 12InthecaseoftheVISarm,the0.6”slitisreplacedwith0.7”.
Articlenumber,page8of17
W.Kauschetal.:Molecfit: Ageneraltoolfortelluricabsorptioncorrection
Table7.Influenceoffittingrangesonthetelluricabsorptioncorrection Table 8. Influence of changing fitting ranges in a molecular band on
oftheNIR-armspectrumdisplayedinFig.2 thetelluricabsorptioncorrectionoftheNIR-armspectrumdisplayedin
Fig.2
Run Rangesa Rel. FWHMb PWV I I
off res
RMS [pixels] [mm] Run Range Rel. FWHMa PWV Ioff Ires
[µm] RMS [pixels] [mm]
1 12345 0.054 3.76 1.46 −0.008 0.235
2 1–––– 0.030 3.19 1.68 +0.085 0.349 2b 1.12−1.13 0.030 3.19 1.68 +0.085 0.349
3 –2––– 0.022 2.60 1.32 −0.063 0.246 2a 1.13−1.14 0.033 3.21 1.72 +0.101 0.399
4 ––3–– 0.028 3.08 1.40 −0.041 0.222 2b 1.14−1.15 0.039 3.03 1.42 +0.061 0.502
5 123–– 0.066 3.79 1.48 −0.004 0.238 2c 1.12−1.15 0.041 3.25 1.56 +0.100 0.494
6 1–––5 0.035 3.29 1.56 +0.039 0.315
3b 1.47−1.48 0.022 2.60 1.32 −0.063 0.246
7 –2–4– 0.034 3.28 1.36 −0.036 0.235
3a 1.46−1.47 0.021 2.78 1.37 −0.044 0.237
3b 1.45−1.46 0.023 2.97 1.35 −0.067 0.256
Notes.
3c 1.44−1.45 0.023 2.97 1.35 −0.067 0.256
(a) Forthewavelengthlimitsofthedifferentrangeswiththeindicated
3d 1.44−1.48 0.036 2.82 1.37 −0.045 0.242
numbers,seeTable4.
(b) TheFWHMisgivenforthecentreofthefullNIR-armwavelength
range,i.e.1.74µm. Notes.
(a)TheFWHMisgivenforthecentreofthefullNIR-armwavelength
range,i.e.1.74µm.
correction for the 5.0” slit. However, except for the value for (b)samerunsasinTable7
the rarely used 5.0” slit, the mean offsets can be considered as
negligible.Nevertheless, the slit width seems to contributeto a
broadeningoftheI distributionoftheentiredataset(seeFig.5
off
andTable5).
AsindicatedbyFig.8andTable6,theintra-binvariationsof
the residuals of the telluric absorption correctionincrease with
decreasing slit width or FWHM. The mean I values range
res
from 0.156 for the 5.0” slit to 0.239 for the 0.4” slit. For the
VIS arm, the corresponding values are 0.153 and 0.219. This
clear dependencebroadensthe distributionof I for the entire
res
data set (see Fig. 5 and Table 5). At first, the trend can be ex-
plained by the expected steepness of the line profiles if a line
comprisesonlyafewpixels(about2.5pixelsforthe0.4”slitof
theNIRarm).Inthiscase,smalldiscrepanciesbetweenthemod-
elledandthetrueprofilecancausesignificantresiduals.Onthe
otherhand,thescatterintheNIR/VISarmiscalculatedforbins
of a width of 1nm/0.5nm (about 17/25 pixels). If the FWHM
islow,more(probablyuncorrelated)resolutionelementsfitinto
thebinrange.ThiseffectcouldalsoaugmentI .
res
4.5.Influenceoffittingranges Fig. 9. Mean counts in ADU and standard deviation relative to mean
countsforagridof1nmbinsofthetelluricabsorptioncorrectedexam-
So far, the discussion has been based on a fixed set of fitting
plespectrum shown inFig.2for threedifferent setsof fittingranges.
ranges(seeTable4andSect.4.1).Inthefollowing,wefocuson
The black spectrum equals the one in Fig. 2 and corresponds to the
changesinthequalityofthetelluricabsorptioncorrectionwhen standardset-upofwindowsdescribedinTable4.Theredandthegreen
these rangesare changed.For this purpose,we tested the NIR- spectrawerecalculatedbyonlyusingasinglefittingrange(seelegend
arm example spectrum shown in Fig. 2, which is characterised andTable7).
by an airmass of 1.32 and a best-fit PWV of 1.46mm. We ran
molecfitfordifferentsubsetsofthefivestandardNIR-armfit-
ting ranges, which had to include at least one range dominated largestdeviationsarefoundforrunsthatwerebasedononlyone
bywatervapourlines. fitting range. For the quality of the telluric absorption correc-
Table7showstheresultsoftheseventestrunsweperformed. tion as measuredby I and I , there is a similar trend. How-
off res
The table indicates the selected fitting ranges (see Table 4 for ever,the quality of the correctionalso strongly dependson the
the numbers),the RMS of the fit residualsrelative to the mean rangesinvolved.WhilethefitonlydependingonRange1(1.12
counts,thebest-fitFWHM,thebest-fitPWV,andthetwoqual- to 1.13µm) is by far the worst (Run 2), the result for Run 4,
ityindicatorsI andI (seeSect.4.1).Thetableentriesforthe whichisonlybasedonRange3(1.80to1.81µm),isremarkably
off res
differentparametersshowacleardifferenceinthequalityofthe good. This is also illustrated by Fig. 9, which shows the mean
fitandthetelluricabsorptioncorrectiondependingonthefitting values and relative standard deviationsfor 1nm bins of the re-
ranges considered. As expected, the RMS of the fit is reduced sultingspectraofRun2and4in comparisonwiththestandard
if the number of the fitting ranges is decreased. The resulting Run 1. Run 2 only led to a good telluric absorption correction
FWHM range from 69% to 101% of the value of the standard inthefittedrange,whereasRun4showsareasonablecorrection
run.ForthePWV, weobtainedvaluesfrom90%to115%.The overtheentirewavelengthrange.
Articlenumber,page9of17
A&Aproofs:manuscriptno.molecfit_paper_2
Table9.InfluenceofwavelengthgridcorrectionbyaChebyshevpoly-
nomialoforderwlc_nonthetelluricabsorptioncorrectionofthespec-
trumdisplayedinFig.2
wlc_n Rel. FWHM PWV I I
off res
RMS [pixels] [mm]
0 0.054 3.76 1.46 −0.008 0.235
1 0.126 7.25 1.51 −0.046 0.456
3 0.121 7.05 1.51 −0.053 0.459
5 0.120 6.98 1.51 −0.050 0.453
Table 10. Influence of wavelength grid correction by a Chebyshev
polynomialoforderwlc_nonthetelluricabsorptioncorrectionofthe
spectrum displayed in Fig. 2 for the fixed best-fit line profile (rel-
res_box=0.560andres_gauss=1.671)asderivedfromthestandard
testrun
Fig.10.MeancountsinADUandstandarddeviationrelativetomean
wlc_n Rel. FWHM PWV Ioff Ires counts for agrid of 1nmbins of the telluricabsorption corrected ex-
RMS [pixels] [mm] amplespectrumshowninFig.2fordifferentordersoftheChebyshev
polynomialforthewavelengthgridcorrectionandfixedlineprofile(see
0 0.054 3.75 1.47 −0.007 0.235
legendandTable10).
1 0.031 3.75 1.44 −0.028 0.195
3 0.040 3.75 1.39 −0.042 0.262
5 0.031 3.75 1.42 −0.021 0.343 4.6.Influenceofinputparameters
Next,weinvestigatetheinfluenceoftheinputfitparameterson
the quality of the telluric absorptioncorrection.In this respect,
our input parameter set (see Table 3) appears to be a reason-
Since the results for the molecfit runs with single fitting able choice (see discussion in Sect. 4.1). However,there could
ranges differ significantly, we performed the model fitting and beacriticalrestrictionofthemaximumorderoftheChebyshev
telluricabsorptioncorrectionforsinglerangesthatcovertelluric polynomialforthecorrectionofthewavelengthgrid.Theselec-
lines in the same bands such as Runs 2 and 3, but with differ- tion wlc_n = 0 only allows a constant shift of the wavelength
ent wavelengthlimits. Only rangeswhere lines of intermediate grid.AsdiscussedinSect. 4.5,thisismostlikelynotsufficient
strengthdominatewereselected(see Fig.1).Forrangeswithin toachievegoodfitsinallthedifferentfittingrangesatthesame
thesameH Oband,Table8revealssimilarvaluesforthelisted time.For thisreason,we studiedtheeffectof thedegreeofthe
2
parameters.Thissuggeststhatchangingcentreandwidthofafit- Chebyshev polynomialon the quality of the fit. Table 9 shows
tingrangeinaband(inareasonableway)haslessofanimpact the results of our investigationof the standard NIR-arm exam-
thanchangingtheband. ple(seeFig.2)forfourdifferentdegreesofthepolynomial.The
resultcolumnsarethesameasinTable7.Thevaluesfortherel-
These results imply that modifying the fitting range within ativeRMS,FWHM,Ioff,andIresclearlyimplythatthefitsofthe
theH Obandat1.13µmdoesnotsignificantlyimprovethequal- runswithwlc_n=1,3,and5failed.ThedoublingoftheFWHM
2
ityofthefit.ThePWV, I ,and I valuesremainunsatisfying fortheserunsindicatesanincreaseofthedegreesoffreedomby
off res
if a fitting range within this band is not combined with ranges theadditionalcoefficientsoftheChebyshevpolynomialcaused
in other molecularbands. Since the line depths of the different degeneracies,which led to an erroneousfit of the instrumental
ranges are comparable, this does not seem to explain the dis- profile.Inotherwords,thefittingalgorithmwasnotabletofind
crepancies.Differencesinthebest-fitlineshapesandwavelength theglobalχ2minimum.
shifts(upto1pixel)forthedifferentmolecfitrunscouldimply To make the wavelength correction more robust, we per-
thattheissueislinkedtothestructureoftheX-Shootercompos- formed a second series of runs with reduced degrees of free-
iteechellespectraconsistingofmanyorders.Atleast,linepro- dom. For this purpose, we fixed the properties of the line pro-
filesinthe1.13µmbandcoverlesspixelsthanthoseinbandsat file.Wetookthebest-fitresultsofthestandardrunandsetrel-
longerwavelengths(see Sect. 4.4).Inview of the uncertainties res_box = 0.560,res_gauss = 1.671, and the correspondingfit
inthelineprofileandwavelengthcalibration,agoodtelluricab- flags to 0 (cf. Table 3). The results for the four different de-
sorptioncorrectionovertheentirewavelengthrange(seeFig.9) greesoftheChebyshevpolynomialarelistedinTable10.Forthe
requiresthat all critical molecularabsorptionbands are probed higherwlc_n,thefitsinthefivefittingrangesarenowbetterthan
byfittingranges.Therefore,ourstandardsetoffittingwindows forthestandardrun,astherelativeRMSindicate.ThePWVval-
(see Table 4) is well defined, even though only low order cor- uesandtherelatedI forsystematicoffsetsarerelativelystable.
off
rectionsofthedifferentkindsofsystematicdeviationsfromthe Thesmall-scaleresidualsindicator I isthelowest(0.195)for
res
atmospherictransmissionmodelarepossible(seeSect.4.6).The a linearwavelengthcorrectionfunction,i.e.wlc_n = 1. Higher
bestfitisalwaystheresultofacompromise,asindicatedbythe ordercorrectionsindicateworseI (0.343forwlc_n=5).They
res
smallerresidualsforindividualfittingrangesinthecorrespond- tendtodeteroriatethetelluricabsorptioncorrection,despitethe
ingwavelengthregimes(seeFig.9). fixed line profile. This is also demonstrated by Fig. 10, which
Articlenumber,page10of17