Table Of ContentAstronomy&Astrophysicsmanuscriptno.18382 (cid:13)c ESO2012
January10,2012
The barium isotopic fractions in five metal-poor stars
A.J.Gallagher1,S.G.Ryan1,A.Hosford1,A.E.Garc´ıaPe´rez2,W.Aoki3,andS.Honda4
1 Centre for Astrophysics Research, School of Physics, Astronomy & Mathematics, University of Hertfordshire, College Lane,
Hatfield,Hertfordshire,AL109AB,UnitedKingdom
email:[a.gallagher, s.g.ryan, a.hosford]@herts.ac.uk
2 DepartmentofAstronomy,P.O.Box400325,UniversityofVirginia,Charlottesville,VA22904-4325,UnitedStates
email:[email protected]
3 NationalAstronomicalObservatory,Mitika,Tokyo,181-8588,Japan
email:[email protected]
4 KwasanObservatory,KyotoUniversity,Ohmine-choKitaKazan,Yamashina-ku,Kyoto,607-8471,Japan
email:[email protected]
2 Received02November2011/Accepted29December2011
1
0
ABSTRACT
2
n Context.Theoryandobservationsofheavyelementnucleosynthesisareinconflictwithone-another.Theorystatesthatinthemost
a metal-poorstars,therapid(r-)neutron-capturenucleosyntheticprocesswouldbedominantovertheslow(s-)process.Themostrecent
J determinationsofr-ands-processyieldsdonotsupportthis.
9 Aims.WeprovidemeasurementsoftheBaisotopicfractionsforfivemetal-poorstarsderivedwithalocalthermodynamicequilibrium
(LTE)analysiswith1Dmodelstellaratmospheres.Thisincreasesthecomparisonswithheavyelementnucleosynthesistheory.
] Methods. We use high resolution (R ≡ λ/∆λ = 90000−95000), very high signal-to-noise (S/N > 500) spectra to determine
R thefractionofodd Ba isotopes(f )bymeasuringsubtleasymmetriesintheprofileoftheBaiilineat4554Å.Wealsousetwo
odd
S different macroturbulent broadening techniques, Gaussian and radial-tangential, to model the Fe lines of each star, and propagate
. eachtechniquetomodelmacroturbulentbroadeninginthe Ba 4554Åline.Weconducta1Dnon-LTE(NLTE)treatmentofthe Fe
h linesintheredgiantHD122563andthesubgiantHD140283inanattempttoimprovethefitting.Wedetermine[Ba/Eu]ratiosfor
p
thetwogiantsinourstudy,HD122563andHD88609,whichcanalsobeusedtodeterminetherelativecontributionofthes-and
- r-processestoheavy-elementnucleosynthesis,forcomparisonwith f .
o odd
Results.Wefindmathematicalsolutionsof f forHD122563,HD88609andHD84937of−0.12±0.07,−0.02±0.09,and−0.05±
r odd
t 0.11respectively.BD+26◦3578yieldedavaluefor f =0.08±0.08.OnlyBD−04◦3208wasfoundtohaveaphysical f ratioof
s odd odd
0.18±0.08.Thismeansthatallstarsexaminedhereshowisotopicfractionsmorecompatiblewithans-processdominatedcomposition.
a
[ The[Ba/Eu]ratiosinHD122563andHD88609arefoundtobe−0.20±0.15and−0.47±0.15respectively,whichindicateinstead
anr-processsignature.WereportabetterstatisticalfittothemajorityofFeprofilesineachstarwhenemployingaradial-tangential
1 broadeningtechniqueduringour1DLTEinvestigation.
v Conclusions.WiththeincreaseofthenumberofstarsforwhichtheBaisotopefraction f hasbeenmeasured,andthenatureoftheir
odd
7 results,thereisnowastrongerargumenttosuggestthatothersynthesiscodesthatemployalternativeapproachestoradiativetransfer
5 (e.g.3Dhydrodynamics)havetobeconsideredtotacklethehighlevelofprecisionrequiredforthedeterminationofisotopicratios.
7 Wehaveshownthat,fromastatisticalpointofview,onemustconsiderusingaradial-tangentialbroadeningtechniqueratherthana
1 GaussianonetomodelFelinemacroturbulenceswhenworkingin1D.NoimprovementtoFelinefittingisseenwhenemployinga
. NLTEtreatmentoftheFelines.
1
0 Keywords.Stars:PopulationII-Stars:abundances-Galaxy:evolution-Nuclearreactions,nucleosynthesis,abundances
2
1
:
v 1. Introduction ofactives-processinginTP-AGBstarscanbeseenthroughab-
i sorption line detections of short lived 98Tc and 99Tc isotopes
X
Nuclei heavier than the Fe-peak are mainly synthesised via (Smith&Lambert1988,andreferencestherein)visibleat4238,
r
a two neutron-capture processes, the slow (s-) and rapid (r-) pro- 4262and4297Å.
cess. For the s-process, neutron-capture rates are much lower There are many candidates for r-process sites including
than β-decay rates in unstable isotopes, whereas for the r- neutron star explosions (Imshennik 1992), neutron star surface
process, neutron-capture rates are higher than β-decay rates. explosions (Bisnovatyi-Kogan & Chechetkin 1979) and neu-
Each n-capture process has a different site for nucleosynthe- tron star winds (Panov & Janka 2009; Wanajo et al. 2001),
sis (Burbidge et al. 1957). Low- to intermediate-mass stars to name a few. However, presently the most favoured sites for
(1M(cid:12) (cid:46) M (cid:46) 8M(cid:12)) evolving along the thermal pulsing ther-processarecore-collapsesupernovae(Wanajo&Ishimaru
asymptotic giant branch (TP-AGB) provide the necessary con- 2006). Extreme temperatures and run away nuclear processes
ditions for the “main” s-process, which is responsible for the produce an extremely high fluence of free neutrons (Wanajo
majority of the s-process elements in the solar-system between etal.2003),whicharenecessaryforr-processnucleosynthesis.
88 ≤ A ≤ 204(Snedenetal.2008),releasingfreeneutronsvia The presence of seed nuclei with high n-capture cross-
12C(p,γ)13N(β+ν )13C(α,n)16O reaction occurring in the He- sections(σ),suchasFe,iscriticalforn-capturenucleosynthesis.
e
richzoneinradiativeconditions(Stranieroetal.1997).Evidence As low- to intermediate-mass stars cannot synthesise nuclides
1
A.J.Gallagheretal.:Thebariumisotopicfractionsinfivemetal-poorstars
uptothe Fe peak,high-σnucleimustbepresentatthetimeof red wing and are further from the line core. As such, when the
the star’s formation for the s-process to occur. High-mass su- oddisotopecontributiontothetotallinestrengthisincreased,the
pernova progenitors (M > 8M(cid:12)) reach high enough tempera- asymmetryintheabsorptionline’sprofileisincreased.WhenBa
tures at the very end of their evolution immediately before the isdominatedbythes-process,moreoftheabundanceisassoci-
supernova explosive phase to synthesise nuclides up to the Fe atedwiththeevenisotopes,whichcontributetothelinenearits
peak.Unlikethes-process,ther-processdoesnotneedthepres- centre; the line profile has a deeper core with shallower wings
ence of high-σ nuclei at the time of formation as they are pro- andtheline’sasymmetryisreduced.
ducedinsitushortlybeforetheendofthelifeofthestar.Also, Thereare,however,difficultiesindeterminingisotopicfrac-
low-tointermediate-massstarsarelonglivedincomparisonto tions in Ba, chief among which is the high precision required
high-massstars.Assuch,r-processenrichmentfromsupernovae in the analysis of f , which demands the highest quality ob-
odd
explosions should dominate in the early universe, i.e. in metal- servationsandradiativetransfermodels.Issuesthenarisewhen
poor regimes, with the s-process signatures becoming increas- complex astrophysical behaviours, such as convection, start to
inglydominantinmoremetal-richregimes.Thistheorywasset becomevisibleinthehighqualitystellardata.Basicassumptions
outbyTruran(1981)andthechemicalevolutionofn-captureel- used in conventional spectrum synthesis codes that assume a
ementsfromBatoEuwasquantifiedbyTravaglioetal.(1999). plane-parallelgeometry(1D)andlocalthermodynamicequilib-
Indications to support this theory can be seen in evidence pre- rium (LTE) cannot actually replicate the observed Baii 4554Å
sentedinFranc¸oisetal.(2007,theirFig.14). lineprofile(Gallagheretal.2010).
AstheGalaxybecomesmoremetal-richovertime,s-process Thewellstudiedmetal-poorsubgiant,HD140283illustrates
signaturesinstarsbegintoincreaserelativetother-processfor the difficulties that are encountered when determining f ,
odd
Ba(Franc¸oisetal.2007).Whenonecomparesthe[Ba/Eu]ratios which has been attempted several times for this star. Gallagher
from Franc¸ois et al. (2007) with those from Mashonkina et al. et al. (2010) find [Fe/H] = −2.59 ± 0.09 and a low [Ba/Fe]
(2003),whostudythemetallicityatwhichthes-processbegins ratio = −0.87 ± 0.14, which seemingly point to an r-process
toincreaserelativetother-processforthehaloandthickdiskre- origin as Ba is mainly an s-process element in the solar sys-
spectively,therearevariationsinstar-to-starcompositionswhich tem. Yet according to their isotopic analysis they find f =
odd
leadtodifferentr-ands-processregimesforagivenmetallicity. 0.02±0.06, which agrees with the result published by Magain
InparticularFranc¸oisetal.(2007)findthatthes-processbegins (1995),whofinds f = 0.08±0.06.Bothisotopefractionsin-
odd
to increase relative to the r-process at [Fe/H] (cid:38) −2.6, whereas dicateafullys-processregime,contradictingtheTruran(1981)
Mashonkinaetal.(2003)findthistooccurat[Fe/H](cid:38)−1.5. model. However, measurements of f in 1D LTE by Lambert
odd
One potential way of detecting r- and s-process signatures & Allende Prieto (2002) and (for the same spectrum) Collet
in a star is to measure the isotopic fractions in heavy elements etal.(2009)showHD140283tobeslightlyr-processdominated
usingtheprofileoftheirabsorptionlines.Therearedifferences with f = 0.30 ± 0.21 and f = 0.33 ± 0.13 respectively,
odd odd
between pure s- and r-process isotope ratios in most heavy el- which contradicts Magain (1995) and Gallagher et al. (2010).
ements, which can be in principle detectable through minute When Collet et al. (2009) reanalysed the same spectrum again
changesinlineasymmetry.Baisanattractiveheavyelementfor using 3D hydrodynamic model stellar atmospheres they found
whichtouseofthismethod,asthehyperfinesplitting(hfs)ofits f = 0.15±0.12, indicating an s-process signature and sup-
odd
4554Ålinefromthesingly-ionisedstageisquitelarge(Rutten portingresultsfromMagain(1995)andGallagheretal.(2010).
1978)anditoffersthepossibilityofmeasuringtheoddfraction If the three studies showing HD140283 to have an s-process
(f 1)viaresolvedasymmetriclines. signature are correct, the contradiction with Truran’s paradigm
odd
The r- and s-process are responsible for five of the seven couldbeexplainedbyhows-andr-processesvarywith[Fe/H],
stable isotopes of Ba (the lightest two, 130,132Ba, arise in the orbytheinhomogeneityoftheinterstellarmedium(ISM)when
so-called p-process (Burbidge et al. 1957)). Whereas the s- thishalostarformed,inwhichcasestar-to-starvariationsofn-
process can synthesise all five Ba n-capture isotopes, shielding capturesignatureswouldbecommon.Thecauseofthediscrep-
by134,136Xe preventsther-processfromsynthesisingtwoofthe ancybetweentheresultsofthevariousstudiesofHD140283is
evenisotopes,134,136Ba. unclear.
Using nucleosynthesis calculations (Arlandini et al. 1999), Unlike Ba, Eu in the solar system has a predominantly r-
thevaluesof f canbedeterminedforther-ands-process.For process contribution, which Arlandini et al. (1999) calculates
odd
a fully s-process regime, f = 0.11±0.01, and in a fully r- to be 94% of the total Eu. Both stable Eu isotopes, 151,153Eu,
odd,s
processregime, f =0.46±0.06.Gallagheretal.(2010)show showsignificantr-processcontributionsrelativetothes-process
odd,r
alinearrelationshipbetween f andr-ands-processcontribu- andtheseoccurinalmostequalamountsataratioof0.48:0.52
odd
tionsfor Ba determinedfromArlandinietal.(1999).Valuesof for 151:153 (Arlandini et al. 1999). High abundances of Eu in
0.0 ≤ f < 0.11 or 0.46 < f ≤ 1.0 are not physical in the metal-poor stars indicate a strong r-process signature (Spite &
odd odd
context of the nucleosynthesis model but are achievable from Spite1978;Snedenetal.2008).Thereforeitiscommonpractice
moreadhocisotopicmixes.However,wehaveassumedthatthe tousethe[Ba/Eu]ratioasanindicatorofastar’sr-ands-process
theoryinArlandinietal.(1999)isaccurateandwestatethrough- ratio(Burrisetal.2000;Hondaetal.2006,2007;Snedenetal.
outourpaperthatanyvalueof f whichliesoutsidethelimits 2008).
odd
0.11≤ f ≤0.46isnon-physical. Limits on [Ba/Eu] abundance ratios can be set for pure s-
odd
From the point of view of spectroscopy, the even Ba iso- and r-processes and are found to be +1.45 and −0.81 respec-
topes contribute principally to the formation of the line centre tively (Burris et al. 2000), which were calculated using solar
in the Baii 4554Å line. The odd isotopes, which are hyperfine abundancesinAnders&Grevesse(1989).Usingthetheoretical
split,contributetothespectralregionclosertothewingsofthe abundancesinArlandinietal.(1999),wefindthe[Ba/Eu]limits
line(seeFig.1).Therelativestrengthoftheoddisotopeslocated forthes-andr-processestobe+1.13and−0.69respectively.
toward the blue wing are smaller than those located toward the Gallagheretal.(2010)highlightedtheissuesthatarisewhen
fitting Fe lines assuming 1D LTE, particularly in the wings of
1 f =[N(135Ba)+N(137Ba)]/N(Ba) theline,andplottedtheaverageresidualforalltheFelinesanal-
odd
2
A.J.Gallagheretal.:Thebariumisotopicfractionsinfivemetal-poorstars
ysed.Theydemonstratedtheasymmetriesthatoccurinlinefor- (2007)andMashonkinaetal.(2008).Mashonkinaetal.(2008)
mation;1DLTEradiativetransfercodescannotreplicateasym- complementthe[Ba/Eu]determinationnicelyinHD84937cal-
metries. Gallagher et al. (2010) speculated that a spectroscopic culating f = 0.43±0.14,indicatinganalmostfullyr-process
odd
analysis based on 3D radiation-hydrodynamic model stellar at- regime.Howevertheyfound f inHD122563tobe0.22±0.15,
odd
mospheres may resolve these problems. In addition they found amostlys-processregime,whichcontradictsthe[Ba/Eu]abun-
irregularitiesbetweentheobservedandsyntheticprofilesinthe dances found in their study and by Honda et al. (2006), see
Feline’score. Table 2. We also calculate f for two more turn-off stars,
odd
Inthispaperwedeterminetheisotopicfractionsof Ba ina BD−04◦3208 and BD+26◦3578, neither of which have previ-
further five metal-poor stars under the assumption of 1D LTE. ousBaandEuanalyses.
Wedescribetheobservationsin§2,andthe1DLTEanalysisof
theBa4554Ålinein§3.Duetothelackofmetalsinmetal-poor
stars,i.e.starswith[Fe/H] < −2,electronnumberdensitiesare Table 2. Results from previous 1D LTE studies to determine
low,whichdrivesdownopacitiesintheatmosphereoflate-type [Ba/Eu]and/or foddforstarsstudiedinthiswork.
stars. Therefore assuming LTE in line forming regions of the
stellaratmosphereisnolongervalid(Mashonkinaetal.2008).In Star [Fe/H] [Ba/Eu] f Reference
odd
§4oftheworkpresentedherewetestwhethertheirregularities HD140283 −2.59 >−0.66 0.01±0.04 (1)
seen in the Fe line residuals are due to LTE departures, using −2.40 ∼−1.05 0.30±0.21 (2)
a non local thermodynamic equilibrium (NLTE) treatment for −2.50 ··· 0.33±0.13 (3)
HD140283andHD122563.Wediscusstheresultsin§5. −2.70 ··· 0.08±0.06 (4)
HD122563 −2.77 −0.50 ··· (5)
−2.53 −0.41 0.22±0.15 (6)
2. Targetselectionandobservations
HD84937 −2.15 −0.69 0.43±0.14 (6)
Thestellarspectrausedinthisstudyarealmostthehighestqual- HD88609 −3.07 −0.48 ··· (7)
ity spectra of very metal-poor stars obtained using the High
Dispersion Spectrograph (HDS) (Noguchi et al. 2002) at the
Subaru8.2mTelescope.Allhavehighresolution(R ≡ λ/∆λ = (1)Gallagheretal.(2010),asmeasuredbythe4554Åline.(2)
90000−95000,calculatedfromthewidthsofseveralhundred Lambert & Allende Prieto (2002). (3) Collet et al. (2009). (4)
ThAr lines),andhighsignal-to-noise(S/N > 500perpixel,as Magain (1995). (5) Honda et al. (2006). (6) Mashonkina et al.
measuredaround4500Å).Suchspectraareessentialforanac- (2008).(7)Hondaetal.(2007).
curatemeasurementof f .Specificsoftheobservationscanbe
odd
foundinTable1.
Table1.Detailsoftheobservationsofthestellarspectra. 3. 1DLTEanalysis
In this section we briefly review the method used to deter-
Star Date Exp.Time(min) S/N R mine the isotopic fractions, abundances and broadening values
HD140283 22/07/01 82 1100 90000 of the stars in our sample. All synthetic spectra in this sec-
tion were created using the ATLAS (Cottrell & Norris 1978)
HD88609 20/04/04 210 750 90000
radiative transfer code with KURUCZ06 model atmospheres
19/10/05
(http://kurucz.harvard.edu/grids.html ). For a more
20/10/05
extensivedescriptionoftheprocessesinvolvedinthefollowing
HD122563 30/04/04 90 850 90000 procedure,wereferthereadertoGallagheretal.(2010).Results
areprovidedinTable3.
HD84937 22/03/03 180 630 95000
BD+26◦3578 17/05/05 130 550 95000 3.1. Bariumlinelists
BD−04◦3208 18/05/05 180 580 95000 Line lists with all hfs components of the Ba line at 4554Å,
19/05/05 whichisusedtodetermine f ,wereconstructedusingisotopic
odd
information from Arlandini et al. (1999) and hfs information
from Wendt et al. (1984) and Villemoes et al. (1993) for pure
s- and pure r-process mixtures (corresponding to f = 0.11
odd
and0.46respectively).Hybridlinelistsfor−0.24≤ f ≤0.46
Table 2 shows previous results on Ba published for four of odd
werecreatedfromthesebyadjustingthelinestrengthsoftheBa
thestarsstudiedinthispaper.Itfurtherillustratesthedifficulties
isotopes.FurtherdetailsonthiscanbefoundinGallagheretal.
indetermining fodd,inthatforHD122563, fodd and[Ba/Eu]do (2010) but we remind the reader that f = 0.11 is the lowest
not support each other2, while for HD140283 there are large odd
valueof f achievedinthes-processofArlandinietal.(1999);
discrepanciesbetween fodddeterminations. f =0.0o0ddisthelowestvalueof f achievableinaneven-only
Thetwogiantsinourstudy,HD122563andHD88609,and odd odd
isotope mix, and that values of f < 0.00 are non-physical,
oneoftheturn-offstars,HD84937,showastrongindicationthat odd
mathematicalsolutionsonly.
Ba should be r-process dominated based upon [Ba/Eu] abun-
Isotopic abundances presented in Arlandini et al. (1999)
dance ratios calculated in Honda et al. (2006), Honda et al.
whichweusetodetermine f and f werenormalised(by
odd,r odd,s
2 One might take the view that these results are consistent with a Arlandini et al. 1999) to the s-process-only isotope 150Sm. We
mixedheavyelementorigin. exploredarenormalisationto134Baand136Ba,butfoundlittleto
3
A.J.Gallagheretal.:Thebariumisotopicfractionsinfivemetal-poorstars
nochangein f :0.49(renormalisedto134Ba)and0.46(renor- prescriptionweadoptforζ assumesequalspeedsintheradial
odd,r RT
malised to 136Ba). The renormalisation does not affect f , andtangentialflows,andequaltemperatures(Gray2008).
odd,s
which remains fodd,s = 0.11. This does not significantly alter ThemodelspectraweresynthesisedwithATLASusingagrid
theinterpretationoftheresultspresentedhere. ofζ valuesrangingfrom4.00kms−1to9.00kms−1instepsof
RT
No attempt was made to determine f for the 4934Å line 0.2kms−1.Theinstrumentalbroadening,determinedfromThAr
odd
because, as showed by Gallagher et al. (2010), analysis of this lines, and represented as a Gaussian, was also included in the
line is extremely difficult and yields large errorbars due to Fe synthesis.Eachlinewasfitusingthesameχ2codethatwasused
blends found in the wings of this line. Nor do we attempt to in§3.2.1.ResultsforζRT canbefoundinTable3(rows(17)to
studyhigherexcitationlinesofBa,astheirhyperfinesplittingis (24)),wherewehavealsolistedthenumberoflinesthatarebest
fitbytheζ approachforeachstar.
muchsmallerthanthatat4554Å. RT
3.3. Theisotopicfractionofbarium
3.2. Determinationofthemacroturbulence
Onceν andζ wereobtainedforthetwobroadeningmech-
To recap on Gallagher et al. (2010), we use a χ2 code (derived conv RT
anisms,theBaii4554Ålinewasanalysedusingaχ2 codevery
fromthatofGarc´ıaPe´rezetal.(2009))tocomparetheobserved
and synthetic spectra of a number of Fei and Feii lines, com- similartotheonedescribedin§3.2tofindvaluesforthefreepa-
puted for different abundances A(Fe)3, wavelength shifts ∆λ, rameters∆λ,A(Ba)and foddthatminimiseχ2forthe4554Åline
and line broadening parameters. Two different broadening ap- in each star. Results for fodd for Gaussian and radial-tangential
broadeningtechniquescanbefoundinTable3.Thebestfit Ba
proaches are used, as described below. We derive, for each Fe
profiles are shown in Fig. 1 (Gaussian) and in Fig. 2 (radial-
lines analysed, the best fitting abundance, wavelength shift and
tangential). From the Gaussian results we find for HD122563,
broadening. An ordinary least squares (OLS) fit is calculated
HD88609, HD84937, BD−04◦3208 and BD+26◦3578 that
through the wavelength-dependence of broadening and A(Fe)
f = −0.12±0.07, −0.02±0.09, −0.05±0.11, 0.18±0.08
valuestodeterminethebestvaluesat4554Å. odd
and0.08±0.08respectively.Theseresultswouldsuggestthatall
starsexaminedhereshowahighs-processfraction.
3.2.1. Gaussianbroadening
One approach to the macroscopic broadening is to adopt a 3.4. The[Ba/Eu]ratio
Gaussian of FWHM = ν , representing the convolution of
conv In our sample only the two giants had Eu line strengths ade-
a Gaussian instrumental profile with a Gaussian macroturbu-
quate to conduct a Eu abundance analysis. This was done by
lent profile. As Lambert & Allende Prieto (2002) show, f
odd examining the Euii 4129Å line. The Euii 4205Å line is not
is extremely sensitive to ν . They found δf /δν =
conv odd conv used in this study as it is blended with a Vii line (Honda et al.
−0.51(kms−1)−1 for HD140283. Gallagher et al. (2010) found
2006;Gallagheretal.2010)thatcanaffectabundancedetermi-
an even larger sensitivity, −0.71(kms−1)−1. The effects of this
nations.Alsonoattemptismadetoanalysetheisotopicsplitting
largesensitivitycanbereducedbyincreasingthenumberof Fe
of 151,153Eu; we assume a fixed 50:50 isotopic split of 151:153
lines, N,usedtoconst√rainνconv,aswetaketheerrorinνconv as whenconstructingthehfs-affected Eu 4129Ålinelist.The Eu
thestandarderror,σ/ N,whereσisthestandarddeviationof
linelistforthesolarr-ands-processratiowasconstructedusing
ν values. In our work, only Fe lines of comparable equiva-
conv
lentwidths(W)totheBaiilineareselected,sotheywouldhave hfsinformationfromBeckeretal.(1993)andKrebs&Winkler
(1960) with loggf values taken from Biemont et al. (1982).
similarformationdepthstotheBaline,implyingthatmacrotur-
bulenteffectson Ba wouldbewelldescribedby Fe.Wealsodo Abundances for Eu are taken as those that satisfy the χ2 min-
not analyse strong lines where uncertain pressure effects in the imum.Fromtheseabundances,andthosefoundbythe Ba anal-
ysis,[Ba/Eu]wascalculatedandtheresultsforbothstarscanbe
linebroadeningbecomesignificant.
foundinTable3,row(10).
Theadoptedatmosphericparametersforeachstararelisted
inTable3(rows(1)to(5))andthederivedbroadeningisgiven
inrow(7). 3.5. Erroranalysis
InGallagheretal.(2010)wedemonstratedhowalteringonestel-
3.2.2. Radial-tangentialmacroturbulentbroadening lar parameter can force other parameters, in particular ν , to
conv
compensate for its effect on f . In that paper we called this
InGallagheretal.(2010)wecomparedthreedifferentbroaden- odd
case1.Thecompensationbyν waswellillustratedwhenone
conv
ing techniques to find out which of them best fit the Fe lines. lookedattheeffectsofchangingthemicroturbulence(ξ).Once
Wefoundthatusingarotationalbroadeningmechanism,where ν wasrecalculatedfromthe Fe lines,theeffectξhadon f
conv odd
the macroturbulent broadening of the star was represented by
was nullified. As ν partially compensates for other changes
conv
νsini only (with the instrumental broadening still represented in the stellar parameters as well, i.e. Teff and logg, their effect
by a Gaussian), almost always gave a worse fit than when we
on f isalsoreduced.
odd
employed a simple Gaussian. However we found that using a
Tocalculatetheerrorin f welookatfivepossiblesources
odd
radial-tangentialmacroturbulentbroadeningtechnique(ζ )al-
RT of error: νconv, ξ, Teff, logg and the Unso¨ld approximation en-
lowed us to fit spectral lines slightly better than the Gaussian hancementfactor,E ,whichenhancestheeffectofγ inthe
γ 6,vdW
mechanism.Asaresult,wehavecontinuedtoemploythisbroad- Van Der Waals calculation, γ = γ E . In our analysis we
6 6,vdW γ
eningtypeinthecurrentinvestigationforallfivestarsandagain haveusedE =2.2.Totesttheeffectithasonν and f we
γ conv odd
for HD140283, as well as the simple Gaussian approach. The havedecreasedthisto1.5.Theeffectofuncertaintiesin[Fe/H]
on f is negligible and as such was ignored (Gallagher et al.
(cid:16) (cid:17) odd
3 A(X)=log N(X) +12. 2010).Itisexpectedthateverystarbelongingtothesamestage
10 N(H)
4
A.J.Gallagheretal.:Thebariumisotopicfractionsinfivemetal-poorstars
Fig.1. The best fit Baii 4554Å lines for each star, using a Gaussian broadening technique. Each figure displays the observed Ba
profile(diamonds)andthebestfitsyntheticprofile(solidline),whichincludestheerroron f (dashedline).Wehavealsoincluded
odd
aschematicoftheoddandevenisotopesforreference.Thelowerpanelofeachfigureshowstheresiduals(obs-syn)ofeachfitasa
percentage.ForreferencewehaveincludedHD140283,whichwasanalysedinGallagheretal.(2010).
5
A.J.Gallagheretal.:Thebariumisotopicfractionsinfivemetal-poorstars
Fig.2.ThebestfitBaii4554Ålinesforeachstar,usingaradial-tangentialbroadeningtechnique.Eachfiguredisplaystheobserved
Ba profile (diamonds) and the best fit synthetic profile (solid line), which includes the error on f (dashed line). We have also
odd
included a schematic of the odd and even isotopes for reference. The lower panel of each figure shows the residuals (obs-syn) of
eachfitasapercentage.
6
A.J.Gallagheretal.:Thebariumisotopicfractionsinfivemetal-poorstars
Table3.Resultsofthe1DLTEanalysisconductedonfivemetal-poorstarsandthevariousparametersusedintheiranalysis.
Parameter HD122563 HD88609 HD84937 BD−04◦3208 BD+26◦3578 HD140283
AtmosphericParameters
(1) Teff (K) 4570±100 4550±100 6290±100 6340±100 6240±100 5750±100
(2) logg(cms−1) 1.1±0.3 1.1±0.3 3.9±0.3 4.0±0.2 3.9±0.2 3.7±0.1
(3) [Fe/H] −2.77±0.19 −3.07±0.20 −2.15±0.30 −2.28±0.20 −2.33±0.20 −2.50±0.20
(4) ξ(kms−1) 2.2±0.5 2.4±0.5 1.2±0.3 1.5±0.2 1.5±0.2 1.4±0.1
(5) AtmosphereReference (1) (2) (3) (4) (4) (5)
Gaussianbroadening
(6) f −0.12±0.07 −0.02±0.09 −0.05±0.11 0.18±0.08 0.08±0.08 0.02±0.06
odd
(7) ν (kms−1) 6.99±0.07 7.03±0.08 6.98±0.06 6.62±0.05 6.41±0.06 5.75±0.02
conv
(8) [Fe/H] −2.90±0.17 −3.17±0.17 −2.24±0.11 −2.42±0.11 −2.45±0.12 −2.59±0.09
(9) [Ba/Fe] −0.85±0.21 −0.91±0.21 0.04±0.15 −0.20±0.15 −0.06±0.16 −0.87±0.14
(10) [Ba/Eu] −0.20±0.15 −0.47±0.15 ··· ··· ··· >−0.66
(11) (cid:104)∆λ(cid:105)(mÅ) −15.86±0.37 −14.70±0.90 −14.69±0.53 −11.47±1.093 −13.29±0.89 −12.67±0.48
(12) δf /δν (kms−1)−1 −0.57 −0.74 −0.89 −0.78 −0.77 −0.71
odd conv
(13) δf /δξ(kms−1)−1 −0.08 −0.08 0.05 0.05 0.05 0.00
odd
(14) δfodd/δTeff (100K)−1 −0.04 −0.05 −0.03 −0.02 −0.02 −0.02
(15) δf /δlogg(dex)−1 0.02 0.02 −0.27 −0.23 −0.23 −0.28
odd
(16) δf /δE (0.7)−1 −0.02 −0.02 −0.05 −0.04 −0.04 ···
odd γ
RadialTangentialbroadening
(17) f −0.16±0.05 −0.11±0.07 −0.02±0.10 0.20±0.10 0.09±0.10 0.02±0.04
odd
(18) ζ (kms−1) 5.69±0.09 5.74±0.09 5.77±0.08 5.36±0.06 5.14±0.07 4.30±0.02
RT
(19) ν (kms−1) 3.32 3.32 3.20 3.20 3.20 3.32
inst
(20) numberofbestfitFelines 53 34 30 28 32 38
(21) δf /δζ (kms−1)−1 −0.30 −0.64 −0.60 −0.73 −0.70 −0.63
odd RT
(22) δf /δξ(kms−1)−1 −0.08 −0.08 0.05 0.05 0.05 0.00
odd
(23) δfodd/δTeff (100K)−1 −0.01 −0.001 −0.05 −0.07 −0.06 0.01
(24) δf /δlogg(dex)−1 −0.01 −0.02 −0.18 −0.22 −0.21 −0.35
odd
Otherspectralinformation
(25) Spectralrange(Å) 3080-4780 3070-4780 4130-6860 4130-5340 4050-5250 4100-6900
(26) Felinesamplesize 54 35 44 36 37 93
(27) W (mÅ) 99.1 93.2 49.7 34.7 42.7 20.1
Ba
(1)Hondaetal.(2006).(2)Hondaetal.(2007).(3)Aokietal.(2009).(4)Garc´ıaPe´rezetal.(2009).(5)Gallagheretal.(2010).
ofevolution,i.e.giant,sub-giantandturn-off,wouldreproduce ThiswasdoneundertheassumptionsofLTE.However,itiswell
comparable sensitivities to each stellar parameter. As such we known that Fei suffers from the effects of NLTE (The´venin &
haveruneachtestfortwoofthefivestars:totestthesensitivity Idiart1999;Shchukinaetal.2005)inmetal-poorstars.Wethere-
of f in the giants we have used HD88609, and for the turn- fore sought to quantify NLTE effects for Fe on the preceding
odd
off stars we have chosen BD−04◦3208. However, we have run analysis,inparticularonthedeterminationofmacroturbulence,
sensitivity tests of ν and ζ for all stars as these parame- andthereforethevalueof f .Noattemptismadetodetermine
conv RT odd
tershavethelargesteffecton f .Theresultsofthesensitivity NLTEcorrectionsfor Ba itself,eitherin f orthe[Ba/Eu]ra-
odd odd
of f can be seen in Table 3, rows (12) to (16) and rows (21) tio. Mashonkina et al. (2008) demonstrated that corrections to
odd
to (24). The tests confirm that the f determinations are es- theabundanceratioarenotsignificantenoughtochangethein-
odd
sentiallyunaffectedbythechoiceof Eγ,Teff orξ,butloggand ferredr-ands-processregimeinastar.Thedeterminationof fodd
themacroturbulentbroadeningeffectsaremoreimportant.Ithas assumingNLTEgoesbeyondthescopeoftheworkpresentedin
beenreportedbyTajitsuetal.(2010)thattheEEV42-80CCDs thissection.
used in the HDS suffer from nonlinearity. By investigating the
differencesbetweenthecorrectedandnon-correctedspectra,we To compute the Fei profiles, a version of the NLTE code
foundthatitseffecton f wasnegligible. MULTI (Carlsson 1986) was used with modifications to include
odd
the effects of line-blanketing, described in Collet et al. (2005).
ThecodeemploysMARCSmodelatmospheres.Themodelatom
usedwasthatadoptedbyHosfordetal.(2010).Foralongerdis-
4. 1DNLTEFelineanalysis
cussiononthemodelatom,processesofNLTEradiativetransfer
InGallagheretal.(2010)weaimedtoconstrainthemacroturbu- anditsimpactonstarsofthistype,seeHosfordetal.(2010).It
lence of HD140283 through the use of the Fe lines. Using the isimportant,however,tomentiontheparameterS ,thescaling
H
samemethod,wehavealsodonethisforfivefurtherstarsin§3. factor for the collisions due to H as described by the approxi-
7
A.J.Gallagheretal.:Thebariumisotopicfractionsinfivemetal-poorstars
mate Drawin formula (Drawin 1968, 1969). Due to the uncer- Table 5. Results from the NLTE analysis and the ATLAS LTE
tainties in the magnitude of the H collisions, the value of S resultsforcomparison.
H
is still uncertain and is treated differently by different works.
Collet et al. (2005) treats it as a free parameter and tests val- Star Run (cid:104)A(Fe)(cid:105) (cid:104)ν (cid:105)(kms−1)
uesS = 1and0.001.Kornetal.(2003)foundahighervalue, conv
H HD140283 LTE 4.96±0.01 6.03±0.04
SH = 3,howeverinmorerecentwork(Mashonkinaetal.2010) S =MU1LTI 5.28±0.01 5.98±0.05
the same group has constrained it to 0.1 based on an improved SH =0.001 5.53±0.01 5.92±0.04
Fe atom. Here we adopt the values 1 and 0.001; this gives us H
LTE 4.92±0.04 5.76±0.09
twosetsofsyntheticspectra,onewiththeDrawin(S = 1)de- ATLAS
H (51linesubset)
scriptionof H collisions,andasecondclosetomaximalNLTE
LTE 4.91±0.01 5.75±0.02
effects(S =0.001).WealsocomputelineprofilesinLTEusing ATLAS
H (93lines)
MULTI.
NLTE calculations of Fei line profiles were performed for HD122563 LTEMULTI 4.58±0.03 7.02±0.10
two stars, the subgiant HD140283 and the giant HD122563. SH =1 4.98±0.03 6.95±0.09
Thefirstwasanalysedsoacomparisoncouldbemadebetween SH =0.001 5.12±0.03 6.91±0.09
this work and the LTE analysis of Gallagher et al. (2010). The LTEATLAS 4.54±0.11 7.06±0.18
second was analysed to understand the NLTE effects on Fei in (31linesubset)
giants,wheretheatmospheresaremoretenuousandalsocooler, LTEATLAS 4.51±0.04 6.99±0.07
toactasacomparisontotheLTEworkinthispaper. (54lines)
ThreesetsofMULTIrunswherecompletedforeachstar,one
inLTE,andtwoinNLTEwiththeS valuesmentionedabove.
H
Aχ2 analysisproceduresimilartotheonedescribedin§3been
used. Synthetic profiles were created over the parameter space
showninTable4.Theextrinsicbroadeningwasrepresentedby A comparison of MULTI LTE and ATLAS LTE results shows
a Gaussian consolidating both macroturbulence and instrumen- that the abundances and extrinsic broadening value are compa-
tal broadening, the values FWHM in Table 4 representing the rable for both cases, the only exception being the broadening
G
FWHMoftheGaussian. valuesofHD140283,whichisthemostimportantparameteras
itdirectlyaffects f .ForHD140283wehavelargervaluesin
odd
NLTE than that of Gallagher et al. (2010). Table 5 shows that
Table4.Rangesofparametersusedtocreatethesyntheticpro-
for HD140283, choosing the same 51 line subset doesn’t “fix”
filesinMULTI. thediscrepancy.ForHD122563thedifferenceismuchsmaller
and is within the errors. One could naively ascribe this differ-
χ2gridparameterranges
encetobediscrepanciesintheMARCSandKURUCZmodelatmo-
A(Fe) FWHM ∆λ spheres, e.g. different temperature gradients and density gradi-
G
Star Run (mÅ) (mÅ) ents. However, a comparison between the MARCS and KURUCZ
HD140283 LTE 4.28−5.28 73−119 ±25 modelatmospherescanbefoundinHosford(2010),whofound
MULTI
S =1 4.66−5.28 73−119 ±25 little to no effect by these parameters. It is most likely that the
H
S =0.001 5.00−5.70 73−119 ±25 differencesarisefromthedifferenttreatmentsofthebroadening
H
HD122563 LTE 4.00−5.58 74−114 ±25 itselfinMULTIandATLAS.Weseecomparablewavelengthshifts
S =MU1LTI 4.00−5.58 74−114 ±25 betweenthetwoanalyses,andcomparableprofilesforeachline.
SH =0.001 4.68−5.50 74−114 ±25 In NLTE we see an increase of abundance with decreasing SH
H duetotheoverionisationeffectsbecomingmorepertinent;thus
a larger positive abundance is needed for neutral lines to com-
pensate.Asaconsistencycheck,NLTEabundancesfromtheχ2
analysiswerecomparedtothosefromanequivalentwidthanal-
TheintentionwastoseeiftheobservedFeiprofilescouldbe ysisandwerefoundtobecomparableateachSHvalue.
betterfitbyspectracomputedinNLTE,inparticularforthegi- Aninterestingthingtonotehereisthesensitivityofνconv to
ants,wherethecooleratmospheresresultinlargerlinestrengths theSH valueandthedifferencebetweenLTEandNLTEvalues.
(atfixed[Fe/H]).Here,thesyntheticLTEcoreistooshallowand Forbothstars,νconvdecreasesby0.1kms−1ingoingfromMULTI
thewingstoobroadevenattheminimumχ2valueoftheline.In LTEtoMULTISH =0.001.Naively,onemightinferfromTable3
switchingtoNLTE,wehopedwemightmodelthe Fe linesbet- thatthiswouldincrease f fromanLTEanalysisofBa4554Å
odd
ter,andhenceobtainbettervaluesofmacroturbulentbroadening between 0.06 and 0.09. However, some of this difference may
and,inlaterworks,amorereliablevalueof f forBa. notfullyapplyto Ba calculatedinLTE,duetodifferentbroad-
odd
Table 5 gives the results from the χ2 analysis using MULTI, ening under NLTE. Nonetheless, it points to the importance of
andtheATLASLTEresultsforcomparison.TheMULTIvaluesare an accurate description of the radiative transfer if one is to be
themeanof51linesforHD140283and31linesforHD122563; abletodetermine f .
odd
errors are the standard error. Fewer lines are used in the MULTI OnehopeoftheNLTEanalysiswasthatitmayaidinfitting
analysisthanintheATLASLTEanalysisduetotheincomplete- thestrongerFelinesofthegiantbyproducingmorerealisticline
ness of the adopted model atom which leads to several of the profiles, and hence reduce the residuals in the Fe analysis (see
lines not being computable in MULTI. Also, after further scruti- Gallagheretal.2010,theirFig.10).InFig.3weregeneratethe
nizing the results, three lines from HD140283 and three lines plot of average residuals for HD140283 using a MULTI analy-
fromHD122563wereremovedfromtheanalysis.Thiswasdue sisof51Felines.Wehaveco-addedtheresidualsfromeachFe
toeitherapoorlydefinedcontinuum,orblendinglinesveryclose linetosmoothoutanyuniquelinedefects.Theresidualsareof
tothelineofstudy. similarmagnitudetothosefromGallagheretal.(2010)andhave
8
A.J.Gallagheretal.:Thebariumisotopicfractionsinfivemetal-poorstars
Fig.3. Plots of average residuals from χ2 analysis of Fe lines in HD140283 and HD122563, for S = 1, 0.001 and LTE using
H
MULTI.ForcomparisonwehavegeneratedthesameplotusingATLASoutputdataforthesamesubsetsoflines.
similarfeatures.Mostimportantly,theMULTIresidualsforNLTE 5.1. Alternativebroadeningtechniques
withdifferentS valuesandforLTEareallverysimilar.There
H
is in fact a very slight worsening of the core fit with increased We have shown that fodd has a high sensitivity to νconv, which
NLTEeffects.ItisalsoseenthattheresidualsforHD122563are we have determined by fitting synthetic 1D LTE (and in §4,
ofasimilarform,albeitwithagreatermagnitude.Thelinesanal- NLTE) profiles to Fe lines. There are several reasons why we
ysedinHD122563arefarstrongerthanthoseinHD140283.As chosetouseFelines.Firstlytheyarethemostabundantspecies
the lines become stronger, they become harder to fit precisely, inametal-poorspectrumandcoveraconsiderablerangeinline
butusingNLTEprofileshasnoeffectonimprovingthis. strength.Asmentionedabove,thesetwoattributesareusefulbe-
causetheyallowustouselinesthatformatsimilardepthstothe
ThefactthattheMULTINLTEanalysishasledtonoimprove- Baline.However,werevisitthisargumentandconsiderwhether
mentovertheMULTILTEanalysisinthefitoftheFelinesisnot Feisasensibleatomicspeciestousetodeterminethemacrotur-
entirelysurprising.InfactwhencomparedtotheATLASanalysis bulenceofanotherspecies.
for the same subset of Fe lines (seen in red) there is a consid- Totestthishypothesis,weanalysedseveralCailinesinthe
erable worsening of the residuals, particularly for HD140283, star with the best quality stellar spectrum, HD140283 (S/N =
although NLTE effects were still important to investigate. The
1100), using the same techniques described in §3. Only seven
effects of NLTE on Fei in metal-poor stars are dominated by
lines were found to be unblended and to have similar strengths
overionisation.Toafirstapproximation,thepopulationsofneu-
to the Ba line (10 ≤ W (mÅ) ≤ 50). This meant that the stan-
tral Fe energylevelscanbeseenasfollowingaBoltzmanndis-
darderrorinν wasmuchlargerforthissetoflinesthanwas
tributionrelativetooneanother,butwithashiftintheionization conv
found for the 93 Fe lines we used in Gallagher et al. (2010).
equilibrium.Theresultsshowthatthisdoesnotaffecttheshape
Wefoundthat(cid:104)ν (cid:105) = 5.63±0.13kms−1.Thisisasmaller
of the profiles, though for a given equivalent width the abun- conv Ca
value than was determined using Fe lines (5.75±0.02 kms−1)
dance needed to reproduce the line increases. The other main
NLTEeffect,achangeinthelineandcontinuumopacitieswith butstillwithinthe1σerror,andthestatisticsofusingonlyseven
heightintheatmospheres,apparentlyhaslittleoveralleffecton linesmeantthatbyusing Ca wewouldgreatlyincreasetheun-
theFeilineprofiles. certaintyin fodd.Neverthelessitwasfoundthat fodd,whichfrom
theFeanalysiswasfoundtobe0.01±0.06(inthe4554Åline4),
In summary, NLTE effects in Fe affect νconv by up to ∼ wouldmovehigherto0.10±0.11.Wecannotsaywhether Ca
0.1kms−1, and may affect fodd for Ba up to 0.06 or 0.09, but isabetteratomicspeciestousethan Fe asthespreadinνconv is
NLTE does not result in a better fit to the Fe lines (Fig. 3). toohigh.
Other mechanisms may come into play, e.g. as represented by
To avoid using other elements to constrain the macroturbu-
3Dmodelatmospheres.Itwouldstillbeinterestingtosee,how-
lent broadening of Ba, we experimented by treating ν as a
ever,howaNLTEtreatmentofBaaffectstheinferred f . conv
odd freeparameterwhilstdetermining f ,thusderivingitfromthe
odd
Ba line.Thiswasdoneforallsixstarsinthisstudy.Resultsare
showninTable6.InTable6wealsogivethestandarddeviation
(s.d.) of the Fe line measurements, as an indication of the un-
certainty associated with the measurement of just one line, e.g.
5. Discussion Ba 4554Å. As shown, νconv is little changed (within 1 s.d.) in
fourstarswhenusingjusttheBaline,andwithin2s.d.inafifth
With the exception of one star, BD−04◦3208, all of the stars star,andthereforethereislittlechangeto fodd.Itisinterestingto
notethattwooftheturn-offstarsandthesubgiant,HD140283,
analysedinthispaperandHD140283,whichwasstudiedinde-
arefoundtohavehigherν values,drivingsmaller f (more
tailinGallagheretal.(2010),showanon-physicalisotoperatio conv odd
non-physical) ratios though in all cases the differences in ν
(f < 0.11)closetothes-process-onlycomposition.Thenon- conv
odd
are comparable to the uncertainty expected for one measure-
physical results for f suggest that applying a 1D LTE treat-
odd
ment. It is therefore still unclear whether the Fe analysis does
menttoanalysetheisotopicfractionofthe Ba 4554Ålinedoes
notappeartobeveryrobust.Thereareseveralpossibilitieswhy
thismightbethecase,andafewpossiblesolutionstotheprob- 4 Table3lists f ascalculatedbyboththe4554and4934Ålines
odd
lem,whichwenowdiscuss. forHD140283.
9
A.J.Gallagheretal.:Thebariumisotopicfractionsinfivemetal-poorstars
Table6.Valuesofν (measuredinkms−1)asdeterminedfrom
conv
Fe linesanddirectlybytheBaii4554Åline.Notethatwecan-
notcalculate f inBD+26◦3578whenweemployν (Ba).
odd conv
Star ν s.d. f ν f
conv odd conv odd
(Fe) (Fe) (Fe) (Ba) (Ba)
HD122563 6.99 0.54 −0.12 6.82 −0.04
HD88609 7.03 0.45 −0.02 6.98 0.01
HD84937 6.98 0.41 −0.05 6.92 −0.03
BD−04◦3208 6.62 0.32 0.18 6.88 −0.01
BD+26◦3578 6.41 0.34 0.02 8.85 ···
HD140283 5.75 0.19 0.01 6.06 −0.23
describetheDopplerbroadeningfor Ba wellornot,butthereis
notstrongevidenceagainstit.
AswellastestingwhetherFewasanadequatespeciestouse,
we also considered whether a simple Gaussian adequately de-
scribesmacroturbulentbroadening.InGallagheretal.(2010)we
showedthataζ macroturbulentbroadeningmechanismbetter
RT
fit several Fe lines than a Gaussian. Therefore we employed a
ζ treatmentforeachstaranalysedinthisinvestigation(§3.2.2,
RT
Fig.2,andTable3).Itwasfoundthatforthegiantstars,aradial-
tangentialfittheFelinesbetter,withonlyonelineineachspec-
trum better fit by a Gaussian. We found that for the three turn-
offstarsaζ techniquefit68%−86%of Fe linesbetter.This
RT
demonstrates a clear reason to consider using ζ when work-
RT
ingin1DLTEoveraGaussianbroadeningmechanism.Thisis
particularly clear with the giant stars, whose Fe line cores are
closer to saturation causing the wings to become more signifi-
cant. Examination of the residual plots in Fig. 4 shows further
theimprovementtothefitswhenusingζ .Howeverwestress
RT
to the reader that whilst using such a technique under the as-
sumptionsof1DLTEseemstoimproveuponfittingerrorsasso-
ciatedwithusingatraditionalGaussian,botharestillsymmetric
profilesandareunabletoremedytheissueofasymmetriesasso-
ciatedwithabsorptionlinesinrealstellarspectra.
5.2. Felineresiduals
Fig.4showstheaverageresidualsofthe Fe linesusedindeter-
mining ν and ζ . It illustrates the difficulties in fitting ab-
conv RT
sorptionlineswith1DLTEsyntheticprofiles.
It is seen that the turn-off and subgiant stars have quite
anasymmetricresidualprofile,withparticularproblemsoccur-
ring in the red wings, 100 to 130mÅ from line centre for all
four stars. This seems to be caused by underlying assumptions
adoptedin1DLTEradiativetransfercodes;realabsorptionlines
arenotperfectlysymmetric.
This investigation is an extension of the asymmetry analy-
sis conducted in Gallagher et al. (2010); the asymmetry seems
tooccurinallfourstars.Severefittingissuesoccurinthegiant
stars,HD122563andHD88609,wherethe Ba (andhence Fe)
lineequivalentwidthsare∼90mÅ(Table3,row(27))andlines
cores begin to saturate so pressure broadening becomes more Fig.4. The average residuals of the Fe lines used to constrain
significant in the wings, and this may explain the symmetric ν andζ .
conv RT
residualsseenat±0.14Å.
10
