Modeling the quantum interference signatures of the Ba II D2 4554 A line in the second solar spectrum
aa r X i v : . [ a s t r o - ph . S R ] M a r Modeling the quantum interference signatures of the Ba ii D H. N. Smitha , K. N. Nagendra , J. O. Stenflo , and M. Sampoorna Indian Institute of Astrophysics, Koramangala, Bangalore, India Institute of Astronomy, ETH Zurich, CH-8093 Zurich, Switzerland Istituto Ricerche Solari Locarno, Via Patocchi, 6605 Locarno-Monti, Switzerland [email protected]; [email protected]; [email protected]; [email protected]
ABSTRACT
Quantum interference effects play a vital role in shaping the linear polarization profiles of solarspectral lines. The Ba ii D line at 4554 ˚A is a prominent example, where the F -state interferenceeffects due to the odd isotopes produce polarization profiles, which are very different from thoseof the even isotopes that have no F -state interference. It is therefore necessary to account for thecontributions from the different isotopes to understand the observed linear polarization profilesof this line. Here we do radiative transfer modeling with partial frequency redistribution (PRD)of such observations while accounting for the interference effects and isotope composition. TheBa ii D polarization profile is found to be strongly governed by the PRD mechanism. We showhow a full PRD treatment succeeds in reproducing the observations, while complete frequencyredistribution (CRD) alone fails to produce polarization profiles that have any resemblance withthe observed ones. However, we also find that the line center polarization is sensitive to thetemperature structure of the model atmosphere. To obtain a good fit to the line center peak ofthe observed Stokes Q/I profile, a small modification of the FALX model atmosphere is needed,by lowering the temperature in the line-forming layers. Because of the pronounced temperaturesensitivity of the Ba ii D line it may not be a suitable tool for Hanle magnetic-field diagnosticsof the solar chromosphere, because there is currently no straightforward way to separate thetemperature and magnetic-field effects from each other. Subject headings: line: profiles — polarization — scattering — methods: numerical — radiative transfer— Sun: atmosphere
1. Introduction
The linearly polarized spectrum of the Sunknown as the Second Solar Spectrum exhibits sig-natures of a number of physical processes not seenin the intensity spectrum and which may also beused to diagnose weak and turbulent magneticfields that are inaccessible with the ordinary Zee-man effect. Many of the most prominent spectrallines in the Second Solar Spectrum, like Na i D and D , Ba ii D and D , and Ca ii H and K,are governed by effects of quantum interferencebetween states of different total angular momen-tum ( J or F states). The profound importance of quantum interference for the formation of theselines was first demonstrated both observationallyand theoretically by Stenflo (1980, see also Stenflo1997).Quantum interference between the J -statesgoverns the linear polarization signatures ofatomic multiplets such as the Ca ii H and K, Na i D and D , and Cr i triplet lines. The theoryof such J -state interference was developed to in-clude the effects of partial frequency redistribution(PRD) by Smitha et al. (2011, 2013). This the-ory was then applied successfully to model thelinear polarization profiles of the Cr i triplet at5204-5208 ˚A by Smitha et al. (2012a).1hen an atom possesses nuclear spin the J states are split into F states (hyperfine structuresplitting). The quantum interference between the F states produces depolarization in the line core.Examples of lines governed by F -state interferenceare the Na i D , Ba ii D , and Sc ii line at 4247 ˚A.The Ba ii D line is due to the transition betweenthe upper fine structure level J = 3 / J = 1 / I s = 3 /
2, resulting in four up-per and two lower F -states (see Figure 1(b)). Thequantum interference between the upper F -statesneeds to be taken into account in the modelingof the Ba ii D line. The odd isotopes contributeabout 18% of the total Ba abundance in the Sun(c.f. Table 3 of Asplund et al. 2009). The remain-ing 82% comes from the even isotopes, which arenot subject to HFS (because I s = 0).The intensity profile of the Ba ii D line hasearlier been studied extensively, for example byHolweger & Mueller (1974) and Rutten (1978, andthe references cited therein). Some of these stud-ies aimed at determining the solar abundance ofBa. Observations with the high precision spectro-polarimeter ZIMPOL by Stenflo & Keller (1997)clearly revealed the existence of three distinctpeaks in the linear polarization ( Q/I ) profiles ofthe Ba ii D line. The nature of these peaks couldsubsequently be theoretically clarified by Stenflo(1997), who used the last scattering approxima-tion to model the Q/I profiles. It was demon-strated that the central
Q/I peak is due to theeven isotopes of Ba, while the two side peaks aredue to the odd isotopes.Using a similar last scattering approximation,the magnetic sensitivity of the Ba line was ex-plored by Belluzzi et al. (2007). Both these papershowever did not account for radiative transfer orPRD effects. The potential of using the Ba ii D line as a diagnostic tool for chromospheric weakturbulent magnetic fields and the important roleof PRD were discussed by Faurobert et al. (2009),but the treatment was limited to the even Baisotopes, for which HFS is absent. In contrast,our radiative-transfer treatment with PRD in thepresent paper includes both even and odd isotopesand the full effects of HFS with F -state interfer-ences. The theory of F -state interference with PRD inthe non-magnetic collisionless regime was recentlydeveloped in Smitha et al. (2012b, herafter P1).The PRD matrix was also incorporated into thepolarized radiative transfer equation. The trans-fer equation was then solved for the case of con-stant property isothermal atmospheric slabs. Inthe present paper we extend the work of P1 tosolve the line formation problem in realistic 1-Dmodel atmospheres in order to model the Ba ii D line profile observed in a quiet region close to thesolar limb.The outline of the paper is as follows: In Sec-tion 2 we present the polarized radiative transferequation which is suitably modified to handle sev-eral isotopes of Ba. In Section 3 we present thedetails of the observations. In Section 4 we dis-cuss the model atom and the model atmosphereused. The results are presented in Section 5 withconcluding remarks in Section 6.
2. Polarized line transfer equation with F -state interference The polarization of the radiation field is ingeneral represented by the full Stokes vector(
I, Q, U, V ) T . However, in the absence of a mag-netic field Stokes U and V are zero in an axisym-metric 1-D atmosphere. Hence in a non-magneticmedium the Stokes vector ( I, Q ) T is sufficient toexpress the polarization state of the radiation field.The transfer equation in the reduced Stokes vectorbasis (see Smitha et al. 2012a) is µ ∂ I ( λ, µ, z ) ∂z = − k tot ( λ, z ) [ I ( λ, µ, z ) − S ( λ, z )] , (1)with positive Q defined to represent linear polar-ization oriented parallel to the solar limb. Thequantities appearing in Equation (1) are defined inthe reference mentioned above. However, we needto generalize the previous definitions of opacityand source vector to handle even and odd isotopecontributions together.The total opacity k tot ( λ, z ) = k l ( z ) φ g ( λ, z ) + σ c ( λ, z ) + k th ( λ, z ), where σ c and k th are the con-tinuum scattering and continuum absorption coef-ficients, respectively. In the present treatment, k th also includes the contribution from the blend lines,which are assumed to be depolarizing and henceare treated in LTE. k l is the wavelength averaged2 A O P S P D D P S F=3F=2F=1F=0F=2F=1
Is=3/2Is=3/2 ; ; A O A O A O A O (a) (b) ( D ) ( D ) Fig. 1.— (a) represents the Ba ii model atom for the even isotopes, while for the odd isotopes the atomicmodel is modified by replacing two of the levels, P / and S / , with their hyperfine structure components,as shown in (b). In (b), I s is the nuclear spin. The energy levels are not drawn to scale.absorption coefficient for the J a → J b transition. J a and J b are the electronic angular momentumquantum numbers of the lower and upper level,respectively. φ g is the Voigt profile function writ-ten as φ g ( λ, z ) = 0 . φ e ( λ, z ) + 0 . φ o ( λ, z ) . (2) φ e ( λ, z ) is the Voigt profile function for the evenisotopes of Ba ii corresponding to the J a = 1 / → J b = 3 / φ o ( λ, z ),which is the weighted sum of the individual Voigtprofiles φ ( λ F b F a , z ) representing each of the F a → F b absorption transitions. Here F a and F b are thetotal angular momentum quantum numbers of theinitial and the intermediate hyperfine split levels,respectively. φ o ( λ, z ) is the same as φ HFS ( λ, z )defined in Equation (7) of P1 and is given by φ o ( λ, z ) = (cid:20) φ ( λ , z ) + 532 φ ( λ , z )+ 532 φ ( λ , z ) + 132 φ ( λ , z )+ 532 φ ( λ , z ) + 1432 φ ( λ , z ) (cid:21) . (3)The 17 .
8% of φ o ( λ, z ) in Equation (2) containscontributions from both the Ba (6.6%) and
Ba (11.2%) odd isotopes.The reduced total source vector S ( λ, z ) appear- ing in Equation (1) is defined as S ( λ, z ) = k l ( z ) S l ( λ, z ) + σ c ( λ, z ) S c ( λ, z ) k tot ( λ, z )+ k th ( λ, z ) S th ( λ, z ) + ǫ k l ( z ) φ g ( λ, z ) S th ( λ, z ) k tot ( λ, z ) , (4)for a two-level atom with an unpolarized lowerlevel. For the case of Ba ii D it was shown byDerouich (2008) that any ground level polariza-tion would be destroyed by elastic collisions withhydrogen atoms (see also Faurobert et al. 2009).In Equation (4), S th = ( B λ , T , where B λ isthe Planck function. S l ( λ, z ) is the line sourcevector defined as S l ( λ, z ) = Z + ∞ Z +1 − e R ( λ, λ ′ , z ) ˆΨ( µ ′ ) × I ( λ ′ , µ ′ , z ) dµ ′ dλ ′ , (5)with e R ( λ, λ ′ , z ) = 0 . f R e ( λ, λ ′ , z )+0 . f R o ( λ, λ ′ , z ) . (6)Here f R o ( λ, λ ′ , z ) is a (2 ×
2) diagonal matrix,which includes the effects of HFS for the odd iso-topes. Its elements are f R o = diag ( R o , R o ), where R Ko are the redistribution function componentsfor the multipolar index K , containing both type-II and type-III redistribution of Hummer (1962).3he expression for R K is obtained by the quantumnumber replacement L → J ; J → F ; S → I s in Equation (7) of Smitha et al. (2012b, see alsoSmitha et al. 2013 and P1). In our present com-putations, we replace the type-III redistributionfunctions by CRD functions. We have verifiedthat both of these give nearly identical results(see also Mihalas 1978; Smitha et al. 2012a) andsuch a replacement drastically reduces the com-putation time. The redistribution matrix for the17 .
8% of the odd isotopes includes the contribu-tions from the individual redistribution matricesfor the
Ba and
Ba isotopes. f R e ( λ, λ ′ , z ) is also a (2 ×
2) diagonal matrix forthe even isotopes without HFS. Its elements R Ke are the redistribution functions corresponding tothe J a = 1 / → J b = 3 / → J f = 1 / I s = 0 in f R o ( λ, λ ′ , z ). An expressionfor f R e ( λ, λ ′ , z ) can be found in Domke & Hubeny(1988) and in Bommier (1997, see also Nagendra1994, Sampoorna 2011) in the Stokes vector basis.It is the angle averaged versions of these quantitiesthat are used in our present computations. As hasbeen demonstrated in Supriya et al. (2013), theuse of the angle-averaged redistribution matrix issufficiently accurate for all practical purposes.Like in Smitha et al. (2012b) we use the twobranching ratios defined by A = Γ R Γ R + Γ I + Γ E ,B ( K ) = Γ R Γ R + Γ I + D ( K ) Γ E − D ( K ) Γ R + Γ I + Γ E . (7)Γ R and Γ I are the radiative and inelastic colli-sional rates, respectively. Γ E is the elastic collisionrate computed from Barklem & O’Mara (1998). D ( K ) are the depolarizing elastic collision rateswith D (0) = 0. The D (2) is computed using (seeDerouich 2008; Faurobert et al. 2009) D (2) = 6 . × − n H ( T / . +7 . × − (1 / . n H ( T / . exp(∆ E/kT ) , (8)where n H is the neutral hydrogen number density, T the temperature, and ∆ E the energy differencebetween the P / and P / fine structure lev-els. In the present treatment we neglect the col-lisional coupling between the P / level and the metastable D / level. The importance of suchcollisions for the line center polarization of Ba ii D has been pointed out by Derouich (2008), whoshowed that the neglect of such collisions wouldlead to an overestimate of the line core polariza-tion by ∼ B turb ) to be overes-timated by ∼ B turb but to ex-plore the roles of PRD, HFS, quantum interfer-ences, and the atmospheric temperature structurein the modeling of the triple peak structure of theBa ii D linear polarization profile.Frequency coherent scattering is assumed inthe continuum (see Smitha et al. 2012a) with itssource vector given by S c ( λ, z ) = 12 Z +1 − ˆΨ( µ ′ ) I ( λ, µ ′ , z ) dµ ′ . (9)The matrix ˆΨ is the Rayleigh scattering phasematrix in the reduced basis (see Frisch 2007).The line thermalization parameter ǫ is defined by ǫ = Γ I / (Γ R + Γ I ). The Stokes vector ( I, Q ) T canbe computed from the irreducible Stokes vector I by simple transformations given by (see Frisch2007) I ( λ, θ, z ) = I ( λ, µ, z )+ 12 √ θ − I ( λ, µ, z ) ,Q ( λ, θ , z ) = 32 √ − cos θ ) I ( λ, µ, z ) , (10)where θ is the colatitude of the scattered ray.The scattering geometry is shown in Figure 1 ofAnusha et al. (2011).
3. Observational details
The observed polarization profiles of the Ba ii D line that are used in the present paper for mod-eling purposes were acquired by the ETH teamof Stenflo on June 3, 2008, using their ZIMPOL-2 imaging polarimetry system (Gandorfer et al.2004) at the THEMIS telescope on Tenerife. Fig-ure 2 shows the CCD image of the data recorded atthe heliographic north pole with the spectrographslit placed parallel to the limb at µ = 0 .
1. The po-larization modulation was done using Ferroelectric4iquid Crystal (FLC) modulators. The spectro-graph slit was 1 ′′ wide and 70 ′′ long on the solardisk. The resulting CCD image has 140 pixels inthe spatial direction and 770 pixels in the spectraldirection. The effective pixel size was 0.5 ′′ spatiallyand 5.93 m˚A spectrally. The observed profilesused to compare with the theoretical ones havebeen obtained by averaging the I and Q/I imagesin Figure 2 over the spatial interval 40 ′′ - 52 ′′ .The recording presented in Figure 2 does notshow much spatial variation along the slit, since itrepresents a very quiet region. However, record-ings near magnetic regions made during the sameobserving campaign with ZIMPOL on THEMISexhibit large spatial variations. It has long beenknown that all strong chromospheric scatter-ing lines (like the Ca i i D , Sr ii ii D line is noexception, which means that it is sensitive to theHanle effect like the other chromospheric lines.Observations of spatial variations of this line havealso been carried out by L´opez Ariste et al. (2009)and Ramelli et al. (2009).
4. Modeling procedure
To model the polarization profiles of theBa ii D line we use a procedure similar tothe one described in Holzreuter et al. (2005, seealso Anusha et al. 2011, Anusha et al. 2010,Smitha et al. 2012a). It involves the computationof the intensity, opacity and collisional rates fromthe PRD-capable MALI (Multi-level ApproximateLambda Iteration) code developed by Uitenbroek(2001, referred to as the RH-code). The codesolves the statistical equilibrium equation andthe unpolarized radiative transfer equation self-consistently. The opacities and the collision ratesthus obtained are kept fixed, while the reducedStokes vector I is computed perturbatively bysolving the polarized radiative transfer equationwith the angle-averaged redistribution matricesdefined in Section 2.Such a procedure requires a model atom and amodel atmosphere as inputs to the RH-code. Thedetails of the model atom and the atmosphere arediscussed in the next subsections. Three different atom models are considered,two for the odd and one for the even isotope. Theatom model for the even isotope (
Ba) is givenby the five levels of Figure 1(a), while for the oddisotopes (
Ba and
Ba) the model is extendedto include the hyperfine splitting as described byFigure 1(b). We neglect the contribution fromother less abundant even isotopes. The wave-lengths of the six hyperfine transitions for the oddisotopes are taken from Kurucz’ database and arelisted in Table 1. These transitions are weightedwith their line strengths given in Equation (3) (seeTable 1).
We present the results computed for some ofthe standard realistic 1-D model atmospheres, likeFALA, FALF, FALC (Fontenla et al. 1993) andFALX (Avrett 1995). Among these four modelsFALF is the hottest and FALX the coolest. Theirtemperature structures are shown in the top panelof Figure 3. However, as will be discussed below,we find that a model atmosphere that is coolerthan FALX is needed to fit the observed profiles.The new model, denoted FALX, is obtained byreducing the temperature of the FALX model byabout 300 K in the height range 500 – 1200 kmabove the photosphere.We have verified that such a modification ofthe FALX model does not significantly affect theintensity spectra. In contrast, the
Q/I spectraturn out to be very sensitive to such tempera-ture changes. Like in Smitha et al. (2012a), wetest the FALX atmosphere by computing the limbdarkening function for a range of wavelengths and µ values and compare it with the observed datafrom Neckel & Labs (1994). This is shown in thebottom panel of Figure 3. One can see that FALXand the standard FALX fit the observed center-to-limb variation equally well. Therefore small modi-fications of the temperature structure to achieve agood fit to the observed Q/I profile can be madewithout affecting the model constraints imposedby the intensity spectrum.
5. Results
In the following we discuss the modeling detailsand the need for a model atmosphere that is cooler5han FALX. This helps us to evaluate the temper-ature sensitivity of the Ba ii D line and its use-fulness for magnetic-field diagnostics. In additionwe demonstrate the profound role that PRD playsfor the formation of the polarized line profile. ii D line profile From the three Ba ii atom models described inSection 4.1 we obtain three sets of physical quan-tities (two for the odd isotopes and one for theeven isotope) from the RH code. These quanti-ties include line opacity, line emissivity, continuumabsorption coefficient, continuum emissivity, con-tinuum scattering coefficient, and the mean inten-sity. The mathematical expressions used to com-pute these various quantities for the even isotopesare given in Uitenbroek (2001). For the odd iso-topes, the profile functions in these expressions arereplaced by φ o ( λ, z ) defined by Equation (3).The three sets of quantities are then combinedin the ratio of their respective isotope abundancesand subsequently used as inputs to the polariza-tion code. The polarization profiles thus computed for thevarious model atmospheres are shown in Figure 4,displayed separately for the even, odd, and com-bined even-odd cases in three different panels. TheStokes
Q/I profiles in Figure 4 are computed bysetting the total abundance of Ba in the Sun equalto the abundance of even isotopes in the firstpanel; the abundance of odd isotopes in the secondpanel; and a fractional abundance of even (82%)and odd (18%) isotopes in the third panel. Theprofiles in the first panel can be compared to theresults presented in Figure 6 of Faurobert et al.(2009). As seen from the first panel, the ampli-tude of the central peak for the even isotopes isvery sensitive to the temperature structure of themodel atmosphere in contradiction with the con-clusions of Faurobert et al. (2009). Also in theirpaper, the amplitude of the central peak obtainedfrom the FALC model is larger than the one ob-tained from FALX, which is opposite to our find-ings (although it could be that the version of theFALC model they used is not identical to the onethat we have used). However, the profile com- puted with the FALX model in first panel of Fig-ure 4 for the even isotopes is in good agreementwith the one given in their paper.The profiles in the second panel of Figure 4,which represent the odd isotopes, also exhibit asimilar large sensitivity to the choice of model at-mosphere. Therefore the combined even-odd iso-topes profiles in the third panel are also very sen-sitive to the temperature structure.For the sake of clarity, let us point out thatthe combined
Q/I profiles in the bottom panel ofFigure 4 differ profoundly from what one wouldobtain from a linear superposition of the corre-sponding profiles for the even and odd isotopesindividually in the two other panels, in propor-tion to their isotope ratios. The reason is that thecombination is highly non-linear, since the linesare formed in an optically thick medium (namelythe radiative transfer effects). While the opacitiesand redistribution matrices are combined in a lin-ear way as described by Equations (2) and (6), theeven and odd isotopes blend with each other in theradiative transfer process, which makes the com-bination as it appears in the emergent spectrumhighly non-linear.The drastic depolarization of
Q/I in the linecore has its origin in the polarizability factor W of the odd isotopes. It is well known that thetrough like suppression of W in the line core forBa ii is formed due to hyperfine structure for theodd isotopes (see Stenflo 1997). In our radia-tive transfer calculations we have a superposition(in the proportion of the isotope ratios), of thetrough-like scattering opacity of the odd isotopes,with the peak-like scattering opacity of the evenisotopes. The shape of the Q/I profile dependson the details of radiative transfer and PRD (seeEquations (2)-(6)) namely on how these two scat-tering opacities non-linearly blend to produce thenet result for the emergent radiation in the opti-cally thick cases.
FALX model
As seen from the last panel of Figure 4, thecentral peak is not well reproduced by any of thestandard model atmospheres. All the models pro-duce a dip at line center. Such a central dip iscommonly due to the effects of PRD, caused bythe properties of the type-II frequency redistribu-6ion. In the case of Ba ii D , the contribution tothis central dip comes mainly from the even iso-topes, as shown in Figure 5. The three rows inthis figure represent the even, odd and combinedeven-odd cases, respectively, for the FALX modelatmosphere. The first column shows the profilescomputed with only type-II redistribution, the sec-ond column those computed with CRD only. TheCRD profiles are obtained by setting the branch-ing ratios A = 0 and B ( K ) = (1 − ǫ ). None of theCRD profiles shows a central dip.The occurrence and nature of this central diphas been explored in detail in Holzreuter et al.(2005), who showed that its magnitude is stronglydependent on the choice of atmospheric parame-ters. This behavior is also evident from Figure 4.The cooler the atmosphere, the smaller is the cen-tral dip. The dip is often smoothed out by instru-mental and macro-turbulent broadening. How-ever, the profiles in Figure 4 have already beensmeared with a Gaussian function having a fullwidth at half maximum (FWHM) of 70 m˚A. Thedip could be suppressed by additional smearing,but such large smearing would also suppress theobserved side peaks of the odd isotopes and wouldmake the intensity profile inconsistent with the ob-served one. The value 70 m˚A has been chosen tooptimize the fit, but it is also consistent with whatwe expect based on the observing parameters andturbulence in the chromosphere.The failure of all the tried standard modelatmospheres therefore leads us to introduce anew model with a modified temperature structure,which is cooler than the standard FALX model.The details of the new cooler FALX model hasbeen given in Section 4.2. This new model at-mosphere succeeds in giving a good fit to both theintensity and the polarization profiles, as shown inFigure 6. To simulate the effects of spectrographstray light on the intensity and polarization pro-files we have applied a spectrally flat unpolarizedbackground of 4% of the continuum intensity levelto the theoretical ( I, Q/I ) profiles. For a good
Q/I line center fit, we find that it is necessary toinclude Hanle depolarization from a non-zero mag-netic field. Our theoretical profiles are based ona micro-turbulent magnetic field of strength B turb with an isotropic angular distribution. Our best fitto the Q/I profile corresponds to a field strengthof B turb = 2 G. The importance of PRD in modeling theBa ii D line has already been demonstrated inFaurobert et al. (2009), although by only consid-ering the even isotopes. Figure 5 demonstratesthe importance of PRD for both the odd and theeven isotopes. As seen from the second column ofthis figure, the Q/I profiles for the odd isotopeswhen computed exclusively in CRD do not pro-duce any side peaks, while the profiles computedwith type-II redistribution exhibits such peaks.Also, by comparing the
Q/I profiles for the evenisotopes in the first row, we see that CRD failsto generate the needed line wing polarization. Acomparison between the observed profiles and thetheoretical profiles based on CRD alone (dottedline) and on full PRD (dashed line) for the FALXmodel is shown in Figure 7. While the inten-sity profile can be fitted well using either PRD orCRD, the polarization profile cannot be fitted atall with CRD alone. PRD is therefore essential tomodel the
Q/I profiles of the Ba ii D line.
6. Conclusions
In the present paper we have for the first timetried to model the polarization profiles of the Ba ii D line by taking full account of PRD, radiativetransfer, and HFS effects. We use the theory of F -state interference developed in P1 in combinationwith different atom models representing differentisotopes of Ba ii and various choices of model at-mospheres. Applications of the well known stan-dard model atmospheres FALF, FALC, FALA,and FALX fail to reproduce the central peak, andinstead produce a central dip mainly due to PRDeffects. We have shown that in the case of Ba ii D the central dip is reduced by lowering the tem-perature of the atmospheric model. We can there-fore achieve a good fit to the observed polarizationprofile by slightly reducing the temperature of theFALX model.In modeling the Ba ii D line we account for thedepolarizing effects of elastic collisions with hy-drogen atoms but neglect the alignment transferbetween the P / level and the metastable D / level. It has been shown by Derouich (2008) thatthis alignment transfer affects the line center po-larization and is needed for magnetic field diagnos-tics. The purpose of the present paper is however7ot to determine magnetic fields but to clarify thephysics of line formation.We demonstrate that PRD is essential to repro-duce the triple peak structure and the line wingpolarization of the Ba ii D line, but find that theline center polarization is very sensitive to the tem-perature structure of the atmosphere, which con-tradicts the conclusions of Faurobert et al. (2009),who find that the barium line is temperature in-sensitive and therefore suitable for Hanle diagnos-tics. This contradiction illustrates that a full PRDtreatment as done in the present paper, includingthe contributions from both the even and odd iso-topes, is necessary to bring out the correct tem-perature dependence of the line. The large tem-perature sensitivity of the Ba ii D line makesit rather unsuited for magnetic-field diagnostics,since there is no known straightforward way toseparate the temperature and magnetic-field ef-fects for this line.We would like to thank Dr. Michele Bianda foruseful discussions. REFERENCES
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This 2-column preprint was prepared with the AAS L A TEXmacros v5.2.
Table 1: Wavelengths (˚A) of the hyperfine transi-tions for the odd isotopes of Ba ii F a F b Ba Ba Line strength1 0 4553.999 4553.995 0.156251 1 4554.001 4553.997 0.062501 2 4554.001 4553.998 0.156252 1 4554.046 4554.049 0.437502 2 4554.059 4554.051 0.156252 3 4554.050 4554.052 0.03125 Fig. 2.— CCD image showing the I and Q/I spec-tra of the Ba ii D line at µ = 0 .
1. The ob-servations were obtained on June 3, 2008, withZIMPOL-2 at the French THEMIS telescope onTenerife.9
ALF FALAFALC FALXFALX
Temperature structure
Fig. 3.—
Top panel:
The temperature structure of some of the standard model atmospheres. FALX rep-resents the model for which the temperature is reduced by about 300 K over a 700 km range around theheight of formation of the Ba ii D line. Bottom panel:
Comparison between the observed center-to-limbvariation (CLV) of the continuum intensity and the predictions from different model atmospheres includingFALX for a wide range of wavelengths from the violet to the IR region of the spectrum. For all the µ valuesthe dashed and the dash-triple dotted lines are practically indistinguishable as the models FALX and FALXproduce nearly identical fits. 10ig. 4.— Comparison between the observed Q/I profile and the theoretical profiles for some of the standardmodel atmospheres, separately displayed for the even, odd, and combined even-odd cases. The theoreticalprofiles represent the non-magnetic case and have been smeared with a Gaussian having a full width at halfmaximum (FWHM) of 70 m˚A to account for instrumental and macro-turbulent broadening.11ig. 5.— Theoretical
Q/I profiles computed for the non-magnetic FALX model for the even (first row),odd (second row), and combined even-odd (third row) isotopes, with only type-II frequency redistribution(first column) and only complete frequency redistribution CRD (second column). A prominent central dipis present for the type-II redistribution profiles although they have been smeared with a Gaussian havingFWHM = 70 m˚A. 12ig. 6.— Fit to the observed profile using the FALX model with and without a micro-turbulent magneticfield B turb . The theoretical profiles have been smeared using a Gaussian with FWHM = 70 m˚A.13ig. 7.— Comparison between the observed Stokes profiles and the profiles computed with CRD (dotted line)and PRD (dashed line) for the FALX model. The theoretical profiles have been smeared with a Gaussianhaving FWHM = 70 m˚A. The strength of the micro-turbulent magnetic field B turbturb