In our previous attempt to model the Stokes profiles of the Cr i triplet at 5204-5208 Å and the Ba ii D2 at 4554 Å, we found it necessary to slightly modify the standard FAL model atmospheres to fit the observed polarization profiles. In the case of Cr i triplet, this modification was done to reduce the theoretical continuum polarization, and in the case of Ba ii D2, it was needed to reproduce the central peak in Q/I. In this work, we revisit both these cases using different standard model atmospheres whose temperature structures closely resemble those of the modified FAL models, and explore the possibility of synthesizing the line profiles without the need for small modifications of the model atmospher

Bianda, M.

Nagendra, K. N.

Ramelli, R.

Sampoorna, M.

Smitha, H. N.

Stenflo, J. O.

RERO DOC Digital Library

Polarimetry: From the Sun to Stars and Stellar EnvironmentsProceedings IAU Symposium No. 305, 2014K. N. Nagendra, S. Bagnulo, R. Centeno &M. J. Mart´ınez Gonza´lez, eds.c© International Astronomical Union 2015doi:10.1017/S1743921315005074A revisit to model the Cr i triplet at5204-5208 A˚ and the Ba ii D2 line at 4554 A˚in the Second Solar SpectrumH. N. Smitha1, K. N. Nagendra1, J. O. Stenﬂo2,3, M. Bianda3,M. Sampoorna1 and R. Ramelli31 Indian Institute of Astrophysics, Koramangala, Bangalore, Indiaemail: smithahn@iiap.res.in; knn@iiap.res.in; sampoorna@iiap.res.in2 Institute of Astronomy, ETH Zurich, CH-8093 Zurich, Switzerlandemail: stenflo@astro.phys.ethz.ch3 Istituto Ricerche Solari Locarno, Via Patocchi, 6605 Locarno-Monti, Switzerlandemail: mbianda@irsol.ch; ramelli@irsol.chAbstract. In our previous attempt to model the Stokes proﬁles of the Cr i triplet at 5204-5208 A˚and the Ba ii D2 at 4554 A˚, we found it necessary to slightly modify the standard FAL modelatmospheres to ﬁt the observed polarization proﬁles. In the case of Cr i triplet, this modiﬁcationwas done to reduce the theoretical continuum polarization, and in the case of Ba ii D2 , it wasneeded to reproduce the central peak in Q/I . In this work, we revisit both these cases usingdiﬀerent standard model atmospheres whose temperature structures closely resemble those ofthe modiﬁed FAL models, and explore the possibility of synthesizing the line proﬁles withoutthe need for small modiﬁcations of the model atmosphere.Keywords. line: formation, line: proﬁles, polarization, radiative transfer, scattering, Sun: at-mosphere1. IntroductionThe Cr i triplet at 5204-5208 A˚ and the Ba ii D2 at 4554 A˚ are some of the wellknown chromospheric lines showing prominent polarization signals in the Second SolarSpectrum. The Cr i triplet proﬁles are governed by J-state interference (Smitha et al.2012) and the Ba ii D2 line is governed by F -state interference (Smitha et al. 2013b).To model the limb observations of Cr i triplet at μ = 0.15 (μ = cos θ, with θ beingthe heliocentric angle), Smitha et al. (2012) had to slightly modify FALF, one of thestandard model atmospheres of Fontenla et al. (1993). This modiﬁcation, in the form ofan increase in the temperature at the continuum formation heights (0-500 km above thephotosphere), was necessary to get a good ﬁt to Q/I in the continuum.In the case of Ba ii D2 4554 A˚ limb observations (μ = 0.1), which were modeled inSmitha et al. (2013b), the temperature of the FALX model (Avrett 1995) had to beslightly reduced at the heights where the line center is formed, in order to reproduce thecentral peak in Q/I. Subsequently it was shown in Smitha et al. (2014a) that althoughthis modiﬁed FALX model could reproduce the observations at μ = 0.1, it could notreproduce the observations at other limb distances.In this paper, we explore the possibility of modeling the above two line proﬁles withthe updated FAL models presented in Fontenla et al. (2009, referred to as the FCHHTmodels). A comparison between the temperature structures of the FAL and the FCHHTmodels is shown in Figure 1 (see also Rutten & Uitenbroek 2012).372at https:/www.cambridge.org/core/terms. https://doi.org/10.1017/S1743921315005074Downloaded from https:/www.cambridge.org/core. University of Basel Library, on 30 May 2017 at 21:30:48, subject to the Cambridge Core terms of use, availableRevisiting the Second Solar Spectrum 373Figure 1. Temperature structures of the FAL and FCHHT models.2. Revisiting the Cr i tripletThe model atmospheres tried in Smitha et al. (2012), namely the FALA, FALC, FALFand FALX, predicted a value of the continuum polarization larger than the one foundfrom observations. This problem of over estimation of the continuum polarization by theone-dimensional model atmospheres was also noted in Stenﬂo (2005). A similar problemwas faced in Smitha et al. (2014b) while modeling the Sc ii 4247 A˚ line.In Smitha et al. (2012), to overcome this, the FALF model was modiﬁed into FALFand the temperature was increased in the deeper layers of the atmosphere to reduce thecontinuum polarization. The FALP model, which is hotter than the FALF model, hasa temperature proﬁle similar to the FALF in these deeper layers. However, the FALPmodel fails to provide as good a ﬁt as FALF.The FCHHT-P model, which represents a plage region and has a temperature struc-ture signiﬁcantly diﬀerent from that of the FALF model, provides a good ﬁt to the Cr itriplet proﬁles observed in a quiet region. For modeling, we use the partial frequencyredistribution (PRD) capable Multi-level Approximate Lambda Iteration code of Uiten-broek (2001) and the PRD theory of J-state interference described in Smitha et al. (2011,2013a). Further details are described in Smitha et al. (2012). A comparison between theproﬁles from the FALP and FCHHT-P is shown in Figure 2. The microturbulent mag-netic ﬁeld strengths used to get the line center amplitude of the three lines are 0G, 2.5Gand 1.8G respectively, for the FCHHT-P model.The diﬀerences in the proﬁles from the models FALF, FALP and FCHHT-P can beunderstood by computing the ratio of the continuum-to-line anisotropy. The left panel ofFigure 3 shows this ratio for the 5206 A˚ line of the Cr i triplet. The FALP model, despitehaving a temperature structure similar to that of FALF at continuum heights (left panelof Figure 1), it does not provide as good a ﬁt as the FCHHT-P model (see Figure 2).The FALP model predicts similar anisotropy to FALF at continuum heights but fails toprovide the required continuum-to-line anisotropy ratio which is necessary to obtain agood ﬁt, and this is provided by the FCHHT-P model. Thus the FALF and FCHHT-Pmodels reproduce the observed Cr i triplet proﬁles at μ = 0.15.As a further test of the model atmosphere, we compared the observed and theoreticalintensity ratio Rλ = (I/Ic)μ/(I/Ic)μ=1. This is shown in the right panel of Figure 3,computed from the FCHHT-P and FALP models. Rλ represents the third solar spectrumdescribed in Stenﬂo (2015). The FCHHT-P model provides as good a ﬁt to the third solarspectrum as it does to the second solar spectrum. The ﬁt from the FALP model is notas good as the one from the FCHHT-P model. However there are small diﬀerences seenbetween the observed and the theoretical proﬁles around the 5206 A˚ and the 5208 A˚ linesat https:/www.cambridge.org/core/terms. https://doi.org/10.1017/S1743921315005074Downloaded from https:/www.cambridge.org/core. University of Basel Library, on 30 May 2017 at 21:30:48, subject to the Cambridge Core terms of use, available374 H. N. Smitha et al.Figure 2. Comparison between the observed and the theoretical Stokes (I, Q/I) proﬁles of theCr i triplet computed using the FCHHT-P and FALP models at μ = 0.15.Figure 3. Left panel : Ratio of continuum to line (5206 A˚) anisotropy (×103 ); Right panel :Comparison between the observed (Stenﬂo 2015) and theoretically computed proﬁles of thethird solar spectrum, Rλ = (I/Ic )μ /(I/Ic )μ=1 with μ = 0.15.which may be improved by including the multidimensional eﬀects. Thus the third solarspectrum now provides an additional constraint to test the reliability of the solar modelatmospheres.3. Revisiting the Ba ii D2 lineModeling the (I,Q/I) observations of the Ba ii D2 line at μ = 0.1, which was attemptedin Smitha et al. (2013b, see also Smitha et al. 2014a), was possible only after a smallmodiﬁcation in the temperature structure of the FALX model at heights where the lineat https:/www.cambridge.org/core/terms. https://doi.org/10.1017/S1743921315005074Downloaded from https:/www.cambridge.org/core. University of Basel Library, on 30 May 2017 at 21:30:48, subject to the Cambridge Core terms of use, availableRevisiting the Second Solar Spectrum 375Figure 4. Comparison between the observed and theoretical (I, Q/I) proﬁles of the Ba ii D2line computed using the FCHHT models. The proﬁles from a 2-component model constructed bycombining FCHHT-F and FCHHT-P models in equal proportion ﬁts the observations at μ = 0.1but fails at higher μ values.core is formed. This modiﬁcation was necessary to reproduce the central peak formeddue to the even isotopes.In this paper, we have revisited the modeling of this line using the FCHHT models. Weﬁnd that four of the ﬁve models produce the central peak in Q/I. The intensity proﬁlesfrom these models match the observed ones well, whereas the Q/I proﬁles are broader(see the top two panels of Figure 4). It is possible to combine the two models FCHHT-Fand FCHHT-P in equal proportion to build a 2-component model like the one describedin Holzreuter et al. (2006) and reproduce the observed Q/I proﬁle at μ = 0.1 (see thebottom panels in Figure 4). However as μ increases, we continue to face problems inreproducing the central peak. At other μ values we may need other combinations of themodel atmospheres. This demonstrates the possibility of modeling the Ba ii D2 proﬁlewithout the need for a modiﬁcation in the standard model atmospheres. However itmay not be possible to ﬁnd a single one-dimensional model atmosphere that ﬁts theobservations at all μ values.4. ConclusionsIn this work, we have explored the possibility of modeling the chromospheric Cr itriplet at 5206 A˚ and the Ba ii D2 at 4554 A˚ line without modifying the standardmodel atmospheres. The updated FCHHT models are able to reproduce both these cases.While the Cr i triplet can be modeled with the FCHHT-P model, the Ba ii D2 needs aat https:/www.cambridge.org/core/terms. https://doi.org/10.1017/S1743921315005074Downloaded from https:/www.cambridge.org/core. University of Basel Library, on 30 May 2017 at 21:30:48, subject to the Cambridge Core terms of use, available376 H. N. Smitha et al.2-component model constructed by combining the FCHHT-F and FCHHT-P models inequal proportion.In the case of Cr i triplet, the FCHHT-P model provides as good a ﬁt as the modiﬁedmodel constructed previously. It also provides a good ﬁt to the third solar spectrum withsmall diﬀerences around the centers of the 5206 A˚ and the 5208 A˚ lines.In the case of Ba ii D2 line, the 2-component model constructed in this paper holdsits validity only at μ = 0.1. For higher μ values we need models constructed from otheratmospheric combinations. Thus it may not be possible to ﬁnd a single 1D model atmo-sphere which can reproduce the observed center-to-limb variation of the Ba ii D2 lineproﬁle.The observed proﬁles of the Cr i triplet and the Ba ii D2 lines in the second andthird solar spectra, and their center-to-limb variations, provide a rich set of complexobservational constraints that should ideally be satisﬁed simultaneously by a given modelatmosphere. Our results here indicate that only multidimensional atmospheric modelingcan have a chance to simultaneously reproduce these constraints.AcknowledgementsWe acknowledge the use of the HYDRA cluster facility at the Indian Institute ofAstrophysics for computing the results presented in the paper. We are grateful to Dr.Han Uitenbroek for providing his realistic atmospheric modeling code.ReferencesAvrett, E. H. 1995, in: J. R. Kuhn & M. J. Penn (eds.), Infrared tools for solar astrophysics:What’s next?, Proc. 15th NSO Sac Peak Workshop, p. 303Fontenla, J. M., Avrett, E. H., & Loeser, R. 1993, ApJ 406, 319Fontenla, J. M., Curdt, W., Haberreiter, M., Harder, J., & Tian, H. 2009, ApJ 707, 482Holzreuter, R., Fluri, D. M., & Stenﬂo J. O. 2006, A&A 449, L41Rutten, R. J. & Uitenbroek, H. 2012, A&A 540, A86Smitha, H. N., Nagendra, K. N., Sampoorna, M., & Stenﬂo, J. O. 2013a, JQSRT 115, 46Smitha, H. N., Nagendra, K. N., Stenﬂo, J. O., Bianda, M., Sampoorna, M., Ramelli, R., &Anusha, L. S. 2012, A&A 541, A24Smitha, H. N., Nagendra, K. N., Stenﬂo, J. O., & Sampoorna, M. 2013b, ApJ 768, 163Smitha, H. N., Nagendra, K. N., Stenﬂo, J. O., & Sampoorna, M. 2014a, in: K. N. Nagendra, J.O. Stenﬂo Z. Q. Qu & M. Sampoorna (eds.), Solar Polarization 7, ASP Conf. Series 489(San Francisco: ASP), p. 213Smitha, H. N., Nagendra, K. N., Stenﬂo, J. O., Bianda, M., & Ramelli, R. 2014b, ApJ 794, 30Smitha, H. N., Sampoorna, M., Nagendra, K. N., & Stenﬂo, J. O. 2011, ApJ 733, 4Stenﬂo, J. O. 2015, A&A 573, A74Uitenbroek, H. 2001, ApJ 557, 389at https:/www.cambridge.org/core/terms. https://doi.org/10.1017/S1743921315005074Downloaded from https:/www.cambridge.org/core. University of Basel Library, on 30 May 2017 at 21:30:48, subject to the Cambridge Core terms of use, available

A revisit to model the Cr i triplet at 5204-5208 Å and the Ba ii D2 line at 4554 Å in the Second Solar Spectrum

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A revisit to model the Cr i triplet at 5204-5208 Å and the Ba ii D2 line at 4554 Å in the Second Solar Spectrum

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