1. A possible mechanism for understanding the enigmatic scattering polarization signals observed in the solar Na I and Ba II D 1 lines Luca Belluzzi 1 and Javier Trujillo Bueno 2 COST Action MP1104 WG2 Meeting: Theory and modelling of polarisation in astrophysics Prague, Czech Republic, 5–8 May 2014 1 Istituto Ricerche Solari Locarno, Switzerland 2 Instituto de Astrofísica de Canarias, Tenerife, Spain

2. From Stenflo & Keller 2000, A&A, 355, 789 Observation near the north polar limb (3 April 1995). From Stenflo & Keller 2000, A&A, 355, 789 Thick line (smaller peak): same as left panel. Thin lines (larger peaks): two observations at different locations near the south polar limb (12 September 1996). Observations of the Na I D 1 line (5896 Å ) Observations in quiet regions close to the limb (  =0.1) with ZIMPOL at NSO Kitt Peak

3. Observations of the Ba II D 1 line (4934 Å) Observations in quiet regions close to the limb (  =0.1) with ZIMPOL at NSO Kitt Peak From Stenflo & Keller 1997, A&A, 355, 789 Observation near the north polar limb (April 1995). From Stenflo & Keller 2000, A&A, 355, 789 Two observations at different locations near the north polar limb (4 and 5 April 1995). Three observations at different locations near the south polar limb (12 September 1996). Thick line: average profile

4. Observations in quiet regions close to the limb (  =0.1) with ZIMPOL at IRSOL From Gandorfer 2000, The Second Solar Spectrum, vol.I Na I D 1 Ba II D 1 Observations from the atlas of the Second Solar Spectrum

5. Observation in a quiet region close to the north polar limb (  =0.1) with ZIMPOL3 at IRSOL Observation carried out on March 13, 2014 Exposure time: 1400s (~23min) Signal averaged over about 8 arcsec A recent observation of the Na I D 1 line at IRSOL

6. The atomic transition J u =1/2 J l =1/2 F u = 2 F u = 1 F u = 2 F u = 1 Sodium (1 stable isotope) 23 Na (100%) I= 3/2 Barium (7 stable isotopes) 130 Ba (0.1%) I= 0 132 Ba (0.1%) I= 0 134 Ba (2.4%) I= 0 135 Ba (6.6%) I= 3/2 136 Ba (7.9%) I= 0 137 Ba (11.2%) I= 3/2 138 Ba (71.7%) I= 0 Levels with J=1/2 cannot harbour atomic alignment (population umbalances between sublevels with different values of |M |) Intrinsically unpolarizable line for linear polarization How can atomic alignment be induced in the upper HFS levels? Non-LTE RT calculations in FAL-C

7. CRD theory of polarization (see Landi Degl’Innocenti & Landolfi 2004) Hypotheses: 1)the various HFS components are “pumped” by the same radiation field (hypothesis required by the CRD theory to hold when F-state interference is included) 2)no atomic polarization is present in the lower level (ground level) No alignment can be induced in the upper HFS F-levels =0 (K=2, J u =1/2) =0 (K=2, J u =1/2)

8. Metalevel theory (coherent scattering) (see Landi Degl’Innocenti et al. 1997) Hypotheses: 1)the various HFS components are “pumped” by the same radiation field 2)no atomic polarization is present in the lower level (ground level) No alignment can be induced in the upper HFS F-levels Wavelength position of the 4 HFS components

9. 2) D 1 +D 2 system studied accounting for interference between magnetic sublevels of different F-levels, pertaining either the same J-level or to different J-levels F u = 2 F u = 1 F l = 2 F l = 1 F u = 2 F u = 0 F u = 1 F u = 3 J l =1/2 J u =1/2 J u =3/2 D2D2 D1D1 3) the various HFS components of each D-line are “pumped” by the same radiation field 4) YES atomic polarization in the lower level (parametrized) The results of Landi Degl’Innocenti (1998) (Nature, 392, 256) Hypotheses: 1)Coherent scattering (metalevel theory) Presence of atomic alignment Repopulation pumping mechanism via the D 2 line (Trujillo Bueno et al. 2002, Casini et al. 2002)

10. BUT: 1)The required amount of atomic polarization in the long-lived lower level is incompatible with the presence of inclined magnetic fields with intensities larger than about 0.01G (lower level Hanle effect). (Landi Degl’Innocenti 1998) This result was later refined by Trujillo Bueno et al. (2002) through a deeper analysis of the sensitivity of the atomic polarization in the levels of the D 1 line to the presence of a magnetic field. (from Landi Degl’Innocenti, 1998)

11. BUT: 2)Kerkeni and Bommier (2002) argued that the required amount of atomic polarization in the long-lived lower level appears to be incompatible with the rates of depolarizing collisions that they obtained through quantum chemistry calculations. (from Landi Degl’Innocenti, 1998)

12. F u = 2 F u = 1 F l = 2 F l = 1 J l =1/2 J u =1/2 D1D1 4) Numerical solution of the full non-LTE problem accounting for the variation of the incident field among the various HFS components. 2) Unpolarized and infinitely-sharp lower levels 1) Two-level model atom with HFS Hypotheses: Missing “ingredient”: accounting for the (small) variation of the incident radiation field among the various HFS components of the D 1 line 3) Coherent scattering in the atom rest frame + Doppler redistribution in the observer’s frame (angle-averaged redistr. matrix derived from metalevel theory)

13. CRD vs CS calculations (FAL-C,  =0.1) Physical origin of the Q/I signal in the CS calculations: different pumping radiation field in the various HFS components.

14. Monochromatic anisotropy at the height where τ =1 for  =0.1 The Q/I signal obtained in the Ba II D 1 line is much larger than the one obtained in the Na I D 1 line because the HFS splitting of the lower level of Ba II is about four times larger than that of the lower level of Na I

15. Calculations in various atmospheric models (  =0.1)

16. Conclusions A mechanism capable of producing a scattering polarization signal in the core of the Ba II and Na I D 1 lines, which does not require the presence of atomic polarization in the lower level, has been identified. 1) Although there is a dependence on the atmospheric model, this mechanism should always be at work, while observations do not always show clear scattering polarization signals in the core of these lines (in particular in the core of the Ba II D 1 line). Problems: 2) The peak of the calculated profiles is slightly shifted with respect to the line center, were the calculated signal is still zero. The observed peaks (in particular the one of Na I D 1 ) are centerd at the line center. 3) The amplitude of the calculated NaI D 1 peak is smaller than that of the observations presented by Stenflo & Keller (1997, 2000).

17. Conclusions -lower level polarization, which may in any case be present (mainly in Na I D 1, though in a less amount than in Landi Degl’Innocenti 1998), and may contribute to produce a symmetric profile; -J-state interference, which, in the case of Na I D 1, are known to significantly modify the overall Q/I pattern across D 1 ; -frequency redistribution of continuum radiation: as pointed out by Del Pino Aleman et al. (2014) redistribution phenomena of the continnum radiation are capable of producing observables symmetric signals in the core of intrinsically unpolarizable lines. This latter mechanism depends on the assumed atmospheric model, but it may well coexist with the mechanism presented in this talk. Our calculations do not include: -depolarization and frequency redistribution effects due to collisions. These effects are expected to be more important in the line core of Ba II D 1, which forms deeper in the atmosphere than Na I D 1 (need of a more appropriate R III redistribution matrix for taking these effects into account). -depolarization effect due to a magnetic field (Hanle effect).

18. Conclusions -the impact of metastable levels (for the case of Ba II D 1 ) J l =1/2 J u =1/2 J u =3/2 D2D2 D1D1 J m =3/2 J m =5/2 J l =1/2 J u =1/2 J u =3/2 D2D2 D1D1 Na I Ba II

20. CRD vs CS vs PRD calculations PRD calculations: Core: PRD ≈ CS Wings: PRD CRD

21. PRD calculations in various atmospheric models (  =0.1)