Measurement of magnetic field by Hanle effect in Na I D 2 T. Anan (Kyoto univ.) 1, review of Holzreuter et al , Hanle effect of Na D2

Observation from Carlos’s slide

Observation from Carlos’s slide

Anisotropy of the radiation field Boundary effect: The intensity from the upper hemisphere is reduced, because the photon mean free path starts to exceed the distance to the upper boundary => A < 0 Optically thin Optically thick Closer to the surface, no coming radiation from above => A 〜 0 Limb darkening Limb brightening In τ > 1, A = Au + Al 〜 0 In τ 〜 1, A < 0 <= boundary effect + limb brightening is larger than limb darkening In surface, A > 0 <= no coming radiation from above Limb brightening Limb darkening S 2 >> S 1 In lower layer, A < 0 In upper layer, A > 0 > S 1 Boundary effect A = 0 A < 0 A 〜 0 A < 0 A > 0 A < 0 A > 0

Selected wavelength to discuss in Holzreuter et al μ = 0.1 μ = 0.5 Wing maximum Minimum Core rise Line center

Continuum ΔS is the largest

Wing maximum

minimum

Core rise

Line center

Polarization profile Method 1.Multi-level RH code (with PRD, Uitenbroek 2001) => intensity, opacity, collision rate 2.Classic formalism with the source function for 2 level atomic model with unpolarized ground level => Scattering polarization with PRD – Keeping intensity, opacity, and collision rate are fixed – Redistribution matrix in line Source function Collisional depolarization PRD Polarizability is calculated for a whole multiplet using the density-matrix formalism with the metalevel approach – Frequency dependent – Lower level atomic polarization – Quantum interferences between fine-structure and hyperfine structure levels Solid line ： PRD Dash-dotted: CRD

Polarization profile Interpretation Anisotropy of radiation field × effective polarizability + PRD Wing – Polarization is only formed in presence of PRD Core – Complicated frequency dependence of the anisotropy (dip and side peaks) + smearing effect of PRD – It is not clear what role the Hanle effect may have played in producing the dip – Hyperfine structure and lower-level polarization change polarization degree The alignment in the ground level of Na I become practically negligible for magnetic field strengths greater than 10 G （ Trujillo Bueno et el ） Solid line ： PRD Dash-dotted: CRD

Calculation of Hanle effect by Anan Code: López Ariste & Casini 2002 – Equations are almost similar with HAZEL – Zeeman effect, (incomplete) Paschen-back effect, atomic polarization by optical pumping by irradiation coming from photosphere, Hanle effect – CRD – Incident radiation field is not polarized, and that it possesses cylindrical symmetry around the local solar vertical – Constant property slab model Plan to use the code – Calculate Hanle effect only in core rise formed in middle choromosphere before smearing by PRD (not include photosphere, because the code cannot produce negative anisotropy of the radiation field, small contribution, and NLTE effect is small) – Not calculate line center, because the code cannot produce negative anisotropy of the radiation field – Not calculate wing, because the code doesn’t have PRD

Core rise Calculate Hanle effect only in core rise formed in middle choromosphere before smearing by PRD (not include photosphere, because the code cannot produce negative anisotropy of the radiation field, small contribution, and NLTE effect is small)

Atmospheric model López Ariste & Casini 2002 Constant property slab model Parameters Optical depth Temperature : 10000K Height of slab θ (angle between LOS and z’) Magnetic field vector

Optical depth 〜 Constant source function ！

Height of slab 〜 0 but anisotropy of the radiation field is slightly large Anisotropy of the radiation field is produced by limb darkening even height is 0 Core rise López Ariste & Casini 2002

B = 0G, μ=0.1 López Ariste & Casini 2002 Parameters Optical depth : 0.3 Temperature : 10000K Height of slab : 0 θ : 84° B = 0G Q/I is 0.4 at core rese in Holzreuter et al Results of the calculation is 2 times larger than that of Holzreuter et al. 2005, because anisotropy of radiation field is small and not smeared by PRD Holzreuter et al. 2005

Hanle depolarization López Ariste & Casini 2002 Parameters Optical depth : 0.3 Temperature : 10000K Height of slab : 0 θ : 84° (μ = 0.1) B directs to observer

Only Zeeman effect From Calros’s calculation B LOS can be measured by longitudinal Zeeman effect Can we measure direction of the magnetic field by Hanle effect?

Hanle diagram 視線方向からの 磁場傾斜角 0° 10° 20° 30° 40° 50° 60° 70° 80° 方位角 2° 刻み

Hanle diagram 視線方向からの 磁場傾斜角 0° 10° 20° 30° 40° 50° 60° 70° 80° 方位角 2° 刻み

Hanle diagram 視線方向からの 磁場傾斜角 0° 10° 20° 30° 40° 50° 60° 70° 80° 方位角 2° 刻み

Hanle diagram 視線方向からの 磁場傾斜角 0° 10° 20° 30° 40° 50° 60° 70° 80° 方位角 2° 刻み

Hanle diagram 視線方向からの 磁場傾斜角 0° 10° 20° 30° 40° 50° 60° 70° 80° 方位角 2° 刻み

Hanle diagram 視線方向からの 磁場傾斜角 0° 10° 20° 30° 40° 50° 60° 70° 80° 方位角 2° 刻み

Hanle diagram 視線方向からの 磁場傾斜角 0° 10° 20° 30° 40° 50° 60° 70° 80° 方位角 2° 刻み

Hanle diagram 視線方向からの 磁場傾斜角 0° 10° 20° 30° 40° 50° 60° 70° 80° 方位角 2° 刻み

議論 このまま検討してもよいだろうか。

Hanle diagram BLOS = I need discussion of my plan to study Hanle effect by using constant slab model, and more samples to show this diagram

Results 1 Q/Imax U/Imax B = 100 G (Hanle saturation) τ = 0.1 T = 10000K H 〜 700km θ = 60° hanlediagram_th00_blos002_1.png

Results 2 Q/Imax U/Imax B = 100 G (Hanle saturation) τ = 0.1 T = 10000K H 〜 700km θ = 0°

Results 3 Q/Imax U/Imax B = G (Hanle depolarization) Θ B =90° Φ B =90° τ = 0.1 T = 10000K H 〜 700km θ = 60°

Results 3 Q/Imax B POS (G) B = G (Hanle depolarization) Θ B =90° Φ B =90° τ = 0.1 T = 10000K H 〜 700km θ = 60°

Results 3 |d Q/Imax| B POS (G) B = G (Hanle depolarization) Θ B =90° Φ B =90° τ = 0.1 T = 10000K H 〜 700km θ = 60° We can distinguish 0G 〜 3G and the others in BPOS in this case by Hanle depolarization