Inversions based on ME atmospheres

1. Inversions based on ME atmospheres Stokes inversions beyond ME atmospheres Luis R. Bellot Rubio Instituto de Astrofísica de Andalucía (CSIC) Granada, Spain

2. Inversions based on ME atmospheres • ME atmosphere: • Source function is linear with optical depth • Absorption matrix does not vary with optical depth • Analytical Stokes profiles • Fast inversion • Smooth maps of physical quantities • Results are easy to interpret • Simplistic treatment of radiation transfer • Little thermal information. No height variations • Cannot account for asymmetric Stokes profiles

3. Asymmetric Stokes profiles • Spatial resolution: 1" • Advanced Stokes Polarimeter • DST, Sac Peak • Footpoints of cool coronal loops Nagata, Bellot Rubio, & Katsukawa (2006)

4. Asymmetric Stokes profiles Fe I 630.15 and 630.25 nm • Spatial resolution: 0.6 arcsec • Spatial resolution: 0.7" • POlarimetric LIttrow Spectrograph + KAOS • VTT, Observatorio del Teide • Temporal evolution of a bipolar MMF Cabrera Solana et al. (in preparation)

5. Asymmetric Stokes profiles + + + + + + • Spatial resolution: 0.4" • KIS/IAA Visible Imaging Polarimeter + TESOS + KAOS • VTT, Observatorio del Teide • Pore near disk center Bellot Rubio et al. (in preparation)

6. Asymmetric Stokes profiles • Spatial resolution: 0.2" • TRIPPEL spectrograph + AO • Swedish 1-m Solar Telescope, La Palma • Dark-cored penumbral filaments Bellot Rubio, Langhans, & Schlichenmaier (2005)

7. ME inversions of asymmetric profiles • Fe I 630.1 and 630.2 profiles degraded to SP pixel size MHD simulations (Vögler et al. 2005) +

8. ME inversions of asymmetric profiles • Fe I 630.1 and 630.2 profiles degraded to SP pixel size • Maps of inferred B and vLOS very similar to real ones! MHD simulations (Vögler et al. 2005) +

9. ME inversions of asymmetric profiles Stokes V/I • Asymmetric profiles not well fitted • ME results are some kind of “average” of physical parameters along the LOS MHD simulations (Vögler et al. 2005) ME inv + ME inv +

10. The origin of asymmetries Different magnetic atmospheres coexisting in resolution element Amplitude asymmetry/ Abnormal Stokes profiles Gradients/discontinuities of physical parameters along LOS Area asymmetry Auer & Heasley (1978) RF of V to B RF of I to vLOS RF of I to vLOS The area asymmetry can be used to derive the height variation of atmospheric parameters Cabrera Solana et al. (2005)

11. Available codes for inversions with gradients SIR Ruiz Cobo& del Toro Iniesta (1992) 1C & 2C atmospheres, arbitrary stratifications, any photospheric line SIR/FT Bellot Rubio et al. (1996) Thin flux tube model, arbitrary stratifications, any photospheric line SIR/NLTE Socas-Navarro et al. (1998) NLTE line transfer, arbitrary stratifications SIR/GAUS Bellot Rubio (2003) Uncombed penumbral model, arbitrary stratifications SPINOR Frutiger & Solanki (2001) 1C & 2C atmospheres, arbitrary stratifications, any photospheric line, molecular lines, flux tube model, uncombed model LILIA Socas-Navarro (2001) 1C atmospheres, arbitrary stratifications MISMA IC Sánchez Almeida (1997) MISMA model, arbitrary stratifications, any photospheric line

12. Accounting for gradients • Inversion codes capable of dealing with gradients • Are based on numerical solution of RTE • Provide reliable thermal information • Use less free parameters than ME codes (7 vs 8) • Infer stratifications of physical parameters with depth • Produce better fits to asymmetric Stokes profiles • Height dependence of atmospheric parameters is needed for • 180o azimuth disambiguation • 3D structure of sunspots and pores • Magnetic flux cancellation events • Polarity inversion lines • Dynamical state of coronal loop footpoints • …..

13. Inversions with gradients • Spatial resolution  0.5" • Intensity profiles of Fe I 557.6 nm • Inversion: SIR with 7 free parameters • Thermal/kinematic structure of AR 0019 at different heights in the photosphere Bellot Rubio, Schlichenmaier, & Tritschler (2006)

14. Inversions with gradients + • Spatial resolution: 0.4" • VIP + TESOS + KAOS • Inversion: SIR with 10 free parameters

15. Retrieving gradients from SOLAR-B/SP data How much do gradients cost? SIR inversion with 10 free parameters Dual Xeon workstation @ 2.8 GHz 2 spectral lines, 136 wavelengths, 4 Stokes parameters, model atmosphere discretized in 41 grid points 0.7 s per pixel 0.5 s per pixel Worst-case scenario (real-time inversions) Instrument Pixels Cost Time Workstations SOLIS/VSM 4 x 105 $50 000 3 hours? 20 POLIS 450 $50 000 10 s 20 SOLAR-B/SP 1000 $200 000 5 s 100

16. Optimizations of SIR • Paralellization (MPI) • Designed for use with Linux clusters • Speed increases linearly with number of processors • Status: Already available (L.Bellot) • Porting source code to Fortran 90 • More flexibility, efficiency, and speed • Better management of memory allocation and array operations • Keep I/O to a minimum • Status: in progress (B. Ruiz Cobo) • Use of look-up tables for spectral syntheses • Pe as a function of T and Pg • Absorption coefficients as functions of T and Pe • Speed gain: a factor 10-20 • Status: Already available (B. Ruiz Cobo)

17. Proposed strategy • Baseline: ME inversions of all SP scans • Identify • Pixels with bad fits and/or large asymmetries • Regions where interesting physical processes occur • Run inversions with gradients on these pixels • Use ME results as initialization • Not only linear stratifications, but also more complex height dependences will often be needed. • Two-component model atmospheres may be required • Critical issues: • Clarify limitations of 6301 and 6302 for quiet Sun magnetic field studies • Development of efficient visualization tools