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

2. Extended SOT#17 meeting, Tokyo, April 2006Luis R. Bellot Rubio 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. Extended SOT#17 meeting, Tokyo, April 2006Luis R. Bellot Rubio Asymmetric Stokes profiles Spatial resolution:  1" Advanced Stokes Polarimeter DST, Sac Peak Footpoints of cool coronal loops Nagata, Bellot Rubio, & Katsukawa (2006)

4. Extended SOT#17 meeting, Tokyo, April 2006Luis R. Bellot Rubio Asymmetric Stokes profiles Spatial resolution: 0.6 arcsec Spatial resolution:  0.7" POlarimetric LIttrow Spectrograph + KAOS VTT, Observatorio del Teide Temporal evolution of a bipolar MMF Fe I 630.15 and 630.25 nm Cabrera Solana et al. (in preparation)

5. Extended SOT#17 meeting, Tokyo, April 2006Luis R. Bellot Rubio 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. Extended SOT#17 meeting, Tokyo, April 2006Luis R. Bellot Rubio 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. Extended SOT#17 meeting, Tokyo, April 2006Luis R. Bellot Rubio Fe I 630.1 and 630.2 profiles degraded to SP pixel size ME inversions of asymmetric profiles MHD simulations (Vögler et al. 2005) +

8. Extended SOT#17 meeting, Tokyo, April 2006Luis R. Bellot Rubio Fe I 630.1 and 630.2 profiles degraded to SP pixel size Maps of inferred B and v LOS very similar to real ones! ME inversions of asymmetric profiles MHD simulations (Vögler et al. 2005) +

9. Extended SOT#17 meeting, Tokyo, April 2006Luis R. Bellot Rubio Asymmetric profiles not well fitted ME results are some kind of “average” of physical parameters along the LOS ME inversions of asymmetric profiles MHD simulations (Vögler et al. 2005) + + ME inv Stokes V/I

10. Extended SOT#17 meeting, Tokyo, April 2006Luis R. Bellot Rubio The origin of asymmetries RF of I to v LOS The area asymmetry can be used to derive the height variation of atmospheric parameters Amplitude asymmetry/ Abnormal Stokes profiles Different magnetic atmospheres coexisting in resolution element Area asymmetry Gradients/discontinuities of physical parameters along LOS RF of I to v LOS RF of V to B Cabrera Solana et al. (2005) Auer & Heasley (1978)

11. Extended SOT#17 meeting, Tokyo, April 2006Luis R. Bellot Rubio 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 LILIA Socas-Navarro (2001)1C atmospheres, arbitrary stratifications SPINOR Frutiger & Solanki (2001)1C & 2C atmospheres, arbitrary stratifications, any photospheric line, molecular lines, flux tube model, uncombed model MISMA IC Sánchez Almeida (1997)MISMA model, arbitrary stratifications, any photospheric line SIR/GAUS Bellot Rubio (2003)Uncombed penumbral model, arbitrary stratifications

12. Extended SOT#17 meeting, Tokyo, April 2006Luis R. Bellot Rubio 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 –180 o azimuth disambiguation –3D structure of sunspots and pores –Magnetic flux cancellation events –Polarity inversion lines –Dynamical state of coronal loop footpoints –….. Accounting for gradients

13. Extended SOT#17 meeting, Tokyo, April 2006Luis R. Bellot Rubio 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. Extended SOT#17 meeting, Tokyo, April 2006Luis R. Bellot Rubio Inversions with gradients Spatial resolution:  0.4" VIP + TESOS + KAOS Inversion: SIR with 10 free parameters +

15. Extended SOT#17 meeting, Tokyo, April 2006Luis R. Bellot Rubio 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 SOLIS/VSM4 x 105 3 hours?20 $50 000 POLIS450 10 s20 $50 000 SOLAR-B/SP1000 5 s100 $200 000 InstrumentPixels Time Workstations Cost Worst-case scenario (real-time inversions)

16. Extended SOT#17 meeting, Tokyo, April 2006Luis R. Bellot Rubio 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 –P e as a function of T and P g –Absorption coefficients as functions of T and P e –Speed gain: a factor 10-20 –Status: Already available (B. Ruiz Cobo) Optimizations of SIR

17. Extended SOT#17 meeting, Tokyo, April 2006Luis R. Bellot Rubio 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 Proposed strategy