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Inversions based on ME atmospheres
Stokes inversions beyond ME atmospheres
Luis R. Bellot RubioInstituto de Astrofísica de Andalucía (CSIC)
Granada, Spain
Extended SOT#17 meeting, Tokyo, April 2006 Luis 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
Extended SOT#17 meeting, Tokyo, April 2006 Luis 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)
Extended SOT#17 meeting, Tokyo, April 2006 Luis 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)
Extended SOT#17 meeting, Tokyo, April 2006 Luis 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)
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Extended SOT#17 meeting, Tokyo, April 2006 Luis 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)
Extended SOT#17 meeting, Tokyo, April 2006 Luis 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)
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Extended SOT#17 meeting, Tokyo, April 2006 Luis R. Bellot Rubio
• Fe I 630.1 and 630.2 profiles degraded to SP pixel size
• Maps of inferred B and vLOS very similar to real ones!
ME inversions of asymmetric profiles
MHD simulations (Vögler et al. 2005)
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Extended SOT#17 meeting, Tokyo, April 2006 Luis 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)
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ME inv
ME inv
Stokes V/I
Extended SOT#17 meeting, Tokyo, April 2006 Luis R. Bellot Rubio
The origin of asymmetries
RF of I to vLOS
The area asymmetry can be used to derive the height variation of
atmospheric parameters
Amplitude asymmetry/
Abnormal Stokes profilesDifferent magnetic atmospheres coexisting in resolution element
Area asymmetry Gradients/discontinuities of physical parameters along LOS
RF of I to vLOS
RF of V to B
Cabrera Solana et al. (2005)
Auer & Heasley (1978)
Extended SOT#17 meeting, Tokyo, April 2006 Luis 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
Extended SOT#17 meeting, Tokyo, April 2006 Luis 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– 180o azimuth disambiguation
– 3D structure of sunspots and pores
– Magnetic flux cancellation events
– Polarity inversion lines
– Dynamical state of coronal loop footpoints
– …..
Accounting for gradients
Extended SOT#17 meeting, Tokyo, April 2006 Luis 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)
Extended SOT#17 meeting, Tokyo, April 2006 Luis R. Bellot Rubio
Inversions with gradients
• Spatial resolution: 0.4"• VIP + TESOS + KAOS• Inversion: SIR with 10 free
parameters
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Extended SOT#17 meeting, Tokyo, April 2006 Luis 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/VSM 4 x 105 3 hours? 20 $50 000
POLIS 450 10 s 20 $50 000
SOLAR-B/SP 1000 5 s 100 $200 000
Instrument Pixels Time Workstations Cost
Worst-case scenario (real-time inversions)
Extended SOT#17 meeting, Tokyo, April 2006 Luis 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– 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)
Optimizations of SIR
Extended SOT#17 meeting, Tokyo, April 2006 Luis 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