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