Si I Atomic Model for NLTE Spectropolarimetric Diagnostics of the 10827 Å line N. Shchukina1, A. Sukhorukov1,2, J. Trujillo Bueno3 1Main Astronomical Observatory, NASU, Kiev, Ukraine 2Institute for Solar Physics, Stockholm University, Sweden 3Instituto de Astrofisica de Canarias, La Laguna, Spain SOLARNET IV MEETING The Physics of the Sun from the Interior to the Outer Atmosphere Lanzarote, Spain, 16-20 January 2017

Science objectives: The spectral region around 10830 Å is a powerful diagnostic window: It contains information coming simultaneously from the chromospheric structures (the He I 10830 Å triplet) & from the photosphere (the Si I 10827 Å).

Applications of these lines in solar physics include: Studies of propagation of waves from the photosphere to the chromosphere in a sunspot umbra, pore, a facula (Centeno et al. 2006, 2009; Bloomfield et al. 2007; Felipe et al. 2010, 2011). Studies of long-term variations of the solar activity (Livingston & Holweger, 1982) Measurements of the solar differential rotation (Pierce & Lopresto, 1984). Simultaneous diagnostics of magnetic fields in the photosphere and the chromosphere (Kuckein et al., 2012, 2015; Xu et al., 2012; Yelles et al., 2012; Solanki et al., 2003; Wiegelmann et al., 2005; Penn & Kuhn, 1995)

The scientiic interest on the spectral region around 10830 Å has been growing over the last fifteen years thanks to advances in instrumentation for spectropolarimetric solar observations: 4-m Daniel K. Inouye Solar Telescope (DKIST, Keil et al., 2011) with the infrared instruments. They will provide unprecedented IR observations on the solar disk, at the limb, and in the corona with the highest spatial resolution one can achieve from the ground.; the 4-m European Solar Telescope (EST, Collados et al., 2013); the 1.5-m GREGOR solar telescope (Denker et al., 2012; Soltau et al., 2012) hosted with IR Spectrograph for spectropolarimetry in the 10 000−18 000 A region; (GRIS, Collados et al., 2012); the Japanese Aerospace Exploration Agency mission Solar-C (Shimizu et al., 2011; Katsukawa et al., 2012) aimed at high spatial resolution, high cadence IR spectropolarimetric observations

Such unprecedented facilities for doing solar IR spectropolarimetric observations requires further development of diagnostic tools.

What we know about the NLTE effects in the SiI 10827 line ? The NLTE intensity is lower than the LTE intensity in the core of this line both in 1D and 3D HD model atmospheres (Bard & Carlsson, 2008; Sukhorukov & Shchukina 2012; Sukhorukov, 2012; Shchukina, Sukhorukov & Trujillo Bueno, 2012). A computationally tractable model of the Si i atom in order to study solar atmospheric dynamics using the Stokes-I profile of this line (1D-case) includes 23 levels and 171 radiative transitions (Bard & Carlsson, 2008). We know nothing about the sensitivity of the Stokes Q, U, V parameters to the NLTE effects

OUR AIMS (1) To quantify the sensitivity of the Stokes parameters I, Q,U, V of the Si I 10827 Å line to NLTE effects. (2) To facilitate NLTE diagnostics of this line, i.e. to develop the simplest possible Si model atom which allows a fast and accurate NLTE inversions of the Si I 10827 Å line.

NLTE modelling We solved the self-consistent statistical and radiative transfer equations applying our multilevel transfer code (Shchukina & Trujillo Bueno, 2001). It allows to compute both the NLTE and LTE Stokes I, Q, U, V parameters of spectral lines by taking the Zeeman effect into account.

We used a 3D MHD snapshot model of the quiet solar atmosphere taken from a magneto-convection simulation with small-scale dynamo action (M.Rempel, 2014). The snapshot model has a vertical unsigned flux density < |Bz| > = 80 G in the visible surface layers and zero net magnetic flux. Surface variations of the modulus B (with Bz sign) at continuum level

Atomic Data

for the diffferent model atoms of silicon. No. bb=4124 No. bb=584 Diagram of the energy levels (red horizontal bars) and radiative transitions for the diffferent model atoms of silicon. No. bb=605 No. bb=6

Comprehensive Si atom model used as standard Atomic Data Comprehensive Si atom model used as standard Reduced Si atom model Simplest Si atom model Si I: 206 levels 206 levels 12 levels Si II: 89 levels 3 parent terms Si III: ground level Ground level BB transitions: 4708 605 (f > 10−4) 6 (4s3Po − 4p3P) 10827→ 4s3Po2 − 4p3P2 BF transitions: 295 295 15

Results

The ubiquitous presence of Zeeman-like signatures in the Stokes V, Q, U Si I 10827 Å profiles Vmax/<Icont> min = –13.8% Max = 14.4% Emergent disk-center Stokes V profiles measured in units of spatially averaged mean continuum <Icont> . Noise-free unsmeared case. LEFT: The wavelength variation of the V/<Icont> along the spectrograph’s slit. RIGHT: The spatially resolved emergent V/<Icont> profiles at each of the surface grid points.

A histogram of the wavelength positions of the NLTE Stokes V amplitude of the SiI 10827 Å line. Histograms of the NLTE heights of formation calculated for three wavelengths of the SiI 10827 Å line intensity profile. Heights of formation are calculated using Eddington-Barbier approximation: heights where

Sensitivity of the Stokes parameters to the NLTE effects

Two NLTE phenomena affect the Stokes I profile: (1) The shift of the line formation region caused by the NLTE effects on the line opacity. (2) The deviation of the line intensity source function from the Planck function The NLTE shifts in the height of formation of the Si i 10 827 A line center (no matter how complex the Si model atom is) never exceed 40 km. In the formation layers of the Si i 10 827 Å line the excitation temperature Tex is always lower than the electron temperature Te. The difference (Tex −Te) varies from −200 K to −800 K along the snapshot surface.

Changes of the emergent Stokes I,Q,U, V profiles of the SiI 1082 Changes of the emergent Stokes I,Q,U, V profiles of the SiI 1082.7 nm line caused by the NLTE effects in the 3D MHD snapshot. Results are shown for the wavelength Δλ=0.1 Å corresponding to the mean wavelength position of the Stokes V peaks in red wings of this line. Left: The snapshot surface maps of the NLTE changes. Right: Scatter plots of the NLTE changes. ΔI/<Ic> ΔQ/<Ic> ΔU/<Ic> In the inner wings the NLTE Stokes profile changes are comparable to the values of Stokes parameters themselves. ΔV/<Ic>

Sensitivity of the NLTE effects to the magnetic field

NLTE changes of the emergent Stokes profiles V in the blue and red wings of the SiI 10827 Å line plotted against the vertical field strength Bz. Left: Results for the blue wing at a wavelength Δλ= −0.08 Å. Right: Results for the right wing at Δλ= 0.1 Å. These wavelengths correspond to the mean wavelength positions of the Stokes V peaks in the blue and red wings of this line. For the Stokes V parameter the magnitude of the NLTE effects correlates with the value of magnetic field strength.

Sensitivity of the Stokes parameters to the choice of the Si model atom

In the inner wings the errors are small: ~1.00% for the Stokes I ΔI/<Ic> Changes of the NLTE Stokes profiles I,Q,U,V of the SiI 10827 Å line at the wavelength Δλ= 0.1 Å caused by using the simplest Si model atom instead of the complicated one (605 bb transitions). Left: maps of the NLTE changes for the snapshot surface. Right: Scatter plots of the changes VS. the NLTE I,Q,U,V values. ΔQ/<Ic> ΔU/<Ic> In the inner wings the errors are small: ~1.00% for the Stokes I ~0.01% for the Stokes Q, U ~0.10% for the Stokes V ΔV/<Ic>

Summary

The NLTE effects should be taken into account when diagnosing the emergent Stokes I profiles of the Si I 10 827 Å line. Their magnitude varies considerably across the solar surface. The differences between the NLTE and LTE intensity profiles indicate a well-pronounced dependence on the line depth. The NLTE impact on the linearly and circularly polarized profiles of this line is significant. In the inner wings, around 0.1 where most of the Stokes Q, U, and V peaks are located, the profile changes caused by deviation from LTE are comparable to the values of the Stokes amplitudes themselves. For the Stokes parameter V, there is a clear correlation of the magnitude of the NLTE effects with the magnetic field strength. The 16-level Si model atom with 6 radiative bound-bound transitions, is suitable to account for the physics of formation of the Si I 10 827 Å line and for modeling and inverting its Stokes profiles without assuming LTE.

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