1. 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, January 2017

2. 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 Å triplet)
&
from
the photosphere
(the Si I Å).

3. 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)

4. The scientiic interest on the spectral region around 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 − 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

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

6. 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

7. OUR AIMS
(1) To quantify the sensitivity of the Stokes parameters I, Q,U, V of the Si I 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 Å line.

8. 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.

9. 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

10. Atomic Data

11. 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

12. 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

13. Results

14. 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.

15. 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 Å line intensity profile.
Heights of formation are calculated using Eddington-Barbier approximation: heights where

16. Sensitivity of the Stokes parameters to the NLTE effects

17. 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 A line center (no matter how complex the Si model atom is) never exceed 40 km.
In the formation layers of the Si i 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.

18. 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 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>

19. Sensitivity of the NLTE effects to the magnetic field

20. NLTE changes of the emergent Stokes profiles V in the blue and red wings of the SiI 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.

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

22. 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 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>

23. Summary

24. The NLTE effects should be taken into account when diagnosing the emergent Stokes I profiles of the Si I 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 Å line and for modeling and inverting its Stokes profiles without assuming LTE.

25. Thank you
for
your attention