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Appendix A: Flare data processing

Some authors have reported an Hα-line impact polarization level below 1% in flares. Others like Bianda et al. (2005) did not find any clear linear polarization signature above a sensitivity level of 0.1% in Hα flare observations.Their measurements were made in filter mode with 1′′ × 1′′ pixels and 2 s integration time. Stokes polarization images were obtained by averaging over a 10′′ × 10′′ area, covered in 40 s. Polarization islands in THEMIS observations do not exceed 4′′ × 4′′; i.e., Bianda et al. integrated their measurements over a six times bigger area. For uniform intensity, after integrating over such extended area, a 6% polarization degree would go down below 1%. Moreover, including brighter flare unpolarized regions in this area − which extends over 24 pixels along the slit − would make the polarization degree go further down to the 0.1 to 0.5% level. A 40 s. integration time would reduce this level even more. Bianda et al. observations and the ones presented here were made in Na D2. The set of THEMIS mutiwavelength simultaneous observations included Hα, Hβ, and Mg lines. All these lines were also found to be polarized (Xu et al. 2005, 2006).

After rebinning, the complementary Bianda et al. spectrograph observation of a X17.1 flare has temporal and spatial resolutions (5 arcsec, 10 s) lower than the ones given by THEMIS. The arguments given above also apply to these measurements. Moreover, the spectrograph entrance slit may not have been put at the right place at the right time.

In high-frequency polarization measurements, Hanaoka (2005) find degrees of polarization in the 0.5 to 1% range. However, these measurements include contributions of all flare kernels over one minute of time. As in Bianda et al. observations, unpolarized bright flare kernel intensity may reduce the flare edge’s polarization signal by one order of magnitude.

These contradictory results justify discussing THEMIS data calibration and Intensity and Stokes V crosstalks below.

Appendix A.1: Flare data calibration

Flat-field and dark-current measurements are made before and after each set of active region observations. These flat-field measurements were used to correct the spectra from line curvature. They were also used for positioning the two spectra in y and correcting for possible y size differences.

The optical paths of the two I ± S beams, where S could be either U or Q, are different. Therefore, even for unpolarized light, as in line wings, observed T = (I + S)/(I − S) intensity ratio differs from unity. Relative correction factors R_l and R_r (R = 1/T) have to be applied to band 0 (I + S) left and right line wings (wavelengths λ_l and λ_r). The correction factor R_λ to apply to band 0 observations along the line profile was obtained by linear interpolation between the right and left wings:

Appendix A.2: Intensity crosstalk

For fast time-varying phenomena like solar flares, simultaneous observations of I ± S are mandatory. Such observations require a perfect relative positioning of these two 2D spectra, in order to avoid an intensity gradient effect spoiling the Stokes parameter measurements. An error δy in relative positioning leads to a spurious /ℐ signal equal to ≅. On each side along y of an I(y) intensity peak, the intensity gradient changes sign, and the resulting spurious /ℐ and /ℐ signals are opposite. This is consequently interpreted as a 90° rotation of the linear polarization direction.

Intensity crosstalk as the source of the observed polarization signal can be easily ruled out, because the association between intensity gradient and polarization orientation is opposite on the two ribbons. Nevertheless, we looked for signatures of a bad relative y positioning of the two I ± S spectra in two other different ways:

	Fig. A.1 and profiles for the best y relative positioning of the two I + S and I − S spectra, where S = U or Q, and for additional ± 0.25 pixels (± 1 arcsec) relative shifts.
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	Fig. A.2 Histograms of the polarization orientation for the best y relative positioning of the two I + S and I − S spectra and for additional ± 0.25 pixels (± 1 arcsec) relative shifts.
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	Fig. A.3 Mean 2D spectrum.
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First, line wings were used. True polarization is expected to be low in the wings. After integration over time and space, the line wings polarization degree does not exceed 0.4%. Therefore, the intensity gradient term may dominate the Stokes one. For every slit position in all time sequences, we shifted one spectrum relative to the other by ±0.25 pixels along the y direction, i.e. ±0.25 arcsec. The resulting mean and profiles are plotted in Fig. A.1. They show a remaining non null polarization that exceeds the 0.4% maximum amplitude in the absence of an imposed δy shift. Consequently, the two I + S and I − S 2D spectra’s relative positioning does not need any correction. The 0.4% polarization degree maximum amplitude, observed in the absence of additional δy shift, gives an estimate of the polarization measurement noise.

Building histograms of the line-center polarization-direction, orientation angular distribution is a second way to check the quality of the relativepositioning. On each side of an I(y) intensity peak, a relative shift in the y direction generates positive and negative intensity gradients and, therefore, radial and tangential polarizations. Consequently, a bad relative positioning of the two I + S and I − S spectra would generate two peaks at these perpendicular radial and tangential directions. As seen in Fig. A.2, shifting one spectrum relative to the other by ± 0.25 arcsec increases significantly the intensities of the polarization-direction orientation angular distribution function at θ = 0 and θ = 90. This, regardless the shift sign. Both these methods lead to the same conclusion; i.e., the observed polarization signal is not due to a bad relative positioning of the I + S and I − S 2D spectra.

Appendix A.3: V crosstalk

Significant V crosstalk requires a magnetic field of significant amplitude to be present at the observed location. V crosstalk does not play any role at line center, where impact polarization is observed. According to the magnetic field polarity, V crosstalk

should affect either the red or the blue wing. This contribution should be constant in time and position. Such time constant line-wing polarization enhancements are not observed. V crosstalk cannot explain the line-center strong polarization signals temporary observed.

Appendix A.4: Polarization fringes

Periodic structures in both the y and the wavelength directions are present in THEMIS spectra (Semel 2003). The false polarization signal that these fringes could introduce in the line 2D spectra, is detectable by adding these spectra over time and over slit positions. For each Stokes parameter, this leads to a mean Stokes S2D spectrum: The resulting mean 2D polarization spectrum is shown in Fig. A.3. This mean spectrum includes erroneous contributions, due to a few deficient couples of CCD pixels, and the contribution of the strongest flare degrees of polarization. Polarization fringes are the main contributors. They have amplitudes lower than 1%.

Fringes and CCD pixel default contributions to the Stokes polarization signal were eliminated by subtracting mean and from all U/I and Q/I 2D-spectra. In this process, the noisy signal, expected to be constant over all the observing time, is eliminated. Flare U_Fl/I and Q_Fl/I Stokes signals, present only during only n_obs observations, are marginally affected by this treatment. These Stokes signals are reduced by n_obs/(Ntime × Nslitpos), where Ntime (= 12) and Nslitpos (=10) are respectively the number of scans and the number of observations per scan. According on the n_obs value, this reduction factor does vary from 1 to 10%. Such a reduction does not significantly affect the flare linear polarization measurements.

© ESO, 2013