Infrequent Occurrence of Significant Linear Polarization in Hα Solar Flares

To reduce the fluctuation, we rebinned the data with the same spatial and temporal samplings as those by Bianda et al. (2005), namely, 10 arcsec and 40 s, respectively. We call this rebinned pixel a macropixel. With these samplings, the typical statistical error of absolute linear polarization ($\sqrt{{Q}^{2}+{U}^{2}}$/I) is 0.04%. The maximum of the systematic errors in our data is 0.61%.

The flaring regions, where we examine the linear polarization, were defined to be the macropixels whose intensities are larger than the threshold of 1.5I_QS. In the 896 images rebinned spatially and temporally, there are 10374 macropixels that were defined as the flaring regions.

To specify the relative timing of the acquisition time of each rebinned image, we defined the normalized timing where the GOES start and peak times are represented by −1 and 0, respectively. For instance, if a strong linear polarization signal is found in the image taken at the GOES start time, the timing of the polarization appearance is −1.

Figures 1(a)–(c) show the histograms of the degree of Hα linear polarization, intensity, and relative timing of the 10374 macropixels in the flaring regions of the 71 flares. Figures 1(d)–(f) show the histograms of heliocentric distance of the 71 flares, GOES peak X-ray flux for the 64 GOES events, and GOES flare duration, which is defined by the elapsed time from the GOES start to end. In each panel, we also show the average and the standard deviation of the data.

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In Figure 1(a), some macropixels show the polarization exceeding the maximum systematic error (0.61%), and they are presumed to be true polarization signals. If we raise the threshold to the sum of the statistical and the systematic errors, i.e., 0.65%, to avoid picking up spurious signals more certainly, there are four macropixels showing the polarization above this value. There are many macropixels of which the degree of polarization is a little below 0.65%. We cannot exclude the possibility that their polarization signals are spurious ones. According to Hanaoka (2006), spurious polarization signals with the opposite signs appear adjacently due to slight outfocus. A careful check of the data revealed that the polarization signals close to the maximum systematic error level are often located at the edge of ribbons and adjacent to another macropixel showing the opposite sign of the polarization. If the polarization measurements were perfect, these signals cancel each other out. We regarded that the polarization signals with the opposite signs are not true signals. On the other hand, all of the four macropixels above 0.65% are observed during event No. 70 in Table 1 in the Appendix, an M6.5 flare. Unlike macropixels below 0.65%, they are isolated from those with the polarization of the opposite sign, and they show net polarization. Therefore, the detection of the polarization in these macropixels is considered to be reliable. These facts confirm that the polarization signals of the four macropixels are true ones, i.e., the solar origin.

The details of the large linear polarization signals in event No. 70 will be examined in the next section, but to clarify if this event has unique characteristics other than the polarization, we also show histograms of event No. 70 alone in Figure 1. As seen in Figure 1(a), there are also macropixels with smaller linear polarization signals in event No. 70. Figure 1(b) shows that the intensity distribution of event No. 70 is (2.03 ± 0.52) × I/I_QS, which is not different from that of the entire flares, (2.02 ± 0.62) × I/I_QS. Figure 1(c) shows that the data of event No. 70 were successfully captured between the onset to peak of the flare. Figure 1(d) shows that location of event No. 70 is 323 arcsec from the disk center and this is not exceptional among the observed flares, whose locations are widely distributed over the center to the limb. Figure 1(e) shows that GOES X-ray flux of event No. 70 was 6.5 × 10⁻⁵ W m⁻², which is relatively strong among the observed data, but is not the strongest (7.1 × 10⁻⁴ W m⁻²). Figure 1(f) shows that the duration of event No. 70 is a typical value among the observed flares, and the event is not a significant long-durational flare as observed by Hanaoka (2003). Summarizing the above, we cannot find any notable characteristics in event No. 70 except the linear polarization.

We investigate more details of the event in this section. The event was an M6.5 class flare occurring in NOAA 10826, located at S03E19. The GOES X-ray flux started to increase at 02:42 UT, peaked at 02:52 UT, and decayed at 03:00 UT. SOHO and RHESSI also observed the flare. We show the light curves of the GOES X-ray flux, RHESSI hard X-ray (25–50 and 50–100 keV) counts, and Hα flux in Figure 2. The FOV-integrated Hα flux shows two peaks at 02:49:30 UT and 02:52:40 UT, which correspond to the RHESSI hard X-ray and GOES soft X-ray peaks, respectively. For this analysis, we used the original temporal resolution of 1 s, but spatially applied a low-pass filter for each image with a cutoff size of 4'' to suppress the noise. In these data, the maximum of systematic errors in linear polarization is 0.81% with the reduced sampling.

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First, we examined the position where the strong polarization signals appear during the flare. Figure 3 shows Stokes IQUV images in Hα at the hard X-ray peak time. The direction of +Q is adopted to be the celestial east–west direction. The figure also shows co-aligned images of SOHO/EIT Fe xii 195 Å, SOHO/MDI continuum intensity and line-of-sight magnetogram, and RHESSI 12–25 and 50–100 keV images during the flare. The RHESSI X-ray images are reconstructed by the PIXON algorithm. Two bright sources appeared in the hard X-ray (50–100 keV) image at (−300'', −90'') and (−290'', −80''), and they were connected by soft X-ray (12–25 keV) loop-like structures. The two hard X-ray sources are located in the opposite magnetic polarities seen in the photospheric line-of-sight magnetogram, and this fact suggests that the soft X-ray loops correspond to the magnetic field lines connecting the two hard X-ray sources. The Hα intensity image shows the brightest source corresponding to the X-ray sources and, in addition, two other bright sources located at (−340'', −87'') and (−265'', −70''). They are in the opposite magnetic polarities and connected by a bright EUV loop seen in the 195 Å image. Thus, we interpreted that small arch structures connect two hard X-ray footpoints and that a loop over the arch structures (Moore et al. 2001) lies approximately along the magnetic neutral line. We show a cartoon of the magnetic configuration based on these observations in Figure 3. Among the four Hα footpoints, strong Q/I and U/I signals of ∼1% appeared at (−340'', −87''), which we interpreted as a footpoint of the EUV loop. The averaged degree of the linear polarization at the hard X-ray sources is less than 0.2%. Another source shows an enhancement of 0.95% outside of the flare brightening at (−350'', 95'') in the U/I map. The V/I map shows an enhancement of ∼0.5% in sunspots, which can be explained by the Zeeman signal emerging due to a slight offset of the transmission wavelength of the Lyot filter from the Hα center. In Figure 4, we showed spatial distributions of the IQU signals along the x-axis at y = −87'', where the strong Q/I and U/I signals appear, at five moments during the flare. Peaks of the Q/I and U/I signals are located at 4'' east from the intensity peak, and the size of the region showing significant polarization is 8'' ± 2'' in the FWHM at 02:52:09 UT. The maximum absolute values of Q/I and U/I are 0.8% ± 0.1% and 1.2% ± 0.2%, respectively. The clear relationship between the macropixels with high polarization signals and the solar structure indicates that the the polarization signals are undoubtedly of solar origin.

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Second, we concentrate on the temporal evolution of two regions where the strong linear polarization appeared (region A) and where the strong hard X-ray emission appeared (region B) individually; the regions are designated in the top panel of Figure 5. We calculated the absolute degree of the linear polarization, $\sqrt{{Q}^{2}+{U}^{2}}$/I, and the direction of the linear polarization, (1/2) arctan(U/Q), at each pixel, and averaged over the pixels with the intensity above 2I/I_QS. The numbers of pixels that we averaged are up to 52 and 233 in regions A and B, respectively, depending on the observation time. Figure 5 shows the temporal evolutions of pixel-averaged intensities, degree of the linear polarization, and direction of the linear polarization measured from the solar north. The averaged intensities of the two regions peaked at 02:49:30 UT and 02:52:40 UT, which correspond to the RHESSI hard X-ray and GOES soft X-ray peaks, respectively. The linear polarization in region A was above the error level between 02:47:40 UT and 02:53:10 UT, and it reached the maximum value of 1.16% ± 0.06% at 02:51:18 UT. On the other hand, in region B, the degree of the linear polarization was almost a constant value of 0.19%, which is regarded as the systematic error. When the degree of the linear polarization in region A reached maximum, the averaged Hα intensity and the direction of the linear polarization were (2.12 ± 0.00)I_QS and −1425 ± 60 from the solar north. The direction of the linear polarization did not change significantly during the flare, and it stayed around −1351 with a standard deviation of 61. In Figure 3, we indicate the direction of −1351 from the solar north in the EIT image. As we see, this direction corresponds the direction of the coronal loop just above the footpoint. Figures 3 and 5 suggest that neither hard X-ray, soft X-ray, nor Hα fluxes correlate with the Hα linear polarization in region A.

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Here, we examine the coronal structure from ultraviolet observations. Figure 6 shows SOHO/EIT 195 Å intensity images, base-subtracted images, and temporal evolution. The base-subtracted images show the difference from image taken at 01:46:55 UT. We integrated positive and negative values over the FOV of the base-subtracted images, and plotted the intensity increase and decrease in Figure 6(a). The base-subtracted images show that strong coronal dimming appears in the west of the active region from 03:10 UT, which is 18 minutes after the GOES peak time. The dimming reached the peak at 04:10 UT, which is 78 minutes after the GOES peak time. Coronal mass ejections (CMEs) are often associated with coronal dimming (Sterling & Hudson 1997). Therefore, in this case, a CME was likely to occur as well, even though the CME catalog³ by the SOHO/Large Angle and Spectrometric COronagraph (LASCO; Brueckner et al. 1995) does not show any CME.

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We found only one event that showed significant linear polarization signals among 71 Hα flares including 64 GOES flares with the spatial and temporal samplings of 10'' × 10'' and 40 s, respectively. Many preceding papers reported the characteristics of the linear polarization in Hα only for the events that show significant polarization signals. In the cases where the polarization was not detected, it has been considered that the sensitivity of the polarimetry was insufficient. On the other hand, Bianda et al. (2005) reported that they did not find significant linear polarization signals in 30 flares, even though they used a high-sensitivity instrument. Based on their preliminary analysis of dozens of flares, Hanaoka (2004, 2005) also found that one flare showed significant linear polarization signals, while most other flares showed none. In our study, we used the polarimeter with higher accuracy described in the papers by Hanaoka (2004, 2005) and confirmed their preliminary results. Furthermore, although the analyzed samples include some large flares such as 4 X- and 13 M-class events, the results are basically negative. The high-frequency modulation techniques reduce spurious signals caused by the seeing effect and by flaring structures evolving in time, and data obtained by these techniques are more reliable than data that were taken by low-frequency modulation techniques. Thus, our results proved that the linear polarization does not appear in most of the flares, but there are a few flares that actually show the polarization.

The reason Bianda et al. (2005) did not find significant linear polarization is thought to be that the binning size of 10'' × 10'' and 40 s was too large to resolve the compact flare kernels (Hénoux & Karlický 2013; Firstova et al. 2014). Our results show that the enhancement of the linear polarization extended 8'' and lasted for 330 s. The polarization with such spatial and temporal sizes is still detectable after the binning done by Bianda et al. (2005). Our results show that the linear polarization signals cover nearly the entire region of one of the Hα footpoints, but are not so high as 10% or highly localized at the edge of the ribbons. Nevertheless, due to the limitation of the observation, we cannot conclude that polarization with a smaller scale and a shorter duration does not exist.

The linear polarization in solar flares observed so far has had the following characteristics: (1) The degree of the polarization is 1%–8% (this study; Henoux et al. 1990; Emslie et al. 2000; Hanaoka 2003). (2) The direction of the polarization is approximately aligned with the coronal loop just above the footpoint (this study; Hanaoka 2003). (3) The degree of the polarization does not correlate with Hα, soft X-ray, or hard X-ray intensities temporally or spatially (this study). (4) Flares with linear polarization in Hα and He i 10830 Å are often associated with eruptions (this study; Hanaoka 2003; Xu et al. 2005; Judge et al. 2015). Some of the characteristics are common in the observed flares, and therefore it is plausible that there is a common mechanism to produce the linear polarization in flares. However, from our statistical results, it was concluded that the linear polarization in Hα with a few percent is rarely observed. The mechanism to produce the Hα linear polarization is not a common phenomenon in ordinary flares. Furthermore, the result that only a minor kernel showed significant polarization means that not all the kernels in a flare necessarily have a common condition relating to the production of the linear polarization.

Let us examine the possibility that the accelerated electrons and the chromospheric dynamics related to the electron injection are the drivers of the linear polarization. They have been considered to produce the linear polarization in many papers. Nonthermal electrons of >50 keV generate hard X-ray photons of 50–100 keV by bremsstrahlung in the dense chromosphere (Koch & Motz 1959). Strong electron injection into the chromosphere can induce rapid evaporation (Fisher et al. 1985) and return current (Emslie 1980). Thus, if anisotropic electrons, return current, or dynamical changes of the chromospheric atmosphere produce linearly polarized photons, linear polarization signals should appear in the same regions as the hard X-ray sources. If the anisotropic radiative field appearing during chromospheric evaporation is the cause of the linear polarization, the linear polarization signals appear at the edge of the flare ribbons (e.g., Štěpán & Heinzel 2013). In our results, however, the linear polarization did not correlate with hard X-ray emission. In the less bright kernels, the linear polarization source was separated 4'' from the intensity peak of the kernel but did not concentrate at the edge of the kernel. Moreover, these mechanisms cannot explain why the significant linear polarization is rarely observed in flares. Thus, the observed linear polarization cannot be caused by anisotropic electrons or the radiation field discussed above.

Here, we focus on other remarkable characteristics of the flares with the linear polarization in Hα, namely, CMEs and eruptions. From some gamma-ray observations of behind-the-limb flares, protons can be accelerated by CME shocks and propagate toward the solar surface along the magnetic field, i.e., toward the footpoints of coronal loops (Cliver et al. 1993; Pesce-Rollins et al. 2015). Actually, the strong linear polarization appeared at one of the footpoints of a coronal loop in the flare studied here, and the direction of polarization was aligned with the coronal loop just above the footpoint. Thus, it is possible that the observed polarization was produced through the impact polarization caused by accelerated protons. Regarding the frequency of observing the proton acceleration, Bai & Sturrock (1989) showed that 14 out of 266 flares were classified as gradual gamma-ray/proton flares by hard X-ray and gamma-ray telescopes on board the Solar Maximum Mission. Based on the result by Bai & Sturrock (1989), the frequency of detecting proton acceleration can be 5.3% ± 1.4% (or higher, because some weaker events were possibly missed due to the limitation of the instrument). To produce the impact polarization, accelerated protons should have an anisotropic pitch angle distribution. Therefore, the probability of detecting the impact polarization is less than the probability of detecting gamma-ray emission. This indirect evidence meets the scenario that linear polarization is produced by impact polarization of accelerated protons, but we cannot explain the degree of the polarization of 1%, as examined by Štěpán et al. (2007). More investigations with highly accurate polarization measurements of solar flares and with numerical simulations of radiative magnetohydrodynamics at flare kernels in the chromosphere are needed to clarify the origin of linear polarization at Hα in solar flares.