Magnetic Field of Solar Dark Filaments Obtained from He I 10830 $\mathrm{\AA}$ Spectro-polarimetric Observation

Solar dark filaments (or prominences seen on the solar limb) are cool ($\sim 10^{4}$ $\mathrm{K}$) and dense ($>10^{9}$ $\mathrm{cm^{-3}}$) plasma suspended in the hot ($>10^{6}$ $\mathrm{K}$) corona. They are supported by a bundle of twisted coronal magnetic field or magnetic flux ropes (MFRs: [Xu et al. (2012)], [Gibson (2018)]). Some of the dark filaments are located in quiet region, and some are in active region. The former filaments are often called as quiescent (QS) filaments, and the latter are called as active region (AR) filaments. Both of the QS and AR filaments locate above the polarity inversion lines (PILs: [Babcock & Babcock (1955)]). The filaments sometimes become unstable and erupt into the interplanetary space, and solar flares are simultaneously observed (Priest & Forbes, 2002). A unified model of filament eruptions and solar flares are reviewed in Shibata & Magara (2011). The eruptive solar flares are sometimes accompanied by the coronal mass ejections (CMEs), and the filaments are observed as a core structure of the CMEs (Parenti, 2014).
  To understand the formation process and the evolution of MFRs in ARs, a number of authors investigated the three-dimentional (3D) coronal magnetic field by using an extrapolation of the nonlinear force-free field (NLFFF: Inoue et al. (2013), Kang et al. (2016), Kawabata et al. (2017), Muhamad et al. (2018),Yamasaki et al. (2021)). In some cases, the NLFFF are used for initial conditions to investigate the dynamics of the erupting MFRs with a magnetohydrodynamic simulation (Jiang et al. (2013), Inoue et al. (2015), Inoue et al. (2018), Inoue & Bamba (2021), Yamasaki et al. (2022b)). However, the NLFFF approximation is not necessarily valid for the lower layer of the solar atmosphere such as the photosphere or low chromosphere. This is because the magnetic pressure is not sufficiently higher than the gas pressure at these heights (Gary, 2001), $i.e.$, the assumption of the force-free is not valid. Kawabata et al. (2020) reported that the shear angle ($i.e.$, angle from the potential field) of the horizontal magnetic field at the height of chromosphere reproduced with the NLFFF was smaller than that determined from observations. Yelles Chaouche et al. (2012) performed two NLFFF extrapolations using observed photospheric and chromospheric magnetic field in dark filament regions independently, and by comparing the results of these two extrapolations they found that the difference in magnetic field structure that supports the filament plasmas; they found highly twisted field lines with more than one turn in the extrapolation from photosphere, but they only found less twisted field lines in the extrapolation from chromosphere. This result suggests that the NLFFF only using a photospheric magnetogram is not suitable for reconstructing filaments’ magnetic field. Thus, direct observations of the magnetic field of the dark filaments are important to understand the structure and the mechanism of instability of the dark filaments.
  In Table 1, we summarized the previous results on the magnetic field of dark filaments and prominences from spectro-polarimetric observations. Regarding QS filaments, most of the studies suggest that the field strength is of the order of $10$ $\mathrm{Gauss}$ (Leroy et al. (1983), Leroy et al. (1984), Bommier et al. (1986), Bommier et al. (1994), Casini et al. (2003), Orozco Suarez et al. (2014), and Martinez Gonzalez et al. (2015)). Wang et al. (2020) reported the field strength of an erupting QS filament was smaller than $100$ $\mathrm{Gauss}$. Regarding AR filaments, some of the previous studies suggest that the field strength is $100-800$ $\mathrm{Gauss}$ (Xu et al. (2012), Kuckein et al. (2009), Sasso et al. (2011), and Sasso et al. (2014)). However, Diaz Baso et al. (2016) pointed out that the observed Stokes profiles from the AR filaments can be explained with a field strength of $10$ $\mathrm{Gauss}$ in the filament if contaminations of observed spectra by the radiation from the background active region with 600 Gauss.
  Besides the field strength of QS and AR filaments, two types of the magnetic field configuration of the filaments are proposed. One is the normal polarity model (Kippenhahn & Schlüter, 1957). In this model, the shear direction of the magnetic field of the filaments is the same as the shear direction of the ambient magnetic field inferred from the photospheric magnetic field (see Figure 1 (a), (c), and (d)). The other model is the reverse polarity model (Kuperus & Raadu, 1974). In this model, the shear direction of the magnetic field of the filaments is opposite to the shear direction of the ambient magnetic field (see Figure 1 (b), (d), and (e)). For QS filaments, Bommier & Leroy (1998) performed a spectro-polarimetric observation of an off-limb prominence in He I D3 line and found that the magnetic field structure was reverse polarity (see also Bommier et al. (1994)). Martinez Gonzalez et al. (2015) performed a spectro-polarimetric observation of an off-limb prominence in He I $10830$ $\mathrm{\AA}$, and they also reported that the structure was the reverse polarity. Wang et al. (2020) obtained the vector magnetic field of an erupting filament and reported that the magnetic field structure was reverse polarity during the eruption process. For AR filaments, Xu et al. (2012) suggested that the magnetic field structure was normal polarity by using a simultaneous observation of He I $10830$ $\mathrm{\AA}$ and Si I $10827$ $\mathrm{\AA}$ lines. Sasso et al. (2014) analyzed the vector magnetic field of filament and concluded that the magnetic field topology was reverse polarity configuration. Yokoyama et al. (2019) studied the photospheric vector magnetic field of a filament channel in an AR and suggested that the field configuration was reverse polarity.
  Diagnostics of the magnetic field structure of the solar filaments require vector magnetic field information. Spectro-polarimetric observation of the absorption line of the He I $10830$ $\mathrm{\AA}$ is one of the most powerful methods to quantitatively obtain the magnetic field of the solar filaments (Hanaoka & Sakurai, 2017). This line is sensitive to magnetic field not only through the Zeeman effect (Zeeman, 1897) but also through the Hanle effect (Hanle, 1924). From the Zeeman effect in this line, the longitudinal components of $10$ $\mathrm{Gauss}$ and transverse components of $200$ $\mathrm{Gauss}$ are detectable at a sensitivity of $0.03\%$ in polarimetric measurements. In contrast, the Hanle effect diagnostics allow us to deduce relatively weak field of $0.1-100$ $\mathrm{Gauss}$. In this study, to clarify not only the magnetic field strength of the filaments but also the magnetic field configuration, we performed a spectro-polarimetirc observation in He I $10830$ $\mathrm{\AA}$ line targeting dark filaments located in quiet regions.
  The rest of this paper is structured as follows; the observation is introduced in Section 2, the analysis is described in Section 3, results are presented in Section 4, and discussion and conclusion on our findings are given in Section 5.

[htb] Past observational works on filament(/prominence) magnetic field

• 1

  Their target was a polar crown.

• 2

  By photospheric magnetic field observation below dark filaments.

Observation was performed by using the newly installed spectro-polarimeter on the Domeless Solar Telescope (DST: Nakai & Hattori (1985)) at Hida Observatory (Ichimoto et al., 2022). The polarimeter consisting of a rotating super achromatic waveplate and a polarizing beam splitter is located just behind the slit of the spectrograph, and it provides efficient modulations for two orthogonally polarized spectra on detectors in wavelength range of $5000-11000$ $\mathrm{\AA}$. In our observation in He I $10830$ $\mathrm{\AA}$, polarimetric sensitivity of $3\times 10^{-4}$ was achieved in a few second with a near-infrared (NIR) camera, the Goldeye G033 SWIR ($640\times 512$ pixels), (see Yamasaki et al. (2022a)).
  Using the spectro-polarimeter, we performed the observations of 8 dark filaments (DFs) on 2022 Apr 9, 2022 Jun 4, 2022 Aug 11, and 2022 Aug 24 JST (see Table 2). Hereafter, we use filament IDs shown in Table 2 to identify each of the target filaments. He I $10830$ $\mathrm{\AA}$ and Si I $10827$ $\mathrm{\AA}$ lines were taken with the NIR camera with an exposure time of $15$ $\mathrm{msec}$ for each frame. We obtained $200$ frames in $3$ $\mathrm{sec}$ for each slit position with $1.0$ $\mathrm{Hz}$ modulation by the rotating waveplate. The slit width and length were $0.1$ and $20$ $\mathrm{mm}$, corresponding to $0^{\prime\prime}.64$ and $128^{\prime\prime}$ on the solar image, respectively. Spatial sampling along the slit is $0^{\prime\prime}.43$ $\mathrm{pixel^{-1}}$, and the spectral sampling is $29$ $\mathrm{m\AA~{}pixel^{-1}}$ while scan step was $1^{\prime\prime}.38$. Fields-of-view along the slit direction ($X$) and the scan direction ($Y$) for each observation is given in Table 2.
  The 8 observational targets are indicated on the full disk H$\alpha$ solar images taken by the Solar Dynamics Doppler Imager (SDDI: Ichimoto et al. (2017)) on the Solar Magnetic Activity Research Telescope (SMART: UeNo et al. (2004)) in Figures 2, 3, 4, and 5 (a). In addition, we also show full disk images of the photospheric magnetic field taken by the Helioseismic and Magnetic Imager (HMI: Scherrer et al. (2012)) onboard the $Solar~{}Dynamics~{}Observatory$ ($SDO$: Pesnell et al. (2012)) in Figures 2, 3, 4, and 5 (b). From the photospheric magnetogram and the H$\alpha$ images, we identified that the DF1, DF3, and DF7 locate in plage regions, the DF2, DF4, DF5, and DF6 locate in quiet regions, and the DF8 locate near an active region.
  Geometrical height of the target filaments is an important parameter for a correct evaluation of the magnetic field by using the Hanle effect. In our study, we estimated the heights of the targets using the SMART-SDDI images days prior or posterior to the DST spectro-polarimetric observation at which they were off-limb prominences. The adopted heights for each filament are shown in Table 2.

[htb] Observational targets

• 1

  The position parameters of $r$, $p$, and $i$ represent the heliocentric distance, polar angle measured from the geographic north, and inclination angle of the slit of spectrograph from the geographical N-S direction, respectively.

• 2

  $X$ is the field view along the slit common for all the targets and $Y$ is the scanning range.

• 3

  Targets locate above plage regions (see Figure 2 for DF1 and DF3 and Figure 4 for DF8).

• 4

  One footpoint of the filament is connected to an active region (see Figure 5).

As we presented in Table 4.3, we found that the field strength ($|\bm{B}|$) of our target filaments is in a range of $8-35$ Gauss. These results are consistent with the previous studies of QS filaments (see Table 1). However, as Diaz Baso et al. (2016) pointed out, the Stokes $V$ signals of dark filament regions can be created by the magnetic field in the photosphere below (see also Diaz Baso et al. (2019a) and Diaz Baso et al. (2019b)). Therefore, since some of our targets are on plage region (DF1, DF3, and DF7) the magnetic field strength of these targets may be overestimated. Regarding the inclination angles of the magnetic field in the local frame, they vary from $63-105^{\circ}$. These results suggest that the magnetic field of dark filaments is more or less horizontal rather than vertical, which is consistent with previous work (e.g. Trujillo Bueno et al. (2002)).
  As we presented in Table 4.3, we found that 7 out of 8 target DFs have reverse polarity configuration (DF1, DF2, DF4, DF5, DF6, DF7, and DF8) and 1 out of 8 targets have normal polarity configuration (DF3). For the other 6 samples besides DF2 and DF3, we display the results in the same manner as Figures 10 and 11 in the Appendix. According to the previous research, Bommier & Leroy (1998) performed a polarimetric observation in the He I D3 $5876$ $\mathrm{\AA}$ line for off-limb prominences and reported that 264 out of 296 QS prominences have reverse polarity in their magnetic field configuration. By observing an off-limb prominence with He I $10830$ $\mathrm{\AA}$ line, Martinez Gonzalez et al. (2015) also reported that the magnetic field configuration of the prominence has the reverse polarity. Our result of the magnetic field configuration of QS filaments is consistent with the result in previous studies. So far most studies for determining the prominence field configuration as one of the normal or reverse polarity types have been conducted with off-limb observations. One exception is the work by Wang et al. (2020) who performed a spectropolarimetric observation in He I $10830$ $\mathrm{\AA}$ line for an on-disk QS filament and reported that the magnetic field configuration was reverse polarity. Our study provides the first observation of multiple on-disk QS filaments and confirmed that the majority of the magnetic field configuration is the reverse polarity.

We thank the staff members and students at Hida observatory for continuous support for our observations. This work was supported by JSPS KAKENHI Grant Number JP21J14036. SDO is a mission of NASA’s Living With a Star Program.