Indication of the Hanle Effect by Comparing the Scattering Polarization Observed by CLASP in the Lyα and Si iii 120.65 nm Lines

Spectropolarimetry is a unique observational technique for determining physical properties of astrophysical plasmas (e.g., magnetic fields). One physical mechanism for producing polarization in spectral lines is the Zeeman effect, which has been widely used. Recently, diagnostic techniques based on the Zeeman effect have been used to interpret high-spatial resolution observations under seeing-free conditions, such as those obtained with the spectropolarimeter (Ichimoto et al. 2008; Lites et al. 2013) of the Solar Optical Telescope (Shimizu et al. 2008; Suematsu et al. 2008; Tsuneta et al. 2008) on board the Hinode satellite (Kosugi et al. 2007) and IMaX (Martínez-Pillet et al. 2011) on board the Sunrise balloon telescope (Solanki et al. 2010). These observations have significantly advanced our empirical understanding of photospheric magnetic fields.

One of the key goals of solar physics is to understand how the hot plasma of the million-degree solar corona is produced and maintained (the so-called "coronal heating problem"). The chromosphere and the transition region, which are the interface layers between the photosphere and the corona, play a critical role in the energy balance of the outer solar atmosphere. Recent space-borne and ground-based observations revealed that this interface region is full of highly dynamic activities such as magneto-acoustic and Alfvén waves and jets, which could contribute to the heating of the upper chromosphere, transition region, and corona (e.g., Katsukawa et al. 2007; Okamoto et al. 2007; Shibata et al. 2007). However, lack of information on the magnetic field in this region limits the ability to quantify these phenomena. In the photosphere, the ratio of gas to magnetic pressure (β) is larger than unity; however, in the chromosphere and in the layers above, the magnetic forces dominate (i.e., β < 1). Hence, the magnetic structure of these upper layers is expected to be radically different from that of the photosphere, which in most cases can be measured using the Zeeman effect. Only by obtaining quantitative information on the strength and direction of the magnetic field in the low β regions of the solar atmosphere (chromosphere, transition region, and corona) will it be possible to decipher the magnetic coupling between the upper atmosphere and the underlying photosphere and to determine the relationship between the magnetic field and the dynamical activity of the upper atmospheric plasma.

The polarization of spectral lines originating in the solar chromosphere and above is sensitive to the presence of magnetic fields. However, because such spectral lines are broad and the magnetic fields there are expected to be weak, the polarization signals induced by the Zeeman effect are too small to be detected outside sunspots. As an alternative method, the Hanle effect (i.e., the magnetic-field-induced modification of the linear polarization caused by the scattering of anisotropic radiation; e.g., Casini & Landi Degl'Innocenti 2008) has been proposed for probing the magnetic field in the low β atmospheric regions because it is generally much more sensitive to weaker magnetic fields than the Zeeman effect. Recent developments in the theory and numerical modeling of polarization in spectral lines have suggested that the solar disk radiation of some ultraviolet (UV) lines that originate in the upper chromosphere and transition region should show measurable polarization signals caused by scattering processes and that, via the Hanle effect, the line-core polarization signals are sensitive to the presence of magnetic fields in such outer atmospheric regions (Trujillo Bueno et al. 2011, 2012; Belluzzi & Trujillo Bueno 2012). The hydrogen Lyα line at 121.57 nm is of particular interest because its core, which originates at the base of the transition region, is sensitive to the presence of magnetic fields with strength between approximately 10 and 100 G. The paper by Trujillo Bueno et al. (2011) motivated the development of the sounding rocket experiment Chromospheric Lyman-Alpha Spectro-Polarimeter (CLASP; see Kano et al. 2012; Kobayashi et al. 2012; Kubo et al. 2014). This rocket experiment was developed to measure the scattering polarization of the Lyα line and probe the magnetic field in the upper chromosphere and transition region via the Hanle effect. The first attempt to detect scattering polarization in UV lines, including Lyα, was conducted by Stenflo et al. (1980) using a slit-less instrument on board the Soviet satellite Intercosmos 16, but the mission was unsuccessful, presumably due to in-flight molecular contamination.

The CLASP instrument was launched on 2015 September 3 from White Sands Missile Range, and it successfully carried out observations during the 320 s of its suborbital flight. The CLASP observations, for the first time, demonstrated that there is indeed scattering polarization in the hydrogen Lyα line of the quiet solar disk radiation and that the measured Q/I and U/I core and wing signals have conspicuous spatial variations with scales of 10''–20'' (Kano et al. 2017). The Lyα wings, which are insensitive to the Hanle effect, showed scattering polarization perpendicular to the solar limb with a clear center-to-limb variation (CLV) and amplitudes as large as 6% near the limb, in agreement with the theoretical predictions (Belluzzi et al. 2012). On the other hand, the line core, where the Hanle effect operates, showed Q/I and U/I signals of the order of 0.1%, but without a clear CLV in Q/I, in contrast with the theoretical line-core polarization signals calculated using state-of-the-art 1D and 3D models of the solar atmosphere (Trujillo Bueno et al. 2011; Belluzzi et al. 2012; Štěpán et al. 2015). This discrepancy suggests that the geometrical complexity of the transition region, which is not realistic in such models, plays an important role on the Lyα scattering polarization (J. Štěpán et al. 2017, in preparation; J. Trujillo Bueno et al. 2017, in preparation).

It is necessary to disentangle the polarization induced by geometrical complexity and that induced by the magnetic field (i.e., the Hanle effect). One potential method is to observe simultaneously at least two spectral lines with different sensitivities to the Hanle effect, and ideally originating in the same region of the upper solar atmosphere (i.e., the so-called "differential Hanle effect"; e.g., Stenflo et al. 1998; Trujillo Bueno et al. 2012). To put it simply, the geometrical complexity would induce near-identical spatial variations of the polarization signals in the two lines, while the magnetic field would induce different modifications of the scattering polarization. Hence, a comparison of the observed polarization in the two lines would be a diagnostic of the magnetic field if the only difference between the two lines is their sensitivity to the magnetic field.

In this paper, we report the first detection of the scattering polarization in the Si iii line at 120.65 nm, along with observational insight on the causal relationship between the intensity and scattering polarization signals observed by CLASP. Finally, by comparing the U/I signals in the Si iii and Lyα lines, which have very different sensitivities to the Hanle effect, we show observational evidence in favor of the operation of the Hanle effect in these UV spectral lines.

2.1. CLASP Observations

On 2015 September 3, CLASP observed a quiet region at the southwest limb during 280 s under stable pointing conditions in a sit-and-stare mode. The slit was roughly perpendicular to the solar limb with one edge covering an off-limb region of ∼20'' (see Figure 1(a)). The slit length is 400'' and its width is 145.

Zoom In Zoom Out Reset image size

CLASP has two optically symmetric channels, which provide two simultaneous measurements of orthogonal polarization states with two cameras (Narukage et al. 2015, 2017). The two cameras recorded the modulated intensity every 0.3 s in synchronization with the waveplate rotation. In addition to the hydrogen Lyα line at 121.57 nm (which was recorded by the two channels), one channel covered the Si iii line at 120.65 nm. After dark current subtraction, gain correction, and tilt correction of the spectrum, polarimetric demodulation was performed to derive the Stokes I, Q/I, and U/I of the Lyα and Si iii lines (see the Appendix). To achieve the required high polarization sensitivity for the demodulation, we used all the exposures taken during the limb observation, resulting in the temporally averaged I, Q/I, and U/I profiles over 280 s. The final Stokes spectra of the hydrogen Lyα and the Si iii lines are shown in Figures 2 and 3, respectively. The positive reference direction for Stokes Q is parallel to the solar limb.

Zoom In Zoom Out Reset image size

The plate scales are 11 per pixel along the slit and 0.0048 nm per pixel in wavelength. The spatial and spectral resolutions are estimated to be about 3'' and 0.01 nm, respectively (Giono et al. 2016b). Prior to the limb observation, CLASP conducted observations of the quiet Sun near the disk center for about 10 s in order to have data suitable for an in-flight polarization calibration (Giono et al. 2017). The Lyα spectra taken at the Sun center were averaged along the slit, and the pixel of the line center of the spatially averaged Lyα line is set to 121.567 nm. The spectra were found to move by 1 and 0.5 pixels along the dispersion direction in the two channels over the total observing duration of 320 s. However, we did not perform any correction for it since the influence of the gradual wavelength shift on the temporally averaged profiles is negligible.

2.2. Data from SDO

2.3. Overview of Observing Region

Figure 3 demonstrates that the core of the Si iii line shows significant linear polarization signals. The Q/I signals are predominantly negative (i.e., perpendicular to the solar limb) except for the region $-650^{\prime\prime} \lt Y\lt -620^{\prime\prime}$. There is a bright structure around the center of this region (Y ∼ −635''), as shown in the intensity spectra (Figure 3(a)), and the positive Q/I signals are found in the dark regions besides the bright structure. This bright structure is indicated by a blue arrow in Figure 1, and it is sandwiched by a small dark filament. The large intensity gradient in these dark regions would induce the positive Q/I signals (a simple explanation is presented in the last paragraph of Section 4). The U/I signals consist of positive and negative patches along the slit, with no preferred sign.

Zoom In Zoom Out Reset image size

Figure 4 shows the spatial variation of I, Q/I, and U/I in the Si iii line as well as in the Lyα core and wing. Since the Si iii line is weak compared with the Lyα line, we perform binning over 7 pixels along the wavelength direction indicated by a blue horizontal bar in the panels of Figure 3. The linear polarization in the Lyα core is of the order of 0.1%, and the I, Q/I, and U/I signals have also been averaged over the central 7 pixels indicated by the red horizontal bar in Figure 2. The Lyα wing I, Q/I, and U/I signals refer to the mean values of the pixels located at ±0.05 nm from the nominal Lyα center, and these pixels are indicated by green lines in Figure 2. In these pixels, the temporally and spatially averaged Q/I profile shows a maximum amplitude (see the lower middle panel of Figure 2). The uncertainties in Q/I and U/I are evaluated by $\sigma \,=\sqrt{{({\sigma }_{\mathrm{phot}})}^{2}+{({\sigma }_{\mathrm{CCD}})}^{2}}$, where ${\sigma }_{\mathrm{phot}}$ and ${\sigma }_{\mathrm{CCD}}$ are the spurious polarizations caused by the photon noise and by the read-out noise of the CCD cameras. The equations to derive ${\sigma }_{\mathrm{phot}}$ and ${\sigma }_{\mathrm{CCD}}$ are the ones in Appendices A.1 and A.2 of Ishikawa et al. (2014b). We employ an averaged read-out noise of six electrons (Champey et al. 2014, 2015), which correspond to six photons. The averaged uncertainty is 0.066% at the Lyα core, 0.18% at the Lyα wing, and 0.50% at the Si iii line. In the Si iii line, ${\sigma }_{\mathrm{phot}}$ and ${\sigma }_{\mathrm{CCD}}$ are comparable, while ${\sigma }_{\mathrm{phot}}$ is dominant both in the Lyα core and in the Lyα wing.

Zoom In Zoom Out Reset image size

The Si iii line intensity observed by CLASP does not show a clear limb brightening or limb darkening. Its spatial variation along the slit is similar to that of the Lyα core and wing, which suggests that the Si iii line also originates in the upper chromosphere and the transition region. A recent theoretical investigation indicates that, at least for close to the limb lines of sight, the Lyα core and the Si iii line share the same region of formation (del Pino Alemán et al. 2017).

The I, Q/I, and U/I signals of the Si iii line show conspicuous spatial variations, and the typical spatial scale of the peak-to-peak variations is 10''–20''. The Q/I signals are dominated by negative values (i.e., linear polarization perpendicular to the solar limb), and they show a clear center-to-limb (CLV) variation, from −6% at Y ∼ −950'' to ∼0% at Y ∼ −600'', while the U/I signals fluctuate around zero (±2%). The dominance of negative Q/I signals with their clear CLV is also seen in the Lyα wing. The conspicuous spatial variation observed in I, Q/I, and U/I, with spatial scales of 10''–20'', is a common characteristic among the Lyα core, the Lyα wing, and the Si iii line.

When the reference direction for Stokes Q positive is chosen parallel to the nearest limb, the Q/I line-center signal produced by scattering process in a plane-parallel atmosphere without magnetic fields is approximately given by (e.g., Trujillo Bueno et al. 2011)

$$\begin{eqnarray}&&\displaystyle \frac{Q}{I}\approx \displaystyle \frac{1}{\sqrt{2}}{\text{}}{W}_{2}({j}_{l},{j}_{u})(1-{\mu }^{2})\displaystyle \frac{{\bar{J}}_{0}^{2}}{{\bar{J}}_{0}^{0}},\end{eqnarray} \tag{ 1 }$$

$$\begin{eqnarray}&&\displaystyle \frac{U}{I}=0,\end{eqnarray} \tag{ 2 }$$

where ${{\rm{W}}}_{2}({j}_{l},{j}_{u})$ is a coefficient whose value depends on the angular momentum (j) of the lower (l) and upper levels (u) of the line under consideration and $\mu =\cos \theta$, with θ the heliocentric angle (Figure 5). While ${\bar{J}}_{0}^{0}$ is the frequency-integrated mean intensity weighted by the absorption profile, ${\bar{J}}_{0}^{2}$ quantifies whether the illumination of the atomic system is preferentially vertical or horizontal and it represents the axial symmetrical component of the anisotropic radiation field. In Equation (1), the degree of anisotropy, ${\bar{J}}_{0}^{2}/{\bar{J}}_{0}^{0}$, which depends on the thermal and dynamic structure of the solar atmosphere, has to be evaluated where the line-center optical depth is unity along the LOS. Equation (1) indicates that Q/I = 0 at the disk center (μ = 1) and that the Q/I amplitude tends to be larger toward the limb (μ ∼ 0). Hence, the presence of CLV in Q/I is a defining characteristic of scattering polarization, whose amplitude is proportional to the anisotropy of the incident radiation field in the line-formation region.

Zoom In Zoom Out Reset image size

The Si iii line at 120.65 nm results from the transition between the ground level 3s^{2 1}S₀ and the $3s3p{}^{1}{{\rm{P}}}_{1}$ excited level (Table 1). The upper level has three magnetic sublevels with $m=-1,0,+1$ (m being the magnetic quantum number), which can harbor population imbalances and quantum coherence induced by the absorption and scattering of anisotropic radiation. Clearly, the linear polarization observed by CLASP in the Si iii line is scattering line polarization.

Table 1.  List of Spectral Lines Studied in This Paper

Wavelength (nm)	Line	Transition	Landé factor of upper level	Aul (s−1)
121.57	H i	$1s{}^{2}{{\rm{S}}}_{1/2}$ − $2p{}^{2}{{\rm{P}}}_{3/2}$	4/3	$6.27\times {10}^{8}$
120.65	Si iii	3s2 1S0 − $3s3p{}^{1}{{\rm{P}}}_{1}$	1	$2.55\times {10}^{9}$

Note. For each entry, we give the wavelength, the line identification, the line transition, the Landé factor of the upper level, and the Einstein A_ul coefficient in s⁻¹. The Landé factor is calculated using the L–S coupling scheme, while the other parameters are from the NIST database. For the hydrogen Lyα line, we only give the transition that contributes to its scattering polarization.

Download table as:  ASCIITypeset image

For spectral lines like Lyα line and Si iii, only the upper level can be polarized, and the critical field strength for the onset of the Hanle effect, B_H (in Gauss), is given by $1.137\times {10}^{-7}{g}_{u}{A}_{{ul}}$, where g_u is the level's Landé factor and A_ul is the Einstein spontaneous emission coefficient in s⁻¹. Using the parameters listed in Table 1, we have ${B}_{{\rm{H}}}=295$ G for the Si iii line and ${B}_{{\rm{H}}}=53$ G for the hydrogen Lyα line. In the Lyα wing, ${B}_{{\rm{H}}}=\infty$, since it is insensitive to the Hanle effect. The Lyα line starts to approach the Hanle saturation regime (i.e., the Q/I and U/I signals are only sensitive to the magnetic-field direction) above ∼50 G (see Ishikawa et al. 2014a). The simultaneous measurements of the scattering polarization in the Lyα and in the Si iii line with different sensitivities to the Hanle effect, provide more information to constrain the magnetic field with a larger sensitivity range than that only with the Lyα line.

In 1D plane-parallel semi-empirical models of the solar atmosphere, without magnetic fields, and taking the reference direction for positive Stokes Q parallel to the nearest solar limb, the U/I signals are zero (Equation (2)). This is because in such atmospheric models the incident radiation field has axial symmetry around the local vertical. The non-zero U/I signals observed by CLASP in the Lyα wing (Figure 2(c)), where the Hanle effect does not operate, suggest that the wing scattering polarization is caused by the symmetry breaking produced by the horizontal atmospheric inhomogeneities of the solar chromospheric plasma (i.e., that there are significant non-axisymmetric radiation fields). This is also supported by the intensity variations observed by CLASP along the slit, with scales of 10''–20'' similar to the variations seen in Q/I and U/I.

Figure 6 provides a detailed comparison between I, Q/I, and U/I at the Lyα wing. Here we focus on the part of the slit where we have quiet-Sun regions (i.e., Y < −710''). The Y locations where the intensity shows a local maximum (i.e., the core of bright structures) are indicated by yellow vertical lines. We find that, except in the gray-shaded areas, the peak locations coincide with those where U/I changes sign. As discussed below, this correspondence between peak intensity locations and zero-crossing points of U/I can be easily interpreted using a simple scattering polarization model where the anisotropy of the local radiation field plays a dominant role.

Zoom In Zoom Out Reset image size

In a three-dimensional (3D) model of the solar atmosphere, the breaking of the axial symmetry of the radiation field illuminating the atomic system at each point within the medium also contributes to the scattering polarization (Manso Sainz & Trujillo Bueno 2011; Štěpán et al. 2015). As a result, Equations (1) and (2) do not hold, since without a magnetic field the mere presence of horizontal inhomogeneities can create U/I signals and modify the Q/I signals (e.g., at the solar disk center Q/I and U/I are not zero, in general). In particular, for the LOS indicated in Figure 5, U/I scattering polarization signals are produced by the presence of horizontal inhomogeneities, unless they are symmetric with respect to the x–z plane, resulting in non-zero U/I values. Here, we consider an isolated bright structure of circular shape observed at the solar disk center (see Figure 7). At the very center of a bright structure, the intensity gradient in the horizontal direction is zero. In other words, the symmetry axis of the radiation field is aligned with the LOS, and Q = U = 0. However, outside the center of the bright structure, the symmetry axis of the radiation field does not coincide with the μ = 1 LOS and non-zero scattering polarization signals arise. The resulting linear polarization is tangential to circles around the center of the bright structure and the Q and U signs are indicated in the lower panels of Figure 7. A similar illustrative example can be found in the bottom left panel of Figure 1 of Štepán & Trujillo Bueno (2012), which shows the disk center scattering polarization in the Lyα line core produced by relatively bright and dark structures of circular shape computed by means of a three-dimensional (3D), non-LTE multilevel radiative transfer code. When the spectrograph's slit hits a bright structure, as indicated by the gray line of Figure 7, we have ${dI}/{dx}=0$ and U = 0 (i.e., U/I changes sign) at x = 0. Hence, the above-mentioned spatial variation of the U/I signals observed by CLASP in the Lyα wing results from the horizontal inhomogeneity caused by local bright structures. However, we also find exceptions at the gray-shaded areas, where the peak intensity locations do not coincide with zero-crossing points in U/I. In these areas the distance between bright structures is relatively small (≤10''), while outside it the typical distance is ∼20'', as shown in the top panel of Figure 6. In addition, the intensity enhancement of the bright structures located inside the gray-shaded areas is not as large as that outside. We speculate that positive and negative U/I signals over a bright structure are merged with positive and negative U/I signals in the next bright structure when the distance is small and a zero-crossing is not clearly visible.

Zoom In Zoom Out Reset image size

Concerning I and Q/I in the Lyα wing, we note that locations with local maximum in intensity roughly correspond to positions showing local maximum or minimum values in Q/I (see Figure 6). The interpretation of the spatial variation of the Q/I signals with respect to that of I is not so straightforward. As shown in Figure 7, in the idealized case of an isolated bright structure, Q has the largest negative value at x = 0 (where intensity is maximum), resulting in a local minimum. Thus, if the Q/I spatial variation is mainly due to the local symmetry breaking caused by bright structures, Q/I should show a local minimum at every U/I zero-crossing point (i.e., at every peak intensity location). Some cases in Figure 6 correspond to this situation (e.g., Y ∼ −812'' and Y ∼ −730''), but in others the peak intensity locations coincide with the locations where the Q/I has a local maximum (e.g., Y ∼ −800'' and Y ∼ −880''). In some cases, we find that the positions with a peak intensity lie between locations where Q/I has a local maximum or minimum value (e.g., Y ∼ −750'' and Y ∼ −925''). The axisymmetric component of the anisotropy ${\bar{J}}_{0}^{2}/{\bar{J}}_{0}^{0}$, which mainly induces the Q/I scattering polarization, could vary over the bright structure. This variation as well as the horizontal inhomogeneity due to the bright structure would contribute to a spatial variation of Q/I resulting in properties that cannot be explained only by the simple example of Figure 7.

The simple scattering polarization model (Figure 7) can also be applied to understand the positive Q/I in the Si iii line (Section 3). Let us assume that the slit crosses the center of the bright structure (i.e., it is located at $y=0$ in Figure 7). In this case, at the edge of the bright structure (i.e., dark regions) along the slit, Q shows the largest positive signals. When the positive Q signals due to this local effect dominate the negative CLV signals, the net Q signals result in positive values even outside the disk center. As pointed out in Section 3, the positive Q/I signals in the Si iii line are found in the dark regions that surround the bright structure, and this observational signature is consistent with this simple model.

5.1. Strategy

5.2. Comparison of Scattering Polarization

5.2.1. Region A

Figure 8(a) shows our first example; it is a bright structure around Y = −813'', indicated by a pink box in Figure 1. This bright structure is also identified in the intensity spectra of the Lyα and the Si iii lines (Figures 8(c) and (e)). The spatial variation of the intensities in the Lyα core, the Lyα wing, and the Si iii line around the bright region are shown in Figure 8(g), clearly indicating that these three spectral windows represent maximum values at Y = −813'' in the Lyα wing and the Si iii line and at Y = −815'' in the Lyα core.

Zoom In Zoom Out Reset image size

Figure 8(d) shows that a bright structure consists of a pair of negative and positive U/I patches in the Lyα wing. The same panel indicates that the U/I signals in the Lyα core also show the same distribution consisting of negative and positive patches. This behavior is also found in the Si iii line (see Figure 8(f)). These similarities in U/I distributions can be confirmed in Figure 8(h), where the U/I signals at three wavelength windows are plotted. The U/I signals in the Lyα core, in the Si iii line, and in the Lyα wing change sign around Y = −813''. Finally, the SDO/HMI magnetogram (Figure 8(b)) does not show any significant photospheric magnetic field.

We define now the following quantity,

$$\begin{eqnarray}&&{P}_{\lambda }=\left|\left[\displaystyle \sum _{k=1}{\left(\displaystyle \frac{U}{I}\right)}_{\lambda ,k}\right]/\left[\displaystyle \sum _{k=1}\left|{\left(\displaystyle \frac{U}{I}\right)}_{\lambda ,k}\right|\right]\right|,\end{eqnarray} \tag{ 3 }$$

with λ = core, wing, or Si iii. Then, ${(U/I)}_{\mathrm{core}}$, ${(U/I)}_{\mathrm{wing}}$, and ${(U/I)}_{\mathrm{Si}{\rm{III}}}$ represent the U/I signals in the Lyα core (red line in Figure 8(h)), in the Lyα wing (green line in Figure 8(h)), and in the Si iii line (blue line in Figure 8(h)), and k indicates pixels inside the gray area of Figure 8(h). Except for Region C where the outer edge is affected by another bright region, we choose pixels sandwiched by the locations where $| U/I|$ becomes maximum in the Lyα wing. With this definition, ${P}_{\lambda }=0$ when the spatial variation is perfectly antisymmetric and ${P}_{\lambda }$ approaches 1 when it deviates from the antisymmetric shape. Indeed, in this region, ${P}_{\lambda }\sim 0$ for all spectral windows; ${P}_{\mathrm{core}}=0.06$, ${P}_{\mathrm{wing}}=0.16$, and ${P}_{\mathrm{Si}{\rm{III}}}=0.05$.

In addition, we calculate the total unsigned magnetic flux in the photosphere as

$$\begin{eqnarray}&&{{\rm{\Phi }}}_{\mathrm{phot}}=\displaystyle \sum _{l}| {B}_{\mathrm{LOS}}| {\rm{\Delta }}s,\end{eqnarray} \tag{ 4 }$$

where B_LOS is the magnetic flux density observed by HMI, Δ s is the geometrical area corresponding to 1 pixel, and l represents the pixel whose absolute magnetic flux density is larger than 33 Mx cm⁻² inside the purple box of Figure 8(b). The criteria of 33 Mx cm⁻² is five times larger than the noise level, and the noise level is estimated by the standard deviation of the temporally averaged HMI magnetogram signals in the area where there is no conspicuous magnetic field (in a very quiet region). The total unsigned magnetic flux of Region A is $1.4\times {10}^{16}$ Mx. The criteria of 33 Mx cm⁻² is stringent, resulting in smaller total magnetic flux, but we employ this criteria in order to take into account only magnetic concentrations that appear to be connected to the upper atmospheric layers.

5.2.2. Region B

The second example (Region B), indicated by a light blue box in Figure 1, consists of a few faint bright structures, as shown in Figure 9(a). By comparing the AIA 30.4 nm image (Figure 9(a)) with HMI magnetograms (Figure 9(b)), it seems that such bright structures are rooted to three magnetic concentrations with negative polarity enclosed by red contours. To calculate the total unsigned magnetic flux ${{\rm{\Phi }}}_{\mathrm{phot}}$, we consider the purple box region indicated in the figure, which includes such magnetic concentrations. The total magnetic flux is about 100 times larger than that of Region A, with ${{\rm{\Phi }}}_{\mathrm{phot}}=1.3\times {10}^{18}$ Mx.

Zoom In Zoom Out Reset image size

One part of these bright structures is seen in the intensity spectra of the Lyα and the Si iii lines (Figures 9(c) and (e)), and all spectral regions show a clear peak around Y = −797'', as shown in Figure 9(g). This bright region shows negative U/I around Y = −795'' (at the disk center side) and positive U/I around Y = −800'' (at the limb side) in the Lyα wing (Figure 9(d)). However, the U/I signal at the Lyα core is almost zero. In the Si iii U/I spectra, the strong negative signals are seen around Y = −795'', but positive and negative signals are mixed around Y = −800'' (Figure 9(f)).

Figure 9(h) shows their spatial variations more clearly. In the Lyα wing, ${(U/I)}_{\mathrm{wing}}$ changes sign around Y = −797'', with negative signals at the disk center side of the bright structure ($-797^{\prime\prime} \lt Y\lt -793^{\prime\prime}$) and positive ones at the limb side ($-803^{\prime\prime} \lt Y\lt -797^{\prime\prime}$). Similarly, ${(U/I)}_{\mathrm{Si}{\rm{III}}}$ shows negative signals at the disk center side ($-798^{\prime\prime} \lt Y\lt -793^{\prime\prime}$) with a maximum amplitude of 1.5%. However, at the limb side (−802'' < Y − 799''), where positive ${(U/I)}_{\mathrm{wing}}$ signals are observed, the ${(U/I)}_{\mathrm{Si}{\rm{III}}}$ signals are fluctuating at ±0.2%. The behavior of the Lyα core is essentially the same as that of the Si iii line; the ${(U/I)}_{\mathrm{core}}$ signals are negative at the disk center side with a maximum amplitude of 0.1% but are fluctuating around zero at the limb side. In summary, negative U/I signals are present, but positive U/I signals are seriously suppressed both in the Si iii and in the Lyα core. The different behavior of the Lyα core and the Si iii line from that of the Lyα wing are clearly indicated also by the ${P}_{\lambda }$ quantity (Equation (3)), which is ${P}_{\mathrm{core}}=0.68$ and ${P}_{\mathrm{Si}{\rm{III}}}=0.88$, while ${P}_{\mathrm{wing}}=0.25$.

5.2.3. Region C

The third example is Region C, indicated by the orange box of Figure 1, while enlarged images of this region are shown in Figure 10. Here we focus on the bright structure located at Y ∼ −771'' (Figure 10(g)). As seen in Figure 10(d), the U/I signal at the Lyα wing changes sign (positive at the disk center side and negative at the limb side) over the bight structure (see also intensity spectra of Figure 10(c)). On the other hand, the Lyα core does not show such a change of the sign, since it is dominated by positive signals. The U/I signal of the Si iii line changes its sign, as shown in Figure 10(f). These behaviors of the U/I signals can also be seen in Figure 10(h). Both, the U/I signals of the Lyα wing and of the Si iii line change sign around Y = −770'', where their intensities are the largest, while the U/I signal of the Lyα core is dominated by positive values.

Zoom In Zoom Out Reset image size

The gray area to calculate ${P}_{\lambda }$ in Region C has been carefully chosen. Region D, which is next to Region C at the disk center side and is brighter than Region C, shows positive U/I at the limb side and negative U/I at the disk center side (see Figure 6). We deduce that the positive U/I signal of Region C at the disk center side is merged with the positive U/I signals of Region D and that it is impossible to identify the pixel where $| U/I|$ becomes maximum. Hence, we choose the location where the gradient of U/I becomes flat (Y = −767'') as the upper boundary of the gray area. Regarding the lower boundary, we investigate the spatial variation of I and U/I in the Lyα core. Around Y = −779'', only the Lyα core intensity shows a peak (Figure 10(g)). At the same location, U/I in the Lyα core crosses zero (Figure 10(h)). Assuming that the negative U/I signal in the Lyα core at −779'' < Y < −774'' is associated with the intensity peak at Y = −779'', we exclude this area to calculate ${P}_{\lambda }$. ${P}_{\lambda }$ for the Lyα wing and the Si iii line are close to zero (${P}_{\mathrm{wing}}=0.25$ and ${P}_{\mathrm{Si}{\rm{III}}}=0.16$) since they show the antisymmetric patterns, but ${P}_{\mathrm{core}}=0.73$.

In the photosphere, negative and positive magnetic concentrations are identified around [X, Y] = [−2'', −765''] and [X, Y] = [−7'', −773''], respectively. The prominent bright structure is elongated in the $X$ direction as shown in the AIA 30.4 nm image of Figure 10(a), and it appears to be associated with the positive magnetic concentration. However, this bright structure is surrounded by a faint bright region, and we cannot deny that the targeting bright structure is not associated with the negative magnetic concentration. Therefore, to calculate total unsigned flux, we employ the purple box, which accommodates both negative and positive magnetic concentrations, resulting in ${{\rm{\Phi }}}_{\mathrm{phot}}=8\times {10}^{17}$ Mx.

5.2.4. Region D

The fourth example is a bright area that spreads throughout the small area of 40'' × 10'' seen in the AIA 30.4 nm image (Figure 11(a)). This bright region consists of elongated structures along the solar radial direction (i.e., the Y axis in the figures), and appears to be rooted in the positive magnetic concentrations at Y ∼ −748'' observed by the HMI magnetogram (Figure 11(b)). As discussed in Section 2.3, these magnetic concentrations correspond to the enhanced network field (see also Figure 1(d)), and the total unsigned magnetic flux is the largest among the four considered regions, with ${{\rm{\Phi }}}_{\mathrm{phot}}=2.0\times {10}^{18}$ Mx.

Zoom In Zoom Out Reset image size

The central part of this bright region can be seen in the intensity spectra of the Lyα and Si iii lines (Figures 11(c) and (e)); its maximum value is located at Y = −751'' in the Lyα core and wing and at Y = −752'' in the Si iii line (Figure 11(g)). Figure 11(d) clearly shows that the U/I signal in the Lyα wing changes sign over the bright structure, being negative at the disk center side and positive at the limb side. However, in the Lyα core and in the Si iii line, U/I is predominantly negative, as shown in Figures 11(d) and (f) (see also Figure 11(h)). In this example, the antisymmetric spatial distribution of the U/I signal in the Lyα core and in the Si iii line is not present, resulting in ${P}_{\mathrm{Si}{\rm{III}}}=0.69$ and ${P}_{\mathrm{core}}=0.99$, while ${P}_{\mathrm{wing}}=0.25$.

5.3. Summary of Four Examples

Figure 12 shows ${P}_{\lambda }$ versus ${{\rm{\Phi }}}_{\mathrm{phot}}$ for the A, B, C, and D selected regions. The quantity ${P}_{\lambda }$ defined in Equation (3) quantifies how close the spatial distribution of the U/I signals is to the antisymmetric shape, while ${{\rm{\Phi }}}_{\mathrm{phot}}$ defined in Equation (4) is the total unsigned photospheric magnetic flux beneath each region. In these regions, the U/I signals in the Lyα wing clearly change sign over the bright structure, and their spatial distributions are antisymmetric. Thus, the ${P}_{\mathrm{wing}}$ quantity shows values close to zero in all regions (green circles in Figure 12).

Zoom In Zoom Out Reset image size

In Region A, where ${{\rm{\Phi }}}_{\mathrm{phot}}$ has its smallest value, the Lyα core and the Si iii line show antisymmetric distributions similar to those seen in the Lyα wing, and ${P}_{\mathrm{core}}$ and ${P}_{\mathrm{Si}{\rm{III}}}$ are also close to zero. No significant photospheric magnetic field is observed in Region A, which can be categorized as an internetwork region. Region C, which has the second lowest ${{\rm{\Phi }}}_{\mathrm{phot}}$, harbors magnetic concentrations that correspond to the network fields. The U/I signal in the Si iii line maintains the antisymmetric shape (${P}_{\mathrm{Si}{\rm{III}}}\sim 0$), while the Lyα core does not (${P}_{\mathrm{core}}\sim 0.75$). In Region B, which has the second highest photospheric magnetic flux, relatively strong network fields are observed. The antisymmetric shape of the U/I spatial distributions is partially lost in the Lyα core and in the Si iii line, resulting in ${P}_{\mathrm{core}}\sim 0.7$ and ${P}_{\mathrm{Si}{\rm{III}}}\sim 0.9$. In Region D, which shows the highest ${{\rm{\Phi }}}_{\mathrm{phot}}$ and corresponds to an enhance network field region, the spatial distributions of U/I in the Lyα core and in the Si iii line do not show the antisymmetric shape, and they have ${P}_{\mathrm{Si}{\rm{III}}}\sim 0.7$ and ${P}_{\mathrm{core}}\sim 1$.

The spatial variation of U/I in the Lyα core is similar to that in the Lyα wing only in the internetwork region (Region A), while the antisymmetric distributions are not seen in Regions B, C, and D, where network elements are present. The spatial variation of U/I in the Si iii line is similar to that in the Lyα wing in two regions with the smallest total unsigned photospheric magnetic fluxes. The deviation from the antisymmetric distribution is the larger the greater the unsigned photospheric magnetic flux.

6.1. Detection of Scattering Polarization in the Si iii 120.65 nm Line

6.2. Scattering Polarization Caused By the Local Anisotropic Radiation Field

6.3. Indication of the Hanle Effect

The Chromospheric Lyman-Alpha Spectropolarimeter (CLASP) team is an international partnership between NASA Marshall Space Flight Center, National Astronomical Observatory of Japan (NAOJ), Japan Aerospace Exploration Agency (JAXA), Instituto de Astrofísica de Canarias (IAC), and Institut d'Astrophysique Spatiale; additional partners include Astronomical Institute ASCR, Istituto Ricerche Solari Locarno, Lockheed Martin, and University of Oslo. The Japanese participation was funded by the basic research program of ISAS/JAXA, internal research funding of NAOJ, and JSPS KAKENHI (Grant Numbers 23340052, 24740134, 24340040, and 25220703). The US participation was funded by NASA Low Cost Access to Space (Award Number 12-SHP 12/2-0283). The Spanish participation was funded by the Ministry of Economy and Competitiveness through project AYA2010-18029 (Solar Magnetism and Astrophysical Spectropolarimetry). The French hardware participation was funded by Centre National d'Etudes Spatiales (CNES). J.Š. acknowledges the financial support by the Grant Agency of the Czech Republic through grant 16-16861S and project RVO:67985815. J.T.B. acknowledges the supercomputing grants provided by the Barcelona Supercomputing Center.

The half-waveplate optimized for the hydrogen Lyα line (Ishikawa et al. 2013) is located at the upstream of the slit. The waveplate continuously rotates at 4.8 s/rotation with a polarization modulation unit (PMU, Ishikawa et al. 2015), which generates a trigger signal regularly every 0.3 s. Each camera in the spectropolarimeter then takes 16 images with an exposure time of 0.3 s for every rotation synchronously with the waveplate rotation. Examples of observed signals in each camera can be found in Table 2 of Ishikawa et al. (2014b, note that the positive direction for Stokes Q in this table is parallel to the slit).

The first data reduction process includes the dark current subtraction, the gain correction, and the tilt correction of the image (i.e., rotate the image so that the dispersion and the slit are aligned to the pixel). After the alignment between the two channels, the demodulation is performed for each channel using all data, and that the positive Q-direction is defined to be perpendicular to the slit;

$$\begin{eqnarray}{Q}_{1} & = & ({D}_{1,{t}_{1}}-{D}_{1,{t}_{2}}-{D}_{1,{t}_{3}}+{D}_{1,{t}_{4}})\\ & & +({D}_{1,{t}_{5}}-{D}_{1,{t}_{6}}-{D}_{1,{t}_{7}}+{D}_{1,{t}_{8}})\,+\cdots ,\end{eqnarray} \tag{ 5 }$$

$$\begin{eqnarray}{Q}_{2} & = & (-{D}_{2,{t}_{1}}+{D}_{2,{t}_{2}}+{D}_{2,{t}_{3}}-{D}_{2,{t}_{4}})\\ & & +(-{D}_{2,{t}_{5}}+{D}_{2,{t}_{6}}+{D}_{2,{t}_{7}}-{D}_{2,{t}_{8}})\,+\cdots ,\end{eqnarray} \tag{ 6 }$$

$$\begin{eqnarray}{U}_{1} & = & ({D}_{1,{t}_{2}}-{D}_{1,{t}_{3}}-{D}_{1,{t}_{4}}+{D}_{1,{t}_{5}})\\ & & +({D}_{1,{t}_{6}}-{D}_{1,{t}_{7}}-{D}_{1,{t}_{8}}+{D}_{1,{t}_{9}})\,+\cdots ,\end{eqnarray} \tag{ 7 }$$

$$\begin{eqnarray}{U}_{2} & = & (-{D}_{2,{t}_{2}}+{D}_{2,{t}_{3}}+{D}_{2,{t}_{4}}-{D}_{2,{t}_{5}})\\ & & +(-{D}_{2,{t}_{6}}+{D}_{2,{t}_{7}}+{D}_{2,{t}_{8}}-{D}_{2,{t}_{9}})\,+\cdots ,\end{eqnarray} \tag{ 8 }$$

$$\begin{eqnarray}{I}_{i} & = & {D}_{i,{t}_{1}}+{D}_{i,{t}_{2}}+{D}_{i,{t}_{3}}+{D}_{i,{t}_{4}}+{D}_{i,{t}_{5}}\\ & & +{D}_{i,{t}_{6}}+{D}_{i,{t}_{7}}+{D}_{i,{t}_{8}}+\cdots ,\end{eqnarray} \tag{ 9 }$$

where ${D}_{i,{t}_{j}}$ indicates the data at the jth exposure in ith channel, and t₁ corresponds to the exposure over the PMU angle from 0° to 225. Finally, we derive fractional polarizations (Q/I and U/I). For the Lyα line,

$$\begin{eqnarray}&&\displaystyle \frac{Q}{I}=\displaystyle \frac{1}{a}\left(\displaystyle \frac{{Q}_{1}/{K}_{1}+{Q}_{2}/{K}_{2}}{{I}_{1}/{K}_{1}+{I}_{2}/{K}_{2}}\right),\end{eqnarray} \tag{ 10 }$$

$$\begin{eqnarray}&&\displaystyle \frac{U}{I}=\displaystyle \frac{1}{a}\left(\displaystyle \frac{{U}_{1}/{K}_{1}+{U}_{2}/{K}_{2}}{{I}_{1}/{K}_{1}+{I}_{2}/{K}_{2}}\right),\end{eqnarray} \tag{ 11 }$$

where a = 2/π is a modulation coefficient resulting from the continuous rotation of the half-waveplate (i.e., phase retardation is equal to 180°) and K_i is the throughput value of each channel derived by summing all signals around the Lyα from the whole observing duration at the limb. For the Si iii line, by forming the single channel demodulation,

$$\begin{eqnarray}&&\displaystyle \frac{Q}{I}=\displaystyle \frac{1}{a^{\prime} }\left(\displaystyle \frac{{Q}_{2}}{{I}_{2}}\right),\end{eqnarray} \tag{ 12 }$$

$$\begin{eqnarray}&&\displaystyle \frac{U}{I}=\displaystyle \frac{1}{a^{\prime} }\left(\displaystyle \frac{{U}_{2}}{{I}_{2}}\right),\end{eqnarray} \tag{ 13 }$$

where $a^{\prime} =1.45/\pi$ is the modulation coefficient for the Si iii line. The birefringence of MgF₂, which is the material of the waveplate, is known to dramatically change in VUV (Johnson 1964; Chandrasekharan & Damany 1969). Using the wavelength variation of the birefringence (Chandrasekharan & Damany 1969; Laporte et al. 1983) the phase retardation at 120.65 nm is estimated to be 117°. Combining on-the-ground and in-flight polarization calibrations, the instrumental polarization was measured to be negligibly small compared to our requirement (Giono et al. 2016a; Giono et al. 2017). Hence we do not apply additional calibration to the demodulated data.

From the CLASP Slit-Jaw (SJ) image, the angle between the slit and the solar radius (Δα) turns out to be 16. This misalignment results in an azimuth error, i.e., $Q\leftrightarrow U$ crosstalk when we define the demodulated Stokes signals as those in the reference frame that the positive reference direction for Stokes Q is parallel to the solar limb. The crosstalk is ∼sin(2Δα)p, where p is the typical linear polarization degree. This crosstalk is comparable to or smaller than the noise level , as is the case with each of the quantities given in Table 2. Hence, we do not perform any additional calibration for the demodulated polarization signals, and the positive Q-direction is defined as the parallel to the solar limb.

Table 2.  Typical Degree of Linear Polarization (p) and Noise Level (ε) in Each Wavelength Range

Wavelength Range	p
Lyα core	≲0.5%	∼0.07%
Lyα wing	≲5%	∼0.2%
Si iii	≲5%	∼0.5%

Download table as:  ASCIITypeset image