DOES THE VARIATION OF THE SOLAR INTRA-NETWORK HORIZONTAL FIELD FOLLOW THE SUNSPOT CYCLE?

As the weakest magnetic field of the Sun, the solar inter-network field consists of vertical and horizontal field components. The inter-network vertical field was found in 1975 (Livingston & Harvey 1975; Smithson 1975), but it was not until the late 1980s that the possible presence of the inter-network horizontal field was suggested by analyzing the visible inter-network longitudinal field from solar disk center to limb (Martin 1988). In fact, the arcsecond scale (typically 1–2 arcseconds or smaller), short-lived (with a lasting lifetime of about 5 minutes) horizontal field was first discovered in 1996 based on the observations from the Advanced Stokes Polarimeter (Lites et al. 1996). With the very sensitivity SOLIS vector spectromagnetograph (Keller et al. 2003), Harvey et al. (2007) deduced the ubiquitous "seething" horizontal field throughout the solar inter-network region. Further evidence of the  inter-network horizontal field is provided by the analysis of the space-borne observations of the Solar Optical Telescope (SOT; Ichimoto et al. 2008; Shimizu et al. 2008; Suematsu et al. 2008; Tsuneta et al. 2008a) on board Hinode (Kosugi et al. 2007). The Spectro-polarimeter (SP) observations have revealed that the inclination angle of the inter-network magnetic field has a peak distribution at 90° (Orozco Suárez et al. 2007; Jin et al. 2012), which corresponds to the horizontal field. The horizontal field primarily concentrates in the patches on the edges of granule (Lites et al. 2008; Jin et al. 2009a), and has a smaller spatial scale than the solar granule (Ishikawa et al. 2008; Jin et al. 2009a).

With the ubiquitous appearance all over the Sun including the polar regions (Tsuneta et al. 2008b; Jin & Wang 2011), the solar inter-network horizontal field contributes 10²⁵ Mx magnetic flux to the solar photosphere per day (Jin et al. 2009b), which is one order of magnitude lower than the contribution from the solar inter-network vertical field ( 10²⁶ Mx; Zhou et al. 2013) but three orders of magnitude higher than that of the ephemeral active region (10²² Mx; Harvey et al. 1975). Moreover, the horizontal field may also contribute to the hidden turbulent flux suggested by studies involving the Hanle depolarization of scattered radiation (Lites et al. 2008). In addition, the magnetic energy provided by the horizontal magnetic field to the quiet Sun is comparable to the total chromospheric energy loss and about 10 times the total energy loss of the corona (Ishikawa & Tsuneta 2009). According to the numerical simulation of quiet magnetism, Rempel (2014) found that 50% of magnetic energy resides on scales smaller than about 0.1 arcsec, which means more magnetic energy is still hidden. Based on the numerical simulations, Steiner et al. (2008) pointed out that the inter-network horizontal field gets pushed to the middle and upper photosphere by overshooting convection, where it forms a layer of horizontal field of enhanced flux density, reaching up into the lower chromosphere. The inter-network horizontal field might play a role in the atmospheric heating.

The identification and critical importance of the inter-network horizontal field have encouraged active studies to understand why so much inter-network horizontal flux is generated and what the ultimate origin of horizontal magnetic field is. The radiative magnetohydrodynamic simulations display that a local dynamo can produce the horizontal field in the quiet Sun (e.g., Schüssler & Vögler 2008). The similar appearance rates of the horizontal field in the quiet region and the plage region discovered by Ishikawa & Tsuneta (2009) suggest that a common local dynamo that is independent of the global dynamo produces the horizontal field. Furthermore, the fraction of selected pixels with polarization signals shows no overall variation by studying the long-term observations (Buehler et al. 2013). However, Stenflo (2012) argued that the global dynamo is still the main source of magnetic flux even in the quiet Sun.

The distinction between the global dynamo, which creates the sunspot cycle, and the local dynamo, which is independent of the sunspot cycle, would provide supporting evidence for the origin of the solar inter-network horizontal field. The long-term SP observations with high spatial resolution and polarization sensitivity provide us with the opportunity to carry out this study. In order to improve the signal-to-noise ratio in the weak field region, we adopt the wavelength-integration method to extract the horizontal magnetic signals observed from 2008 April to 2015 February, roughly from the solar minimum to the maximum of the current cycle.

The next section is devoted to describing the observations and data analysis. In Section 3, we present the result of cyclic invariance of the inter-network horizontal field, and discuss some possible uncertainties of our result.

The SOT/SP measurements provide high spatial resolution and polarization sensitivity observations since 2006 November. These observations were recorded by 112 wavelength points covering the spectral range from 630.08 to 630.32 nm, including the entire information of Stokes parameters (I, Q, U, and V) in two magnetic sensitivity Fe ii lines. However, because of the telemetry problems, dual mode images were unavailable after 2008 January. In order to keep consistency of image quality, the present study utilizes the observations taken after 2008 January because the uniform single mode images have been adopted since then. Avoiding those regions that were close to the solar limb and polar region, a total of 430 SP measurements of quiet Sun are selected in this study, which covers the period from 2008 April to 2015 February. In order to compare the inter-network horizontal fields in different magnetic environments, 146 active regions and 109 plage regions are also selected in the same period. The exposure time of all these magnetograms is 3.2 s.

In order to enhance the sensitivity of weak polarization signals in the presence of measurement noise, the linear polarization signal is extracted based on the method of wavelength integration (Lites et al. 2008). The method avoids the problems of non-convergence and non-uniqueness that arise in the inversions of noisy profiles, and provides the optimal sensitivity to the weak polarization signal.

Just as accounted by Buehler et al. (2013) and Lites et al. (2014), the rms contrast of Stokes I is not constant but shows a fluctuation due to the temperature fluctuation on the spacecraft during long-term observations. In order to examine the instrumental effect, we first show the rms intensity contrast as a function of the mean distance from the solar disk center, which is shown in the left panel of Figure 1. An obvious dropping of the rms intensity contrast is found when the observed regions were far away from the solar disk center. However, within the distance of 0.2 solar radius, the changing of intensity contrast is not obvious. To examine the long-term variation of rms contrast, we selected all quiet magnetograms from the SP measurement within the distance of 0.2 solar radius, and analyzed the rms contrast in the period of investigation. The result is shown in the middle panel of Figure 1. The fluctuation reaches as much as 1.1%, confirming the result of Buehler et al. (2013) and Lites et al. (2014). To reduce the fluctuation, we degrade all observations spatially by a 3 × 3 smoothing average, and the result is shown in the right panel of Figure 1. It can be found that the average fluctuation has a slight decline, falling down to 0.7% after smoothing, while the average rms contrast drops to 5.23 from the original value of 6.99. Furthermore, during the investigation, the rms contrast does not show regular variation but a fluctuation around a constantly horizontal line with time. Therefore, we do not make further instrumental amendments except for the spatial smoothing.

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In this study, not all observations are located on the disk center, so the center-limb effect of magnetic field needs to be considered. The limb-weakening of circular polarization has been identified (e.g., Jin & Wang 2011; Lites et al. 2014). However, there are still few analyses on the center-limb effect of the linear polarization. Here, we adopt two methods to analyze the variation of linear polarization when the observed regions were far away from solar disk center. On the one hand, we assume that there are only two possible cyclic variations of the horizontal field in the quiet Sun: linear correlation (i. e., the positive and negative correlations) with the sunspot cycle and keeping constant in the sunspot cycle. Based on this assumption, we analyze these magnetograms of the quiet Sun observed from 2008 April to 2009 July, an interval of the invariant sunspot number. The result is shown in the top panel of Figure 2. We can find that moving far away from solar disk center, the horizontal field in quiet Sun does not display obvious changes. On the other hand, we avoid the observation from the solar polar region, and study these local observations of the quiet Sun from solar disk center to limb in a few days, i.e., a period from 2008 December 29 to 2009 January 4. These magnetograms locate at almost the same magnetic environment of the Sun's disk, resembling a series of observations from solar center to limb at the same time. The corresponding result is shown in the bottom panel of Figure 2. For the magnetic distribution from the solar disk center to the limb, the variation of horizontal field is still not obvious. Therefore, in this study, the magnitude of the horizontal field is considered to be independent of observational location on the solar disk.

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The pixel area in each magnetogram is corrected by $\mathrm{cos}(\alpha )$, where α is the heliocentric angle. We identify the horizontal magnetic structures by setting the thresholds of 0.2 Mm² on the area (i.e., equivalent to the area of four pixels) and 1.5 times the noise level, where the magnetic noise of the horizontal field is about 50 G. Note that, unlike the vertical field B_v, the horizontal field B_h times the pixel area is not the measurement of magnetic flux since the field is transverse to the line of sight. We first adopt the equivalent spatial scale of the horizontal magnetic structures in the transverse surface, i.e., $d=\sqrt{S/\pi }\times 2$, where S is the area of horizontal magnetic structure in the transverse surface. Then we assume a vertical height of h = 100 km (Lites et al. 1996; Jin et al. 2009b), which is comparable to the photospheric scale height, and compute the area of horizontal magnetic structures by d × h. Finally, we obtain the magnetic flux of these horizontal magnetic structures by considering their average flux density and area. In order to avoid the effect from the solar network field and plage regions as well as active regions, we exclude those horizontal magnetic structures with larger spatial scales and stronger magnetic flux densities by considering a magnetic flux larger than $5.0\times {10}^{17}$ Mx. The identification of the IN region is displayed in Figure 3. The region within the red contours represents the horizontal magnetic structures in the active region, the plage region as well as the network region. The average area ratio of the inter-network region to the entire SP quiet magnetogram reaches 98.0%, and exceeds 42.7% even through in the measurement including the active region.

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In this study, we set a threshold of 1.5 times the noise level on the inter-network horizontal magnetic field to analyze its flux density. On average, 17.7% of pixels in a quiet map carry the significant horizontal magnetic signal, and the average area ratio of significant horizontal magnetic signals also reaches 13.7% in a magnetogram including the active region. These magnetograms are also analyzed by using different thresholds, such as the 2 and 2.5 times of noise level, but the results display no obvious dependence of the threshold choice. Higher thresholds severely reduce the area occupancy of magnetic signals and enhance the magnetic flux density, and result in significantly poorer statistics. Because our results are not affected, the description of employing higher thresholds is not discussed in this study.

We first compute the horizontal magnetic flux density of each quiet magnetogram for the identified solar inter-network region, and obtain the monthly average distribution and the standard deviation of the inter-network horizontal field, which is shown by the black symbol in the top panel of Figure 4. The corresponding monthly average sunspot number in this period is displayed in the bottom panel of Figure 4. The average inter-network horizontal flux density reaches 87 ± 1 G. Comparing the inter-network vertical flux density above 1.5 times the noise level, the obvious imbalance between vertical and horizontal flux densities is confirmed. Furthermore, it can be found that the imbalance is invariable, i.e., a constant of 8.7 ± 0.5, during the ascending phase of solar cycle 24, which is shown in the middle panel of Figure 4. Within the scope of deviation, the distribution of the inter-network horizontal field does not vary from the solar minimum to the current maximum of cycle 24 either. The fact of no cyclic variation of inter-network horizontal field suggests that it is predominantly governed by a process that is independent of the global solar cycle.

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Due to the randomness of SP local observations, it is necessary to examine whether the local information of the horizontal field can represent its full disk information. We choose two target regions: one inter-network region close to an active region and another within a large-scale quiet region. The two target regions may suffer from different influences caused by either strong or weak surrounding flux distributions from flux diffusion or magnetic interaction. Based on this consideration, we also analyze the inter-network horizontal measurements surrounding the active region or the plage region. The result is shown by green symbols in the top panel of Figure 4. It can be found that the IN horizontal field surrounding the active region does not display the cyclic variation either. Comparing the cyclic variations of the inter-network horizontal field in the large-scale quiet region and at the surroundings of active or plage regions, we can find that their variational ranges are almost the same. Just like the cyclic behavior of the longitudinal field (Jin et al. 2011), the diffusion of the active region is likely to have an obvious effect only on the strong network field. The diffusion of the active region seems to be little and even insignificant for the inter-network field.

Our results also indirectly confirm early findings obtained by Ito et al. (2010) and Shiota et al. (2012) who found the invariance of the inter-network magnetic field in the solar polar region by analyzing Hinode/SOT data. Some detailed analyses of the solar inter-network region have strongly suggested the presence of the local dynamo (Lites 2011; Buehler et al. 2013; Lites et al. 2014). Furthermore, the numerical simulation of the local dynamo can reproduce the process of generating the solar inter-network horizontal field (Vögler & Schüssler 2007; Schüssler & Vögler 2008). Such a local dynamo process seems to naturally explain the cyclic invariance of the inter-network horizontal field.

The conclusion still needs to be examined by observations with a large field of view and continuous temporal coverage. In a sense, the partition of network and inter-network regions only by the magnitude of magnetic flux is uncertain. The magnetic flux of network magnetic structures in the rapid evolving phase is sometimes very weak, and the magnetic flux of some inter-network magnetic structures is even larger than that of network magnetic structures (Wang et al. 1995; Zhou et al. 2013). The observations with full-disk coverage and high spatial resolution and polarization sensitivity are still needed to examine our result.

The authors are grateful to the team members who have made great contributions to the Hinode mission. Hinode is a Japanese mission developed and launched by ISAS/JAXA, with NAOJ as domestic partner and NASA and STFC (UK) as international partners. It is operated by these agencies in co-operation with ESA and NSC (Norway). The work is supported by the National Basic Research Program of China (G2011CB811403) and the National Natural Science Foundation of China (11003024, 11373004, 11322329, 11221063, KJCX2-EW-T07, and 11025315).