Magnetic field measurements in the upper chromosphere and above, where the gas-to-magnetic pressure ratio $beta$ is lower than unity, are essential for understanding the thermal structure and dynamical activity of the solar atmosphere. Recent develop
ments in the theory and numerical modeling of polarization in spectral lines have suggested that information on the magnetic field of the chromosphere-corona transition region could be obtained by measuring the linear polarization of the solar disk radiation at the core of the hydrogen Lyman-$alpha$ line at 121.6~nm, which is produced by scattering processes and the Hanle effect. The Chromospheric Lyman-$alpha$ Spectropolarimeter (CLASP) sounding rocket experiment aims to measure the intensity (Stokes $I$) and the linear polarization profiles ($Q/I$ and $U/I$) of the hydrogen Lyman-$alpha$ line. In this paper we clarify the information that the Hanle effect can provide by applying a Stokes inversion technique based on a database search. The database contains all theoretical $Q/I$ and $U/I$ profiles calculated in a one-dimensional semi-empirical model of the solar atmosphere for all possible values of the strength, inclination, and azimuth of the magnetic field vector, though this atmospheric region is highly inhomogeneous and dynamic. We focus on understanding the sensitivity of the inversion results to the noise and spectral resolution of the synthetic observations as well as the ambiguities and limitation inherent to the Hanle effect when only the hydrogen Lyman-$alpha$ is used. We conclude that spectropolarimetric observations with CLASP can indeed be a suitable diagnostic tool for probing the magnetism of the transition region, especially when complemented with information on the magnetic field azimuth that can be obtained from other instruments.
We obtained a long exposure vector magnetogram of the quiet Sun photosphere at the disk center with wide FOV of $51 times 82$. The observation was performed at Fe I 525.0 nm with the shutter-less mode of the Narrow Band Filter Imager of the Solar Opt
ical Telescope (SOT) on board Hinode satellite. We summed the linear polarization ($LP$) maps taken with time cadence of 60 seconds for 2 hours to obtain a map with as long an exposure as possible. The polarization sensitivity would be more than 4.6 (21.2 in exposure time) times the standard observation with the SOT spectro-polarimeter. The $LP$ map shows a cellular structure with a typical scale of $5 - 10$. We find that the enhanced $LP$ signals essentially consist of the isolated sporadic transient horizontal magnetic fields (THMFs) with life time of 1-10 min, and are not contributed by long-duration weak horizontal magnetic fields. The cellular structure coincides in position with the negative divergence of the horizontal flow field, i.e., mesogranular boundaries with downflows. Azimuth distribution appears to be random for the scale size of the mesogranules. Some pixels have two separate appearances of THMFs, and the measured time intervals are consistent with the random appearance. THMFs tend to appear at the mesogranular boundaries, but appear randomly in time. We discuss the origin of THMFs based on these observations.
Vertical magnetic fields have been known to exist in the internetwork region for decades, while the properties of horizontal magnetic fields have recently been extensively investigated with textit{Hinode}. Vertical and horizontal magnetic fields in t
he internetwork region are considered to be separate entities and have thus far not been investigated in a unified way. We discover clear positional association between the vertical and horizontal magnetic fields in the internetwork region with textit{Hinode}. Essentially all of the horizontal magnetic patches are associated with the vertical magnetic patches. Alternatively, half of the vertical magnetic patches accommodate the horizontal magnetic patches. These horizontal patches are located around the borders of the vertical patches. The intrinsic magnetic field strength as obtained with the Stokes $V$ line ratio inside the horizontal patches is weak, and is in sub-equipartition field regime ($B<700$ G), while the field strength outside the horizontal patches ranges from weak to strong (kG) fields. Vertical magnetic patches are known to be concentrated on mesogranular and supergranular boundaries, while the horizontal magnetic patches are found only on the mesogranular boundaries. These observations provide us with new information on the origin of the vertical and horizontal internetwork magnetic fields, in a unified way. We conjecture that internetwork magnetic fields are provided by emergence of small-scale flux tubes with bipolar footpoints, and the vertical magnetic fields of the footpoints are intensified to kG fields due to convective collapse. Resultant strong vertical fields are advected by the supergranular flow, and eventually form the network fields.
Properties of transient horizontal magnetic fields (THMFs) in both plage and quiet Sun regions are obtained and compared. Spectro-polarimetric observations with the Solar Optical Telescope (SOT) on the Hinode satellite were carried out with a cadence
of about 30 seconds for both plage and quiet regions located near disk center. We select THMFs that have net linear polarization (LP) higher than 0.22%, and an area larger than or equal to 3 pixels, and compare their occurrence rates and distribution of magnetic field azimuth. We obtain probability density functions (PDFs) of magnetic field strength and inclination for both regions.The occurrence rate in the plage region is the same as for the quiet Sun. The vertical magnetic flux in the plage region is ~8 times larger than in the quiet Sun. There is essentially no preferred orientation for the THMFs in either region. However, THMFs in the plage region with higher LP have a preferred direction consistent with that of the plage-regions large-scale vertical field pattern. PDFs show that there is no difference in the distribution of field strength of horizontal fields between the quiet Sun and the plage regions when we avoid the persistent large vertical flux concentrations for the plage region. The similarity of the PDFs and of the occurrence rates in plage and quiet regions suggests that a local dynamo process due to the granular motion may generate THMFs all over the sun. The preferred orientation for higher LP in the plage indicates that the THMFs are somewhat influenced by the larger-scale magnetic field pattern of the plage.
