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Register a new userThe Solar Cycle Variation of Topological Structures in the Global Solar Corona
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The distribution of magnetic flux across the solar photosphere results in a complex web of coronal magnetic field structures. To understand this complexity, the magnetic skeleton of the coronal field can be calculated. The skeleton highlights the separatrix surfaces that divide the field into topologically distinct regions, allowing open-field regions on the solar surface to be located. Furthermore, separatrix surfaces and their intersections (separators) are important likely energy release sites. This paper investigates, throughout the solar cycle, the nature of coronal magnetic-field topologies that arise under the potential-field source-surface approximation. In particular, we characterise the typical global fields at solar maximum and minimum. Global magnetic fields are extrapolated from observed Kitt Peak and SOLIS synoptic magnetograms, from Carrington rotations 1645 to 2144, using the potential-field source-surface model. Hence, variations in the coronal skeleton are studied over three solar cycles. Key building blocks which make up magnetic fields are identified and classified according to the nature of their separatrix surfaces. The magnetic skeleton reveals that, at solar maximum, the global coronal field involves a multitude of topological structures at all latitudes. Many open-field regions exist originating anywhere on the photosphere. At solar minimum, the coronal topology is heavily influenced by the solar dipole. A strong dipole results in a simple large-scale structure involving just two large polar open-field regions, but, at short radial distances between plus or minus 60 deg latitude, the small-scale topology is complex. If the solar dipole if weak, as in the recent minimum, then the low-latitude quiet-sun magnetic fields may be globally significant enough to create many disconnected open-field regions at low latitudes, in addition to the two polar open-field regions.
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Solar-cycle related variation of differential rotation is investigated through analyzing the rotation rates of magnetic fields, distributed along latitudes and varying with time at the time interval of August 1976 to April 2008. More pronounced differentiation of rotation rates is found to appear at the ascending part of a Schwabe cycle than at the descending part on an average. The coefficient $B$ in the standard form of differential rotation, which represents the latitudinal gradient of rotation, may be divided into three parts within a Schwabe cycle. Part one spans from the start to the $4^{th}$ year of a Schwabe cycle, within which the absolute $B$ is approximately a constant or slightly fluctuates. Part two spans from the $4^{th}$ to the $7^{th}$ year, within which the absolute $B$ decreases. Part three spans from the $7^{th}$ year to the end, within which the absolute $B$ increases. Strong magnetic fields repress differentiation of rotation rates, so that rotation rates show less pronounced differentiation, but weak magnetic fields seem to just reflect differentiation of rotation rates. The solar-cycle related variation of solar differential rotation is inferred to the result of both the latitudinal migration of the surface torsional pattern and the repression of strong magnetic activity to differentiation of rotation rates.
We present observations of the extended solar cycle activity in white-light coronagraphs, and compare them with the more familiar features seen in the Fe XIV green-line corona. We show that the coronal activity zones seen in the emission corona can be tracked high into the corona. The peak latitude of the activity, which occurs near solar maximum, is found to be very similar at all heights. But we find that the equatorward drift of the activity zones is faster at greater heights, and that during the declining phase of the solar cycle, the lower branch of activity (that associated with the current cycle) disappears at about 3 Ro. This implies that that during the declining phase of the cycle, the solar wind detected near Earth is likely to be dominated by the next cycle. The so-called rush to the poles is also seen in the higher corona. In the higher corona it is found to start at a similar time but at lower latitudes than in the green-line corona. The structure is found to be similar to that of the equatorward drift.
By defining an appropriate field line helicity, we apply the powerful concept of magnetic helicity to the problem of global magnetic field evolution in the Suns corona. As an ideal-magnetohydrodynamic invariant, the field line helicity is a meaningful measure of how magnetic helicity is distributed within the coronal volume. It may be interpreted, for each magnetic field line, as a magnetic flux linking with that field line. Using magneto-frictional simulations, we investigate how field line helicity evolves in the non-potential corona as a result of shearing by large-scale motions on the solar surface. On open magnetic field lines, the helicity injected by the Sun is largely output to the solar wind, provided that the coronal relaxation is sufficiently fast. But on closed magnetic field lines, helicity is able to build up. We find that the field line helicity is non-uniformly distributed, and is highly concentrated in twisted magnetic flux ropes. Eruption of these flux ropes is shown to lead to sudden bursts of helicity output, in contrast to the steady flux along the open magnetic field lines.
Understanding many physical processes in the solar atmosphere requires determination of the magnetic field in each atmospheric layer. However, direct measurements of the magnetic field in the Suns corona are difficult to obtain. Using observations with the Coronal Multi-channel Polarimeter, we have determined the spatial distribution of the plasma density in the corona, and the phase speed of the prevailing transverse magnetohydrodynamic waves within the plasma. We combine these measurements to map the plane-of-sky component of the global coronal magnetic field. The derived field strengths in the corona from 1.05 to 1.35 solar radii are mostly 1-4 Gauss. These results demonstrate the capability of imaging spectroscopy in coronal magnetic field diagnostics.
The latitudinal distributions of the yearly mean rotation rates measured respectively by Suzuki in 1998 and 2012 and Pulkkinen $&$ Tuominen in 1998 are utilized to investigate internal-cycle variation of solar differential rotation. The rotation rate at the solar Equator seems to decrease since cycle 10 onwards. The coefficient $B$ of solar differential rotation, which represents the latitudinal gradient of rotation, is found smaller in the several years after the minimum of a solar cycle than in the several years after the maximum time of the cycle, and it peaks several years after the maximum time of the solar cycle. The internal-cycle variation of the solar rotation rates looks similar in profile to that of the coefficient $B$. A new explanation is proposed to address such a solar-cycle related variation of the solar rotation rates. Weak magnetic fields may more effectively reflect differentiation at low latitudes with high rotation rates than at high latitudes with low rotation rates, and strong magnetic fields may more effectively repress differentiation at relatively low latitudes than at high latitudes. The internal-cycle variation is inferred to the result of both the latitudinal migration of the surface torsional pattern and the repression of strong magnetic activity to differentiation.
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