Solar Intranetwork Magnetic Elements: Intrinsically Weak or Strong?

The high spatial resolution observation of a quiet region taken with the Solar Optical Telescope/Spectro-Polarimeter aboard the Hinode spacecraft is analyzed. Based on the Milne?CEddington atmospheric model, the vector magnetic field of the quiet region is derived by fitting the full Stokes profiles of the Fe i 630 nm line pair. We extract intranetwork (IN) region from the quiet region and identify 5058 IN magnetic elements, and study their magnetic properties. As a comparison, the magnetic properties of network (NT) region are also analyzed. The main results are as follows. i)?The IN area displays a predominance of weak (hecto-gauss) field concentration, i.e., 99.8?% of IN area shows the weak field. Moreover, the vector magnetic field exhibits concentration toward horizontal direction. However, for the NT region, we discover the coexistence of weak field and strong (kilo-gauss, kG) field. In the IN and NT regions, the filling factor shows almost the same probability distribution function with the peak at about 0.28. ii)?All IN magnetic elements show field strength less than 1?kG. However, some NT elements display the coexistence of weak field and strong field. Regardless of NT or IN elements, about 20?% of elements lies in the Doppler blue-shift region. Our results imply that not all magnetic elements lie in the down-draft sites.     

Magnetic Field Elements at High Latitude: Lifetime and Rotation Rate

Using one-minute cadence time-series full disk magnetograms taken by the SOHO/MDI, we have studied the magnetic field elements at high latitude (poleward of 65° in latitude). It is found that an average lifetime of the magnetic field elements is 16.5 h during solar minimum, much longer than that during solar maximum (7.3 h). During solar minimum, number of the magnetic field elements with the dominant polarity is about 3 times as that of the opposite polarity elements. Their lifetime is 21.0 h on average, longer than that of the opposite polarity elements (2.3 h). It is also found that the lifetime of the magnetic field elements is related with their size, consistent with the magnetic field elements in the quiet sun at low latitude found by Hagenaar et al. (Astrophys. J. 511:932, 1999). During solar maximum, the polar regions are equally occupied by magnetic field elements with both polarities, and their lifetimes are roughly the same on average. No evidence shows there is a correlation between the lifetime and size of the magnetic field elements. Using an image cross-correlation method, we also measure the solar rotation rate at high latitude, up to 85° in latitude. The rate is ω=2.914−0.342sin ² φ−0.482sin ⁴ φ μrad s⁻¹ sidereal. It agrees with previous studies using the spectroscopic and image cross-correlation methods, and also agrees with the results using the element tracking method when the sample of the tracked magnetic field elements is large. The consistency of those results strongly suggests that this rate at high latitude is reliable.     

Solar Cycle Variation of Magnetic Flux Ropes in a Quasi-Static Coronal Evolution Model

The structure of electric current and magnetic helicity in the solar corona is closely linked to solar activity over the 11-year cycle, yet is poorly understood. As an alternative to traditional current-free “potential-field” extrapolations, we investigate a model for the global coronal magnetic field which is non-potential and time-dependent, following the build-up and transport of magnetic helicity due to flux emergence and large-scale photospheric motions. This helicity concentrates into twisted magnetic flux ropes, which may lose equilibrium and be ejected. Here, we consider how the magnetic structure predicted by this model – in particular the flux ropes – varies over the solar activity cycle, based on photospheric input data from six periods of cycle 23. The number of flux ropes doubles from minimum to maximum, following the total length of photospheric polarity inversion lines. However, the number of flux rope ejections increases by a factor of eight, following the emergence rate of active regions. This is broadly consistent with the observed cycle modulation of coronal mass ejections, although the actual rate of ejections in the simulation is about a fifth of the rate of observed events. The model predicts that, even at minimum, differential rotation will produce sheared, non-potential, magnetic structure at all latitudes.     

Cross Helicity and Turbulent Magnetic Diffusivity in the Solar Convection Zone

In a density-stratified turbulent medium, the cross helicity 〈u′⋅B′〉 is considered as a result of the interaction of the velocity fluctuations and a large-scale magnetic field. By means of a quasilinear theory and by numerical simulations, we find the cross helicity and the mean vertical magnetic field to be anti-correlated. In the high-conductivity limit the ratio of the helicity and the mean magnetic field equals the ratio of the magnetic eddy diffusivity and the (known) density scale height. The result can be used to predict that the cross helicity at the solar surface will exceed the value of 1 gauss km s⁻¹. Its sign is anti-correlated to that of the radial mean magnetic field. Alternatively, we can use our result to determine the value of the turbulent magnetic diffusivity from observations of the cross helicity.     

Investigation of the Solar Differential Rotation of Compact Magnetic Elements for 1966 – 1986

The differential rotation of compact magnetic elements during activity cycles 20 and 21 (1966 – 1986) is studied by using solar synoptic charts. For each hemisphere the compact magnetic elements with the polarity of the circumpolar magnetic field have larger rotation rates than the elements with the opposite polarity. This difference in rotation rates is present during the whole cycle except during the polarity reversal of the circumpolar field.     

Microwave and Hard X-Ray Spectral Evolution for the 13 December 2006 Solar Flare

This paper explores the time evolution of microwave and hard X-ray spectral indexes in the solar flare observed by Nobeyama Radio Polarimeters (NoRP) and the Ramaty High Energy Solar Spectroscopy Imager (RHESSI) on 13 December 2006. The microwave spectral index, γ _MW, is derived from the emissions at two frequencies, 17 and 35 GHz, and hard X-ray spectral index, γ _HXR, is derived from RHESSI spectra. Fifteen subpeaks are detected at the microwave and hard X-ray emissions. The microwave spectral indexes tend to be harder than hard X-ray spectral indexes during the flare, which is consistent with previous findings. All detected subpeaks follow the soft-hard-soft spectral behaviours in the hard X-ray rise-peak-decay phases. However, the corresponding microwave subpeaks display different spectral behaviour, such as soft-hard-soft, soft-hard-harder, soft-hard-soft + hard or irregular patterns. These contradictions reveal the complicated acceleration mechanism for low- and high-energy electrons during this event. It is also interesting that the microwave interpeak spectral indexes are much more consistent with one another.     

The Rotation Rates of Solar Magnetic Fields During Solar Cycles 21 – 23

Employing the synoptic maps of the photospheric magnetic fields from the beginning of solar cycle 21 to the end of 23, we first build up a time – longitude stackplot at each latitude between ±35°. On each stackplot there are many tilted magnetic structures clearly reflecting the rotation rates, and we adopt a cross-correlation technique to explore the rotation rates from these tilted structures. Our new method avoids artificially choosing magnetic tracers, and it is convenient for investigating the rotation rates of the positive and negative fields by omitting one kind of field on the stackplots. We have obtained the following results. i) The rotation rates of the positive and negative fields (or the leader and follower polarities, depending on the hemispheres and solar cycles) between latitudes ±35° during solar cycles 21–23 are derived. The reversal times of the leader and follower polarities are usually not consistent with the years of the solar minimum, nevertheless, at latitudes ±16°, the reversal times are almost simultaneous with them. ii) The rotation rates of the three solar cycles averaged over each cycle are calculated separately for the positive, negative and total fields. The latitude profiles of rotation of the positive and negative fields exhibit equatorial symmetries with each other, and those of the total fields lie between them. iii) The differences in rotation rates between the leader and follower polarities are obtained. They are very small near the equator, and increase as latitude increases. In the latitude range of 5° – 20°, these differences reach 0.05 deg day⁻¹, and the mean difference for solar cycle 22 is somewhat smaller than cycles 21 and 23 in these latitude regions. Then, the differences reduce again at latitudes higher than 20°.     

Phase Space Analysis: The Equilibrium of the Solar Magnetic Cycle

We present the results of a statistical study of the solar cycle based on the analysis of the superficial toroidal magnetic field component phase space. The magnetic field component used to create the embedded phase space was constructed from monthly sunspot number observations since 1750. The phase space was split into 32 sections (or time instants) and the average values of the orbits on this phase space were calculated (giving the most probable cycle). In this phase space it is shown that the magnetic field on the Sun’s surface evolves through a set of orbits that go around a mean orbit (i.e., the most probable magnetic cycle that we interpret as the equilibrium solution). It follows that the most probable cycle is well represented by a van der Pol oscillator limit curve (equilibrium solution), as can be derived from mean-field dynamo theory. This analysis also retrieves the empirical Gnevyshev – Ohl’s rule between the first and second parts of the solar magnetic cycle. The sunspot number evolution corresponding to the most probable cycle (in phase space) is presented.     

3D Coronal Structures and Magnetic Field During the Total Solar Eclipse of 29 March 2006

The good quality of the observing sequence of about 60 photographs of the white-light corona taken during the total solar eclipse observations on 29 March 2006, in Al Sallum, Egypt, enable us to use a new method of image processing for enhancement of the fine structure of coronal phenomena. We present selected magnetic-field lines derived for different parameters of the extrapolation model. The coincidence of the observed coronal white-light fine structures and the computed field-line positions provides a 3D causal relationship between coronal structures and the coronal magnetic field.     

Current Helicity and Twist as Two Indicators of the Mirror Asymmetry of Solar Magnetic Fields

A comparison between the two tracers of magnetic field mirror asymmetry in solar active regions – twist and current helicity – is presented. It is shown that for individual active regions these tracers do not possess visible similarity but averaging by time over the solar cycle, or by latitude, reveals similarities in their behavior. The main property of the data set is antisymmetry over the solar equator. Considering the evolution of helical properties over the solar cycle we find signatures of a possible sign change at the beginning of the cycle, though more systematic observational data are required for a definite confirmation. We discuss the role of both tracers in the context of solar dynamo theory.     

Multispacecraft Observations of Magnetic Clouds and Their Solar Origins between 19 and 23 May 2007

We analyze a series of complex interplanetary events and their solar origins that occurred between 19 and 23 May 2007 using observations by the STEREO and Wind satellites. The analyses demonstrate the new opportunities offered by the STEREO multispacecraft configuration for diagnosing the structure of in situ events and relating them to their solar sources. The investigated period was characterized by two high-speed solar wind streams and magnetic clouds observed in the vicinity of the sector boundary. The observing satellites were separated by a longitudinal distance comparable to the typical radial extent of magnetic clouds at 1 AU (fraction of an AU), and, indeed, clear differences were evident in the records from these spacecraft. Two partial-halo coronal mass ejections (CMEs) were launched from the same active region less than a day apart, the first on 19 May and the second on 20 May 2007. The clear signatures of the magnetic cloud associated with the first CME were observed by STEREO B and Wind while only STEREO A recorded clear signatures of the magnetic cloud associated with the latter CME. Both magnetic clouds appeared to have interacted strongly with the ambient solar wind and the data showed evidence that they were a part of the coronal streamer belt. Wind and STEREO B also recorded a shocklike disturbance propagating inside a magnetic cloud that compressed the field and plasma at the cloud’s trailing portion. The results illustrate how distant multisatellite observations can reveal the complex structure of the extension of the coronal streamer into interplanetary space even during the solar activity minimum. Electronic Supplementary Material  The online version of this article () contains supplementary material, which is available to authorized users.     

Combined Analysis of Solar Neutrino and Solar Irradiance Data: Further Evidence for Variability of the Solar Neutrino Flux and Its Implications Concerning the Solar Core

A search for any particular feature in any single solar neutrino dataset is unlikely to establish variability of the solar neutrino flux since the count rates are very low. It helps to combine datasets, and in this article we examine data from both the Homestake and GALLEX experiments. These show evidence of modulation with a frequency of 11.85 year⁻¹, which could be indicative of rotational modulation originating in the solar core. We find that precisely the same frequency is prominent in power spectrum analyses of the ACRIM irradiance data for both the Homestake and GALLEX time intervals. These results suggest that the solar core is inhomogeneous and rotates with a sidereal frequency of 12.85 year⁻¹. From Monte Carlo calculations, it is found that the probability that the neutrino data would by chance match the irradiance data in this way is only 2 parts in 10 000. This rotation rate is significantly lower than that of the inner radiative zone (13.97 year⁻¹) as recently inferred from analysis of Super-Kamiokande data, suggesting that there may be a second, inner tachocline separating the core from the radiative zone. This opens up the possibility that there may be an inner dynamo that could produce a strong internal magnetic field and a second solar cycle.     

Modeling of Local Magnetic Field Enhancements within Solar Flux Ropes

To model and study local magnetic-field enhancements in a solar flux rope we consider the magnetic field in its interior as a superposition of two linear (constant α) force-free magnetic-field distributions, viz. a global one, which is locally similar to a part of the cylinder, and a local torus-shaped magnetic distribution. The newly derived solution for a toroid with an aspect ratio close to unity is applied. The symmetry axis of the toroid and that of the cylinder may or may not coincide. Both the large and small radii of the toroid are set equal to the cylinder’s radius. The total magnetic field distribution yields a flux tube which has a variable diameter with local minima and maxima. In principle, this approach can be used for the interpretation and analysis of solar-limb observations of coronal loops.     

Statistical Comparison of Magnetic Clouds with Interplanetary Coronal Mass Ejections for Solar Cycle 23

We compare the number and characteristics of interplanetary coronal mass ejections (ICMEs) to those of magnetic clouds (MCs) by using in-situ solar wind plasma and magnetic field observations made at 1 AU during solar cycle 23. We found that ≈ 28% of ICMEs appear to contain MCs, since 103 magnetic clouds (MCs) occurred during 1995  – 2006, and 307 ICMEs occurred during 1996 – 2006. For the period between 1996 and 2006, 85 MCs are identified as part of ICMEs, and six MCs are not associated with ICMEs, which conflicts with the idea that MCs are usually a subset of ICMEs. It was also found that solar wind conditions inside MCs and ICMEs are usually similar, but the linear correlation between geomagnetic storm intensity (Dst _min) and relevant solar wind parameters is better for MCs than for ICMEs. The differences between average event duration (Δt) and average proton plasma β (〈β〉) are two of the major differences between MCs and ICMEs: i) the average duration of ICMEs (29.6 h) is 44% longer than for MCs (20.6 hours), and ii) the average of 〈β〉 is 0.01 for MCs and 0.24 for ICMEs. The difference between the definition of a MC and that for an ICME is one of the major reasons for these average characteristics being different (i.e., listed above as items i) and ii)), and it is the reason for the frequency of their occurrences being different.     

On the Origin, 3D Structure and Dynamic Evolution of CMEs Near Solar Minimum

We have conducted a statistical study 27 coronal mass ejections (CMEs) from January 2007 – June 2008, using the stereoscopic views of STEREO SECCHI A and B combined with SOHO LASCO observations. A flux-rope model, in conjunction with 3D triangulations, has been used to reconstruct the 3D structures and determine the actual speeds of CMEs. The origin and the dynamic evolution of the CMEs are investigated using COR1, COR2 and EUVI images. We have identified four types of solar surface activities associated with CMEs: i) total eruptive prominence (totEP), ii) partially eruptive prominence (PEP), iii) X-ray flare, and iv) X-type magnetic structure (X-line). Among the 27 CMEs, 18.5% (5 of 27) are associated with totEPs, 29.6% (8 of 27) are associated with PEPs, 26% (7 of 27) are flare related, and 26% (7 of 27) are associated with X-line structures, and 43% (3 of 7) are associated with both X-line structures and PEPs. Three (11%) could not be associated with any detectable activity. The mean actual speeds for totEP-CMEs, PEP-CMEs, flare-CMEs, and X-line-CMEs are 404 km?s^?1,247 km?s^?1,909 km?s^?1, and 276 km?s^?1, respectively; the average mean values of edge-on and broadside widths for the 27 CMEs are 52 and 85 degrees, respectively. We found that slow CMEs (V≤400 km?s^?1) tend to deflect towards and propagate along the streamer belts due to the deflections by the strong polar magnetic fields of corona holes, while some faster CMEs show opposite deflections away from the streamer belts.     

The Magnetic Field at the Inner Boundary of the Heliosphere Around Solar Minimum

STEREO A and B observations of the radial magnetic field between 1 January 2007 and 31 October 2008 show significant evidence that in the heliosphere, the ambient radial magnetic field component with any dynamic effects removed is uniformly distributed. Based on this monopolar nature of the ambient heliospheric field we find that the surface beyond which the magnetic fields are in the monopolar configuration must be spherical, and this spherical surface can be defined as the inner boundary of the heliosphere that separates the monopole-dominated heliospheric magnetic field from the multipole-dominated coronal magnetic field. By using the radial variation of the coronal helmet streamers belts and the horizontal current – current sheet – source surface model we find that the spherical inner boundary of the heliosphere should be located around 14 solar radii near solar minimum phase.     

Grand Minima of Solar Activity and the Mean-Field Dynamo

We demonstrate that a simple solar dynamo model, in the form of a Parker migratory dynamo with random fluctuations of the dynamo governing parameters and algebraic saturation of dynamo action, can at least qualitatively reproduce all the basic features of solar Grand Minima as they are known from direct and indirect data. In particular, the model successfully reproduces such features as an abrupt transition into a Grand Minimum and the subsequent gradual recovery of solar activity, as well as mixed-parity butterfly diagrams during the epoch of the Grand Minimum. The model predicts that the cycle survives in some form during a Grand Minimum, as well as the relative stability of the cycle inside and outside of a Grand Minimum. The long-term statistics of simulated Grand Minima appears compatible with the phenomenology of the Grand Minima inferred from the cosmogenic isotope data. We demonstrate that such ability to reproduce the Grand Minima phenomenology is not a general feature of the dynamo models but requires some specific assumption, such as random fluctuations in dynamo governing parameters. In general, we conclude that a relatively simple and straightforward model is able to reproduce the Grand Minima phenomenology remarkably well, in principle providing us with a possibility of studying the physical nature of Grand Minima.     

Extraction of Solar Coronal Magnetic Loops with the Directional 2D Morlet Wavelet Transform

We present an automated extraction method based on the continuous wavelet transform (CWT) for analyzing solar magnetic loops. The aim of the work is to extract, from the images taken from solar EUV telescopes, the traces of bright loops presumably shaped by the magnetic field of the solar corona. The technique is that of wavelet analysis, using the two-dimensional Morlet wavelet, because of its efficiency in detecting oriented features, which allows us to follow closely the curvature of the loops. Next, we segment the wavelet modulus image and we threshold it, both globally and locally (i.e., adaptively), in order to eliminate the remaining noise. Altogether, our method performs well, it is robust and fast, and could be used as a standard tool for analyzing large data sets expected from missions like SDO.