C. E. Parnell

Statistical Analysis of the Energy Distribution of Nanoflares in the Quiet Sun

For many years it has been debated whether the quiet solar corona is heated by nanoflares and microflares or by magnetic waves. In this paper TRACE data of events with energies in the range 1023-1026 ergs are investigated. A new stable and objective statistical technique is proposed to determine the index, -γ, of a power-law relation between the frequency of the events and their energy. We find that γ is highly dependent on the form of the line-of-sight depth assumed to determine the event energies. If a constant line-of-sight depth is assumed, then γ lies between 2.4 and 2.6; however, if a line-of-sight depth of the form (Ae/k2)1/2 is assumed, where Ae is event area and k is a constant, then γ lies between 2.0 and 2.1. In all cases the value of γ is greater than 2 and therefore implies that the events with the lowest energies dominate the heating of the quiet solar corona. Moreover, there are strong indications that there is insufficient energy from events with nanoflare energies (i.e., energies in the range 1024-1027 ergs) to explain the total energy losses in the quiet corona. However, our results do not rule out the possibility that events with picoflare energies (i.e., energies in the range 1021-1024 ergs) heat the quiet corona. From analysis of the spatial distribution of the events, we find that events are mainly confined to regions with the brightest EUV emission, which are presumably the regions connected to the strongest magnetic fields. Indeed, just 16% of the quiet corona possesses such events.

The structure of three‐dimensional magnetic neutral points

The local configurations of three‐dimensional magnetic neutral points are investigated by a linear analysis about the null. It is found that the number of free parameters determining the arrangement of field lines is four. The configurations are first classified as either potential or non‐potential. Then the non‐potential cases are subdivided into three cases depending on whether the component of current parallel to the spine is less than, equal to or greater than a threshold current; therefore there are three types of linear non‐potential null configurations (a radial null, a critical spiral and a spiral). The effect of the four free parameters on the system is examined and it is found that only one parameter categorizes the potential configurations, whilst two parameters are required if current is parallel to the spine. However, all four parameters are needed if there is current both parallel and perpendicular to the spine axis. The magnitude of the current parallel to the spine determines whether the n...

NANOFLARE STATISTICS FROM FIRST PRINCIPLES: FRACTAL GEOMETRY AND TEMPERATURE SYNTHESIS

We derive universal scaling laws for the physical parameters of flarelike processes in a low-� plasma, quan- tified in terms of spatial length scales l, area A, volume V, electron density ne, electron temperature Te, total emission measure M, and thermal energy E. The relations are specified as functions of two independent input parameters, the power index a of the length distribution, Nðl Þ/ la , and the fractal Haussdorff dimension D between length scales l and flare areas, Aðl Þ/ l D. For values that are consistent with the data, i.e., a ¼ 2:5 � 0:2 and D ¼ 1:5 � 0:2, and assuming the RTV scaling law, we predict an energy distribution NðE Þ/ E � � with a power-law coefficient of � ¼ 1:54 � 0:11. As an observational test, we perform statistics of nanoflares in a quiet-Sun region covering a comprehensive temperature range of Te � 1 4M K. We detected nanoflare events in extreme-ultraviolet (EUV) with the 171 and 195 Afilters from the Transition Region and Coronal Explorer (TRACE), as well as in soft X-rays with the AlMg filter from the Yohkoh soft X-ray telescope (SXT), in a cospatial field of view and cotemporal time interval. The obtained frequency dis- tributions of thermal energies of nanoflares detected in each wave band separately were found to have power- law slopes of � � 1:86 � 0:07 at 171 A ˚ (Te � 0:7 1:1 MK), � � 1:81 � 0:10 at 195 A ˚ (Te � 1:0 1:5 MK), and � � 1:57 � 0:15 in the AlMg filter (Te � 1:8 4:0 MK), consistent with earlier studies in each wavelength. We synthesize the temperature-biased frequency distributions from each wavelength and find a corrected power- law slope of � � 1:54 � 0:03, consistent with our theoretical prediction derived from first principles. This analysis, supported by numerical simulations, clearly demonstrates that previously determined distributions of nanoflares detected in EUV bands produced a too steep power-law distribution of energies with slopes of � � 2:0 2:3 mainly because of this temperature bias. The temperature-synthesized distributions of thermal nanoflare energies are also found to be more consistent with distributions of nonthermal flare energies deter- mined in hard X-rays (� � 1:4 1:6) and with theoretical avalanche models (� � 1:4 1:5). Subject headings: Sun: corona — Sun: flares — Sun: UV radiation — Sun: X-rays, gamma rays

A POWER-LAW DISTRIBUTION OF SOLAR MAGNETIC FIELDS OVER MORE THAN FIVE DECADES IN FLUX

Solar flares, coronal mass ejections, and indeed phenomena on all scales observed on the Sun, are inextricably linked with the Sun’s magnetic field. The solar surface is covered with magnetic features observed on many spatial scales, which evolve on differing timescales: the largest features, sunspots, follow an 11-year cycle; the smallest seem to follow no cycle. Here, we analyze magnetograms from Solar and Heliospheric Observatory (SOHO)/Michelson Doppler Imager (full disk and high resolution) and Hinode/Solar Optical Telescope to determine the fluxes of all currently observable surface magnetic features. We show that by using a “clumping” algorithm, which counts a single “flux massif” as one feature, all feature fluxes, regardless of flux strength, follow the same distribution—a power law with slope −1.85 ± 0.14—between 2 × 10 17 and 10 23 Mx. A power law suggests that the mechanisms creating surface magnetic features are scale-free. This implies that either all surface magnetic features are generated by the same mechanism, or that they are dominated by surface processes (such as fragmentation, coalescence, and cancellation) in a way which leads to a scale-free distribution.

A contemporary view of coronal heating

Determining the heating mechanism (or mechanisms) that causes the outer atmosphere of the Sun, and many other stars, to reach temperatures orders of magnitude higher than their surface temperatures has long been a key problem. For decades, the problem has been known as the coronal heating problem, but it is now clear that ‘coronal heating’ cannot be treated or explained in isolation and that the heating of the whole solar atmosphere must be studied as a highly coupled system. The magnetic field of the star is known to play a key role, but, despite significant advancements in solar telescopes, computing power and much greater understanding of theoretical mechanisms, the question of which mechanism or mechanisms are the dominant supplier of energy to the chromosphere and corona is still open. Following substantial recent progress, we consider the most likely contenders and discuss the key factors that have made, and still make, determining the actual (coronal) heating mechanism (or mechanisms) so difficult.

Solar Magnetic Tracking. I. Software Comparison and Recommended Practices

Feature tracking and recognition are increasingly common tools for data analysis, but are typically implemented on an ad hoc basis by individual research groups, limiting the usefulness of derived results when selection effects and algorithmic differences are not controlled. Specific results that are affected include the solar magnetic turnover time, the distributions of sizes, strengths, and lifetimes of magnetic features, and the physics of both small scale flux emergence and the small-scale dynamo. In this paper, we present the results of a detailed comparison between four tracking codes applied to a single set of data from SOHO/MDI, describe the interplay between desired tracking behavior and parameterization tracking algorithms, and make recommendations for feature selection and tracking practice in future work.

The three-dimensional structures of X-ray bright points

Recently, the Converging Flux Model has been proposed for X-ray bright points and cancelling magnetic features. The aim of this peice of work is to try and model theoretically specific X-ray bright points in the framework of the Converging Flux Model. The observational data used includes a magnetogram showing the normal component of the magnetic field at the photosphere and a high-resolution soft X-ray image from NIXT showing the brightenings in the lower solar corona. By approximating the flux concentrations in the magnetograms with poles of the appropriate sign and sense, the overlying three-dimensional potential field structure is calculated. Deduction of plausible motions of the flux sources are made which produce brightenings of the observed shape due to reconnection between neighbouring flux regions. Also the three-dimensional separarix and separator structure and the way the magnetic field lines reconnect in three dimensions is deduced.

A trilinear method for finding null points in a three-dimensional vector space

Null points are important locations in vector fields, such as a magnetic field. A new technique (a trilinear method for finding null points) is presented for finding null points over a large grid of points, such as those derived from a numerical experiment. The method was designed so that the null points found would agree with any field lines traced using the commonly used trilinear interpolation. It is split into three parts: reduction, analysis, and positioning, which, when combined, provide an efficient means of locating null points to a user-defined subgrid accuracy. We compare the results of the trilinear method with that of a method based on the Poincare index, and discuss the accuracy and limitations of both methods.

Recursive Reconnection and Magnetic Skeletons

By considering a simple driven model involving the resistive 3D MHD interaction of magnetic sources, it is shown that it is essential to know the magnetic skeleton to determine (1) the locations of reconnection, (2) type of reconnection, (3) the rate of reconnection, and (4) how much reconnection is occurring. In the model, two opposite-polarity magnetic fragments interact in an overlying magnetic field with reconnection, first closing and then opening the magnetic field from the sources. There are two main reconnection phases: the first has one reconnection site at which the flux is closed, and the second has three sites. The latter is a hybrid case involving both closing and reopening reconnection processes. Each reconnection site coincides with its own separator, and hence all reconnection is via separator reconnection. All the separators connect the same two nulls and thus mark the intersection between the same four types of flux domain. In the hybrid state, the two competing reconnection processes (which open and close flux connecting the same two source pairs) run simultaneously, leading to recursive reconnection. That is, the same flux may be closed and then reopened not just once, but many times. This leads to two interesting consequences: (1) the global reconnection rate is enhanced and (2) heating occurs for a longer period and over a wider area than in the single-separator case.

A new view of quiet-Sun topology from Hinode/SOT

Context. With the recent launch of the Hinode satellite our view of the nature and evolution of quiet-Sun regions has been improved. In light of the new high resolution observations, we revisit the study of the quiet Sun’s topological nature. Aims. Topology is a tool to explain the complexity of the magnetic field, the occurrence of reconnection processes, and the heating of the corona. This Letter aims to give new insights to these different topics. Methods. Using a high-resolution Hinode/SOT observation of the line-of-sight magnetic field on the photosphere, we calculate the three dimensional magnetic field in the region above assuming a potential field. From the 3D field, we determine the existence of null points in the magnetic configuration. Results. From this model of a continuous field, we find that the distribution of null points with height is significantly different from that reported in previous studies. In particular, the null points are mainly located above the bottom boundary layer in the photosphere (54%) and in the chromosphere (44%) with only a few null points in the corona (2%). The density of null points (expressed as the ratio of the number of null points to the number of photospheric magnetic fragments) in the solar atmosphere is estimated to be between 3% and 8% depending on the method used to identify the number of magnetic fragments in the observed photosphere. Conclusions. This study reveals that the heating of the corona by magnetic reconnection at coronal null points is unlikely. Our findings do not rule out the heating of the corona at other topological features. We also report the topological complexity of the chromosphere as strongly suggested by recent observations from Hinode/SOT.