The Parker Problem Revisited: Response to the Interpretation of Low (2010)

This paper responds to points made by Low (Solar Phys. 2010. doi:) with regard to the Parker problem as formulated in Craig and Sneyd (Solar Phys. 232, 41, 2005). We first point out that, since Low focuses mainly on interpreting approximate linearized solutions to the Parker problem, his approach cannot address key issues relating to the finite amplitude stability and dynamic accessibility of potential equilibria. Further difficulties are shown to surround Low’s assertion that non-linear equilibria derived by magneto-frictional relaxation of the Parker problem should be discounted. We conclude that both linear and non-linear approaches to the Parker problem appear remarkably consistent: they demonstrate the development of smooth 3D equilibria as opposed to the routine collapse to singular current sheets.     

Re-Evaluation of the Flare–Type II–CME Association

We have re-evaluated the association of type II solar radio bursts with flares and/or coronal mass ejections (CMEs) using the year 2000 solar maximum data. For this, we consider 52 type II events whose associations with flares or CMEs were absent or not clearly identified and reported. These events are classified as follows; group I: 11 type IIs for which there are no reports of GOES X-ray flares and CMEs; group II: 12 type IIs for which there are no reports of GOES X-ray flares; and group III: 29 type IIs for which the flare locations are not reported. By carefully re-examining their association from GOES X-ray and H, Yohkoh SXT and EIT-EUV data, we attempt to answer the following questions: (i) if there really were no X-ray flares associated with the above 23 type IIs of groups I and II; (ii) whether they can be regarded as backside events whose X-ray emission might have been occulted. From this analysis, we have found that two factors, flare background intensity and flare location, play important roles in the complete reports about flare–type II–CME associations. In the above 23 cases, for more than 50% of the cases in total, the X-ray flares were not noticed and reported, because the background intensity of X-ray flux was high. In the remaining cases, the X-ray intensity might be greatly reduced due to occultation. From the H flare data, Yohkoh SXT data and EIT-EUV data, we found that ten cases out of 23 might be frontside events, and the remaining are backside events. While the flare–type II association is found to be nearly 90%, the type II–CME association is roughly around 75%. This analysis might be useful to reduce some ambiguities regarding the association among type IIs, flares and CMEs.     

The Wave–Driver System of the Off-Disk Coronal Wave of 17 January 2010

We study the 17 January 2010 flare–CME–wave event by using STEREO/SECCHI-EUVI and -COR1 data. The observational study is combined with an analytic model that simulates the evolution of the coronal wave phenomenon associated with the event. From EUV observations, the wave signature appears to be dome shaped having a component propagating on the solar surface ( $\overline{v}\approx280~\mathrm{km}\,\mathrm{s}^{-1}$ ) as well as one off-disk ( $\overline{v}\approx 600~\mathrm{km}\,\mathrm{s}^{-1}$ ) away from the Sun. The off-disk dome of the wave consists of two enhancements in intensity, which conjointly develop and can be followed up to white-light coronagraph images. Applying an analytic model, we derive that these intensity variations belong to a wave–driver system with a weakly shocked wave, initially driven by expanding loops, which are indicative of the early evolution phase of the accompanying CME. We obtain the shock standoff distance between wave and driver from observations as well as from model results. The shock standoff distance close to the Sun (<?0.3 R _⊙ above the solar surface) is found to rapidly increase with values of ≈?0.03?–?0.09 R _⊙, which gives evidence of an initial lateral (over)expansion of the CME. The kinematical evolution of the on-disk wave could be modeled using input parameters that require a more impulsive driver (duration t=90 s, acceleration a=1.7 km?s^?2) compared to the off-disk component (duration t=340 s, acceleration a=1.5 km?s^?2).     

Source Region of the Decameter–Hectometric Type II Radio Burst: Shock–Streamer Interaction Region

D–H type II radio bursts are widely thought to be caused by coronal mass ejections (CMEs). However, it is still unclear where the exact source of the type IIs on the shock surface is. We identify the source regions of the decameter–hectometric (D–H) type IIs based on imaging observations from SOHO/LASCO and the radio dynamic spectrum from Wind/Waves. The analysis of two well-observed events suggests that the sources of these two events are located in the interaction regions between shocks and streamers, and that the shocks are enhanced significantly in these regions.     

The solar coronal mass ejection of 20–21 November, 1973

The coronal transient event of 20–21 November is unusual in that its appearance is distinctly non-loop-like; rather, the transient resembles a confined ray or fan-like volume. Studies of the distribution of the coronal material with time indicate that this is a mass ejection event, involving about 1 × 10¹⁵ g of material from the lower corona. Analysis of the polarization signal of the event suggests that the event is associated with chromospheric activity in a region near longitude E68. The observed properties (distributions in brightness and polarization) of the transient are compared with the properties of a well-studied event of typical loop-like appearance, but rotated to simulate an edge-on appearance; the differences suggest that the 20–21 November event is not such an edge-on, loop-like transient, but rather is most simply described as an axisymmetric-cylindrical or conical volume, the boundaries of which remain constant over the events' lifetime. On this basis, the variation of the transient spatial density with height and the variation of density with time can be specified rather more certainly than for previously-studied coronal mass ejection events. Densities are found to range from 3 × 10^–16 g cm^–3 at 2.1 R heliocentric height early in the event to 1 × 10^–18 g cm^–3 at 4.0 R late in the event. Typical temporal variations of the ejected material (at a given heliocentric height) are found to be on the order of 10^–18 g cm^–3 s^–1. The mass and momentum balance in the event have been estimated from the observed parameters, employing a multiparameter approach. We find that a model with modest mass flux typified by material speed u ₀ 50 km s^–1 and a near balance between the event's pressure gradient force and gravity — with possibly a small hydromagnetic wave contribution to the total pressure — is consistent with the observations. The kinetic energy of the event, determined from the motion of the center of mass of the ejected material, is only about 10²⁶ ergs, and thus is the smallest for any solar mass ejection studied to date.The National Center for Atmospheric Research is sponsored by the National Science Foundation.     

Topology of Magnetic Field and Coronal Heating in Solar Active Regions – II. The Role of Quasi-Separatrix Layers

The photospheric vector magnetic fields, H and soft X-ray images of AR 7321 were simultaneously observed with the Solar Flare Telescope at Mitaka and the Soft X-ray Telescope of Yohkoh on October 26, 1992, when there was no important activity in this region. Taking the observed photospheric vector magnetic fields as the boundary condition, 3D magnetic fields above the photosphere were computed with a new numerical technique. Then quasi-separatrix layers (QSLs), i.e., regions where 3D magnetic reconnection takes place, were determined in the computed 3D magnetic fields. Since Yohkoh data and Mitaka data were obtained in well-arranged time sequences during the day, the evolution of 3D fields, H features and soft X-ray features in this region can be studied in detail. Through a comparison among the 3D magnetic fields, H features and soft X-ray features, the following results have been obtained: (a) H plages are associated with the portions of QSLs in the chromosphere; (b) diffuse coronal features (DCFs) and bright coronal features (BCFs) are morphologically confined by the coronal linkage of the field lines related to the QSLs; (c) BCFs are associated with a part of the magnetic field lines related to the QSLs. These results suggest that as the likely places where energy release may occur by 3D magnetic reconnection, QSLs play an important role in the chromospheric and coronal heating in this active region.     

The Effect of Flows on Transverse Oscillations of Coronal Loops

In this paper we study kink oscillations of coronal loops in the presence of flows. Using the thin-tube approximation we derive the general governing equation for kink oscillations of a loop with the density varying along the loop in the presence of flows. This equation remains valid even when the density and flow are time dependent. The derived equation is then used to study the effect of flows on eigenfrequencies of kink oscillations of coronal loops. The implication of the obtained results on coronal seismology is discussed.     

Timing irregularities of PSR J1705–1906

Timing analysis of PSR J1705–1906 using data from Nanshan 25-m and Parkes 64-m radio telescopes, which span over fourteen years, shows that the pulsar exhibits significant proper motion, and rotation instability. We updated the astrometry parameters and the spin parameters of the pulsar. In order to minimize the effect of timing irregularities on measuring its position, we employ the Cholesky method to analyse the timing noise. We obtain the proper motion of \(-77(3)\) mas?yr^?1 in right ascension and \(-38(29)\) mas?yr^?1 in declination. The power spectrum of timing noise is analyzed for the first time, which gives the spectral exponent \(\alpha =-5.2\) for the power-law model indicating that the fluctuations in spin frequency and spin-down rate dominate the red noise. We detect two small glitches from this pulsar with fractional jump in spin frequency of \(\Delta \nu /\nu \sim 2.9 \times 10^{-10}\) around MJD 55199 and \(\Delta \nu /\nu \sim 2.7\times 10^{-10}\) around MJD 55953. Investigations of pulse profile at different time segments suggest no significant changes in the pulse profiles around the two glitches.     

Studying the Equilibrium Points of the Modified Circular Restricted Three-body Problem: The Case of Sun–Haumea System

We intend to study a modified version of the planar Circular Restricted Three-Body Problem(CRTBP) by incorporating several perturbing parameters. We consider the bigger primary as an oblate spheroid and emitting radiation while the small primary has an elongated body. We also consider the perturbation from a disk-like structure encompassing this three-body system. First, we develop a mathematical model of this modified CRTBP.We have found there exist five equilibrium points in this modified CRTB...     

The Family P12 of the Three-body Problem – The Simplest Family of Periodic Orbits, with Twelve Symmetries Per Period

A beautiful plane eight-shaped orbit has been found by Alain Chenciner, Richard Montgomery and Carles Simo through the minimisation of the action between suitable limit conditions. The three masses are equal and chase each other along the eight shape. This procedure can be generalized and leads to a family of three-dimensional periodic orbits with three equal masses and with 12 space-time symmetries per period. The property of a unique orbit for the three masses is conserved in a suitable uniformly rotating set of axes. The eight-shaped orbit represents the end of the family, its beginning being the classical Lagrangian solution with three equal masses and with a uniformly rotating equilateral triangle.     

Coronal Faraday rotation of the Crab Nebula, 1971–1975

We observed Faraday rotation of linearly polarized radio waves from the Crab Nebula (Tau A) at 4170 MHz during solar coronal occultations in June 1971–75. Mean amplitudes of the variations of position angle are larger in an active phase of the solar cycle than in a quiet phase. In occultations in 1971 and 1973, the position angle of the polarization varied oscillatory by 20–50 degrees due to local magnetic structures in the corona with a typical scale-length of about 0.5 R . In 1974, we observed a typical variation of position angle of polarization which is expected from a Y-shaped field configuration in coronal streamers.The Faraday rotation is enhanced when the line of sight to Tau A passes through strong coronal magnetic fields computed from magnetograph observations, while the rotation is suppressed when the line of sight passes through large coronal holes observed in X-rays. Short-time oscillation of the rotation angle observed in 1971 and 1973 suggests that neutral sheets in coronal streamers oscillate at a period of 3 hours with an amplitude of 1 R at a distance of 10 R from the Sun.     

The Craig – Sneyd Analytic Solutions to the Parker Problem

This paper follows up on the conclusion by Craig and Sneyd (2005) that the solutions to a linearized magnetostatic problem are counterexamples to the magnetostatic model of Parker (1972), demonstrating a general absence of continuous equilibrium for a magnetic field with an arbitrarily prescribed topology. The analysis presented here shows that Craig and Sneyd had incorrectly rejected an important subset of those solutions in a misunderstanding of the Parker model. The complete set of solutions when correctly interpreted is, in fact, physically consistent with the Parker model. A general discussion of the Parker theory of spontaneous current sheets is given.     

The thermal structure of Jupiter II. Observations and analysis of 8–14 micron radiation

Observations of Jovian limb structure at 8.11 and 8.45 microns are reported. These are used along with other limb structure and spectral data in the 8–14 micron region to derive a model of the thermal and cloud structure within the 1.0-0.01 bar pressure regime. The model is generally consistent with models derived from Pioneer 10 infrared radiometer data reported by Orton (1975b). The temperature is about 165K at 1.00 bar, 108K at 0.01 bar, and 143K at 0.03 bar. In zones, an optically opaque cloud of NH₃ exists near the 143K (0.60 bar) level. A partly transparent haze of solid NH₃ particles overlies the cloud. Belts are free of the cloud and have a much lower abundance of NH₃ haze than the zones. The data are consistent with an NH₃ gas abundance defined by saturation equilibrium, with a mixing ratio of 1.5 × 10^?4 deep in the atmosphere, and with a CH₄ mixing ratio of 2 × 10^?3, about three times the currently accepted value.     

Damping of Longitudinal Magneto–Acoustic Oscillations in Slowly Varying Coronal Plasma

We investigate the propagation of MHD waves in a magnetised plasma in a weakly stratified atmosphere, representative of hot coronal loops. In most earlier studies, a time-independent equilibrium was considered. Here we abandon this restriction and allow the equilibrium to develop as a function of time. In particular, the background plasma is assumed to be cooling due to thermal conduction. The cooling is assumed to occur on a time scale greater than the characteristic travel times of the perturbations. We investigate the influence of cooling of the background plasma on the properties of magneto–acoustic waves. The MHD equations are reduced to a 1D system modelling magneto–acoustic modes propagating along a dynamically cooling coronal loop. A time-dependent dispersion relation that describes the propagation of the magneto–acoustic waves is derived using the WKB theory. An analytic solution for the time-dependent amplitude of waves is obtained, and the method of characteristics is used to find an approximate analytical solution. Numerical calculations of the analytically derived solutions are obtained to give further insight into the behaviour of the MHD waves in a system with a variable, time-dependent background. The results show that there is a strong damping of MHD waves and the damping also appears to be independent of the position along the loop. Studies of MHD wave behaviour in a time-dependent backgrounds seem to be a fundamental and very important next step in the development of MHD wave theory that is applicable to a wide range of situations in solar physics.     

Effect of Electron Pressure on the Grad–Shafranov Reconstruction of Interplanetary Coronal Mass Ejections

We investigate the effect of electron pressure on the Grad–Shafranov (GS) reconstruction of Interplanetary Coronal Mass Ejection (ICME) structures. The GS method uses in situ magnetic field and plasma measurements to solve for a magnetohydrostatic quasi-equilibrium state of space plasmas. For some events, a magnetic flux-rope structure embedded within the ICME can be reconstructed. The electron temperature contributes directly to the calculation of the total plasma pressure, and in ICMEs its contribution often substantially exceeds that of proton temperature. We selected ICME events observed with the Wind spacecraft at 1 AU and applied the GS reconstruction method to each event for cases with and without electron temperature measurements. We sorted them according to the proton plasma β (the ratio of proton plasma pressure to magnetic pressure) and the electron-to-proton temperature ratio. We present case studies of three representative events, show the cross sections of GS reconstructed flux-rope structure, and discuss the electron pressure contribution to key quantities in the numerical reconstruction procedure. We summarize and compare the geometrical and physical parameters derived from the GS reconstruction results for cases with and without electron temperature contribution. We conclude that overall the electron pressure effect on the GS reconstruction results contributes to a 10?–?20 % discrepancy in some key physical quantities, such as the magnetic flux content of the ICME flux rope observed at 1 AU.     

Detection of Coronal Mass Ejections Using Multiple Features and Space–Time Continuity

Coronal Mass Ejections (CMEs) release tremendous amounts of energy in the solar system, which has an impact on satellites, power facilities and wireless transmission. To effectively detect a CME in Large Angle Spectrometric Coronagraph (LASCO) C2 images, we propose a novel algorithm to locate the suspected CME regions, using the Extreme Learning Machine (ELM) method and taking into account the features of the grayscale and the texture. Furthermore, space–time continuity is used in the detection algorithm to exclude the false CME regions. The algorithm includes three steps: i) define the feature vector which contains textural and grayscale features of a running difference image; ii) design the detection algorithm based on the ELM method according to the feature vector; iii) improve the detection accuracy rate by using the decision rule of the space–time continuum. Experimental results show the efficiency and the superiority of the proposed algorithm in the detection of CMEs compared with other traditional methods. In addition, our algorithm is insensitive to most noise.     

The Interaction Between Coronal Mass Ejections and Streamers: A Statistical View over 15 Years (1996 – 2010)

We report on the statistical analysis of the interaction between coronal mass ejections (CMEs) and streamers based on 15 years (from 1996 to 2010 inclusive) of observation of the solar corona with the LASCO-C2 coronagraph. We used synoptic maps and improved the method of analysis of past investigations by implementing an automatic detection of both CMEs and streamers. We identified five categories of interaction based on photometric and geometric variations between the pre- and post-CME streamers: “brightening”, “dimming”, “emergence”, “disappearance”, and “deviation”. A sixth category, “no change”, included all cases where none of the above variations is observed. A “global set” of 21?242 CMEs was considered as well as a subset of the 10 % brightest CMEs (denoted “top-ten”) and three typical periods of solar activity: minimum, intermediate, and maximum. We found that about half of the global population of CMEs are not associated with streamers, whereas 93 % of the 10 % brightest CMEs are associated. When there is a CME-streamer association, approximately 95 % of the streamers experience a change, either geometric or radiometric. The “no change” category therefore amounts to approximately 5 %, but this percentage varies from 1?–?2 % during minimum to 7?–?8 % during intermediate periods of activity; values of 3?–?5 % are recorded during maximum. Emergences and disappearances of streamers are not dominant processes; they constitute 16?–?17 % of the global set and 23 % (emergence) and 28 % (disappearance) of the “top-ten” set. Streamer deviations are observed for 57 % and 70 % of, respectively, the global set and “top-ten” CMEs. The cases of dimming and brightening are roughly equally present and each case constitutes approximately 30?–?35 % of either set, global or “top-ten”.     

Observational Signatures of Impulsively Heated Coronal Loops: Power-Law Distribution of Energies

It has been established that small scale heating events, known as nanoflares, are important for solar coronal heating if the power-law distribution of their energies has a slope α steeper than −2 (α<−2). Forward modeling of impulsively heated coronal loops with a set of prescribed power-law indices α is performed. The power-law distribution is incorporated into the governing equations of motion through an impulsive heating term. The results are converted into synthetic Hinode/EIS observations in the 40″ imaging mode, using a selection of spectral lines formed at various temperatures. It is shown that the intensities of the emission lines and their standard deviations are sensitive to changes in α. A method based on a combination of observations and forward modeling is proposed for determining whether the heating in a particular case is due to small or large scale events. The method is extended and applied to a loop structure that consists of multiple strands.