Solar Magnetic Carpet II: Coronal Interactions of Small-Scale Magnetic Fields

This paper is the second in a series of studies working towards constructing a realistic, evolving, non-potential coronal model for the solar magnetic carpet. In the present study, the interaction of two magnetic elements is considered. Our objectives are to study magnetic energy build-up, storage and dissipation as a result of emergence, cancellation, and flyby of these magnetic elements. In the future these interactions will be the basic building blocks of more complicated simulations involving hundreds of elements. Each interaction is simulated in the presence of an overlying uniform magnetic field, which lies at various orientations with respect to the evolving magnetic elements. For these three small-scale interactions, the free energy stored in the field at the end of the simulation ranges from 0.2 – 2.1×10²⁶ ergs, whilst the total energy dissipated ranges from 1.3 – 6.3×10²⁶ ergs. For all cases, a stronger overlying field results in higher energy storage and dissipation. For the cancellation and emergence simulations, motion perpendicular to the overlying field results in the highest values. For the flyby simulations, motion parallel to the overlying field gives the highest values. In all cases, the free energy built up is sufficient to explain small-scale phenomena such as X-ray bright points or nanoflares. In addition, if scaled for the correct number of magnetic elements for the volume considered, the energy continually dissipated provides a significant fraction of the quiet Sun coronal heating budget.     

High-Latitude Solar Rotation Traced by Magnetic Elements

Sequential observations at Huairou Solar Observation Station, China, and Kitt Peak, U.S.A., show that polar magnetic elements can live from several to more than 58 hours. This enables measurement of the solar rotation rate near the polar region by tracing magnetic element motions. With observations carried out on 8–15 July 1997, we identify and trace more than 1300 elements at north heliographic latitudes between 55°–85° using two methods, and fit the mean sidereal rotation rate as =14.0±0.54–(2.24±1.22)sin²–(1.78±0.79)sin⁴ deg per day.     

On Three-Dimensional Magnetic Skeleton Elements Due to Discrete Flux Sources

The magnetic field in the solar corona plays an important role in coronal heating, flaring activity and many other phenomena studied on the Sun. Magnetic topology is frequently used to understand complicated coronal magnetic fields. By calculating the skeleton of a field, it is possible to build up a sophisticated representation of the key elements of a field’s configuration. This paper determines a simple relation between the numbers of separators (X), coronal null points (N_c), flux domains (D) and flux sources (S) in such a configuration: D=X+S−N_c−1. This equation is used to explain the behaviour of some of the bifurcations found in Magnetic Charge Topology, and to show that a one-to-one relationship exists between the number of circuits in the domain graph and the augmented null graph. Finally, it is shown that in quiet-Sun regions, the number of separators is approximately proportional to the number of flux sources.     

On the Power in the Legendre Modes of the Solar Radial Magnetic Field

The power in the different modes of an expansion of the solar radial magnetic field at the surface in terms of Legendre polynomials,P , is calculated with the help of a solar dynamo model studied earlier. The model is of the Babcock–Leighton type, i.e., the surface eruptions of the toroidal magnetic field – through the tilt angle, , formed by the magnetic axis of a bipolar magnetic region with the east-west line – are the sources for the poloidal field. In this paper it is assumed that the tilt angle is subject to fluctuations of the form, = ()+ <> where <> is the average value and () is a random normal fluctuation with standard deviation which is taken from Howard's observations of the distribution of tilt angles. For numerical considerations, negative values of were not allowed. If this occurred, was recalculated. The numerical integrations were started with a toroidal magnetic field antisymmetric across the equator, large enough to generate eruptions, and a negligible poloidal field. The fluctuations in the tilt angle destroy the antisymmetry as time increases. The power of the antisymmetric modes across the equator (i.e., odd values of ) is concentrated in frequencies, _p, corresponding to the cycle period. The maximum power lies in the =3 mode with considerable power in the =5 mode, in broad agreement with Stenflo's results who finds a maximum power at =5. For the symmetric modes, there is considerable power in frequencies larger than _p, again in broad agreement with Stenflo's power spectrum.     

Lifetime of Intranetwork Magnetic Elements

Using a 10-hour time sequence of very deep magnetograms of Big Bear Solar Observatory, we have studied the lifetime of Intranetwork Magnetic Elements for the first time. The analysis reveals the following results:(1) The lifetime of intranetwork elements ranges from 0.2 hr to 7.5 hr with the mean of 2.1 hr. There appears to be a quasi-linear dependence of the lifetime on the total flux of elements. (2) Most intranetwork elements appear as a cluster of mixed polarities from an emergence center somewhere within the network boundary and are destroyed by three mechanisms: merging with intranetwork or network elements of the same polarity, cancellation of opposite polarity elements, or separation and disappearance at the position where they appear. (3) We estimate that the total energy released from the recycling of IN elements isinebreak1.6 × 10²⁸ ergs s^-1, which seems to be comparable to the energy required to heat the corona.     

Independent Global Modes of Solar Magnetic Field Fluctuations

Observed solar, interplanetary and geomagnetic time series contain quasi periodicities on scales of 1–2.5 years. The further discovery of 1.3 year fluctuations in helioseismic observations suggests that a variety of signals may be related to the underlying dynamo in the Sun. We use independent component analysis to study the temporal and spatial variations of a few statistically independent global modes of the axisymmetric solar magnetic field over a period of 25 years. Five modes capture the salient properties of the data. Two modes describe the polar and high latitude fields, and present 1–1.5 year quasi periodicities. The other three modes correspond to low and mid-latitude phenomena and show both 1.3 and 1.7-year variations. By comparing the characteristic time scales, dates of occurrence and heliocentric latitudes of these modes, we connect them to their manifestations in heliospheric time series.     

Classical Calculations of Scattering Signatures from a Gravitational Singularity or the Scattering and Absorption Cross-Sections of a Black Hole

Within the context of general relativity theory we calculate, analytically, scattering signatures around a gravitational singularity: angular and time distributions of scattered massive objects and photons and the time and space modulation of Doppler effects. Additionally, the scattering and absorption cross sections for the gravitational interactions are calculated. The results of numerical simulations of the trajectories are compared with the analytical results.     

Interaction and Dynamics of the Photospheric Network Magnetic Elements

Small-scale magnetic elements in the quiet photospheric network are believed to play a key role in the energy flow from the solar surface to upper layers of atmosphere. Their intense hydro-magnetic activity includes merging and fragmentation of same polarity fluxes, `total' or partial cancellation of neighboring flux elements of opposite polarity, dynamic appearance and disappearance of compact bipoles, etc. We study the general features of these processes, and show that non-collinearity of flux tubes, sharp stratification of low atmosphere and finite plasma beta lead to several specific effects in the interacting flux tubes that may explain the morphological properties of network magnetic field and also provide a mechanism for the energy build up and release in the nearby chromosphere and transition region. We show that during the collision of flux tubes in the photosphere reconnection occurs regardless of whether the flux tubes are of opposite or of the same polarity. But the dynamics of reconnection products are significantly different and lead to different macroscopic effects that can be observed.     

Hardening of Thermal Photons Through Inverse Compton Scattering in Strong Magnetic Fields

A new spectrum function is obtained by use of the Compton scattering cross section in the laboratory frame dervied earlier. This spectrum function, besides some modifications in the coefficients of the resonant term, contains also a non-resonant term which is inversely proportional to the square of the magnetic field. Based on this spectrum function, the hardening of thermal photons through inverse Compton scattering by relativistic electron beams on the surface of a strongly magnetized neutron star is investigated. Two new features are found. First, there is a maximum scattered photon energy for a given resonant scattering, beyond which resonance disappears. This maximum depends on the electron energy and the magnetic field, but is independent of the incident photon energy. Second, Beyond each resonant scattering, there is a high-energy tail, resulting from non-resonant scattering. It is also found that all the tails have a common upper limit which is the highest scattered photon energy for the given incident photon and electron energies. These two new features are absent in the Monte Carlo simulations and therefore, may have physical implications for γ-ray emissions.     

强磁场中的逆Compton散射与γ射线爆能谱

本文认为强磁场中的逆Compton散射可能是γ射线爆的主要辐射机制.其能谱是由源区质子产生的低频光子经强磁场中非热电子的Compton散射形成的.我们利用非相对论情形(B/B_(cr)≤1,hv_i/m_ec~2≤1)下强磁场中的Compton散射微分截面,导出了上述Compton散射的辐射谱公式,由此很好地拟合了典型γ射线爆GB811016的观测能谱.     

A Multispacecraft Analysis of a Small-Scale Transient Entrained by Solar Wind Streams

The images taken by the Heliospheric Imagers (HIs), part of the SECCHI imaging package onboard the pair of STEREO spacecraft, provide information on the radial and latitudinal evolution of the plasma compressed inside corotating interaction regions (CIRs). A plasma density wave imaged by the HI instrument onboard STEREO-B was found to propagate towards STEREO-A, enabling a comparison between simultaneous remote-sensing and in situ observations of its structure to be performed. In situ measurements made by STEREO-A show that the plasma density wave is associated with the passage of a CIR. The magnetic field compressed after the CIR stream interface (SI) is found to have a planar distribution. Minimum variance analysis of the magnetic field vectors shows that the SI is inclined at 54° to the orbital plane of the STEREO-A spacecraft. This inclination of the CIR SI is comparable to the inclination of the associated plasma density wave observed by HI. A small-scale magnetic cloud with a flux rope topology and radial extent of 0.08 AU is also embedded prior to the SI. The pitch-angle distribution of suprathermal electrons measured by the STEREO-A SWEA instrument shows that an open magnetic field topology in the cloud replaced the heliospheric current sheet locally. These observations confirm that HI observes CIRs in difference images when a small-scale transient is caught up in the compression region.     

磁场中p模/s模的转换及黑子对声波的吸收

在柱坐标下将黑子周围的环形区域（黑子除外）内的振荡分解为朝向黑子传播的（入射的）波和离开黑子传播的（出射的）波。对无黑子的环形区域内的振荡也进行了同样的分解。将黑子周围的入射波看成是被黑子磁流管磁化了的介质（介质内的磁场基本是水平的）中的波。而无黑子区的入射波看成是非磁化介质中的波。比较这两种波在固定波数下功率随频率的分布发现，在磁化介质中不同径向除ｎ的声波（ｐ模）频率系统降低，同时功率也降低，降低的功率最高达非磁化介质中波的功率的３０％。而比较在固定频率下功率随波数的分布发现，磁场中ｆ模及ｎ＝１，２，３的ｐ模的脊向高波数方向位移，功率的降低受频率调制，即声波在某些有限的频带中被吸收。这些观测表明，在磁场中ｐ模与磁声重力波（ＭＡＧ）产生了模式混合或耦合。模式混合的存在支持了模式转换作为ｐ模式被黑子吸收的机制的解释。此外，本文还分析了转换的ＭＡＧ波进入黑子磁流管（其中的磁场基本上是垂直的）后进一步被吸收，吸收的功率最高达ＭＡＧ波的２０％。在磁流管内没有进一步观测到模式的转换     

New Approach to Study Extended Evolution of Supergranular Flows and Their Advection of Magnetic Elements

Using velocity and magnetogram data extracted from the full-disk field of view of MDI during the 1999 Dynamics Program, we have studied the dynamics of small-scale magnetic elements (3–7 Mm in size) over time periods as long as six days while they are readily visible on the solar disk. By exploiting concurrent time series of magnetograms and Doppler images, we have compared the motion of magnetic flux elements with the supergranular velocity field inferred from the correlation tracking of mesogranular motions. Using this new method (which combines the results from correlation tracking of mesogranules with detailed analysis of simultaneous magnetograms), it is now possible to correlate the motions of the velocity field and magnetic flux for long periods of time and at high temporal resolution. This technique can be utilized to examine the long-term evolution of supergranulation and associated magnetic fields, for it can be applied to data that span far longer time durations than has been possible previously. As tests of its efficacy, we are able to use this method to verify many results of earlier investigations. We confirm that magnetic elements travel at approximately 350 m s ^–1 throughout the duration of their lifetime as they are transported by supergranular outflows. We also find that the positions of the magnetic flux elements coincide with the supergranular network boundaries and adjust as the supergranular network itself evolves over the six days of this data set. Thus we conclude that this new method permits us to study the extended evolution of the supergranular flow field and its advection of magnetic elements. Since small-scale magnetic elements are strongly advected by turbulent convection, their dynamics can give important insight into the properties of the subsurface convection.     

On the Excitation of Leaky Modes in Cylindrical Loops

The role of leaky waves in the coronal loop oscillations observed by TRACE is not yet clearly understood. In this work, the excitation of fast waves in solar coronal loops modelled as dense plasma cylindrical tubes in a uniform straight magnetic field is investigated. We study the trapped and especially leaky modes (whose energy escapes from the tube) that result from an initial disturbance by solving the time-dependent problem numerically. We find that the stationary state of the tube motion is given by the trapped normal modes. By contrast, the transient behaviour between the initial and the stationary phase is dominated by wave leakage. The so-called trig leaky modes are clearly identified since the transient behaviour shows periods and damping times that are in agreement with the values calculated from the normal-mode analysis. Consequently, these radiating modes have physical significance. However, we have not found any evidence for the excitation of other types of modes, such as the principal leaky kink mode. J. Andries is postdoctoral Fellow of the National Fund for Scientific Research – Flanders (Belgium) (F.W.O.-Vlaanderen).     

Mode Conversion of Solar p Modes in non-Vertical Magnetic Fields – i. two-Dimensional Model

Sunspots absorb incident p modes. The responsible mechanism is uncertain. One possibility is mode conversion to slow magnetoacoustic–gravity waves. In vertical field mode conversion can adequately explain the observed f-mode absorption, but is too inefficient to explain the absorption of p modes. In this investigation we calculate the efficiency of fast-to-slow magnetoacoustic–gravity wave conversion in non-vertical field. We assume two-dimensional propagation where the Alfvén waves decouple. It is found that resultant p-mode absorption is significantly enhanced for moderate inclinations at higher frequencies, whereas for p modes at lower frequencies, and the f mode in general, there is no useful enhancement. However, the enhancement is insufficient to explain the observed p-mode absorption by sunspots. Paper II considers the efficiency of mode conversion in non-vertical field with three-dimensional propagation, where fast and slow magnetoacoustic–gravity waves and Alfvén waves are coupled.     

Thermophysical Modelling of Comet P/Borrelly Effects of Volume Energy Absorption and Volume Sublimation

In this work, we continue revising the theoretical basis ofnumerical models describing the transport of matter andenergy inside a porous dust-ice mixture at low temperature. Amodel of a light-absorbing near-surface layer of a comet nucleus isinvestigated. Gas transport is considered simultaneously with thesolution of the general heat transfer equation. Thequasi-stationary temperature distribution and the H₂O massflux and sublimation rate are computed for a nucleus model ofcomet 19P/Borrelly at the Deep Space 1 (DS1) encounter. Theenergy is deposited in a layer of about 20 particle radii: Thiscorresponds to a solid-state greenhouse effect. The surfacetemperature of the layer-absorbing model as well as the gasproduction rate are significantly smaller than the ones in thesurface-absorbing model. An active fraction of 40–50% would berequired to explain the observed water production rate ofP/Borrelly with our layer-absorption model at the time of the DS1encounter.     

Small-Scale Topography of 433 Eros from Laser Altimetry and Imaging

The NEAR laser rangefinder (NLR) obtained more than 16 million range returns from asteroid 433 Eros. We present the first results from analyses of topographic profiles interpreted with the aid of simultaneous, boresighted images obtained by the NEAR multispectral imager (MSI). The location of the NLR boresight relative to that of MSI is determined by detailed correlations of ranging data and simultaneous images, including cases where the laser boresight slewed off and on the limb of the asteroid and cases where the laser illuminated a boulder close to the time of an image. In the data presented, the precision of the range measurements is about 1 m, with the minimum spot diameter under 5 m, and successive spots are contiguous or overlapping. Elevation on the irregular object Eros is given with respect to the gravitational and centrifugal potential. Landslides in craters are characterized. Possible crater benches are identified. Examples of infilled craters are presented. These observations suggest a depth of unconsolidated regolith, which is subject to sliding, of typically a few tens of meters. An example of structurally controlled cratering is presented. Examples of tectonic features are described. Surface roughness on Eros is approximately self-affine from scales of a few meters to hundreds of meters. A comparison of fractal statistics shows that Eros is extremely rough on observed scales, when compared to terrestrial a'a lava on submeter scales and undisturbed lunar regolith on subcentimeter scales.     

Collective Spectra of Resonant Inverse Compton Scattering of Assembly of Relativistic Electrons in Intense Magnetic Fields*

The resonant inverse Compton scattering (RICS) of relativistic electrons in intense magnetic fields is an efficient mechanism for producing the highenergy γ-rays. In our previous work it is suggested that the early-stage γ-ray radiation of γ-ray bursts (GRBs) may be mainly produced by this mechanism. By using this mechanism, some puzzles in the study of GRBs can be clarified, e.g., the origin of the Amati relation obtained from the statistics of observations, the formation of the observed two-segment (broken) power-law spectra, the relevant “deadline problem”, the polarization property, etc. Herein our discussion will be focused on the formation of the broken power-law spectra. Based on the formula of the RICS spectral power of individual fast electrons, we have derived the simplified analytical formula of the collective RICS radiation spectrum (RICS spectral luminosity) produced by the assembly of relativistic electrons in an intense magnetic field when they pass through the ambient low-frequency radiation field, and applied it to several typical low-frequency radiation fields (e.g., the black-body radiation field, power-law radiation field and thermal bremsstrahlung field) around the central neutron star, for the convenience of comparison with the observed spectra. Our calculations indicate that the RICS radiation mechanism has a very high efficiency in the hard X-ray and γ-ray wavebands, if the matching condition (i.e., the condition approximate to resonance) is satisfied, and that independent of the ambient radiation field, the produced spectra are commonly the two-segment power-law spectra. Additionally, it is suggested that the RICS mechanism might be an ideal highly-efficient radiation mechanism for the high-energy emissions (hard X-rays and γ-rays) of the GRBs, soft γ-ray repeated bursts (SGRs) and γ-ray pulsars (GRPs).     

Scattering by nonspherical particles and optical properties of Martian dust

Ultraviolet spectral reflectance data obtained from the Mariner 9 during the 1971 Mars dust storm were analyzed at two wavelengths to deduce the complex index of refraction of Martian dust. Martian dust particles were considered to be irregularly shaped and randomly oriented nonspherical particles. The analysis shows that the Mariner 9 data are consistent with the scattering by irregular particles with an index of refraction m = 1.59 ? 0.0015i at λ = 0.305 μm and m = 1.55 ? 0.004i at λ = 0.268 μm. Both the real and the imaginary parts of refractive index found are considerably smaller than previously reported results using a spherical shape model for Martian dust particles.