Regularized Reconstruction of the Differential Emission Measure from Solar Flare Hard X-Ray Spectra

We address the problem of how to test whether an observed solar hard X-ray bremsstrahlung spectrum (I(∊)) is consistent with a purely thermal (locally Maxwellian) distribution of source electrons, and, if so, how to reconstruct the corresponding differential emission measure (ξ(T)). Unlike previous analysis based on the Kramers and Bethe-Heitler approximations to the bremsstrahlung cross-section, here we use an exact (solid-angle-averaged) cross-section. We show that the problem of determining ξ(T) from measurements of I(∊) invOlves two successive inverse problems: the first, to recover the mean source-electron flux spectrum ( [`(F)]\overline{F} (E)) from I(∊) and the second, to recover ξ(T) from [`(F)]\overline{F} (E). We discuss the highly pathological numerical properties of this second problem within the framework of the regularization theory for linear inverse problems. In particular, we show that an iterative scheme with a positivity constraint is effective in recovering δ-like forms of ξ(T) while first-order Tikhonov regularization with boundary conditions works well in the case of power-law-like forms. Therefore, we introduce a restoration approach whereby the low-energy part of [`(F)]\overline{F} (E), dominated by the thermal component, is inverted by using the iterative algorithm with positivity, while the high-energy part, dominated by the power-law component, is inverted by using first-order regularization. This approach is first tested by using simulated [`(F)]\overline{F} (E) derived from a priori known forms of ξ(T) and then applied to hard X-ray spectral data from the Reuven Ramaty High Energy Solar Spectroscopic Imager (RHESSI).     

Dynamic Three-Dimensional Tomography of the Solar Corona

Empirical, three-dimensional electron-density maps of the solar corona can be tomographically reconstructed using polarized-brightness images measured from ground- and space-based observatories. Current methods for computing these reconstructions require the assumption that the structure of the corona is unchanging with time. We present the first global reconstructions that do away with this static assumption and, as a result, allow for a more accurate empirical determination of the dynamic solar corona. We compare the new dynamic reconstructions of the coronal density during February 2008 to a sequence of static reconstructions. We find that the new dynamic reconstructions are less prone to certain computational artifacts that may plague the static reconstructions. In addition, these benefits come without a significant increase in computational cost.     

Differential Rotation of the Solar Corona from Magnetic Field Data

A method for investigating the differential rotation of the solar corona using the coronal magnetic field as a tracer is proposed. The magnetic field is calculated in the potential approximation from observational data at the photospheric level. The time interval from June 24, 1976, to December 31, 2004, is considered. The magnetic field has been calculated for all latitudes from the equator to ±75? with a 5? step at distances from the base of the corona 1.0 R_⊙ to 2.45 R_⊙ near the source surface. The coronal rotation periods at 14 distances from the solar center have been determined by the method of periodogram analysis. The coronal rotation is shown to become progressively less differential with increasing heliocentric distance; it does not become rigid even near the source surface. The change in the coronal rotation periods with time is considered. At the cycleminimumthe rotation has been found to bemost differential, especially at small distances from the solar center. The change in coronal rotation with time is consistent with the tilt of the solar magnetic equator. The results from the magnetic field are compared with those obtained from the brightness of the green coronal Fe XIV 530.3 nm line. The consistency between these results confirms the reliability of the proposed method for studying the coronal rotation. Studying the rotation of the coronal magnetic field gives hope for the possibility of using this method to diagnose the differential rotation in subphotospheric layers.     

Rotational Tomography For 3d Reconstruction Of The White-Light And Euv Corona In The Post-Soho Era

Improving our understanding of the mechanisms that energize the solar wind and heat structures in the solar corona requires the development of empirical methods that can determine the three-dimensional (3D) temperature and density distributions with as much spatial and temporal resolution as possible. This paper reviews the solar rotational tomography (SRT) methods that will be used for 3D reconstruction of the solar corona from data obtained by the next generation of space-based missions such as the Solar and Terrestrial Relations Observatory (STEREO), Solar-B and the Solar Dynamics Observatory (SDO). In the next decade, SRT will undergo rapid advancement on several frontiers of 3D image reconstruction:

1. Electron density reconstruction from white-light coronagraph images.
2. Differential emission measure (DEM) reconstruction from EUV images.
3. Dual-spacecraft (STEREO) observing geometry.
4. Fusion of data from multiple spacecraft with differing instrumentation.
5. Time-dependent estimation methods.

Although the principles described apply to many different wavelength regimes, this paper concentrates on white-light and EUV data. Previous work on all of these subjects is reviewed, and major technical issues and future directions are discussed.     

Variation of Emission Line Width in Mid- and High-Latitude Corona

Spectroscopic studies of the solar corona, using the high spatial and spectral resolution 25-cm coronagraph at the Norikura Solar Observatory for equatorial off-limb observations, indicated that the variation of radiance and line width with height is different for different temperature lines. The line width of the forbidden red emission line [Fe x] 6374 Å was found to increase with height, and that of the green emission line [Fe xiv] 5303 Å decreased with height. This had been interpreted in terms of the interaction between different temperature plasmas but needed to be confirmed. Further observations were made on several days during 2004, in two emission lines simultaneously covering the mid-latitude and polar regions to investigate the existence of the observed variation in other parts of the solar corona. In this study, we have analysed several raster scans that cover mid- and high-latitude regions of the off-limb corona in all four bright emission lines [Fe x] 6374 Å, [Fe xi] 7892 Å, [Fe xiii] 10747 Å, and [Fe xiv] 5303 Å. We find that the FWHM of the red line increases with height and that of the green line decreases with height, similar to the observations in the equatorial regions. The line widths are higher in the polar regions for all of the observed emission lines except the green line. Higher values of FWHM in polar regions may imply higher non-thermal velocities, which could be further linked to a non-thermal source powering the solar-wind acceleration, but the reason for the behaviour of the green emission line remains to be explored.     

Neutral Hydrogen and Its Emission Lines in the Solar Corona

Since the Lyman-\(\alpha\) rocket observations of Gabriel (Solar Phys. 21, 392, 1971), it has been realized that the hydrogen (H) lines could be observed in the corona and that they offer an interesting diagnostic for the temperature, density, and radial velocity of the coronal plasma. Moreover, various space missions have been proposed to measure the coronal magnetic and velocity fields through polarimetry in H lines. A necessary condition for such measurements is to benefit from a sufficient signal-to-noise ratio. The aim of this article is to evaluate the emission in three representative lines of H for three different coronal structures. The computations have been performed with a full non-local thermodynamic-equilibrium (non-LTE) code and its simplified version without radiative transfer. Since all collisional and radiative quantities (including incident ionizing and exciting radiation) are taken into account, the ionization is treated exactly. Profiles are presented at two heights (1.05 and 1.9 solar radii, from Sun center) in the corona, and the integrated intensities are computed at heights up to five solar radii. We compare our results with previous computations and observations (e.g. L\(\alpha\) from Ultraviolet Coronal Spectrometer) and find a rough (model-dependent) agreement. Since the H\(\alpha\) line is a possible candidate for ground-based polarimetry, we show that in order to detect its emission in various coronal structures, it is necessary to use a very narrow (less than 2 Å wide) bandpass filter.     

The EUV Unresolved Corona

The unresolved corona for three active regions (ARs) above the solar limb is investigated. Intensities measured for ions formed above 1 MK are presented as a function of height above the solar surface. The observed decrease in intensity with altitude is found to be best fit by an exponential. Furthermore, this exponential decrease is approximately the decrease in emission expected for a hydrostatic planar geometry atmosphere, where the scale height temperature is dependent on the dynamics of the AR. For two of the ARs analyzed, we have found that the best-fit temperature derived from the exponential fits is consistent with an isothermal hydrostatic unresolved corona.     

The Magnetic Field of the Solar Corona from Pulsar Observations

We present a novel experiment with the capacity to independently measure both the electron density and the magnetic field of the solar corona. We achieve this through measurement of the excess Faraday rotation resulting from propagation of the polarised emission from a number of pulsars through the magnetic field of the solar corona. This method yields independent measures of the integrated electron density, via dispersion of the pulsed signal and the magnetic field, via the amount of Faraday rotation. In principle this allows the determination of the integrated magnetic field through the solar corona along many lines of sight without any assumptions regarding the electron density distribution. We present a detection of an increase in the rotation measure of the pulsar J1801-2304 of approximately 170 rad m² at an elongation of 0.96° from the centre of the solar disc. This corresponds to a lower limit of the magnetic field strength along this line of sight of >41.8 nT. The lack of precision in the integrated electron density measurement restricts this result to a limit, but application of coronal plasma models can further constrain this to approximately 0.5 μT, along a path passing 2.7 solar radii from the solar limb, which is consistent with predictions obtained using extensions to the source surface models published by the Wilcox Solar Observatory.     

TRACE-derived Temperature and Emission Measure Profiles along Long-lived Coronal Loops: The Role of Filamentation

Near-infrared spectroscopic observations of a sample of very cool, low-mass objects are presented with higher spectral resolution than in any previous studies. Six of the objects are L dwarfs, ranging in spectral class from L2 to L8/9, and the seventh is a methane or T dwarf. These new observations were obtained during commissioning of the near-infrared spectrometer (NIRSPEC), the first high-resolution near-infrared cryogenic spectrograph for the Keck II 10 m telescope on Mauna Kea, Hawaii. Spectra with a resolving power of R approximately 2500 from 1.135 to 1.360 μm (approximately J band) are presented for each source. At this resolution, a rich spectral structure is revealed, much of which is due to blending of unresolved molecular transitions. Strong lines due to neutral potassium (K i) and bands due to iron hydride (FeH) and steam (H2O) change significantly throughout the L sequence. Iron hydride disappears between L5 and L8, the steam bands deepen, and the K i lines gradually become weaker but wider because of pressure broadening. An unidentified feature occurs at 1.22 μm that has a temperature dependence like FeH but has no counterpart in the available FeH opacity data. Because these objects are 3-6 mag brighter in the near-infrared compared with the I band, spectral classification is efficient. One of the objects studied (2MASSW J1523+3014) is the coolest L dwarf discovered so far by the 2 Micron All-Sky Survey (2MASS), but its spectrum is still significantly different from the methane-dominated objects such as Gl 229B or SDSS 1624+0029.     

The Green Corona and Magnetic Fields

We present results of a study of the green corona (530.3 nm, Fexiv) and photospheric magnetic fields over the period 1976–1999 when both quantities were observed by ground-based observatories. By comparing both the limb green-line intensities and photospheric magnetograms we have found a relation between the strength of magnetic field and coronal intensities. This relation enables us to extend solar surface magnetic fields since 1976 back to 1939. From 1947 to 1992 the magnetic field strength grew at the cycle maxima by a factor of 1.5–2. On the other hand, both the green corona intensity and magnetic field strength in the present cycle are smaller compared to cycle 22, by a factor of 2. No relationship was found between the green corona intensities and magnetic field polarity as was previously supposed. Behavior for the green corona intensities is different between high-latitude and mid-latitude regions, and this break occurs at the heliographic latitude of ± 45°. Homogeneous coronal data set cannot be directly used to derive `the tilt angle', even though some similarities between the green coronal holes, poleward branches in the green corona and prominences and the tilt angle can be found.     

Magnetic Field as a Tracer for Studying the Differential Rotation of the Solar Corona

The characteristics of differential rotation of the solar corona for the period 1976?–?2004 were studied as a function of the distance from the center of the Sun. For this study, we developed a method using the coronal magnetic field as a tracer. The field in a spherical layer from the base of the corona up to the source surface was determined from photospheric measurements. Calculations were performed for 14 heliocentric distances from the base of the corona up to 2.45 \(R_{\odot }\) solar radii (the vicinity of the source surface) and from the equator to \(\pm 75^{\circ }\) of latitude at \(5^{\circ }\) steps. For each day, we calculated three spherical components, which were then used to obtain the field strength. The coronal rotation periods were determined by the periodogram method. The rotation periods were calculated for all distances and latitudes under consideration. The results of these calculations make it possible to study the distribution of the rotation periods in the corona depending on distance, time, and phase of the cycle. The variations in the coronal differential rotation during the time interval 1976?–?2004 were as follows: the gradient of differential rotation decreased with the increase of heliocentric distance; the rotation remaining differential even in the vicinity of the source surface. The highest rotation rates (shortest rotation periods) were recorded at the cycle minimum at small heliospheric distances, i.e. small heights in the corona. The lowest rotation rate was observed at the middle of the ascending branch at large distances. At the minimum of the cycle, the differential rotation is most clearly pronounced, especially at small heliocentric distances. As the distance increases, the differential rotation gradient decreases in all phases. The results based on magnetic data and on the brightness of the coronal green line 530.3 nm Fe xiv used earlier show a satisfactory agreement. Since the rotation of the magnetic field at the corresponding heights in the corona is probably determined by the conditions in the field generation region, an opportunity arises to use this method for diagnostics of differential rotation in the subphotospheric layers.     

Solar Corona: from Shklovsky to our Days

Fundamental advances in the physics of the solar corona from the 1960's to the present time are briefly reviewed. Progress in coronal investigations has mainly been associated with major space missions, which have discovered such new phenomena as coronal holes and coronal mass ejections, and have enabled detailed study of coronal arch systems. The role of magnetic fields on various scales in quasi-steady-state phenomena is discussed for various phases of the solar activity cycle.     

一类X射线发射度在脉冲相具有显著指数增长特征的太阳耀斑

太阳耀斑脉冲相的X射线光变曲线的复杂性表明此阶段有多种物理过程参与其中.基于某些显著的观测特征对耀斑分类可以用来探索这些特征的物理起源.对GOES (Geostationary Operational Environmental Satellite)卫星观测数据的分析表明有一类X射线发射度在脉冲相呈显著指数增长的耀斑.指数增长阶段的平均温度为正态分布.在此温度分布1σ之内的大多数耀斑属于B级或C级耀斑,其GOES低通道流量的峰值分布为对数正态分布.指数增长相的增长率和持续时间也遵循对数正态分布.持续时间分布范围大概为几十秒到几千秒.正如所预期的,增长时标同软X射线的衰减时标具有相关性.此外,指数增长相的增长率与持续时间呈强烈的反相关,而且随增长率的增大,对应的平均温度也有缓慢增大的趋势.     

Solar Flares with an Exponential Growth of the Emission Measure in the Impulsive Phase Derived from X-ray Observations

The light curves of solar ?ares in the impulsive phase are complex in general, indicating that multiple physical processes are involved in. With the GOES (Geostationary Operational Environmental Satellite) observations, we ?nd that there are a subset of ?ares, whose impulsive phases are dominated by a period of exponential growth of the emission measure. The ?ares occurred from January 1999 to December 2002 are analyzed, and the results from the observations made with both GOES 8 and GEOS 10 satellites are compared to estimate the instrumental uncertainties. Their mean temperatures during this exponential growth phase have a normal distribution. Most ?ares within the 1σ range of this temperature distribution belong to the GOES class B or C, with the peak ?uxes at the GOES low-energy channel following a log-normal distribution. The growth rate and duration of the exponential growth phase also follow a log- normal distribution, in which the duration is distributed in the range from half a minute to about half an hour. As expected, the growth time is correlated with the decay time of the soft X-ray ?ux. We also ?nd that the growth rate of the emission measure is strongly anti-correlated with the duration of the exponential growth phase, and the mean temperature increases slightly with the increase of the growth rate. The implications of these results on the study of energy release in solar ?ares are discussed in the end.     

The Global Dynamics of the High-Temperature Corona

This paper surveys coronal motions detected by the Yohkoh soft X-ray telescope SXT, emphasizing `global restructuring'. Large-scale structures in the solar corona can persist for time scales much longer than those of the supergranulation, and may have larger spatial scales. Flares and coronal mass ejections (CMEs) can disrupt these structures. A grazing-incidence telescope such as SXT provides a view of the corona biased in temperature towards the hotter components, but in a thick `observing slice' (spatial contribution function). This helps in seeing excitation (energy release) but may conceal some of the structural changes. The observations of restructuring largely appear to consist of expanding or outwards magnetic motions, which are endoergic. This suggests a conjecture regarding the existence of magnetic implosions on scales not yet detected, as a source of free energy.     

色球和冕层加热机制

简要回顾了近年来恒星色球和恒星冕层加热机制研究的一些重要成果和进展.恒星高层大气具有多种加热方式,在非磁区域和磁性区域的加热机制有所不同.主要讨论了稳定的恒星色球和冕层加热机制,包括传统的非磁区域的声波加热,磁性作用下的快慢磁声波加热,阿尔芬波加热,磁重联加热以及费米加热等.     

脉冲星的γ辐射

本文根据Ｒ－Ｓ模型讨论脉冲星的γ辐射，在讨论光子被电磁场吸收时，我们把中子星磁层分成两部分，一部分以电场吸收为主，另一部分以磁场吸收为主。本文以电子在电磁场中的级联过程为基础，计算了Ｃｒａｂ、Ｖｅｌａ等六个已知γ射线脉冲星的一些物理量，发现与观测基本相符。另外我们还预言了一些很可能是γ射线脉冲星的候选者。