On-Orbit Sensitivity Evolution of the EUV Imaging Spectrometer on Hinode

Since its launch on 22 September 2006, the EUV Imaging Spectrometer onboard the Hinode satellite has exhibited a gradual decay in sensitivity. Using spectroheliograms taken in the Fe viii 185.21 Å and Si vii 275.35 Å emission lines in quiet regions near Sun center we characterize that decay. For the period from December 2006 to March 2012, the decline in the sensitivity can be characterized as an exponential decay with an average time constant of 7358±1030 days (20.2±2.8 years). Emission lines formed at temperatures ??10^6.1 K in the quiet Sun data exhibit solar-cycle effects.     

Fundamental Emission of Type III Bursts Produced in Non-Maxwellian Coronal Plasmas with Kappa-Distributed Background Particles

Detailed simulations based on quasi-linear theory are presented for fundamental ( $f_{\rm p}$ ) emission of type III bursts produced in non-Maxwellian, suprathermal, background coronal plasma by injection of energetic electrons during flares with a power-law or Maxwellian velocity distribution, where $f_{\rm p}$ is the electron plasma frequency. The background plasma is assumed to have a kappa (κ) distribution, as inferred from solar wind data and proposed by theories for the corona and solar wind. The predicted type III beam speeds, Langmuir wave levels, and the drift rate and flux of $f_{\rm p}$ emission are strongly sensitive to the presence of suprathermal background electrons in the corona. The simulations show the following results. i) Fast beams with speeds $v_{\rm b}>0.5c$ are produced for coronal background electrons with small κ (κ?5) by injected electrons with power-law spectra. ii) Moderately fast beams with $v_{\rm b} \approx0.3\,\mbox{--}\,0.5c$ are generated in coronal plasma with κ?8 by injections of power-law or Maxwellian electrons. iii) Slow beams with $v_{\rm b}<0.3c$ are produced for coronal background electrons with large κ (κ>8), including the asymptotic limit κ→∞ where the electrons are Maxwellian, for both power-law and Maxwellian injections. The observation of fast type III beams (with $v_{\rm b}>0.5c$ ) thus suggests that these beams are produced in coronal regions where the background electron distribution has small κ by injected electrons with power-law spectra, at least when such beams are observed. The simulations, from the viewpoint of type III bursts, thus support: i) the presence, at least sometimes, of suprathermal background electrons in the corona and the associated mechanisms for coronal heating and solar wind acceleration; ii) power-law spectra for injected energetic electrons, consistent with observations of such electrons in situ and of X-ray emission.     

The Effect of Helicity Dissipation on the Critical State of an Avalanche Model for Solar Flares

We perform numerical simulations using an avalanche model for solar flares, in which the effect of avalanche event duration is included and the lateral boundary condition can be either open or periodic. The results from the simulations show that self-organized criticality (SOC) exists under a variety of conditions of helicity dissipation, and they are similar in the sense that the indices of power-law distributions of avalanche sizes are the same, while the duration and waiting time distributions differ little. Of interest are: (1) if there exists helicity dissipation in the course of avalanches, SOC exists only when the amount of helicity dissipation per avalanche is small; (2) sudden reductions in the total helicity of the system do not severely disturb SOC, if the amount reduced is moderate; (3) the distribution of waiting times is shown to be exponential, in consistent with the Poisson statistics other avalanche models have predicted, and the exponent increases as the effect of event duration becomes larger. The self-similar structure of the avalanche time series is also examined. These results imply that, although helicity is dissipated in resistive diffusion of flares, the amount of dissipation should be small and the conservation law of helicity thus holds in an approximate sense. Also, the coronal mass ejections (CMEs), observed to take helicity out of the solar corona in an eruptive way, may disrupt the statistical equilibrium of the corona only temporarily.     

Investigation of the X-Ray Emission of the Large Arcade Flare of 2 March 1993

A large arcade flare, occurring on 2 March 1993, has been investigated using X-ray observations recorded by the Yohkoh and GOES satellites and the Compton Gamma Ray Observatory. We analyzed the quasi-periodicity of the hard-X-ray (HXR) pulses in the impulsive phase of the flare and found a close similarity between the quasi-periodic sequence of the pulses to that observed in another large arcade flare, that of 2 November 1991. This similarity helped to explain the strong HXR pulses which were recorded at the end of the impulsive phase as due to the inflow of dense plasma (coming from the chromospheric evaporation) into the acceleration volume inside the cusp. In HXR images a high flaring loop was seen with a triangular cusp structure at the top, where the electrons were efficiently accelerated. The sequence of HXR images allowed us to investigate complicated changes in the precipitation of the accelerated electrons toward the flare footpoints. We have shown that all these impulsive-phase observations can be easily explained in terms of the model of electron acceleration in oscillating magnetic traps located within the cusp structure. Some soft-X-ray (SXR) images were available for the late decay phase. They show a long arcade of SXR loops. Important information about the evolution of the flare during the slow decay phase is contained in the time variation of the temperature, T(t), and emission measure, EM(t). This information is the following: i) weak heating occurs during the slow decay phase and it slowly decreases; ii) the decrease in the heating determines a slow and smooth decrease in EM; iii) the coupling between the heating and the amount of the hot plasma makes the flare evolve along a sequence of quasi-steady states during the slow decay phase (QSS evolution).     

RHESSI Microflares: I. X-Ray Properties and Multiwavelength Characteristics

We study the general X-ray and multiwavelength characteristics of microflares of GOES class A0.7 to B7.4 (background subtracted) detected by the Reuven Ramaty High Energy Solar Spectroscopic Imager (RHESSI) on 26 September 2003 comparing them with the properties of regular flares. All the events for which X-ray imaging was feasible originated in one active region and were accumulated in areas with intermixed magnetic polarities. During the events’ rise and peak phase, the RHESSI X-ray spectra show a steep nonthermal power-law component (4?γ?10) for energies ??10 keV. Further evidence for the presence of electron beams is provided by the association with radio type III bursts in 5 out of 11 events where AIP radio spectra were available. The strongest event in our sample shows radio signatures of a type II precursor. The thermally emitting flare plasma observed by RHESSI is found to be hot, 11?T?15 MK, with small emission measures, 10⁴⁶?EM?10⁴⁷ cm^?3, concentrated in the flare loop. In the EUV (TRACE 171 Å), the UV (TRACE 1600 Å) and Kanzelhöhe Solar Observatory Hα, impulsive brightenings at both ends of the RHESSI 3?–?6 keV X-ray loop source are observed, situated in opposite magnetic polarity fields. During the decay phase, a postflare loop at the location of the RHESSI loop source is observed in the TRACE 171 Å? channel showing plasma that is cooled from ??10 MK to ≈?1 MK. Correlations between various thermal and nonthermal parameters derived from the RHESSI microflare spectra compared to the same correlations obtained for a set of small and large flares by Battaglia et al. (Astron. Astrophys. 439, 737, 2005) indicate that the RHESSI instrument gives us a spectrally biased view since it detects only hot (T?10 MK) microflares, and thus the correlations between RHESSI microflare parameters have to be interpreted with caution. The thermal and nonthermal energies derived for the RHESSI microflares are \(\bar{E}_{\mathrm{th}}=7\times 10^{27}\) ergs and \(\bar{E}_{\mathrm{nth}}=2\times 10^{29}\) ergs, respectively. Possible reasons for the order-of-magnitude difference between the thermal and nonthermal microflare energies, which was also found in previous studies, are discussed. The determined event rate of 3.7 h^?1 together with the average microflare energies indicate that the total energy in the observed RHESSI microflares is far too small to account for the heating of the active region corona in which they occur.     

A Nonlinear Force-Free Magnetic Field Approximation Suitable for Fast Forward-Fitting to Coronal Loops. II. Numeric Code and Tests

Based on a second-order approximation of nonlinear force-free magnetic field solutions in terms of uniformly twisted field lines derived in Paper I, we develop here a numeric code that is capable to forward-fit such analytical solutions to arbitrary magnetogram (or vector magnetograph) data combined with (stereoscopically triangulated) coronal loop 3D coordinates. We test the code here by forward-fitting to six potential field and six nonpotential field cases simulated with our analytical model, as well as by forward-fitting to an exactly force-free solution of the Low and Lou (Astrophys. J. 352, 343, 1990) model. The forward-fitting tests demonstrate: i) a satisfactory convergence behavior (with typical misalignment angles of μ≈1^°?–?10^°), ii) relatively fast computation times (from seconds to a few minutes), and iii) the high fidelity of retrieved force-free α-parameters (α _fit/α _model≈0.9?–?1.0 for simulations and α _fit/α _model≈0.7±0.3 for the Low and Lou model). The salient feature of this numeric code is the relatively fast computation of a quasi-force-free magnetic field, which closely matches the geometry of coronal loops in active regions, and complements the existing nonlinear force-free field (NLFFF) codes based on photospheric magnetograms without coronal constraints.     

Excitation of Langmuir waves by the lower energy cutoff behavior of power-law electrons

Langmuir waves (LWs), which are believed to play a crucial role in the plasma emission of solar radio bursts, can be excited by streaming instability of energetic electron beams. However, solar hard X-ray observations imply that the energetic flare electrons usually have a power-law energy distribution with a lower energy cutoff. In this paper, we investigate LWs driven by the power-law electrons. The results show that power-law electrons with the steepness cutoff behavior can excite LWs effectively because of the population inversion distribution below the cutoff energy (E _c ). The growth rate of LWs increases with the steepness index (δ) and decreases with the power-law index (α). The wave number of the fastest growing LWs (kλ _D ), decreases with the characteristic velocity of the power-law electrons ( \(v_{c}=\sqrt{2E_{c}/m_{e}}\) ) and increases with the thermal velocity of ambient electrons (v _T ). This can be helpful for us to understand better the physics of LWs and the dynamics of energetic electron beams in space and astrophysical plasmas.     

Scalar field power-law cosmology with spatial curvature and dark energy-dark matter interaction

We consider a late closed universe of which scale factor is a power function of time using observational data from combined WMAP5+BAO+SN Ia dataset and WMAP5 dataset. The WMAP5 data give power-law exponent, α=1.01 agreeing with the previous study of H(z) data while combined data gives α=0.985. Considering a scalar field dark energy and dust fluid evolving in the power-law universe, we find field potential, field solution and equation of state parameters. Decaying from dark matter into dark energy is allowed in addition to the non-interaction case. Time scale characterizing domination of the kinematic expansion terms over the dust and curvature terms in the scalar field potential are found to be approximately 5.3 to 5.5 Gyr. The interaction affects in slightly lowering the height of scalar potential and slightly shifting potential curves rightwards to later time. Mass potential function of the interacting Lagrangian term is found to be exponentially decay function.     

Are There Different Populations of Flux Ropes in the Solar Wind?

Flux ropes are twisted magnetic structures that can be detected by in-situ measurements in the solar wind. However, different properties of detected flux ropes suggest different types of flux-rope populations. As such, are there different populations of flux ropes? The answer is positive and is the result of the analysis of four lists of flux ropes, including magnetic clouds (MCs), observed at 1 AU. The in-situ data for the four lists were fitted with the same cylindrical force-free field model, which provides an estimate of the local flux-rope parameters such as its radius and orientation. Since the flux-rope distributions have a broad dynamic range, we went beyond a simple histogram analysis by developing a partition technique that uniformly distributes the statistical fluctuations across the radius range. By doing so, we found that small flux ropes with radius R<0.1 AU have a steep power-law distribution in contrast to the larger flux ropes (identified as MCs), which have a Gaussian-like distribution. Next, from four CME catalogs, we estimated the expected flux-rope frequency per year at 1 AU. We found that the predicted numbers are similar to the frequencies of MCs observed in-situ. However, we also found that small flux ropes are at least ten times too abundant to correspond to CMEs, even to narrow ones. Investigating the different possible scenarios for the origin of these small flux ropes, we conclude that these twisted structures can be formed by blowout jets in the low corona or in coronal streamers.     

Spatially Resolved Microwave Observations of Multiple Periodicities in a Flaring Loop

Quasi-periodic pulsations (QPPs) with at least three simultaneously existing spectral components with periods P≥30 s, P≈20 s, and about P≈10 s were detected during the decay phase of a solar flare on 3 July 2002, observed with the Nobeyama Radioheliograph (NoRH). A detailed study of the spatial structure of the Fourier amplitudes of QPPs along a flaring loop has revealed different spatial distributions of the three components. It is shown that the source of the QPPs with period P≥30 s has its maximum amplitude in the inner region of the loop, between the footpoints. QPPs with period P≈20 s are localized at the periphery of the loop, mainly in the outer parts of the footpoints. The spatial distribution of oscillations with period about P≈10 s contains three regions of high QPP amplitudes: two near the footpoints and one in the middle of the flaring region. It is shown that the observed properties of the spectral components are most accurately described by the fundamental, second, and third harmonics of the kink mode standing waves. This is the first identification of the kink mode in flare loops which is based on strict limitations derived from data on the spatial structure of a pulsating flare region.     

Analysis of the time profile of type III bursts at meter wavelengths

The time profile of two sets of isolated type III bursts, observed in the meter wavelength range at the Trieste Astronomical Observatory, was analyzed using a Fourier transform technique in order to accurately determine the decay constant of the exponential phase and to derive the exciter time profile. The decay constant () was found to be correlated with the exciter duration (D _e ), suggesting that the damping of plasma waves is not of collisional origin and confirming results obtained by previous authors at lower frequencies. In particular, two distributions can be identified in the ( – D _e ) plane and fitted by two nearly parallel lines, which could be the signature of different decay processes. Moreover, the damping constant observed at higher frequencies (327 and 408 MHz) has the same dependence on exciter duration as that at the lower frequency (237 MHz), also in disagreement with the collisional hypothesis.     

Cosmological implications of exponential harmonic field with collisional matter

We have studied the evolution of cosmological parameters by considering exponential harmonic field with collisional matter. A comparison has been made with the behavior of these parameters in the presence of ordinary matter and the model \(\Lambda CDM\). We have also compared the evolution of these parameters with the ones obtained in the modified gravity f(R) and f(R, T) theory case. The results are in line with those of the modified gravity so that the harmonic exponential field can be used to explain why the Universe has gone from the deceleration phase to the acceleration phase.     

Peak Frequency Dynamics in Solar Microwave Bursts

We analyze the dynamics of the broadband frequency spectrum of 338 microwave bursts observed in the years 2001?–?2002 with the Owens Valley Solar Array. A subset of 38 strong microwave bursts that show a single spectral maximum are studied in detail. Our main goal is to study changes in spectral peak frequency ν _pk with time. We show that, for a majority of these simple bursts, the peak frequency shows a high positive correlation with flux density – it increases on the rise phase in ≈83% of 24 bursts where it could be cleanly measured, and decreases immediately after the peak time in ≈62% of 34 bursts. This behavior is in qualitative agreement with theoretical expectations based on gyrosynchrotron self-absorption. However, for a significant number of events (≈30?–?36%) the peak frequency variation is much smaller than expected from self-absorption, or may be entirely absent. The observed temporal behavior of ν _pk is compared with a simple model of gyrosynchrotron radio emission. We show that the anomalous behavior is well accounted for by the effects of Razin suppression, and further show how an analysis of the temporal evolution of ν _pk can be used to uniquely determine the relative importance of self-absorption and Razin suppression in a given burst. The analysis technique provides a new, quantitative diagnostic for the gyrosynchrotron component of solar microwave bursts. Applying this analysis technique to our sample of bursts, we find that in most of the bursts (60%) the spectral dynamics of ν _pk around the time of peak flux density is caused by self-absorption. On the other hand, for a significant number of events (≈70%), the Razin effect may play the dominant role in defining the spectral peak and dynamics of ν _pk, especially on the early rise phase and late decay phase of the bursts.     

On the power-law distributions of X-ray fluxes from solar flares observed with GOES

The power-law frequency distributions of the peak flux of solar flare X-ray emission have been studied extensively and attributed to a system having self-organized criticality(SOC).In this paper,we first show that,so long as the shape of the normalized light curve is not correlated with the peak flux,the flux histogram of solar flares also follows a power-law distribution with the same spectral index as the powerlaw frequency distribution of the peak flux,which may partially explain why power-law distributions are ubiquitous in the Universe.We then show that the spectral indexes of the histograms of soft X-ray fluxes observed by GOES satellites in two different energy channels are different:the higher energy channel has a harder distribution than the lower energy channel,which challenges the universal power-law distribution predicted by SOC models and implies a very soft distribution of thermal energy content of plasmas probed by the GOES satellites.The temperature(T) distribution,on the other hand,approaches a power-law distribution with an index of 2 for high values of T.Hence the application of SOC models to the statistical properties of solar flares needs to be revisited.     

Oscillations in Solar Faculae. III. The Phase Relations Between Chromospheric and Photospheric Line-of-Sight Velocities

An analysis of line-of-sight velocity oscillation in nine solar faculae was undertaken with the aim of studying phase relations between chromospheric (He?i 10830?Å line) and photospheric (Si?i 10827 Å line) five-minute oscillations. We found that the time lag of the chromospheric signal relative to photospheric one varies from ?12 to 100 seconds and is about 50 seconds on average. We assume that the small observed lag can have three possible explanations: i) convergence of formation levels of He?i 10830?Å and Si?i 10827?Å in faculae; ii) significant increase of five-minute oscillation propagation velocity above faculae; iii) simultaneous presence of standing and travelling waves.     

A Statistical Study of Rhessi Flares

A statistical analysis of RHESSI X-ray flares in the 12–25 keV band during the period from February 2002 to June 2005 is presented. We found that a power-law with an index of 1.80± 0.02 can fit well the frequency distribution of the peak count rates. This power-law does not change significantly with time. However, the frequency distribution of the flare durations cannot be fitted well by a single power-law. There is a weak correlation between the peak count rates and the characteristic times like rise times, decay times, or durations. But the correlation between the rise times and decay times seems to be strong. We discuss the results obtained and compare them with previous works. The frequency distribution of rise times for the sub-group events with a similar magnitude of peak count rates is also shown. In particular, we propose a new parameter R _a , the growth factor of the count rate, defined as the peak count rate divided by the rise time, to reflect the characteristics of the rising phases of flares. The distribution of R _a is shown and discussed.     

Extreme Ultraviolet Late-Phase Flares: Before and During the Solar Dynamics Observatory Mission

The solar extreme-ultraviolet (EUV) observations from the Solar Dynamics Observatory (SDO) have revealed interesting characteristics of warm coronal emissions, such as Fe xvi 335 Å emission, which peak soon after the hot coronal X-ray emissions peak during a flare and then sometimes peak for a second time hours after the X-ray flare peak. This flare type, with two warm coronal emission peaks but only one X-ray peak, has been named the EUV late phase (Woods et al., Astrophys. J. 739, 59, 2011). These flares have the distinct properties of i) having a complex magnetic-field structure with two initial sets of coronal loops, with one upper set overlaying a lower set, ii) having an eruptive flare initiated in the lower set and disturbing both loop sets, iii) having the hot coronal emissions emitted only from the lower set in conjunction with the X-ray peak, and iv) having the first peak of the warm coronal emissions associated with the lower set and its second peak emitted from the upper set many minutes to hours after the first peak and without a second X-ray enhancement. The disturbance of the coronal loops by the eruption is at about the same time, but the relaxation and cooling down of the heated coronal loops during the post-flare reconnections have different time scales with the longer, upper loops being significantly delayed from the lower loops. The difference in these cooling time scales is related to the difference between the two peak times of the warm coronal emission and is also apparent in the decay profile of the X-ray emissions having two distinct decays, with the first decay slope being steeper (faster) and the delayed decay slope being smaller (slower) during the time of the warm-coronal-emission second peak. The frequency and relationship of the EUV late-phase decay times between the Fe xvi 335 Å two flare peaks and X-ray decay slopes are examined using three years of SDO/EUV Variability Experiment (EVE) data, and the X-ray dual-decay character is then exploited to estimate the frequency of EUV late-phase flares during the past four solar cycles. This study indicates that the frequency of EUV late-phase flares peaks before and after each solar-cycle minimum.     

Frequency dependence of solar flare occurrence rates—inferred from power-law distribution

Based on the frequency dependence of the power-law distribution of the peak fluxes in 486 radio bursts in 1–35 GHz observed by Nobeyama Radio Polarimeters (see Song et al. in Astrophys. J. 750:160, 2012), we have first suggested in this paper that the events with power-law behaviors may be emitted from the optically-thin regions, which can be considered as a good measure for the flare energy release. This result is supported by that both the power-law and optical-thin events gradually increase with radio frequencies, which are well fitted by a power-law function with similar indices of 0.48 and 0.80, respectively. Moreover, a flare occurrence rate is newly defined by the power-law event number in per unit frequency. Its values in lower frequencies are evidently larger than those in higher frequencies, which just imply that most flares are trigged in higher corona. Hence, the frequency variation of power-law event number may indicate different energy dissipation rates on different coronal heights.     

Statistical Survey of Type III Radio Bursts at Long Wavelengths Observed by the Solar TErrestrial RElations Observatory (STEREO)/Waves Instruments: Radio Flux Density Variations with Frequency

We have performed a statistical study of 152 Type III radio bursts observed by Solar TErrestrial RElations Observatory (STEREO)/Waves between May 2007 and February 2013. We investigated the flux density between 125 kHz and 16 MHz. Both high- and low-frequency cutoffs were observed in 60 % of events, suggesting an important role of propagation. As already reported by previous authors, we observed that the highest flux density occurs at 1 MHz on both spacecraft. We developed a simplified analytical model of the flux density as a function of radial distance and compared it with the STEREO/Waves data.     

Evidence for energy injection and a fine-tuned central engine at optical wavelengths in GRB 070419A

We present a comprehensive multiwavelength temporal and spectral analysis of the 'fast rise exponential decay' GRB 070419A. The early-time emission in the γ-ray and X-ray bands can be explained by a central engine active for at least 250 s, while at late times the X-ray light curve displays a simple power-law decay. In contrast, the observed behaviour in the optical band is complex (from 10² up to 10⁶ s). We investigate the light-curve behaviour in the context of the standard forward/reverse shock model; associating the peak in the optical light curve at ∼450 s with the fireball deceleration time results in a Lorenz factor  Γ≈ 350  at this time. In contrast, the shallow optical decay between 450 and 1500 s remains problematic, requiring a reverse shock component whose typical frequency is above the optical band at the optical peak time for it to be explained within the standard model. This predicts an increasing flux density for the forward shock component until   t ∼ 4 × 10⁶ s  , inconsistent with the observed decay of the optical emission from   t ∼ 10⁴ s  . A highly magnetized fireball is also ruled out due to unrealistic microphysic parameters and predicted light-curve behaviour that is not observed. We conclude that a long-lived central engine with a finely tuned energy injection rate and a sudden cessation of the injection is required to create the observed light curves, consistent with the same conditions that are invoked to explain the plateau phase of canonical X-ray light curves of γ-ray bursts.