Diagnostics of magnetic flux tube oscillations on the Sun based on fine-structure characteristics of the radio spectrum

The possibility of obtaining information about oscillation processes in magnetic flux tubes on the Sun by analyzing the undulating frequency drift of the zebra pattern in the dynamic spectrum of solar radio emission is discussed. It is shown that the oscillatory variation in the frequency of zebra stripes can be associated with fast magnetoacoustic (FMA) oscillations in a flux tube, which lead to oscillations in the magnetic field strength and electron number density. The October 25, 1994 event recorded by the radio spectrograph of the Astrophysical Institute Potsdam is used as an example to demonstrate the possibility of determining the parameters of FMA oscillations and the physical conditions in coronal magnetic loops from the observed zebra-pattern characteristics.     

Unusual Zebra Patterns in the Decimeter Wave Band

An analysis of new observations showing fine structures consisting of narrowband fiber bursts as substructures of large-scale zebra-pattern stripes is carried out. We study four events using spectral observations taken with a newly built spectrometer located at the Huairou station, China, in the frequency range of 1.1 – 2.0 GHz with extremely high frequency and time resolutions (5 MHz and 1.25 ms). All the radio events were analyzed by using the available satellite data (SOHO LASCO, EIT, and MDI, TRACE, and RHESSI). Small-scale fibers always drift to lower frequencies. They may belong to a family of ropelike fibers and can also be regarded as fine structures of type III bursts and broadband pulsations. The radio emission was moderately or strongly polarized in the ordinary wave mode. In three main events fiber structure appeared as a forerunner of the entire event. All four events were small decimeter bursts. We assume that for small-scale fiber bursts the usual mechanism of coalescence of whistler waves with plasma waves can be applied, and the large-scale zebra pattern can be explained in the conventional double plasma resonance (DPR) model. The appearance of an uncommon fine structure is connected with the following special features of the plasma wave excitation in the radio source: Both whistler and plasma wave instabilities are too weak at the very beginning of the events (i.e., the continuum was absent), and the fine structure is almost invisible. Then, whistlers generated directly at DPR levels “highlight” the radio emission only from these levels owing to their interaction with plasma waves.     

Superfine Temporal Structure of the Microwave Burst on 21 April 2002: What Can We Learn about the Emission Mechanism?

Zebra pattern is observed as a number of almost parallel bright and dark stripes in the dynamic spectrum of solar radio emission. Recent observations show that zebra patterns in the microwave range often have superfine temporal structure, when the zebra stripes consist of individual short pulses similar to millisecond spikes. In this article, the burst on 21 April 2002 is investigated. The burst with a distinct superfine structure was detected at the Huairou Station (China) in 2.6?–?3.8 GHz frequency range. It is found that the emission pulses are quasi-periodic, the pulse period is about 25?–?40 ms and decreases with an increase of the emission frequency. The degree of circular polarization of zebra pattern increases with an increase of the emission frequency, it varies from moderate (about 20%) to relatively high (>60%) values. The temporal delay between the signals with left- and right-handed polarization is not found. The conclusion is made that the emission is generated by plasma mechanism at the fundamental plasma frequency in a relatively weak magnetic field. The observed polarization of the emission is formed during its propagation due to depolarization effects. A model is proposed in which the superfine temporal structure is formed due to modulation of the emission mechanism by downward propagating MHD oscillations; this model allows us to explain the observed variation of the pulse period with the emission frequency.     

Reversed Drifting Quasi-periodic Pulsating Structure in the X1.3 Solar Flare on 30 July 2005

Based on the analysis of the microwave observations at the frequency range of 2.60 – 3.80 GHz in the solar X1.3 flare event observed at the Solar Broadband RadioSpectrometer in Huairou (SBRS/Huairou) on 30 July 2005, an interesting reversed drifting quasi-periodic pulsating structure (R-DPS) is confirmed. The R-DPS is mainly composed of two drifting pulsating components: one is a relatively slow very short-period pulsation (VSP) with a period of about 130 – 170 ms, the other is a relatively fast VSP with a period of about 70 – 80 ms. The R-DPS has a weak left-handed circular polarization. Based on the synthetic investigations of Reuven Ramaty High Energy Solar Spectroscopic Imaging (RHESSI) hard X-ray, Geostationary Operational Environmental Satellite (GOES) soft X-ray observations, and magnetic field extrapolation, we suggest that the R-DPS possibly reflects flaring dynamic processes of the emission source regions.     

On the superfine structure of solar microwave bursts

Solar microwave bursts with a zebra pattern commonly exhibit a superfine time structure: the zebra stripes consist of separate spike-like pulses. We investigate the superfine structure in the April 21, 2002 event. The emission pulses are shown to exhibit a high periodicity (with a period of about 30 ms); there is a clear correlation between the individual zebra stripes. This structure of the dynamic spectra most likely reflects a periodic injection of electron beams, which generate emission at the double plasma resonance levels.     

Time-Dependent Stochastic Modeling of Solar Active Region Energy

A time-dependent model for the energy of a flaring solar active region is presented based on an existing stochastic jump-transition model (Wheatland and Glukhov in Astrophys. J. 494, 858, 1998; Wheatland in Astrophys. J. 679, 1621, 2008 and Solar Phys. 255, 211, 2009). The magnetic free energy of an active region is assumed to vary in time due to a prescribed (deterministic) rate of energy input and prescribed (random) jumps downwards in energy due to flares. The existing model reproduces observed flare statistics, in particular flare frequency – size and waiting-time distributions, but modeling presented to date has considered only the time-independent choices of constant energy input and constant flare-transition rates with a power-law distribution in energy. These choices may be appropriate for a solar active region producing a constant mean rate of flares. However, many solar active regions exhibit time variation in their flare productivity, as exemplified by NOAA active region (AR) 11029, observed during October – November 2009 (Wheatland in Astrophys. J. 710, 1324, 2010). Time variation is incorporated into the jump-transition model for two cases: (1) a step change in the rates of flare transitions, and (2) a step change in the rate of energy supply to the system. Analytic arguments are presented describing the qualitative behavior of the system in the two cases. In each case the system adjusts by shifting to a new stationary state over a relaxation time which is estimated analytically. The model exhibits flare-like event statistics. In each case the frequency – energy distribution is a power law for flare energies less than a time-dependent rollover set by the largest energy the system is likely to attain at a given time. The rollover is not observed if the mean free energy of the system is sufficiently large. For Case 1, the model exhibits a double exponential waiting-time distribution, corresponding to flaring at a constant mean rate during two intervals (before and after the step change), if the average energy of the system is large. For Case 2 the waiting-time distribution is a simple exponential, again provided the average energy of the system is large. Monte Carlo simulations of Case 1 are presented which confirm the estimate for the relaxation time and the expected forms of the frequency – energy and waiting-time distributions. The simulation results provide a qualitative model for observed flare statistics in AR 11029.     

The efficiency of electron acceleration in solar type-IV radio pulsations with a zebra pattern

Based on a comprehensive analysis of the October 25, 1994 event, we consider the balance of energetic particles in a type-IV solar radio emission source with a zebra-type fine structure (in a coronal magnetic loop). The zebra pattern is formed through the injection of fast electrons into a trap and the formation of a ring-type nonequilibrium electron distribution function. We estimated the characteristic zebra-pattern lifetime, which is determined by the escape of fast particles from the trap into the loss cone. In addition, we determined the number of fast particles that must be injected into the trap to provide the observed radio brightness temperature in zebra-pattern stripes by analyzing the plasma emission mechanism responsible for the zebra-pattern generation. As a result, we estimated the efficiency of the electron acceleration mechanism in coronal magnetic loops at the post-flare evolutionary phase of an active region.     

Investigation of Quasi-periodic Variations in Hard X-Rays of Solar Flares. II. Further Investigation of Oscillating Magnetic Traps

In our recent paper (Jakimiec and Tomczak, Solar Physics 261, 233, 2010) we investigated quasi-periodic oscillations of hard X-rays during the impulsive phase of solar flares. We have come to the conclusion that they are caused by magnetosonic oscillations of magnetic traps within the volume of hard-X-ray (HXR) loop-top sources. In the present paper we investigate four flares that show clear quasi-periodic sequences of the HXR pulses. We also describe our phenomenological model of oscillating magnetic traps to show that it can explain the observed properties of the HXR oscillations. The main results are the following: i) Low-amplitude quasi-periodic oscillations occur before the impulsive phase of some flares. ii) The quasi-periodicity of the oscillations can change in some flares. We interpret this as being due to changes of the length of oscillating magnetic traps. iii) During the impulsive phase a significant part of the energy of accelerated (non-thermal) electrons is deposited within a HXR loop-top source. iv) The quick development of the impulsive phase is due to feedback between the pressure pulses by accelerated electrons and the amplitude of the magnetic-trap oscillation. v) The electron number density and magnetic field strength values obtained for the HXR loop-top sources in several flares fall within the limits of N≈(2 – 15)×10¹⁰ cm⁻³, B≈(45 – 130) gauss. These results show that the HXR quasi-periodic oscillations contain important information about the energy release in solar flares.     

Short-Term Periodicities in Sunspot Activities During the Descending Phase of Solar Cycle 23

In the present study, the short-term periodicities in the daily data of the sunspot numbers and areas are investigated separately for the full disk, northern, and southern hemispheres during Solar Cycle 23 for a time interval from 1 January 2003 to 30 November 2007 corresponding to the descending and minimum phase of the cycle. The wavelet power spectrum technique exhibited a number of quasi-periodic oscillations in all the datasets. In the high frequency range, we find a prominent period of 22 – 35 days in both sunspot indicators. Other quasi-periods in the range of 40 – 60, 70 – 90, 110 – 130, 140 – 160, and 220 – 240 days are detected in the sunspot number time series in different hemispheres at different time intervals. In the sunspot area data, quasi-periods in the range of 50 – 80, 90 – 110, 115 – 130, 140 – 155, 160 – 190, and about 230 days were noted in different hemispheres within the time period of analysis. The present investigation shows that the well-known “Rieger periodicity” of 150 – 160 days reappears during the descending phase of Solar Cycle 23, but this is prominent mainly in the southern part of the Sun. Possible explanations of these observed periodicities are delivered on the basis of earlier results detected in photospheric magnetic field time series (Knaack, Stenflo, and Berdyugina in Astron. Astrophys. 438, 1067, 2005) and solar r-mode oscillations.     

The Ly α and Ly β Profiles in Solar Prominences and Prominence Fine Structure

Ly α and Ly β line profiles in a solar prominence were observed with high spatial and spectral resolution with SOHO/SUMER. Within a 60-arcsec scan, we measure a very large variety of profiles: not only reversed and nonreversed profiles but also red-peaked and blue-peaked ones in both lines. Such a spatial variability is probably related to both the fine structure in prominences and the different orientations of mass motions. The usage of integrated-intensity cuts along the SUMER slit allowed us to categorize the prominence in three regions. We computed average profiles and integrated intensities in these lines in the range 2.36 – 42.3 W m⁻² sr⁻¹ for Ly α and 0.027 – 0.237 W m⁻² sr⁻¹ for Ly β. As shown by theoretical modeling, the Ly α/Ly β ratio is very sensitive to geometrical and thermodynamic properties of fine structure in prominences. For some pixels, and in both lines, we found agreement between observed intensities and those predicted by one-dimensional models. But a close examination of the profiles indicated a rather systematic disagreement concerning their detailed shapes. The disagreement between observations and thread models (with ambipolar diffusion) leads us to speculate about the importance of the temperature gradient between the cool and coronal regions. This gradient could depend on the orientation of field lines as proposed by Heinzel, Anzer, and Gunár (Astron. Astrophys. 442, 331, 2005).     

Evidence of Traveling Waves in Filament Threads

High-resolution Hα filtergrams (0.2″) obtained with the Swedish 1-m Solar Telescope resolve numerous very thin, thread-like structures in solar filaments. The threads are believed to represent thin magnetic flux tubes that must be longer than the observable threads. We report on evidence for small-amplitude (1 – 2 km s⁻¹) waves propagating along a number of threads with an average phase velocity of 12 km s⁻¹ and a wavelength of 4″. The oscillatory period of individual threads vary from 3 to 9 minutes. Temporal variation of the Doppler velocities averaged over a small area containing a number of individual threads shows a short-period (3.6 minutes) wave pattern. These short-period oscillations could possibly represent fast modes in accordance with numerical fibril models proposed by Díaz et al. (Astron. Astrophys. 379, 1083, 2001). In some cases, it is clear that the propagating waves are moving in the same direction as the mass flows.     

Examining Periodic Solar-Wind Density Structures Observed in the SECCHI <Emphasis Type="Italic">Heliospheric Imagers</Emphasis>

We present an analysis of small-scale, periodic, solar-wind density enhancements (length scales as small as ≈ 1000 Mm) observed in images from the Heliospheric Imager (HI) aboard STEREO-A. We discuss their possible relationship to periodic fluctuations of the proton density that have been identified at 1 AU using in-situ plasma measurements. Specifically, Viall, Kepko, and Spence (J. Geophys. Res. 113, A07101, 2008) examined 11 years of in-situ solar-wind density measurements at 1 AU and demonstrated that not only turbulent structures, but also nonturbulent, periodic density structures exist in the solar wind with scale sizes of hundreds to one thousand Mm. In a subsequent paper, Viall, Spence, and Kasper (Geophys. Res. Lett. 36, L23102, 2009) analyzed the α-to-proton solar-wind abundance ratio measured during one such event of periodic density structures, demonstrating that the plasma behavior was highly suggestive that either temporally or spatially varying coronal source plasma created those density structures. Large periodic density structures observed at 1 AU, which were generated in the corona, can be observable in coronal and heliospheric white-light images if they possess sufficiently high density contrast. Indeed, we identify such periodic density structures as they enter the HI field of view and follow them as they advect with the solar wind through the images. The smaller, periodic density structures that we identify in the images are comparable in size to the larger structures analyzed in-situ at 1 AU, yielding further evidence that periodic density enhancements are a consequence of coronal activity as the solar wind is formed.     

Positively Drifting Structures During the 18 March 2003 Solar Flare

We analyze the high-frequency drift radio structures observed by the spectrometer at Purple Mountain Observatory (PMO) over the frequency range of 4.5 – 7.5 GHz during the 18 March 2003 solar flare. The drifting structures take place before the soft X-ray maximum, almost at the maximum of hard X-ray flux at 25 – 50 keV. For the first time, the positive drift in this kind of radio structures is detected in such a high frequency range. Their global drifting rate is roughly estimated as 3.6 GHz s⁻¹. They appear in four groups, lasting in total for less than 6 s, and have a broad bandwidth of more than 2 GHz but a smaller ratio of the bandwidth of the drifting structures to mean frequency than that of the lower frequency range. The lifetime of each individual burst in this event can be derived by using the high temporal resolution of the spectrometer at PMO and has an average value of 36.3 ms. Since the negative drifting structures observed in the 0.6 – 4.5 GHz frequency range were interpreted to be a radio signature of a plasmoid ejected upward (moving out of the Sun), the present observation may imply that it is possible for a plasmoid to move downward during a solar flare. However, for a confirmation of this suggestion direct radio imaging observation would be needed.     

Investigation of Long-Period Oscillations of Sunspots with Ground-Based (Pulkovo) and SOHO/MDI Data

We applied special data-processing algorithms to the study of long-period oscillations of the magnetic-field strength and the line-of-sight velocity in sunspots. The oscillations were investigated with two independent groups of data. First, we used an eight-hour-long series of solar spectrograms, obtained with the solar telescope at the Pulkovo Observatory. We simultaneously measured Doppler shifts of six spectral lines, formed at different heights in the atmosphere. Second, we had a long time series of full-disk magnetograms (10 – 34 hour) from SOHO/MDI for the line-of-sight magnetic-field component. Both ground- and space-based observations revealed long-period modes of oscillations (40 – 45, 60 – 80, and 160 – 180 minutes) in the power spectrum of the sunspots and surrounding magnetic structures. With the SOHO/MDI data, one can study the longer periodicities. We obtained two new significant periods (> 3σ) in the power spectra of sunspots: around 250 and 480 minutes. The power of the oscillations in the lower frequencies is always higher than in the higher ones. The amplitude of the long-period magnetic-field modes shows magnitudes of about 200 – 250 G. The amplitude of the line-of-sight velocity periodicities is about 60 – 110 m s⁻¹. The absence of low-frequency oscillations in the telluric line proves their solar nature. Moreover, the absence of low-frequency oscillations of the line-of-sight velocity in the quiet photosphere (free of magnetic elements) proves their direct connection to magnetic structures. Long-period modes of oscillation observed in magnetic elements surrounding the sunspot are spread over the meso-granulation scales (10″ – 12″), while the sunspot itself oscillates as a whole. The amplitude of the long-period mode of the line-of-sight velocity in a sunspot decreases rapidly with height: these oscillations are clearly visible in the spectral lines originating at heights of approximately 200 km and fade away in lines originating at 500 km. We found a new interesting property: the low-frequency oscillations of a sunspot are strongly reduced when there is a steady temporal trend (strengthening or weakening) of the sunspot’s magnetic field. Another important result is that the frequency of long-period oscillations evidently depends on the sunspot’s magnetic-field strength.     

A physical explanation of solar microwave Zebra pattern with the current-carrying plasma loop model

The microwave Zebra pattern structure is an intriguing fine structure on the dynamic spectra of solar type IV radio bursts. Up to now, there is no perfect physical model for the origin of the solar microwave Zebra pattern. Recently, Ledenev et al. (Sol. Phys. 233:129, 2006) put forward an interference mechanism to explain the features of microwave Zebra patterns in solar continuum events. This model needs a structure with a multitude of discrete narrow-band sources of small size. Based on the model of a current-carrying plasma loop and the theory of tearing-mode instability, we propose that the above structure does exist and may provide the main conditions for the interference mechanism. With this model, we may explain the frequency upper limit, the formation of the parallel and equidistant stripes, the superfine structure and intermediate frequency drift rate of the Zebra stripes. If this explanation is valid, the Zebra pattern structures can reveal some information of the motion and the inner structures of the coronal plasma loops.     

Comparison of the Characteristics of Magnetic Clouds and Magnetic Cloud-Like Structures for the Events of 1995 – 2003

Using nine years of solar wind plasma and magnetic field data from the Wind mission, we investigated the characteristics of both magnetic clouds (MCs) and magnetic cloud-like structures (MCLs) during 1995 – 2003. A MCL structure is an event that is identified by an automatic scheme (Lepping, Wu, and Berdichevsky, Ann. Geophys. 23, 2687, 2005) with the same criteria as for a MC, but it is not usually identifiable as a flux rope by using the MC (Burlaga et al., J. Geophys. Res. 86, 6673, 1981) fitting model developed by Lepping, Jones, and Burlaga (Geophys. Res. Lett. 95(11), 957, 1990). The average occurrence rate is 9.5 for MCs and 13.6 for MCLs per year for the overall period of interest, and there were 82 MCs and 122 MCLs identified during this period. The characteristics of MCs and MCL structures are as follows: (1) The average duration, Δt, of MCs is 21.1 h, which is 40% longer than that for MCLs (Δt=15 h); (2) the average (minimum B _z found in MC/MCL measured in geocentric solar ecliptic coordinates) is −10.2 nT for MCs and −6 nT for MCLs; (3) the average Dst_min (minimum Dst caused by MCs/MCLs) is −82 nT for MCs and −37 nT for MCLs; (4) the average solar wind velocity is 453 km s⁻¹ for MCs and 413 km s⁻¹ for MCLs; (5) the average thermal speed is 24.6 km s⁻¹ for MCs and 27.7 km s⁻¹ for MCLs; (6) the average magnetic field intensity is 12.7 nT for MCs and 9.8 nT for MCLs; (7) the average solar wind density is 9.4 cm⁻³ for MCs and 6.3 cm⁻³ for MCLs; and (8) a MC is one of the most important interplanetary structures capable of causing severe geomagnetic storms. The longer duration, more intense magnetic field and higher solar wind speed of MCs, compared to those properties of the MCLs, are very likely the major reasons for MCs generally causing more severe geomagnetic storms than MCLs. But the fact that a MC is an important interplanetary structure with respect to geomagnetic storms is not new (e.g., Zhang and Burlaga, J. Geophys. Res. 93, 2511, 1988; Bothmer, ESA SP-535, 419, 2003).     

The Growth rate of upper-hybrid waves and dynamics of microwave zebra structures

The growth rate of the upper-hybrid waves with different velocities of superthermal electrons is computed considering a finite temperature of the background plasma and relativistic corrections. Based on these computations two examples of high-frequency zebra structures are interpreted. The sequence of the continuum, zebra structure, and continuum observed in the 29 October 2000, event is explained as an increase and following decrease of the velocity of superthermal electrons in the range of v=0.1–0.3 c. On the other hand, the zebra structure observed during the 18 March 2003 event represents an example with fast electron acceleration.     

The RHESSI Microflare Height Distribution

We present the first in-depth statistical survey of flare source heights observed by RHESSI. Flares were found using a flare-finding algorithm designed to search the 6 – 10 keV count-rate when RHESSI’s full sensitivity was available in order to find the smallest events (Christe et al. in Astrophys. J. 677, 1385, 2008). Between March 2002 and March 2007, a total of 25 006 events were found. Source locations were determined in the 4 – 10 keV, 10 – 15 keV, and 15 – 30 keV energy ranges for each event. In order to extract the height distribution from the observed projected source positions, a forward-fit model was developed with an assumed source height distribution where height is measured from the photosphere. We find that the best flare height distribution is given by g(h)∝exp (−h/λ) where λ=6.1±0.3 Mm is the scale height. A power-law height distribution with a negative power-law index, γ=3.1±0.1 is also consistent with the data. Interpreted as thermal loop-top sources, these heights are compared to loops generated by a potential-field model (PFSS). The measured flare heights distribution are found to be much steeper than the potential-field loop height distribution, which may be a signature of the flare energization process.     

Radio Observations of the 20 January 2005 X-class Flare

We present a multi-frequency and multi-instrument study of the 20 January 2005 event. We focus mainly on the complex radio signatures and their association with the active phenomena taking place: flares, CMEs, particle acceleration, and magnetic restructuring. As a variety of energetic-particle accelerators and sources of radio bursts are present, in the flare – ejecta combination, we investigate their relative importance in the progress of this event. The dynamic spectra of ARTEMIS-IV – Wind/Waves – HiRAS, with 2000 MHz – 20 kHz frequency coverage, were used to track the evolution of the event from the low corona to the interplanetary space; these were supplemented with SXR, HXR, and γ-ray recordings. The observations were compared with the expected radio signatures and energetic-particle populations envisaged by the Standard Flare – CME model and the reconnection outflow termination shock model. A proper combination of these mechanisms seems to provide an adequate model for the interpretation of the observational data.     

Spiky Fine Structure of Type III-like Radio Bursts in Absorption

An uncommon fine structure in the radio spectrum consisting of bursts in absorption was observed with the Chinese Solar Broadband Radiospectrometer (SBRS) in the frequency range of 2.6?–?3.8 GHz during an X3.4/4B flare on 13 December 2006 in active region NOAA 10930 (S05W33). Usual fine structures in emission such as spikes, zebra stripes, and drifting fibers were observed at the peak of every new flare brightening. Within an hour at the decay phase of the event we observed bursts consisting of spikes in absorption, which pulsated periodically in frequency. Their instantaneous frequency bandwidths were found to be in the 75 MHz range. Moreover, in the strongest Type III-like bursts in absorption, the spikes showed stripes of the zebra-pattern (ZP) that drifted to higher frequencies. All spikes had the duration as short as down to the limit of the instrument resolution of ≈8 ms. The TRACE 195 Å images indicate that the magnetic reconnection at this moment occurred in the western edge of the flare loop arcade. Taking into account the presence of the reverse-drifting bursts in emission, in the course of the restoration of the magnetic structures in the corona, the acceleration of the beams of fast particles must have occurred both upward and downward at different heights. The upward beams will be captured by the magnetic trap, where the loss-cone distribution of fast particles (responsible for the emission of continuum and ZP) were formed. An additional injection of fast particles will fill the loss-cone later, breaking the loss-cone distribution. Therefore, the generation of continuum will be quenched at these moments, which was evidenced by the formation of bursts in absorption.