Oscillations of coronal loops and second pulsations of solar radio emission

The dispersion properties of the sausage eigenmodes of oscillations in a thin magnetic flux tube are numerically analyzed in terms of ideal magnetohydrodynamics (MHD). The period of the modes accompanied by the emission of MHD waves into the surrounding medium, which leads to acoustic damping of oscillations, is determined by the radius of the tube, not by its length. The dissipation of the sausage oscillations in comparatively high (?0.7R _⊙) and tenuous (?6 × 10⁸ cm^?3) coronal loops is considered. Their Q factor has bound found to be determined by the acoustic damping mechanism. The ratio of the plasma densities outside and inside the loop and the characteristic height of the emission source have been estimated by assuming the quasi-periodic pulsations of meter-wavelength radio emission to be related to the sausage oscillations.     

Observations of Double-Periodic X-Ray Emission in Interacting Systems of Solar Flare Loops

We investigate the M1.8 solar flare of 20 October 2002. The flare was accompanied by quasi-periodic pulsations (QPP) of both thermal and nonthermal hard X-ray emissions (HXR) observed by RHESSI in the 3?–?50 keV energy range. Analysis of the HXR time profiles in different energy channels made with the Lomb periodogram has indicated two statistically significant time periods of about 16 and 36 s. The 36 s QPP were observed only in the nonthermal HXR emission in the impulsive phase of the flare. The 16 s QPP were found in thermal and nonthermal HXR emission both in the impulsive and in the decay phases of the flare. Imaging analysis of the flare region, the determined time periods of the QPP, and the estimated physical parameters of the flare loops allowed us to interpret the observed QPP in terms of MHD oscillations excited in two spatially separated, but interacting systems of flaring loops.     

Waves and Oscillations in the Corona – (Invited Review)

It has long been suggested on theoretical grounds that MHD waves must occur in the solar corona, and have important implications for coronal physics. An unequivocal identification of such waves has however proved elusive, though a number of events were consistent with an interpretation in terms of MHD waves. Recent detailed observations of waves in events observed by SOHO and TRACE removes that uncertainty, and raises the importance of MHD waves in the corona to a higher level. Here we review theoretical aspects of how MHD waves and oscillations may occur in a coronal medium. Detailed observations of waves and oscillations in coronal loops, plumes and prominences make feasible the development of coronal seismology, whereby parameters of the coronal plasma (notably the Alfvén speed and through this the magnetic field strength) may be determined from properties of the oscillations. MHD fast waves are refracted by regions of low Alfvén speed and slow waves are closely field-guided, making regions of dense coronal plasma (such as coronal loops and plumes) natural wave guides for MHD waves. There are analogies with sound waves in ocean layers and with elastic waves in the Earth's crust. Recent observations also indicate that coronal oscillations are damped. We consider the various ways this may be brought about, and its implications for coronal heating.     

Transverse oscillations in coronal loops observed with TRACE – I. An Overview of Events,Movies, and a Discussion of Common Properties and Required Conditions

We study transverse loop oscillations triggered by 17flares and filament destabilizations; only 2 such cases have been reported in the literature until now. Oscillation periods are estimated to range over a factor of ∼15, with most values between 2 and 7 min. The oscillations are excited by filament destabilizations or flares (in 6% of the 255 flares inspected, ranging from about C3 to X2). There is no clear dependence of oscillation amplitude on flare magnitude. Oscillations occur in loops that close within an active region, or in loops that connect an active region to a neighboring region or to a patch of strong flux in the quiet Sun. Some magnetic configurations are particularly prone to exhibit oscillations: two active regions showed two, and one region even three, distinct intervals with loop oscillations. The loop oscillations are not a resonance that builds up: oscillations in loops that are excited along their entire length are likely to be near the fundamental resonance mode because of that excitation profile, but asymmetrically excited oscillations clearly show propagating waves that are damped too quickly to build up a resonance, and some cases show multiple frequencies. We discuss evidence that all oscillating loops lie near magnetic separatrices that outline the large-scale topology of the field. All magnetic configurations are more complicated than a simple bipolar region, involving mixed-polarities in the interior or vicinity of the region; this may reflect that the exciting eruptions occur only in such environments, but this polarity mixing likely also introduces the large-scale separatrices that are involved. Often the oscillations occur in conjunction with gradual adjustments in loop positions in response to the triggering event. We discuss the observations in the context of two models: (a) transverse waves in coronal loops that act as wave guides and (b) strong sensitivity to changes in the field sources for field lines near separatrices. Properties that favor model b are (1) the involvement of loops at or near separatrices that outline the large-scale topology of the field, (2) the combined occurrence of oscillations and loop translations, (3) the small period spread and similar decay time scale in a set of oscillating loops in one well-observed event, and (4) the existence of loops oscillating in antiphase with footpoints close together in two cases. All other properties are compatible with either model, except the fact that almost all of the oscillations start away from the triggering event, suggestive of an outward-pushing exciting wave more in line with model a. The spread in periods from event to event suggests that the oscillations may reflect the properties of some driver mechanism that is related to the flare or mass ejection. Supplementary material to this paper is available in electronic form at http://dx.doi.org/10.1023/A:1014957715396     

Global Coronal Seismology

Following the observation and analysis of large-scale coronal-wave-like disturbances, we discuss the theoretical progress made in the field of global coronal seismology. Using simple mathematical techniques we determine average values for the magnetic field together with a magnetic map of the quiet Sun. The interaction between global coronal waves and coronal loops allows us to study loop oscillations in a much wider context, i.e. we connect global and local coronal oscillations.     

Resonant interactions of modes in coronal magnetic flux tubes

Nonlinear resonant interactions of different kinds of fast magnetosonic (FMS) waves trapped in the inhomogeneity of a low- plasma density, stretched along a magnetic field (as, for example, in coronal loops) are investigated. A set of equations describing the amplitudes of interactive modes is derived for an arbitrary density profile. The quantitative characteristics of such interactions are found. The decay instability of the wave with highest frequency is possible in the system. If amplitudes of interactive modes have close values, the long-period temporal and spatial oscillations are in the system.For a quantitative illustration, the parabolic approximation of the transverse density profile has been chosen. Dispersion relations of FMS waves trapped in a low- plasma slab with a parabolic transverse density profile are found. The transverse structure of the waves in this case can be expressed through Hermitian polynomials. The interaction of kink and sausage waves is investigated. The sausage wave, with a sufficiently large amplitude, may be unstable with respect to the decay into two kink waves, in particular. The spatial scale of a standing wave structure and the time spectrum of radiation are formed due to the nonlinear interactions of loop modes which contain information about the parameters of the plasma slab.     

Oscillatory Behavior in the Corona

We detect and analyze the oscillatory behavior of waves using a coronal seismology tool on sequences of coronal images. We study extreme-ultraviolet image sequences of active and quiet Sun regions and of coronal holes we identify 3- and 5-minute periodicities. In each studied region the 3- and 5-minute periodicities are similarly frequent. The number of pixels exhibiting a 3-minute periodicity is between 6 %?–?8 % and those pixels exhibiting a 5-minute periodicity is between 5 %?–?9 % of the total number of observed pixels. Our results show 3-minute oscillations along coronal loop structures but do not show 5-minute oscillations along these same loop structures. The number of pixels exhibiting 3- and 5-minute periodicities in one type of region (active Sun, quiet Sun, and coronal holes) is roughly the same for all observed regions, leading us to infer that the 3- and 5-minute oscillations are the result of a global mechanism.     

Slow-mode oscillations of large-scale coronal loops

On several occasions, repetitive X-ray brightenings, sometimes accompanied by mass injections into adjacent loops, appeared quasi-periodically with mean periods close to 20 minutes. In all cases when X-ray images were available, the sites of these brightenings were in active regions which were associated with large-scale coronat loops of length (2 – 3) × 10⁵ km. Therefore, the primary source of these long-periodic pulsations might be slow-mode oscillations in these large-scale loops. Free MHD oscillations, proposed earlier by Roberts, Edwin, and Benz (1984), may fit the observed data.     

Radial oscillations of current-carrying coronal loops

The radial oscillations of coaxial magnetic flux tubes with an azimuthal field in the shell modeling current-carrying coronal loops are studied in the cool plasma approximation. Since the concept of current-carrying coronal loops provides a theoretical basis for studying simple loop flares, finding their parameters by means of coronal seismology is a topical problem of modern solar physics. The dispersion equation for radial oscillations is derived and the dispersion curves are constructed. Oscillations with arbitrarily long periods are shown to exist at the fundamental radial mode.     

Propagating disturbances along fan-like coronal loops in an active region

Propagating disturbances are often observed in active region fan-like coronal loops. They were thought to be due to slow mode magnetohydrodynamic waves based on some of the observed properties. However, recent studies involving spectroscopy indicate that they could be due to high speed quasi-periodic upflows which are difficult to distinguish from upward propagating slow waves. In this context, we have studied a fan loop structure in the active region AR 11465 using simultaneous spectroscopic and imaging observations from the Extreme Ultraviolet Imaging Spectrometer onboard Hinode and Atmospheric Imaging Assembly onboard Solar Dynamics Observatory. Analysis of the data shows significant oscillations at different locations. We explore the variations in different line parameters to determine whether the waves or flows could cause these oscillations to improve the current understanding of the nature of these disturbances.     

Nature of Quiet Sun Oscillations Using Data from the Hinode, TRACE, and SOHO Spacecraft

We study the nature of quiet-Sun oscillations using multi-wavelength observations from TRACE, Hinode, and SOHO. The aim is to investigate the existence of propagating waves in the solar chromosphere and the transition region by analyzing the statistical distribution of power in different locations, e.g. in bright magnetic (network), bright non-magnetic and dark non-magnetic (inter-network) regions, separately. We use Fourier power and phase-difference techniques combined with a wavelet analysis. Two-dimensional Fourier power maps were constructed in the period bands 2??C?4?minutes, 4??C?6?minutes, 6??C?15?minutes, and beyond 15?minutes. We detect the presence of long-period oscillations with periods between?15 and 30?minutes in bright magnetic regions. These oscillations were detected from the chromosphere to the transition region. The Fourier power maps show that short-period powers are mainly concentrated in dark regions whereas long-period powers are concentrated in bright magnetic regions. This is the first report of long-period waves in quiet-Sun network regions. We suggest that the observed propagating oscillations are due to magnetoacoustic waves, which can be important for the heating of the solar atmosphere.     

On the role of hydromagnetic waves in the corona and the base of the solar wind

Hydromagnetic waves are of interest for heating the corona or coronal loops and for accelerating the solar wind. This paper enumerates some of the limitations that must be considered before hydromagnetic waves are taken seriously. In the lowest part of the corona, waves interact so that a significant fraction of the coronal wave flux should have periods as 10 s. If the problem of interest determines either a flux of wave energy or a dissipation rate, the distance that each wave mode can travel can be specified, and for at least one mode it must be consistent with the size and location of the region where the waves are to act. Heating of coronal loops observed by X-rays can be explained if the strength of the magnetic field along the loop lies within a rather narrow range and if the wave period is sufficiently short. In general, Alfvén waves travel furthest and reach high into the corona and into the solar wind. The radial variation of the magnetic field is the most important parameter determining where the waves are dissipated. Heating of coronal helmets by Alfvén waves is probable.The National Center for Atmospheric Research is sponsored by the National Science Foundation.     

Periodic variations of the Hα profile width in the chromosphere of coronal holes as a possible indicator of Alfvén waves

We analyze the oscillations of the Hα profile width based on our observations of the chromosphere at the base of solar coronal holes. The maximum oscillation amplitude averaged over ten time series is 64 m 0 A. Direct calculations show that this value cannot be reached through temperature oscillations, because the periodic intensity fluctuations observed during our experiment did not exceed 5%, corresponding to Hα profile broadening only by 1.5–2 m Å. We hypothesize that the observed variations can result from the propagation of torsional Alfvén waves in the chromosphere of coronal holes.     

A new family of solutions of the force-free field equation

In this paper, we determine the temperature profile along the footpoints of large coronal loops observed by TRACE in both the 171 Å and 195 Å passbands. The temperature along the lower part of these coronal loops only shows small variations and can probably be considered to be isothermal. Using the obtained temperature profile T(s) and an estimate of the column depth along the loop, we then determine the pressure along the lower part of the observed coronal loops and hence the value of the pressure scale length. The obtained scale lengths correspond in order-of-magnitude with the theoretically predicted gravitational scale height. We show that the differences between the observed and predicted scale heights are unlikely to be caused by (significant) flows along the loops but could possibly be a consequence of the inclination of the loops. This implies that the quasi-periodic intensity oscillations observed in the loops are most probably caused by compressive waves propagating upward at the coronal sound speed.     

Location of Decimetric Pulsations in Solar Flares

This work investigates the spatial relation between coronal X-ray sources and coherent radio emissions, both generally thought to be signatures of particle acceleration. Two limb events were selected during which the radio emission was well correlated in time with hard X-rays. The radio emissions were of the type of decimetric pulsations as determined from the spectrogram observed by Phoenix-2 of ETH Zurich. The radio positions were measured from observations with the Nançay Radioheliograph between 236 and 432 MHz and compared to the position of the coronal X-ray source imaged with RHESSI. The radio pulsations originated at least 30?–?240 Mm above the coronal hard X-ray source. The altitude of the radio emission increases generally with lower frequency. The average positions at different frequencies are on a line pointing approximately to the coronal hard X-ray source. Thus, the pulsations cannot be caused by electrons trapped in the flare loops, but are consistent with emission from a current sheet above the coronal source.     

Simultaneous geomagnetic and ionospheric oscillations caused by hydromagnetic waves

During magnetically quiet or slightly disturbed nights, closely correlated oscillations of the geomagnetic field and the F-layer were observed by means of magnetometers and a vertical-icidence continuous-wave Doppler sounder at 3.57 MHz. The magnetic oscillations were mostly Pi2 pulsations with periods from 0.5 to 2 min, and an amplitude of 10^?9 T corresponding to a Doppler shift of the order of 0.3 Hz. The observations cannot be explained by a dynamo-motor hypothesis assuming that the magnetic and ionospheric oscillations are caused by alternating E-layer currents, but they agree well with the theory of downgoing hydromagnetic waves. In particular, this theory explains the observed effects due to sporadic E-layer ionization and ion-neutral collisions. The results are found to differ substantially from those of other authors.     

Numerical Simulations of Impulsively Generated Magnetosonic Waves in a Coronal Loop

We consider impulsively excited magnetosonic waves in a highly magnetized coronal loop that is approximated by a straight plasma slab of enhanced mass density. Numerical results reveal that wavelet spectra of time signatures of these waves possess characteristic shapes that depend on the position of the initial pulse: in the case of a pulse launched inside the slab, these spectra are of a tadpole shape, while for a pulse excited in the ambient medium these spectra display more complex structures with branches of long and short-period waves. These short period oscillations correspond to waves that are trapped inside the slab, and the long-period oscillations are associated with waves that propagate through the ambient medium and reach the detection point. These findings are compatible with recent theoretical studies and observations by the solar eclipse coronal imaging system (SECIS).     

日冕分米波射电甚短周期脉动的观测证据

利用国家天文台云南天文台“分米波(700—1500MHz)射电频谱仪”和“四波段太阳射电高时间分辨率同步观测系统”分别于2001年6月24日和1990年7月30日观测到了两个稀少事件，前者是一个小射电爆发，其上升相伴随有短周期(约29、40和100毫秒)的脉动，后者是一个射电大爆发，在2840MHz上产生了周期约30毫秒的射电脉动，还着重讨论其甚短周期(如29—40毫秒)的脉动现象，甚短周期脉动可能是归因于起源在日冕深处不稳定区域的哨声波束周期链对射电辐射的调制，或沉降电子束驱动的静电高混杂波，经由波-波非线性相互作用导致甚短周期的射电脉动。     

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).     

Coherent oscillations from X-ray burst sources

The possible origin or coherent oscillations in X-ray bursters is discussed. Such oscillations with a period of the order of 10 ms have recently been observed. At this point it seems impossible to draw final conclusions on their nature. Nevertheless, it is shown that nonradial pulsations of a neutron star or torsional oscillations of a neutron star's crust seem to be an attractive possibility.