Slow Magnetoacoustic Waves in Two-Ribbon Flares

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Introduction

The physical processes operating in solar energy releases are still unclear and under very active scrutiny. The understanding of three-dimensional morphology and dynamics of large, eruptive, two-ribbon flares can shed light on this problem. This Nugget aims to discuss one aspect of flare development in three-dimensional space, namely the processes of energy release source motions along the magnetic neutral line.

According to the more or less "standard picture" of large eruptive flares oppositely directed magnetic field lines being in the form of arcade of magnetic loops are stretched by some non-stationary agent (e.g. by an erupting twisted magnetic flux rope or filament) to form a quasi-vertical current sheet in the corona. Here, in the current sheet, magnetic field lines can reconnect converting free magnetic energy to thermal and kinetic energy of plasma and charged particles causing a multitude of secondary flaring effects.

Unfortunately, the "standard picture" is essentially two- or two-point-five-dimensional, implying translational symmetry along the flare arcade axis. Being capable to represent a lot of observational effects in the planes of magnetic loops, it does not represent any flare development in the third direction ortogonal to the loop planes - along the flaring arcade axis and the magnetic neutral line. But often large, eruptive, two-ribbon flares develop predominantly just in this direction - in a number of observations energy release is seen to propagate mainly along the flaring arcade axis. In particular, RHESSI made a great contribution in this issue observing an impressive motions of non-thermal hard X-ray sources along the flare arcade axis, the flare ribbons, and the neutral line (e.g. see Nugget 4 and Nugget 6, and Figure 1 below).

Two Bright Peculiarities of the Energy Release Source Motions Along the Flare Arcade Axis

Such type of energy release source motions in eruptive, two-ribbon solar flares has two bright and exciting features:

  1. the still unknown triggering disturbances observed to propagate along the flare arcade axis at the speed of a few tens km/s, well below the Alfven and sound speeds;
  2. it is often accompanied by wavetrains of quasi-periodic pulsations with typical periods from a few seconds up to several tens of seconds observed in light curves of non-thermal hard X-ray and microwave emissions, and each pulsation is emitted sequentially from different magnetic loops of the flaring arcade.

The second feature is illustrated on Figure 1 below using an example of the January 19, 2005 eruptive, two-ribbon solar flare. One can see obvious quasi-periodic pulsations with a period of about 160 s by the naked eye. The presence of quasi-periodicity in the light curves of non-thermal hard X-ray and microwave emissions is clearly confirmed by the standard time-series analysis, such as calculation of Power Spectra or the Normalised Lomb Periodograms. Also one can see that the sources of non-thermal hard X-ray emission (50-100 keV) move predominantly along the main flare ribbons (with an average speed of about 60 km/s) during the time interval, when quasi-periodic pulsations are observed. (See also Nugget 4 and Nugget 6 for example of the flare with the very similar properties.)

Figure 1: Observations of January 19, 2005 X1.3 class solar flare. (Left panel) Light curves of hard X-ray (RHESSI) and microwave (The Learmonth Radio Telescope) emissions. (Central panel) Dynamics of sources of thermal (6-12 keV; circles) and non-thermal (50-100 keV; crosses) hard X-ray emission superimposed on TRACE 160 nm image, which indicates two main flare ribbons. (Right panel) Time-series analysis of 50-100 keV hard X-ray emission light curve obtained by RHESSI during the time interval marked by two vertical dashed red lines on the Left panel, when quasi-periodic pulsations are clearly visible.

Cartoon of the processes of energy release source movement along the flare arcade axis accompanied by quasi-periodic pulsations of non-thermal hard X-ray emission is shown in Figure 2.

Figure 2: Cartoon. Hypothetical energy release sources near (or above) the apexes of different magnetic loops of the flaring arcade are depicted schematically by red circles.

Possible Interpretation II: Slow Magnetoacoustic Waves Propagation in the Flaring Arcade

Here we would like to propose an alternative scenario, connected with the possible propagation of a slow magnetoacoustic wave across the magnetic field of the flaring arcade (a fast magnetoacoustic wave, which propagates across the magnetic field, i.e. along the flare arcade axis, should be ruled out immediately as its speed is super-sonic and super-Alfvenic, that is in contradiction with the feature 1). The presence of plasma non-uniformities is known to modify the MHD wave propagation significantly, causing wave dispersion, appearance of cut-offs and modification of the direction of wave propagation. In particular, one of the cornerstones of MHD coronal seismology is the propagation of fast magnetoacoustic waves along the magnetic field, which is impossible in a uniform medium. For the slow waves in two-ribbon arcades, the wave-guiding effect is connected with the reflection of the waves from the footpoints, on the sharp gradients of the sound speed in the transition region.

In essence, our mechanism (illustrated on Figure 3 below) is based on the statement that the wave-guiding effect allows the slow waves to propagate across the magnetic field (of arcade), at the group speed significantly lower than both the sound and Alfven speeds. This can be verified solving the magnetoacoustic wave equation written for the disturbed equilibrium of the homogeneous magnetic arcade. From this solution one can also obtain an important feature: the maximum value of the perpendicular (to the magnetic field) group speed of the slow magnetoacoustic wave is reached for the propagation angle of about 25-28 degrees to the magnetic field. Hence, the corresponding angular spectral components of the wave-packet, excited by an elementary burst somewhere at the top of an arcade, are the fastest to propagate down the footpoints, get reflected and reach the top of the arcade again. There they can trigger another "elementary" flare burst by several different mechanisms (see below), reinforcing the slow wave and hence compensating the dissipative and scattering losses, and so on. The period of the thus generated quasi-periodic pulsations is then determined by the ratio of the travel path and the speed of the triggering slow magnetoacoustic wave. Hence, it is similar to the period of the second harmonics of the longitudinal mode of a coronal loop, estimated in the range 10–300 s.

Moreover, the proposed scenario can easily explain another frequently observed feature of quasi-periodic pulsations in flares - the presence of double maxima in the elementary bursts (see e.g. light curves of hard X-ray emission on Figure 1). This can occur due to some asymmetry in the positioning of the wave source or in the arcade. In this case, the slow wave pulses, reflected from the opposite footpoint ribbons, arrive at the arcade top and trigger the next "elementary" flare bursts at slightly different times and at slightly different locations (this would be the case, when green and blue dashed lines do not intersect in red circles on Figure 3).

Figure 3: Schematic illustration of the proposed mechanism based on the slow-magnetoacoustic wave-guide effect in the flaring arcade. Hypothetical energy release sources near (or above) the apexes of different magnetic loops of the flaring arcade are depicted by red circles. By grey circles we depict regions where energy could be hypothetically released, but did not do this because the wave-packets did not come here. Blue and green dashed lines indicate trajectories of the triggering wave-disturbances.

We would like to emphasize here that the value of the wave propagation angle (25-28 degrees) is consistent with the observed geometry of two-ribbon flare arcades. As a rule, their spatial extent along the magnetic neutral line is typically comparable or larger than the length of the loops, which form the arcade. Hence, the propagation angle of 25-28 degrees to the field allows slow waves to make several bounces, progressing along the arcade axis. But previous observational and theoretical studies demonstrated that coronal slow magnetoacoustic waves are subject to strong damping. However, the typical damping time is usually longer than one period of the oscillation, hence the waves are able to complete one bounce from the footpoints and reach the top of the arcade. There the waves can trigger another "elementary" flare burst, which will excite another slow magnetoacoustic pulse, repeating the cycle.

Mechanisms of energy release triggering by the slow waves

Similarly to the tether cutting scenario proposed in Nugget 6 we also imply that the current sheet, X-points (X-lines), or 3D null-points are created in the vicinity of the flare arcade apex by some mechanisms, such as prominence eruption or some others (but we do not discuss this problem here). One can suggest that getting to the neighborhood of these magnetic peculiarities the slow magnetoacoustic waves can trigger the acts of energy release at least by two mechanisms:

Conclusion

We have discussed two possible scenarios of the eruptive two-ribbon solar flare development in the direction parallel to the flaring arcade axis: 1) one is based on the tether cutting scenario firstly proposed in Nugget 6, 2) and the other is based on the slow magntoacoustic wave-guide effect in the flaring arcade (proposed here). Unfortunately, at this moment it is not possible to select a preferred one mainly due to the lack of detailed spatially resolved observations. Let's hope that new and more advantageous observations of the Solar Dynamic Observatory jointly with new RHESSI data will bring us more rigorous information.

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