Quasi-Periodic Pulsations in Solar and Stellar Flares: A Review of Underpinning Physical Mechanisms and Their Predicted Observational Signatures

Abstract

The phenomenon of quasi-periodic pulsations (QPPs) in solar and stellar flares has been known for over 50 years and significant progress has been made in this research area. It has become clear that QPPs are not rare—they are found in many flares and, therefore, robust flare models should reproduce their properties in a natural way. At least fifteen mechanisms/models have been developed to explain QPPs in solar flares, which mainly assume the presence of magnetohydrodynamic (MHD) oscillations in coronal structures (magnetic loops and current sheets) or quasi-periodic regimes of magnetic reconnection. We review the most important and interesting results on flare QPPs, with an emphasis on the results of recent years, and we present the predicted and prominent observational signatures of each of the fifteen mechanisms. However, it is not yet possible to draw an unambiguous conclusion as to the correct underlying QPP mechanism because of the qualitative, rather than quantitative, nature of most of the models and also due to insufficient observational information on the physical properties of the flare region, in particular the spatial structure of the QPP source. We also review QPPs in stellar flares, where progress is largely based on solar-stellar analogies, suggesting similarities in the physical processes in flare regions on the Sun and magnetoactive stars. The presence of QPPs with similar properties in solar and stellar flares is, in itself, a strong additional argument in favor of the likelihood of solar-stellar analogies. Hence, advancing our understanding of QPPs in solar flares provides an important additional channel of information about stellar flares. However, further work in both theory/simulations and in observations is needed.

Model-Property Table

Here, in Table 1, we summarize the main expected properties of models (mechanisms) [1]-[15] discussed in Sects. 2.3.1-2.3.3. Since most of the models are not yet fully developed, it is necessary to consider the given properties as preliminary and possible, but not as final and irrevocable (see discussion in Sect. 2.3.4). This table is a rough guide only and should be used with care when choosing the model to interpret the observations of QPPs in a particular flare. This table also partly reflects the current state of development of the models. In particular, it can be seen that analytical formulas for the periods of QPPs are not yet available for all models. Thus, the table also indicates the possible gaps and directions of development of the models.

As a rule of thumb, the more observational manifestations of the mechanism under consideration, indicated in Table 1, are found in the study of a particular flare, the more likely this mechanism is applicable to explain the QPPs in this flare.

Below we consider a virtual example to demonstrate the application of this table. Suppose that from observations of integral fluxes from the Sun, the QPP period of several tens of seconds in both thermal and non-thermal radiations is available. Then one can choose almost equivalently from mechanisms [1], [2], [5], [6], [7], [8], [9], [11], [12], [13], and [15]. Let the QPPs have an irregular structure (e.g. amplitude and time intervals between successive peaks are not stable) and the modulation depth of the intensity of non-thermal radiation (e.g., hard X-rays) reaches 90%, which are the signs of non-stationary magnetic reconnection. Then mechanisms [1], [2], [5], [11], and [13] can be excluded (see the second column in Table 1), while mechanisms [6], [7], [8], [9], [12], and [15] still remain possible. If, in addition, the sources of individual pulsations are spatially resolved and seen to systematically move along the PIL, then we can further narrow the list of candidate mechanisms to [7], [8], [15]. On the other hand, if the QPP sources do not exhibit systematic motion along the PIL (e.g. they appear randomly in different locations in the flare region), then only mechanisms [6], [9], and [12] can be considered. And if there is no other information, then, at the moment, it is practically impossible to make a reliable choice among the remaining mechanisms and they are practically equally applicable to the QPP event under consideration.

If, additionally, a loop is found in the flare region, kink-oscillating with a period close to the period of QPPs, then mechanism [6] could be the most likely candidate. It must be also remembered that the detection of the oscillating loop does not guarantee the unambiguous applicability of mechanism [6] here. It may turn out that the loop oscillations are not a trigger of quasi-periodic reconnection and particle acceleration, but, on the contrary, the quasi-periodic energy release of the flare excites oscillations in one of the nearby loops, the period of the eigenmode of which coincides or is close to the QPP period. To resolve the dilemma, one must try to establish a causal relationship, in particular, which process begins earlier – the QPPs or the loop oscillations (for this one can analyze the time-distance maps). However, despite a significant progress in the analysis and understanding of MHD waves and oscillations in coronal loops and other plasma structures, this is not a trivial task given the available data level.

As another example, we consider the case when QPPs are detected only in the thermal radiation of a flare, e.g., in the soft X-ray and EUV ranges. In this case we can consider mechanisms [1], [4], [5], [10], [13], and [14] for consideration. If the period is several minutes or longer and the QPPs show only a few cycles (peaks) and quickly decay, then it is most likely to be caused by mechanism [4]. To confirm it, it is necessary to compare the found period with the theoretical one, if it is possible to identify the QPP-emitting loop and measure its length and temperature of plasma in it. Also, if spectrally resolved observations in one or several lines are available, then it is necessary to check the additional observational properties of the slow mode, indicated in the column ‘Peculiarities’ in Table 1 (and others properties known from the theory and simulations of this mode).

If the QPP period is a few seconds, then it is more reasonable to consider mechanisms [1] and [14]. To choose between them, one should try to find additional observational signatures of these mechanisms. In particular, for the same length of the flare loop, the global trapped sausage mode will have a longer period compared to the period of the fast standing wave trapped at the loop-top in mechanism [14]. However, the harmonics of the sausage mode can have a comparable period with the period in mechanism [14]. To move a step forward in making a decision, one could use the fact that the sausage mode probably has a higher quality factor, so that a relatively larger number of the QPP peaks can be expected for it.

If the QPP period is from tens of seconds to a few minutes and the QPPs have a high quality factor, then mechanisms [1] and [5] can be considered as the most likely. Next, one should try to estimate from observations and magnetic field reconstruction the parameters of the flare loop used to calculate the QPP periods in these mechanisms. The main difficulty here is to reliably estimate the flare loop minor radius (and cross-section area), the magnitudes of the magnetic field and longitudinal electric current in it. The latter is especially difficult if the flare is located near the limb and vector magnetograms are not available. In this case, one needs to look for additional observational signatures of the mechanisms, e.g., the specific phase difference of the intensity and Doppler shift favouring the interpretation in terms of mechanism [1] (see the rightmost column in Table 1). However, observational signatures of mechanism [5] are still poorly understood, since its forward modeling has not been performed yet. This task is pending.