66. Evidence for similar processes occurring in stellar superflares and solar flares

Author: Chloe E. Pugh, Valery M. Nakariakov & Anne-Marie Broomhall at the University of Warwick.

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Many stars similar to the Sun produce flares several orders of magnitude more powerful than any solar flare on record [1], which raises the question of whether one of these potentially devastating ‘superflares’ could occur on the Sun. We observe multiple periods in the decay phase of a stellar superflare light curve, the most likely explanation of which is MHD oscillations, which suggests that the physical processes in stellar superflares are similar to those observed in solar flares.

Solar flares are frequently observed to undergo quasi-periodic pulsations (QPPs), which are time variations in the intensity of light emitted. QPPs have also been observed in stellar flares (e.g. [2,3]), in a variety of wavebands. Several mechanisms have been proposed to explain why QPPs occur, which fall into one of two categories: ‘magnetic dripping’ mechanisms or magnetohydrodynamic (MHD) oscillations. The magnetic dripping mechanisms are based on the idea that a continuous supply of magnetic energy could cause magnetic reconnection to occur repetitively each time a threshold energy is surpassed, resulting in pulsations of the flare. On the other hand, MHD oscillations of the flaring active region could cause the plasma parameters such as magnetic field strength and density, or the charged particle acceleration efficiency to vary, resulting in modulation of the radiation emission.

Occasionally solar flares with QPPs are observed to have multiple periods, which hold additional information about the cause of the QPPs and the plasma parameters in the flaring region. In this nugget we report one of the first stellar flares to show two simultaneous statistically significant stable periods [4], observed by NASA’s Kepler mission.

Analysis of the flare

Kepler has made high-precision white-light photometric observations of around 150,000 stars over the course of 4 years. The flare of interest occurred on the star KIC 9655129, and can be found in the high (1 minute) cadence light curve from Kepler quarter 14b. The left-hand panel of Figure 1 shows a section of light curve containing the flare, and the right-hand panel shows just the decaying phase of the flare.

Fig. 1: Left: a section of the short-cadence light curve of KIC 9655129, which contains three flares. Right: a shorter section showing the decaying phase of the central flare in the plot on the left. The peak intensity the flare is at time t = 0. The red over-plotted line is the result of a least-squares fit to the flare decay and quasi-periodic pulsations.

To find the QPPs, the flare decay trend was fitted with an exponential decay function using a least-squares method. The fit was then subtracted from the light curve to remove the trend, and hence emphasise short-term variability. The resulting time series is shown in the left-hand panel of Figure 2. A wavelet transform, which is useful for visualising how modes of oscillation in a time series evolve with time, was then performed. The right-hand panel of Figure 2 shows the wavelet spectrum, which has a clear feature above the 99% confidence level at a period of 84+25-19 minutes. The bright feature appears to split into two bands, with the second period appearing at 32 ± 7 minutes.

Fig. 2: Left: the de-trended flare decay light curve, with a fit to the main oscillation over-plotted in red. The peak of the flare is at the time t = 0. Right: the wavelet spectrum of the plot on the left, where the beginning of the time series has been padded with zeros in order to bring the features of interest into the centre of the cone of influence. The brightest feature has a period of 84+25-19 minutes. The far-right panel shows the time-average, or global wavelet spectrum.

Since the resolution of wavelet spectra is limited, estimates of the two detected periods were made by fitting a function, combining an exponential decay with two exponentially damped sinusoids, to the flare decay phase and performing Monte Carlo simulations. The result of this fit is shown by the red curve in the right-hand panel of Figure 1, where the periods are 78 ± 12 and 32 ± 2 minutes.

Properties of the two periodicities

The simultaneous presence of multiple periods in the light curve is difficult to explain with the magnetic dripping mechanisms, which suggests that MHD oscillations are the cause of the QPPs in this flare (although it is also possible that one period is due to a magnetic dripping mechanism, and the other due to an MHD oscillation). The two detected periods could also be time harmonics of a non-linear MHD wave, as such a signal can be decomposed into different sine/cosine waves (a Fourier series expansion). Hence its spectrum would have multiple peaks, and the phases of the time harmonics would be connected. On the other hand, if the signal belongs to different MHD modes or their spatial harmonics, they may have phases disconnected from one another. The phase differences were found to be disconnected, suggesting that the signal is linear, and that the periods are spatial harmonics or the result of different MHD modes. Also the exponential decay time constant of the shorter period variation is 77 ± 29 minutes, compared to 80 ± 12 minutes for the longer one. If the shorter period corresponded to a higher harmonic of a non-linear signal it would be expected to decay faster than the fundamental harmonic, which does not to appear to be the case here.

The ratio of the detected periods is 2.4 ± 0.4. If both of the periods are associated wth MHD oscillations, the ratio can give us seismological information about transverse structuring (if the oscillations are sausage modes) or the field-aligned stratification (if the oscillations are longitudinal).


The QPPs detected in the light curve of a flare on KIC 9655129 were found to be consistent with the presence of two spatial harmonics of an MHD wave, or two separate MHD waves. The properties of the QPPs in this flare are similar to those observed in some solar flares (e.g. [5]), which suggests that the underlying physics in solar flares and stellar superflares could be similar.


  • [1] Maehara, H., Shibayama, T., Notsu, S., Notsu, Y., et al. 2012, Nature, 485, 478
  • [2] Balona, L. A., Broomhall, A.-M., Kosovichev, A., et al. 2015, MNRAS, 450, 956
  • [3] Anfinogentov, S., Nakariakov, V. M., Mathioudakis, M., et al. 2013, ApJ, 773, 156
  • [4] Pugh, C. E., Nakariakov, V. M., Broomhall, A.-M. 2015, ApJ, 813, L5
  • [5] Kolotkov, D. Y., Nakariakov, V. M., Kupriyanova, E. G., et al. 2015, A&A, 574, A53