Quasi-Periodic Energy Release in a Three-Ribbon Solar Flare

Abstract

Quasi-periodic pulsations (QPPs) are found in solar flares of various magnetic morphologies, e.g. in two-ribbon or circular-ribbon flares, and the mechanisms of their generation are not yet clear. Here we present the first detailed analysis of QPPs (with a period $P = 54 \pm 13$ seconds) found in the Ramaty High Energy Solar Spectroscopic Imager (RHESSI) observations of a relatively rare three-ribbon M1.1 class flare that occurred on 5 July 2012 (SOL2012-07-05T06:49). QPPs are manifested in the temporal profiles of temperature [$T$] and emission measure [$EM$] of “super-hot” ($T_{ \mathrm{s}} \approx 30$ – 50 MK) plasma but are almost invisible in the profiles of “hot” ($T_{\mathrm{h}} \approx 15$ – 20 MK) plasma parameters when approximating X-ray spectra of the flare with the bremsstrahlung spectrum of a two-temperature thermal (Maxwellian) plasma. In addition, QPPs with a similar period are found in the temporal profiles of the flux and spectral index of nonthermal electrons if the observed X-ray spectra are approximated by a combination of the bremsstrahlung spectra of a single-temperature plasma and nonthermal electrons with a power-law energy distribution. QPPs are not well expressed in the X-ray flux according to RHESSI and GOES data, or in radio data. The QPPs are accompanied by apparent systematic movement of a single X-ray source at a low speed of $34 \pm 21$ km s⁻¹ along the central flare ribbon over a narrow ($<5$ Mm) “tongue” of negative magnetic polarity, elongated ($\approx 20$ Mm) between two areas of positive polarity. The results of magnetic extrapolation in the nonlinear force-free field (NLFFF) approximation show that the X-ray source could move along curved and twisted field lines between two sheared flare arcades. It is worth noting that in the homologous three-ribbon M6.1 flare (SOL2012-07-05T11:39), which occurred in the same region about five hours later, the X-ray sources moved much less systematically and did not produce similar QPPs. We interpret the observed QPPs as a result of successive episodes of energy release in different spatial locations. In each pulsation, ≈(1 – 4)$\times 10^{29}$ erg is released in the form of thermal energy of hot and super-hot plasmas (or accelerated electrons), which is comparable with the energy of a microflare. The total kinetic energy released during all QPPs is ≈(0.7 – 3.5)$\times 10^{30}$ erg, which is about an order of magnitude less than the free magnetic energy $\approx 1.56 \times 10^{31}$ erg released in the flare region. We discuss possible propagating triggers of the quasi-periodic energy release (slow magnetoacoustic waves, asymmetric rise of curved/twisted field lines, flapping oscillations, and thermal instability in a reconnecting current sheet) and argue that the current state of available mechanisms and observations does not allow us to reach an unambiguous conclusion.

Appendix

Here we address the question of whether the quasi-periodic variations (or QPPs) of the model parameters found from the X-ray spectra fitting could be a result of a known artifact in the RHESSI data. Inglis et al. (2011) found that count rates of the RHESSI detectors can contain artificial oscillations with period $P_{\mathrm{art}} \approx 75$ seconds. In some flares, these oscillations are more pronounced, in others less so, or almost invisible. Since the period ($P_{\mathrm{QPP}} = 54 \pm 13$ seconds) of the quasi-periodic variations is close to $P_{\mathrm{art}}$, it makes sense to check whether they correspond to these artificial oscillations or not.

The RHESSI spacecraft rotates with a period of $\approx 4$ seconds and experiences nutation. This motion produces oscillations of the telescope imaging axis with respect to the spacecraft spin axis (these axes do not coincide with each other; see Fivian et al., 2002). The axis of each collimator deviates slightly from the imaging axis, and this deviation is different for different collimators. For Detector 5 ($\mathrm{D5}$) the deviation is one of the largest, and hence the amplitude of the artificial-count rate oscillations of this detector can also be one of the largest (see Inglis et al., 2011).

Figure 18b shows the temporal profile of the angular distance [$d\left ( t\right )$] between the RHESSI imaging-axis direction and the mean flare position in the image plane. It has a time step of one second, and it is smoothed over four seconds, i.e. about one period of the RHESSI rotation. The fast variations can be seen on top of the smoother sinusoidal variations with an amplitude of about 250 arcseconds. The fast variations have a period of about four seconds and are a consequence of the rotation of the spacecraft, while longer variations have a period of about 75 seconds, i.e. around $P_{\mathrm{art}}$, and they are a consequence of nutation. The Fourier spectrum of this signal is shown in Figure 18a, where one can see two sharp peaks corresponding to periods of about 2 and 4 seconds and one wider peak at about 75 seconds. For comparison, Figures 18c and 18d show the count rates averaged over the RHESSI detectors and the temporal profile of the super-hot plasma temperature [$T_{2}\left ( t\right )$] obtained in the 2vth model, respectively.

Figure 18

(a) Fourier spectrum of the smoothed temporal dependence of the angular distance between the RHESSI imaging-axis direction and the average position of the M1.1 flare studied. This temporal dependence smoothed over four seconds is shown in (b). Three spectral peaks with periods of 2, 4, and 75 seconds are indicated in (a) with vertical dotted blue, green, and red lines, respectively. (c) Count rates with the time step of four seconds averaged over the RHESSI’s front detectors in five energy ranges 3 – 6 (dark blue), 6 – 12 (black), 12 – 25 (cyan), 25 – 50 (red), and 50 – 100 (green) keV. (d) Temporal profile of the super-hot plasma temperature determined within the 2vth model. Peaks of pulsations $\mathrm{P_{1}}$ – $\mathrm{P_{7}}$ are shown with the red vertical dashed lines in (b – d).

Overall, Figure 18 shows the following: i) unlike an almost sinusoidal signal $d\left ( t\right )$ with a period $P_{\mathrm{art}} \approx 75$ seconds, variations in $T_{2}\left ( t\right )$ are unstable, i.e. have a variable period and amplitudes, ii) the temporal profiles $d\left ( t\right )$ and $T_{2}\left ( t\right )$ are not in phase, the peaks of $T_{2}\left ( t\right )$ fall on different phases of the $d\left ( t\right )$ oscillations, iii) no oscillations are seen in the averaged count rates of the RHESSI detectors. The oscillations with a period of $P_{\mathrm{art}} \approx 75$ seconds are also not visible in the count rates of individual detectors $\mathrm{D1}, \mathrm{D2}, \ldots , \mathrm{D9}$ in different energy ranges from 3 to 100 keV (Figure 19). The oscillations are not even visible in the count rates of the $\mathrm{D5}$ detector, for which the largest amplitude would be expected.

Figure 19

Count rates of RHESSI’s front detectors $\mathrm{D1}, \mathrm{D2}, \ldots , \mathrm{D9}$ (shown by different colors from black to red and indicated on (a)) with temporal cadence of four seconds in five energy ranges: 3 – 6 (a), 6 – 12 (b), 12 – 25 (c), 25 – 50 (d), and 50 – 100 (e) keV. (f) The four-second smoothed time dependence of the angular distance between the RHESSI imaging-axis direction and the average position of the M1.1 flare studied.

Thus, in the event under consideration, this artifact practically did not appear, and the arguments stated above oppose the possibility that the QPPs found may be a consequence of the artifact considered in the RHESSI data.