Are Quasi-periodic Pulsations Independent of Loop Oscillations in Solar Flare?

We investigated oscillations in an M8.7 solar flare (SOL2014-10-22), including quasi-periodic pulsations (QPPs) in light curves and Doppler shift oscillations in the flare loops. Using Bayesian-based Markov Chain Monte Carlo, Fast Fourier Transform, and wavelet analysis method, QPPs were identified at microwave and hard X-ray wave bands during the impulsive phase, and the dominant period is 40–50 s. They should be associated with a repetitive energy release process, which accelerates nonthermal electrons periodically. On the other hand, we cannot rule out the possibility of the modulation of external waves because of the lower temporal resolution of spectroscopic observation. However, almost immediately after QPPs, a minority of flare loops display their Doppler velocity oscillations with a significant period of ∼4 minutes, which are observed by the Interface Region Imaging Spectrograph at the coronal line Fe xxi 1354.08 Å (T ∼ 107 K), while its intensity and width show no similar oscillation. Our observations suggest that flare loop oscillations are most likely the fast kink mode waves with a phase speed of ∼840 km s−1. The magnetic field strength in flare loops was estimated to be 54–69 G via the coronal seismology. The QPPs and loop oscillation could be independent of each other in this event.


Introduction
Quasi-periodic pulsations (QPPs) are typical features of the flare energy release process.Generally, they are identified as regular fluctuations of flare light curves with at least three complete cycles.They were detected in a broad range of electromagnetic waves: microwave (Melnikov et al. 2005;Kupriyanova et al. 2010;Dolla et al. 2012;Kolotkov et al. 2015), visible lights (Li et al. 2020b;Hong et al. 2021), extreme-ultraviolet (EUV) and ultraviolet (UV; Su et al. 2012;Li et al. 2020d;Lu et al. 2021;Shi et al. 2022a), soft X-ray (SXR) and hard X-ray (HXR; Inglis & Nakariakov 2009;Reznikova & Shibasaki 2011;Ning et al. 2022), and γ-ray (Nakariakov et al. 2010;Li et al. 2020c;Li & Chen 2022).QPPs can occur in different phases of flares (Simões et al. 2015;Hayes et al. 2016Hayes et al. , 2019Hayes et al. , 2020)).Their characteristic periods range from subseconds to several minutes, and usually have multiple periods (Tan et al. 2010;Van Doorsselaere et al. 2016;McLaughlin et al. 2018;Kupriyanova et al. 2020;Zimovets et al. 2021).Short-period QPPs are usually detected in radio and HXR wave bands thanks to high temporal cadence and likely arise from the interaction between plasma waves and accelerated particles (Aschwanden 1987;Nakariakov et al. 2018).For those longer period QPPs, i.e., at least tens of seconds, they are mainly interpreted in terms of magnetohydrodynamic (MHD) oscillations in coronal magnetic loops or repetitive magnetic reconnection.In the regime of MHD oscillations, slow modes (Wang et al. 2021), fast kink modes (Nakariakov et al. 2021), and fast sausage modes (Li et al. 2020a) are all possible candidates for the QPPs mechanisms.In the regime of repetitive magnetic reconnection (McLaughlin et al. 2012;Thurgood et al. 2019;Karampelas et al. 2022), nonthermal particles are accelerated by intermittent reconnection and then naturally produce periodic emissions.However, due to the lack of sufficient observed information, a mechanism may successfully explain the main features in an event, but usually cannot explain all the features.Thus, the nature of QPPs has not yet been conclusively determined.
QPPs or oscillations are also seen in flare loops, and they are usually detected through spectroscopic measurements and interpreted as MHD waves.Wang et al. (2003) reported the first detection of postflare loop oscillations seen in both Doppler shift and intensity, which were recorded in a Fe XIX line (T ∼ 6.3 × 10 6 K) and explained as slow-mode standing waves.The sausage oscillations of flare loops were identified by Tian et al. (2016) via the analysis of hot line Fe XXI 1354.08 Å (T ∼ 10 7 K).They also found that sausage modes can be the cause of QPPs.Using the same Fe XXI, kink oscillations of flare loops were reported, which were found to be associated with QPPs (Li et al. 2018), or unrelated to QPPs (Li et al. 2017a).
Compared to high-temperature flare loops, oscillations in warm coronal loops are more common, in which kink waves are most frequently modes.These kink oscillations can be detected as transverse displacements of loops through imaging observations (Aschwanden et al. 1999;Nakariakov et al. 1999;Schrijver et al. 2002) and Doppler shift oscillations in the spectroscopic measurements (Tian et al. 2012;Yuan & Van Doorsselaere 2016).Currently, two regimes of kink oscillations are distinguished, namely decaying and decayless.Decaying oscillations will experience rapid damping within only a few cycles starting from Original content from this work may be used under the terms of the Creative Commons Attribution 4.0 licence.Any further distribution of this work must maintain attribution to the author(s) and the title of the work, journal citation and DOI.large amplitude, and they are always related to nearby eruptions (Zimovets & Nakariakov 2015;Zhang et al. 2020;Dai et al. 2021;Li et al. 2023).In the regime of decayless, coronal loops have small displacement amplitude (generally smaller than crosssection radius), and they can last for several complete cycles without significant damping (Wang et al. 2012;Nisticò et al. 2013;Anfinogentov et al. 2015;Afanasyev et al. 2020;Shi et al. 2022b;Li & Long 2023).
In this paper, we investigated oscillations in an M-class flare, including QPPs in light curves detected at multiwavelengths during the impulsive phase, and the following flare loop oscillations.In Section 2, we describe the observations and instruments, which are followed by methodology and data analysis in Sections 3 and 4. The discussion and summary are presented in Sections 5 and 6, respectively.

Observations and Instruments
On 2014 October 22, an M8.7 solar flare occurred in active region NOAA 12192 (S13E21).According to SXR observation from X-ray Sensors (XRS) on board Geostationary Operational Environmental Satellite (GOES), it started at 01:16 UT, peaked at around 01:59 UT, and ended at 02:28 UT.This event was also detected by several other instruments, as shown in GOES/XRS recorded the full-disk radiation with a temporal cadence of ∼2 s.In this study, we utilize the GOES 0.5-4 Å channel, which is similar to the 3-25 keV energy band, mainly consisting of SXR components.Fermi/GBM will quicken its temporal cadence automatically when solar flares happen.We utilize the higher temporal cadence HXR data with a fixed energy band of 50-101 keV.Then, we interpolate the time series to a uniform cadence of 1 s, which is enough to analyze periods exceeding tens of seconds (e.g., Li et al. 2015a;Ning 2017;Li et al. 2022).
SDO/AIA provided full-disk images in seven EUV and two UV channels with a pixel scale of 0 6.The temporal cadence is 12 s for EUV and 24 s for UV.However, due to the strong emissions of saturated images, which are excluded from our analysis, we use a time series with a cadence of 24 s for all EUV channels.The AIA 304 Å (T ∼ 5 × 10 4 K) passband can detect the chromosphere and transition region.AIA 94 (T ∼ 6 × 10 6 K) and 131 Å (T ∼ 10 7 K) were dominated by emissions of hot plasmas (O'Dwyer et al. 2010), while emissions of AIA 171 (T ∼ 7 × 10 5 K), 193 (T ∼ 1.6 × 10 6 K), 211 (T ∼ 2 × 10 6 K), and 335 Å (T ∼ 2.5 × 10 6 K) mainly from warm plasmas.Two UV channels (AIA 1600: UV continuum, C IV and some chromospheric lines; 1700: UV continuum and some chromospheric lines; Simões et al. 2019) mainly reflect the photosphere and temperature minimum (T ∼ 5 × 10 3 K).
A sit-and-stare observation of IRIS was performed during this event.The temporal cadence of SG and SJI is ∼16.5 s and ∼33 s, respectively.The spatial scale is ∼0 166 per pixel.The spectral scale is ∼12.8 mÅ per pixel in the far-ultraviolet (FUV; 1332-1358 Å) wavelengths.Fe XXI 1354.08 Å is a broad line formed at high temperature (T ∼ 10 7 K) and can be seen in the O I (1355.60Å) spectral window.This broad line is always blended with other narrow lines, such as C I 1352.73 and 1354.29 Å,  Fe II 1353.02,1354.01,1354.75, and 1354.85Å, Si II 1352.73 and  1353.72 Å, as well as unknown lines (Innes et al. 2003;Tian et al. 2014;Young et al. 2015;Polito et al. 2015;Graham & Cauzzi 2015;Li et al. 2015cLi et al. , 2017a)).On the other hand, the Fe XXI 1354.08 Å was found much stronger than other lines in flare loops (Tian et al. 2016;Li et al. 2018).IRIS/SJI 1330 Å (mainly UV continuum and C II) is sensitive to the plasma range from 10,000 to 30,000 K, and shows the chromosphere and low transition region.The calibrated level 2 data were used in this study.We also checked the accurate wavelength calibration using the O I 1355.60Å.

Methodology
Bayesian-based Markov Chain Monte Carlo (MCMC) is an efficient mathematical tool to estimate the desired posterior distributions for multiparameter models (Vaughan 2005(Vaughan , 2010;;Gregory 2010).In the detection of periodic signals, MCMC fits the Fourier power spectral density (PSD) of a time series with a model and determines the best-fit parameters.This method has been applied to analyze QPPs signal of solar flares and its details have been described (Inglis et al. 2015(Inglis et al. , 2016;;Hayes et al. 2019Hayes et al. , 2020;;Yuan et al. 2019;Liang et al. 2020;Guo et al. 2023).The procedures of this method can be summarized as follows.
1. Normalize the input signal, multiply it by a window function, and then calculate its Fourier PSD. 2. Select candidate model M. 3. Set prior probability distribution for parameters of model M.

Set initial parameter values and perform MCMC simula-
tions to obtain the posterior probability distribution of parameters, and hence the best fit of PSD can be derived.5. Compare different models using Bayesian information criterion (BIC).6. Calculate the test statistic values (T R , p) for the preferable model to check if it is extreme.
In this paper, two candidate models are utilized.The first model M 0 consists of a power law and a constant, which includes three parameters (A, α, and C), where f is the Fourier frequency, and Af −α and C reflect the properties of red and white noise in Fourier PSD, respectively.
The second model M 1 is the M 0 plus an additional Gaussian component, which includes six parameters (A, α, C, B, β, and σ),  where B, β, and σ are the amplitude, central log frequency, and width of the Gaussian component, respectively.This model illustrates a possible oscillation signal (i.e., QPPs) above the noise.
The BIC can be used to determine which model is preferable (Schwarz 1978;Burnham & Anderson 2004).The smaller the BIC, the better the model.Thus, we define The test statistic T R reflects the maximum deviation between the observed value (i.e., PSD) and the model (Vaughan 2010).The Bayesian p-value is calculated by integrating T R from T R obs to infinity, which represents the tail area probability in the distribution of test statistic T R .A model with 0.01 < p < 0.99 is considered appropriate (Inglis et al. 2016;Guo et al. 2023).

QPPs in Light Curves
Figure 2 (top panel) plots the full-disk normalized light curves between 01:15 and 02:30 UT, including the NoRP 3.75 GHz (magenta), 9.40 GHz (cyan), Fermi 50-101 keV (black), and GOES 0.5-4 Å (red), as well as local light curves of AIA 94 (green), 171 (brown), 211 (pink), 304 (sky blue), 335 (blue), 1600 (purple), and 1700 Å (gold), which were integrated over the whole region in Figure 1.It is interesting that two small peaks appear at 01:25 and 01:32 UT, which seems to be two small eruptions near the southwest ribbon according to the animation of Figure 1.It is also obvious that light curves exhibit two large peaks around 01:38 UT, which correspond to the sudden brightening of double ribbons.Meanwhile, there is a strong enhancement of emission lines in the O I spectral window, followed by the appearance of Fe XXI 1354.08 Å accompanied by visible flare loops.In addition to light curves around 01:38 UT, multiple prominent and regular peaks were also detected by NoRP microwave and Fermi HXR between 01:42 and 01:52 UT, and these peaks occur simultaneously with a certain period.
In order to analyze this periodicity, we first choose NoRP 9.40 GHz and Fermi 50-101 keV to perform the MCMC simulations mentioned above.Figures 3(a , and the test statistic pvalue is 0.92 for M 0 .However, in the fitting of model M 1 , the same best-fit period of ∼39.5 s as Fermi HXR suggests that the oscillation may indeed be present with insufficient power to be definitely detected (Inglis et al. 2015).Moreover, it is clear that the AIA channels (temporal resolution of 24 s) do not have sufficient cadence for a robust investigation of periods in the order of 40-50 s, as found in the microwave and HXR data.
After identifying the 40-50 s periodic signal, it is natural to filter the signal with a certain method.Here we utilize the Fast Fourier Transform (FFT) to decompose the original light curves in Figure 2 top panel.FFT has been applied to detrend the light curves in previous studies (e.g., Ning 2014Ning , 2017).The 100 s (0.01 Hz) is selected as the cutoff threshold between rapidly (high-) and slowly varying (low-frequency) components, which is enough to filter the 40-50 s signal.Periods below 100 s are considered as rapidly varying.The Figure 2 middle panel presents the high-frequency components between 01:37 and 01:52 UT, including NoRP microwave, Fermi HXR, and GOES SXR.Microwave and HXR show similar QPPs at two time intervals, i.e., 01:38-01:40 and 01:42-01:52 UT.The oscillation amplitudes of the microwave in the 01:38-01:40 UT are much larger than that in the 01:42-01:52 UT, and hence we magnify the signals of the latter interval to see more evident oscillation.As noted earlier, the power of QPPs in GOES SXR is not strong enough to be unambiguously detected via the MCMC method, but the filtered GOES SXR components show consistent oscillation with HXR in the 01:42-01:52 UT, which further demonstrates that QPPs may indeed be present in GOES SXR.Next, we perform Morlet wavelet analysis on the rapidly varying component of Fermi 50-101 keV, as shown in the bottom panel of Figure 2. The method and routines were provided by Torrence & Compo (1998).The bottom panel also plots the 99.7% significance level over the wavelet power spectrum, as well as shows the significant period of 40 s, which is consistent with above 40-50 s.Wavelet power is dependent on the oscillation amplitude and hence the signal during 01:38-01:40 UT is not as strong as the latter peaks but also shows a similar period.
Figures 4(a)-(c) plot the cross-correlations between intensity fluctuations at Fermi HXR and at NoRP microwave and GOES SXR.The black and red represent data in 01:38-01:40 and 01:42-01:50 UT, respectively.The maximum correlation coefficient (CC) is also given.In panel (c), the Fermi data are interpolated to the same temporal cadence as GOES.These diagrams show well positive correlations; excluding 01:38-01:40 UT in Figure 4(c), all CCs are greater than 0.66.The correlation between HXR and SXR indicates the inphase oscillation behaviors, which once again demonstrates that QPPs may indeed be present in SXR. Figure 4(d) gives the microwave spectra of NoRP with a similar shape at two times, corresponding to the form of the gyrosynchrotron mechanism (Ning 2007a(Ning , 2007b(Ning , 2008;;White et al. 2011).Therefore, the oscillation behaviors at NoRP microwave and Fermi HXR should originate from a nonthermal process, i.e., the periodic accelerated electrons during the impulsive phase.

Oscillations in Flare Loops
Flare loops are visible at the coronal line Fe XXI 1354.08 Å after 01:39 UT.From the animation of Figure 1, the flare loop system moves south in the plane of sky.Then, we apply Gaussian fitting (Li et al. 2015a(Li et al. , 2015b;;Jeffrey et al. 2018) to the line profiles in the range of 1353.0-1355.0Å, as shown in Figure 5, which presents six samples of the fitting results.These samples are selected from the region below where Doppler velocity oscillation occurred.In order to improve the signal-to-noise ratio, we apply a running average over five pixels along the Y-axis, as marked between two green horizontal lines.The observed data are indicated in orange profiles, and bad pixels are manually removed in the fitting process.The black horizontal dashed line is the linear background emission.The magenta and cyan profiles represent the fitting of Fe XXI 1354.08 Å and C I 1354.29 Å, respectively.Two vertical red lines show their reference rest wavelengths.The black profile is the sum of fitting components.Next, the fitting parameters of Fe XXI 1354.08 Å, including the peak intensity, Doppler velocity, and line width (FWHM), are shown in the figure.We also calculated the 3σ uncertainties via the errors derived from the parameter fitting process Figure 6 gives the time-distance diagrams of Fe XXI 1354.08 Å parameters along the IRIS slit from 01:36 to 02:30 UT, the peak intensity in the top panel, Doppler velocity Local normalized light curves in AIA 94 (green), 171 (brown), 211 (pink), 304 (sky blue), 335 (blue), 1600 (purple), and 1700 Å (gold), which were integrated over the whole region in Figure 1.The gray and yellow background represent the time interval of QPPs and loop oscillations, respectively.Middle panel: the corresponding rapidly varying components between 01:37 UT and 01:52 UT.Bottom panel: the Morlet wavelet spectrum of the rapid-varying component of Fermi 50-101 keV and its global power spectrum.The 99.7% significance level is also marked. in the middle panel, and line width in the bottom panel.Low signal-to-noise ratio points are shown in white in the Dopplergram and black in other panels, and the vertical line at 02:15 UT is caused by the lack of observed data.Figure 1 shows that the IRIS slit locates at the flare ribbon (i.e., between −300″ and −280″) and loops (i.e., between −360″ and −300″ on the Y-axis in Figure 6).The corona above the flare ribbon is heating rapidly and is first seen at the high-temperature line Fe XXI, which displays the bright intensity and broad width and blueshift from 01:39 to 01:44 UT, indicating a chromospheric evaporation process (Tian et al. 2014;Li et al. 2015bLi et al. , 2017bLi et al. , 2019)), namely the dense plasma with high temperatures move from the loop footpoint (or ribbon) to the loop top.Our observation shows the evaporation with an interval of about 5 minutes and a maximum evaporation speed above 60 km s −1 .After 01:44 UT, the evaporation decreases and plasma downflow starts gradually.Thus, Fe XXI exhibits the redshift and its speed increases with time, and the maximum downflow speed is about 20 km s −1 around 01:55 UT.
As mentioned before, flare loops move from north to south along the IRIS slit, and Fe XXI detects that the loops gradually appear from 01:44 to 01:58 UT between −360″ and −300″ in Figure 6.These loops are filled with hotter plasma, which results in Fe XXI with a broad width at the beginning, as shown in Figure 6(c1).There is a hot loop system between −340″ and −325″ along the IRIS slit combining the AIA 131 Å observation.It lasts for more than 0.5 hr from 01:57 to 02:30 UT, and its line width is broader than others.From flare images, the IRIS slit is just located at the top of this loop system, and Fe XXI displays the blueshift suggesting the evaporation process around the loop top during the flare decay phase.
Additionally, there are some red and blue slanted patterns around −320″ in the Dopplergram in Figure 6(b1), which is an indication of loop oscillation.According to AIA images, this oscillation region is located at the flare loop top.Then, we select this region for further analysis, as revealed by two magenta lines (speed is ∼5.3 km s −1 , loops move to the south in the plane of sky). Figure 6(b2) plots the oscillation behaviors of the Fe XXI velocity integration between two lines, i.e., from 01:52 to 02:14 UT.The oscillation period is typically ∼4 minutes and velocity amplitude is about 10 km s −1 , whatever blueshift or redshift.This speed is consistent with previous observations in flare loops (Tian et al. 2016).However, such oscillation is not seen at Fe XXI intensity and width, as plotted in Figure 6(a2) and (c2).The oscillating loops show that their intensity increases with time and reaches the maximum at 02:06 UT, while the width decreases with time.

Discussion
The 40-50 s QPPs were identified at microwave and HXR during the impulsive phase.It is widely known that the microwave emissions in the impulsive phase are generated by the gyrosynchrotron emission of nonthermal electron beams trapped in flare loops (Kundu et al. 1984(Kundu et al. , 1994;;White et al. 2003;Reznikova & Shibasaki 2011;Kumar et al. 2016).HXR emissions in large solar areas arise from thick-target bremsstrahlung of nonthermal electrons (Hoyng et al. 1981;Kundu et al. 1984Kundu et al. , 1994;;Kosugi et al. 1988).Overall, electrons with energy above 30 keV will produce gyrosynchrotron radio emission in flare loops in the corona, and bremsstrahlung HXR when they precipitate into the dense chromosphere (White et al. 2011).In our observation, HXR shows a good correlation with microwaves, which agrees with the above physical process.Furthermore, a similar oscillation period may indeed be present in SXR thermal emission, which also could be associated with nonthermal electron beams heating flaring plasma, i.e., the emissions are attributed to the increased plasma density and temperature.GOES/XRS data have a better signal-to-noise ratio and cadence than AIA for this analysis, and it is clear that the AIA channels do not have sufficient cadence for a robust investigation of periods in the order of 40-50 s.
Is the quasi-period of 40-50 s modulated by an external MHD wave?For instance, sausage modes of flare loops could modulate the electron trapping and precipitation (Nakariakov & Melnikov 2009).Or electron beams modulated by kink modes, as reported by Li et al. (2022), found that a 45 ± 10 s period is most likely to originate from repetitive magnetic reconnection modulated by kink modes.Figure 6 shows the time-distance diagrams of the Fe XXI observation.In the QPPs interval-1, i.e., 01:38-01:40 UT, there is strong chromospheric evaporation in the flare ribbon.In interval-2, i.e., 01:42-01:52 UT, no apparent oscillation signal was detected in loops (−325″ to −300″), but show a majority of redshift with broad line width.As noted in Table 1, IRIS/SG only had a temporal cadence of ∼16.5 s during this observation, while the 40-50 s period is close to the Nyquist frequency of the sampling of IRIS/SG, thus the presence of oscillation cannot be conclusively determined.
However, we found that a minority of flare loops show clear oscillations after the 40-50 s QPPs, as shown in the oscillation region labeled by magenta lines, which are always related to MHD processes, such as slow mode waves, fast sausage mode waves, and fast kink mode waves.The IRIS slit was located at the loop top, meaning that they are most likely global standing modes.The oscillatory loops show consistent behavior and have a similar length, and hence can be considered as a single fat loop.The phase speed (C p ) of the global standing mode can be calculated as Equation (3), that is, twice the loop length (L) divided by the period (P) (Nakariakov & Ofman 2001), From the imaging of the flare, the double footpoints of the oscillatory loop are located near (−360″, − 310″) and (−275″, − 320″), then we can obtain the loop length of ∼100 Mm based on an assumption of semicircular shape.Combining the observed ∼4 minutes period, the phase speed can be estimated to be ∼840 km s −1 , which is larger than the local sound speed (∼500 km s −1 ) at 11 MK (Nakariakov & Ofman 2001;Li et al. 2017a), that is, they are not standing slow mode waves.The phase speed of global sausage mode waves was found to be above 2400 km s −1 (Melnikov et al. 2005;Tian et al. 2016), much higher than what we have observed.Both slow and sausage modes belong to compressible modes and their density fluctuations are expected (Roberts 2000;Nakariakov & Verwichte 2005;Nakariakov 2007).In our study, we do not see any clear signatures of intensity fluctuations, which further rules out the possibility of slow and sausage modes.Alternatively, the observed oscillations are global standing fast kink modes.They are generally weakly compressive (Nakariakov et al. 2021), and our result matches this feature.The phase speed of ∼840 km s −1 is consistent with the range of kink speed (Li et al. 2017a(Li et al. , 2018(Li et al. , 2022)).
In such a case, the internal Alfvén speed (C Ai ) can be determined by the phase speed (C p ), and the magnetic field strength (B) in flare loops can be estimated (Nakariakov & Ofman 2001;White & Verwichte 2012;Nisticò et al. 2013).Li et al. 2017aLi et al. , 2018Li et al. , 2022)), then the C Ai is in a range of 600-604 km s −1 , which indicates that we can take the typical 600 km s −1 for the estimation of the magnetic field: where μ 0 , m p , and m are magnetic permeability in a vacuum, the proton mass, and the mean molecular weight ( ˜1.27; m = Nakariakov & Ofman 2001; White & Verwichte 2012).The typical number density (n e ) of corona is ∼10 15 m −3 , and hence the n i is 3 × 10 16 -5 × 10 16 m −3 based on the above density contrast.Therefore, the magnetic field strength B in flare loops can be estimated to be 54-69 G, which is close to previous analyses (Qiu et al. 2009;Li et al. 2017a).

Summary
We investigated oscillations in an M8.7 flare SOL2014-10-22, including QPPs in light curves and Doppler shift oscillations in the flare loops.In this event, we do not find observational evidence to show the correlation between QPPs and loop oscillation.It is possible that both QPPs and loop oscillation are independent of each other.However, they appear in the sequence during this solar flare indicating a certain physical relationship.More such observations should be analyzed to understand the physical process.The main conclusions are as follows: 1.The 40-50 s QPPs were identified at microwave and HXR between 01:37 and 01:52 UT, and they should originate from periodic accelerated electrons during the impulsive phase.The QPPs may also indeed be present in SXR but at insufficient power to be definitely detected.Furthermore, due to the limitation of temporal resolution of IRIS/SG, we cannot draw a conclusive conclusion about whether QPPs were modulated by external MHD waves.2. The ∼4 minute Doppler shift oscillations of Fe XXI 1354.08 Å in flare loops were detected by IRIS/SG The former should be produced by periodic accelerated electrons, while the latter is most likely due to the MHD waves, indicating that they could be independent of each other, although they were observed in the same event.
presents AIA and IRIS images taken near the flare maximum.Panel (a) illustrates the double-ribbon structure of this flare.The white box represents the field-of-view (FOV) of IRIS, and the central white line indicates the location of the slit.Panel (b) is the IRIS/SJI 1330 Å image in the smaller FOV (∼120″ × 120″), which also shows a similar structure to AIA 304 Å. Panel (c) exhibits the O I spectral window, from which we can see three main emission lines: Fe XXI 1354.08 Å, C I 1354.29 Å, and O I 1355.60Å. Figures 1(d)-(i) display that flare loops connect two ribbons, and the slit across through both flare loops and the western ribbon.

Figure 1 .
Figure 1.(a)-(i) AIA 304 Å, SJI 1330 Å, O I spectral window, AIA 94, 131, 171, 193, 211, and 335 Å images taken around flare peak time.The white box shows the field of view of IRIS, and the central white line indicates the slit location of the spectrograph.An animation of this figure is available.The animation runs from 01:15 to 02:30 UT on 2014-10-22.The video duration is 8 s. (An animation of this figure is available.) Figure2(top panel) plots the full-disk normalized light curves between 01:15 and 02:30 UT, including the NoRP 3.75 GHz (magenta), 9.40 GHz (cyan), Fermi 50-101 keV (black), and GOES 0.5-4 Å (red), as well as local light curves of AIA 94 (green), 171 (brown), 211 (pink), 304 (sky blue), 335 (blue), 1600 (purple), and 1700 Å (gold), which were integrated over the whole region in Figure1.It is interesting that two small peaks appear at 01:25 and 01:32 UT, which seems to be two small eruptions near the southwest ribbon according to the animation of Figure1.It is also obvious that light curves exhibit two large peaks around 01:38 UT, which correspond to the sudden brightening of double ribbons.Meanwhile, there is a strong enhancement of emission lines in the O I spectral window, followed by the appearance of Fe XXI 1354.08 Å accompanied by visible flare loops.In addition to light curves around 01:38 UT, multiple prominent and regular peaks were also detected by NoRP microwave and Fermi HXR between 01:42 and 01:52 UT, and these peaks occur simultaneously with a certain period.In order to analyze this periodicity, we first choose NoRP 9.40 GHz and Fermi 50-101 keV to perform the MCMC simulations mentioned above.Figures3(a)-(f) plot their PSD (blue), best-fit (red solid), and test statistic results.The red dashed line is the 95% confidence level (or 5% significance level).As shown in panels (b) and (e), the positive BIC M M 0 1 λ, λ 0 , and c are the fitting line center, the rest reference wavelength, and the speed of light.The 3σ uncertainty of Doppler velocity is v c σ is the error for line center fitting.Compared to line parameter values, the uncertainties are negligible.Although we attempt to fit line profiles of Fe XXI 1354.08 Å and C I 1354.29 Å with double Gaussian functions, there are still some cases that are fitted only by single Gaussian perfectly, such as Figures 5(b), (d), and (e), which should be caused by the extremely large intensity ratio of Fe XXI and C I in flare loops.From the six samples in Figure 5, Fe XXI 1354.08 Å displays its peak position oscillating around the rest wavelength, indicating that flare loops are oscillating in the line of sight.

Figure 3 .
Figure 3. (a) The NoRP 9.40 GHz PSD and its best fit for model M 0 .The red dashed line represents the 95% confidence level (or 5% significance level).(b) The PSD and its best fit for model M 1 .The positive BIC M M 0 1 ρ i and ρ e are internal and external mass density, and n i and n e are internal and external electron number density.If we assume a density contrast (n i /n e ) of 30-50 (Tian et al. 2016; 4. intensity fluctuations at Fermi 50-101 keV vs. at NoRP 9.40 GHz (a), NoRP 3.75 GHz (b), and GOES 0.5-4 Å (c).Black and red represent the data in the corresponding time interval.The maximum correlation coefficient (CC) is also given.(d) The microwave spectra at 01:40 and 01:47 UT corresponding to the form of the gyrosynchrotron spectra.

Figure 5 .
Figure5.(a)-(f) Six samples of observed spectra and their Gaussian fitting results.The orange profile is the original spectrum at the Y-axis marked by two green lines.The magenta and cyan profiles represent the fitting of Fe XXI 1354.08 Å and C I 1354.29 Å in a linear background (black horizontal dashed line), respectively.Two vertical red lines show their reference rest wavelengths.The black profile is the sum of fitting components.The line parameters and uncertainties are also given.