Doppler Shift Oscillations from a Hot Line Observed by IRIS

Figure 3 shows the spacetime images of Doppler velocity (upper) and line-integrated intensity (lower) at Fe xxi 1354.09 Å. The selected loop-top area is bounded by two green lines, and the plus signs ("+") mark the time of the flare spectra in Figure 2. A pronounced Doppler shift oscillation is observed in the loop-top area from about 00:20 UT to 00:25 UT. It begins from a redshifted velocity, and then changes to a blueshifted velocity. Such oscillatory behavior repeats at least two times, as indicated by the solid arrows in the upper panel. In other words, the oscillatory behaviors last for at least two cycles if we define one cycle as a pair of red- and blueshifts. After two visible changes from red- to blueshifts, the Doppler shifts become very weak. However, no such obvious oscillations can be seen in the spacetime image of line-integrated intensity during the same time intervals, as seen in the lower panel.

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The upper panel in Figure 4 shows the time series of Doppler shift (black) and line-integrated intensity (turquoise), they are averaged over the IRIS slit positions between two green lines in Figure 3. As a comparison, the SXR light curves at 1.0−8.0 Å (black) and 0.5−4.0 Å (turquoise) from GOES and normalized microwave fluxes at 17 GHz (solid purple) and 34 GHz (dash purple) from the NoRH are also given in the lower panel of Figure 4. The time series of Doppler shift exhibit six pronounced and regular peaks between around 00:10 UT−00:25 UT, which are labeled by the number ticks. The oscillations during the peaks "5" and "6" exhibit the changing from red to blue wings, as marked by the solid arrows. The same oscillations can be observed during the peaks "1" and "2," which also display a change from red to blue wings. However, there are only redshifted oscillations during peaks "3" and "4," and they are always dominated by red wings. It is also noted that the onset of these Doppler shift oscillations occurs in the impulsive phase of this flare. On the other hand, none of the similar oscillatory signature is revealed in the line-integrated intensity of Fe xxi 1354.09 Å, normalized microwave fluxes and SXR light curves. But the enhancement of line-integrated intensity is simultaneous with the appearance of Doppler shift oscillations, e.g., in peaks "1" and "5." In peak "4," the line-integrated intensity decreases when the Doppler shift tends to be redshifted. It is well known that the microwave emissions are produced by the nonthermal electron beams trapped in a flare loop during the impulsive phase of the solar flare (see Kundu et al. 1994; White et al. 2003; Reznikova & Shibasaki 2011; Dolla et al. 2012; Asai et al. 2013; Kumar et al. 2016). Although our observations do not show in-phase oscillations in the normalized microwave fluxes at 17 and 34 GHz, it is interesting to note that the pulse peaks of microwave emissions proceed the onset of Doppler shift oscillations by ∼1 minute, indicating the nonthermal electrons produced by magnetic reconnection before Doppler shift oscillations in this flare.

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To obtain the oscillatory period, a wavelet analysis method is used (Torrence & Compo 1998; Yuan et al. 2011; Tian et al. 2012; Li & Zhang 2017). First, a 5 minute running average in the time series of Doppler velocity is considered as a background emission, as indicated by the green profile in the upper panel of Figure 4. Second, the detrended time series of Doppler velocity is calculated from the original time series by removing the background emission (5 minute running average). Figure 5(a) shows the detrended velocity, and they exhibit six distinct peaks, which are well matched with those peaks in the upper panel of Figure 4, as labeled by the number ticks. Figures 5(b) and (c) display wavelet power spectrum and global wavelet, respectively. The oscillatory period can be measured from the peak value of the global wavelet power, and the uncertainty is thought to be the half width at half-maximum value (Tian et al. 2016). Finally, a dominant period with an error bar can be estimated for the detrended Doppler velocity of Fe xxi 1354.09 Å, which is about 3.1 ± 0.6 minutes. The wavelet power spectrum shows that these Doppler shift oscillations are from ∼00:10 UT to ∼00:25 UT, which correspond to the time interval during the six peaks in the time series of Doppler velocity (see Figure 4).

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Thanks to the high spatial resolution of imaging observations, we are able to study the morphological structure of the oscillatory positions. Due to data gaps in XRT observations, only a few XRT images are presented to show the flare loop structure at high temperature during the time interval of the pronounced oscillations. The SXR and EUV images are carefully selected to avoid data saturation (see also Li et al. 2015a; Ning 2017) and plotted with the Y-axis along the direction of the IRIS slit, e.g., 45° rotation. Figure 6 displays the loop structure and its movement from peak "5" to peak "6" at XRT Be_med filter and AIA 193 Å, it also shows the line-of-sight (LOS) magnetogram with the same FOV. Figure 6 shows that double footpoints, which are connected by this flare loop are rooted in the positive and negative magnetic fields, respectively. We trace this flare loop in XRT images and overlaid on each AIA 193 Å image (purple line). The region of interested is the loop-top area, which is bounded by two green lines here. The bright loop in AIA 193 Å images is cospatial with the overlaid SXR loop. It is noted that the bright loop-top region (outlined with two green lines) is crossed by the slit of IRIS (turquoise line).

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Furthermore, we also calculate some parameters of this flare loop. The apparent loop length is estimated to be ∼54 Mm according to the XRT images in Figure 6, as shown by the purple line. Then we can obtain the deprojected loop length (L ≈ 81 Mm) when considering the projection effect due to the derived position of the solar flare (Aschwanden et al. 2002; Kumar et al. 2013; Li 2017). The loop width (w) is also calculated from the XRT images. We first average the intensities between two green lines and obtain the flux along the X-direction. Then we fit the flux with a Gaussian function. Finally, the full width at half maximum (FWHM) of the Gaussian function is considered to be the loop width, which is about 9.8 Mm. Thus, the geometric ratio between loop width and length (w/L) is around 0.12. This geometric ratio is quite reasonable, given $w=2\times r$ (r is the radius of flare loop); therefore, the aspect ratio between loop radius and length (r/L) is about 0.06, which is consistent with previous findings in the coronal loops (Aschwanden et al. 2002).

To investigate the temperature structure of this flare loop, we perform the differential emission measure (DEM) analysis using AIA data at six EUV wavelengths (see Cheng et al. 2012; Sun et al. 2014; Shen et al. 2015). Figures 7(a)–(e) show the DEM profiles in the loop-top region (marked by the red box of pi in Figure 6) with an FOV of 24×24 at the selected time. While Figure 7(f) gives the DEM profiles outside of the flare loop, as indicated by the red box of po. The average temperature (T) and emission measure (EM) at each time are estimated within a confident temperature (log T) range of 5.5–7.5 (Ning et al. 2016). The best-fitted DEM solution of the observation is indicated by the black profile. Then the Monte Carlo (MC) realizations of the observations are applied to estimate the DEM uncertainty, as indicated by the top and bottom color rectangles (see Cheng et al. 2012; Li et al. 2016b, 2016c, 2016d). It gives a much lower value of the uncertainty on our DEM analysis, especially at the high temperature regions, i.e., panels (c) and (d).

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The upper panel of Figure 8 is the time series of the Doppler shift and temperature at the flare loop-top region, and the lower panel shows the EM variation and EUV fluxes at AIA 193 Å (∼20 MK), 131 Å (∼11 MK), 94 Å (∼6.3 MK), 211 Å (∼2.0 MK), and 171 Å (∼0.63 MK) (Lemen et al. 2012). The temperature rises rapidly at the onset of Doppler shift oscillations (e.g., peak "1" and "5"), which is almost in phase with the enhancement of the EUV fluxes at the AIA 131 and 193 Å passbands (≥11 MK). The temperature increases here might be due to hot emission from the loop top that are clearly seen in the XRT Be_med and AIA 193 Å images (Figure 6) and also crossed by the slit of IRIS. However, the EUV fluxes in other channels lag by several minutes and such in-phase correspondence cannot be found, implying that the Doppler shift oscillations only take place in the hot loop, i.e., at least 11 MK. The EM varies very slowly throughout the entire impulsive phase. It keeps nearly constant during the occurrence of Doppler shift oscillations, suggesting the incompressible flare loop. The average EM in the flare loop-top area between ∼00:20 UT and ∼00:25 UT is estimated to be ∼3 × 10³⁰ cm⁻⁵. We further estimate the average number density from Equation (1) (see also Zhang & Ji 2014; Su et al. 2015; Ning et al. 2016; Zhang et al. 2016a), which is about 5.5 × 10¹⁰ cm⁻³. This value agrees well with previous findings in flare loops (Aschwanden & Benz 1997), for example, ${n}_{e}\,\approx$ (2−25) × 10¹⁰ cm⁻³ in SXR loops.

$$\begin{eqnarray}&&{n}_{e}=\sqrt{\displaystyle \frac{\mathrm{EM}}{w}}.\end{eqnarray} \tag{ 1 }$$

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We notice that the Doppler velocities shown in Figure 4 are not pronounced. For example, they are no more than ±25 km s⁻¹ during the Doppler shift oscillations. The Doppler velocity in this study is calculated from the subtraction between the fitting line center and the rest wavelength, and there could be two quantities producing the errors. One is the fitting line center derived from the multi-Gaussian fitting method. The multi-Gaussian fitting procedure (for details, see Li et al. 2015b, 2016a) used to obtain the Fe xxi 1354.09 Å here has included as much as possible the known/unknown blending emission lines in this data set. The final fit as well as the extracted Fe xxi 1354.09 Å line profile (see Figure 2) appear to be successful at the selected positions. Thus the derived fitting line center is convincing. The other one is the rest wavelength. The formation temperature of Fe xxi 1354.09 Å is ∼11 MK, which is too hot to be observed in the quiet-Sun spectrum. In this paper, we set the rest wavelength as 1354.09 Å, which is the average value from the recent IRIS spectral observations, i.e., 1354.08–1354.1 Å (e.g., Polito et al. 2015; Sadykov et al. 2015; Tian et al. 2015; Brosius et al. 2016). The uncertainty is around ±0.01 Å, which corresponds to the Doppler shift of about ±2.2 km s⁻¹. This uncertainty on the rest wavelength of Fe xxi 1354.09 Å might change the Doppler shift slightly but does not have a significant impact on our results. On the other hand, Tian et al. (2016) find that the Doppler velocity of Fe xxi 1354.09 Å in a flare loop is much smaller than that in the flare ribbons, which is similar to our results.

The oscillations in flare/coronal loops are usually related to MHD processes (Roberts 2000; De Moortel & Nakariakov 2012; Tian et al. 2016), such as slow magnetoacoustic waves, fast sausage waves, and fast kink waves. In this paper, the loop oscillations are observed in the Doppler shift of Fe xxi 1354.09 Å, but there are no apparent corresponding intensity fluctuations in line-integrated intensity of Fe xxi 1354.09 Å (Figure 4) or AIA EUV fluxes (Figure 8). In DEM analysis, the EM is also relatively stable during the Doppler shift oscillations. These facts suggest that the flare loop oscillates in an incompressible mode, and further rule out the possibility of slow magnetoacoustic waves because they are compressible magnetoacoustic waves (Roberts 2000; Wang et al. 2002, 2003; Aschwanden 2005). The loop oscillations are unlikely to be interpreted as fast sausage waves either. The sausage oscillations within short periods (<60 s) are often decayless or weakly damping when the cutoff condition and those within long periods (>60 s) are substantially compressible and transverse (Gruszecki et al. 2012; Vasheghani Farahani et al. 2014; Tian et al. 2016). Moreover, they could produce density variation, which can easily modulate the periodic oscillations in microwave emission (Rosenberg 1970; Aschwanden 2005; Antolin & Van Doorsselaere 2013; Reznikova et al. 2015). The loop oscillations here are incompressible, damping, and no corresponding intensity fluctuations are detected in EUV and microwave emissions. All those theoretical predictions of fast sausage waves argue against our observations.

The observed loop oscillations are most probably fast kink waves. The oscillations produced by kink waves can produce the intensity and Doppler shift based on the column depth from different viewing angles. If the spectral slit is aligned along the loop, only Doppler shift oscillations are expected from the LOS direction (Yuan & Van Doorsselaere 2016a). In addition, the kink oscillations can also decay rapidly (Nakariakov et al. 1999; Aschwanden 2005; Zimovets & Nakariakov 2015; Yuan et al. 2016). All these theories are consistent with our observations. In this event, a flare loop is detected to be corresponding to the Doppler shift oscillations. The observed oscillatory period in this flare loop is ∼3.1 ± 0.6 minutes. That is to say, the dominant period of kink oscillations is ∼3.1 minutes. On the other hand, according to the period (P_k) of the standing kink oscillations, we can diagnose the magnetic field strength (B) in this flare loop from Equation (2) (Roberts et al. 1984; Nakariakov & Ofman 2001; Wang et al. 2002; Aschwanden 2005; Tian et al. 2012).

$$\begin{eqnarray}&&B\approx \displaystyle \frac{{v}_{A}}{2.18\times {10}^{11}}{n}_{e}^{\tfrac{1}{2}},\,{v}_{A}={v}_{k}{\left(\displaystyle \frac{2}{1+{n}_{0}/{n}_{e}}\right)}^{-\tfrac{1}{2}},\,{v}_{k}=\displaystyle \frac{2L}{{P}_{k}}.\end{eqnarray} \tag{ 2 }$$

Here, v_A is the local Alfvén speed, v_k is the phase speed of the standing kink wave in its fundamental mode, n_e and n₀ are the electron densities inside and outside of the flare loop, respectively. As mentioned in Section 3, the deprojected length (L) of this flare loop (Figure 6) is ∼81 Mm, thus the kink speed can be estimated to be ∼870 km s⁻¹. Meanwhile, the number density (n_e) inside the flare loop can be estimated from Equation (1). However, it is impossible to find a loop width (w) outside of the flare loop. Therefore, the effective LOS depth ($l\sim \sqrt{H\pi r}$) is used to estimate the number density outside the flare loop region (po), which is ∼4 × 10¹⁰ cm (Zucca et al. 2014; Su et al. 2016). Then we can obtain the density ratio (${n}_{0}/{n}_{e}\sim 0.03$) between outside (po) and inside (pi) flare loop at about 00:24:13 UT, as seen in Figures 7(d) and (f). The Alfvén speed can be estimated to be about 630 km s⁻¹, and the magnetic field strength in this flare loop can be estimated to be ∼68 G, which agrees with previous results, i.e., 60−120 G in the flare loop (see Qiu et al. 2009). In our observations, the density ratio (${n}_{0}/{n}_{e}$) around the flare loop is less than the typical density ratio (i.e., 0.1–0.5) around the coronal loop (Aschwanden 2005), suggesting that the number density in the flare loop is higher than that in the coronal loop.

The upper panel in Figure 4 exhibits that there are at least two oscillatory periods in the time series of Doppler shift of Fe xxi 1354.09 Å. One is the shorter period (∼3.1 minutes), which has been obtained in Section 3.1. The other one seems to be a longer period, and the time series of line-integrated intensity also displays a similar longer period. To extract the longer period, we perform a Fourier analysis using the method described by Yuan et al. (2011), which is based on the Lomb–Scargle periodogram technique (Scargle 1982; Horne & Baliunas 1986).

Figure 9 shows the results of spectral analysis. The Fourier analysis is applied to the detrended time series after removing the background emission, which is the 12 minute running average of the time series (see Tian et al. 2012; Li & Zhang 2017). Here, a different averaging time window only results in changing in relative power of the peaks (Yuan et al. 2011). Panel (a) gives the normalized power spectrum of detrended Doppler shift. From which, we can extract at least two components of periods, P₁ and P₂. We also calculate the error bars as the uncertainties of periods, which are the half width at half-maximum value of the Fourier power (Yuan et al. 2011; Tian et al. 2016). The shorter dominant period (P₁) within an error bar is around 3.1 ± 0.6 minutes. The dominant period of P₁ agrees well with the wavelet analysis result (Figure 5). While the longer dominant period (P₂) within an error bar is about 10 ± 4 minutes. This longer period can also be detected from the detrended time series of line-integrated intensity of Fe xxi 1354.09 Å (b). To illustrate this longer period, we also perform Fourier analysis of the detrended fluxes from GOES 1.0–8.0 Å (c), 0.5–4.0 Å (d) in SXR passbands, and AIA 193 Å (f), 131 Å (f) in EUV wavelengths. The normalized power spectra show that all these detrended fluxes display a longer dominant period of ∼10 minutes, which is the same as that in the Doppler shift of Fe xxi 1354.09 Å. On the other hand, the shorter period cannot be detected in these detrended fluxes, which further confirms that the 3.1 minute oscillations can only be observed in the Doppler shift of Fe xxi 1354.09 Å.

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As mentioned above, the Doppler shift oscillations within a period of ∼3.1 minutes (P₁) can be interpreted as the standing kink oscillations in the hot flare loop. On the other hand, the longer period (P₂) is different from the shorter one (P₁), because it can be observed simultaneously in SXR and EUV fluxes, as well as in the time series of Doppler shift and line-integrated intensity of Fe xxi 1354.09 Å. Those facts imply the process of periodic energy release in this flare (Tian et al. 2015; Li et al. 2017b). The longer period is most likely to be linked to the quasi-periodic pulsations during the solar flare, which seems to be caused by an MHD wave in the slow mode (Fang et al. 2015; Van Doorsselaere et al. 2016). Based on the formation temperature ($T\sim$ 11 MK) of Fe xxi 1354.09 Å, the local sound speed (v_s ≈ $152\sqrt{T/{\bf{MK}}}$) in the flare loop is estimated to be ∼500 km s⁻¹ (e.g., Nakariakov & Ofman 2001; Kumar et al. 2013, 2015). While the deprojected length (L) and longer period (P₂) of this flare loop have been identified as ∼81 Mm and ∼10 ± 4 minutes, then the phase speed of this flare loop (v_h = 2L/P₂) can be estimated as about 200−450 km s⁻¹. This phase speed is slower than the local sound speed, implying it might be a slow MHD wave (Mandal et al. 2016). In other words, the longer period (P₂) might be explained as the MHD wave in a slow mode.

To compare the Doppler shift oscillations, we also use the sine function with a damping amplitude (Equation (3)) to fit the time series of Doppler shift during peaks "5" and "6" (e.g., Nakariakov et al. 1999; Wang et al. 2002; Anfinogentov et al. 2015), because the Doppler shift oscillations are most pronounced during this time interval. Figure 8 (upper) shows the fitting result, the overlaid turquoise profile gives the best fitting, and it appears to match well with the Doppler velocities (black).

$$\begin{eqnarray}&&v(t)={v}_{0}+{v}_{m}\sin \left(\displaystyle \frac{2\pi }{{P}_{1}}t+\psi \right){e}^{-\tfrac{t}{\tau }}.\end{eqnarray} \tag{ 3 }$$

Here, v₀ is the initial Doppler velocity, v_m is the initial oscillatory amplitude, and P₁, ψ, and τ are the shorter dominant period, initial phase, and decay time of the oscillations, respectively.