Recurrently Propagating Intensity Disturbances along Polar Plumes Observed in White Light and Extreme Ultraviolet

We study properties of intensity disturbances along polar coronal rays that are associated with plumes below. For this, we draw azimuth–time images of extreme ultraviolet (EUV) emission of 171 Å band observed by the SDO/AIA and white light (WL) observed by the SOHO/LASCO C2 in 2020 July. From the azimuth–time image, we define two tracks in which the EUV intensities were recurrently enhanced during two weeks. The two EUV tracks are rooted at 78.°8 and 81.°4 latitudes, but their projected azimuth angles are changed with time as the Sun rotates. Coherent WL tracks at different altitudes are determined by scaling the azimuth angles of the EUV tracks, accounting for the effect of inclination of coronal rays. From this, we construct time–distance images of WL intensities along WL tracks, whose projected azimuth angle changes along time and altitude, but the intensities are correlated with the EUV intensities measured below. The time–distance images of WL show repeated and inclined intensity features. The propagation speeds in the altitude range 2.3–6 solar radii are calculated to be 159 ± 8 km s−1 and 300 ± 24 km s−1. The EUV and WL intensities are found to be coherent at 1–2 day periods. It is also found that dynamic burst events along the EUV track are responsible for the enhanced emission. We conclude that the variation of the WL intensity along the polar coronal rays is related with the evolution of the EUV intensity below.


Introduction
Solar coronal plumes are thin and ray-like structure in polar regions, typically observed in white light (WL), extreme ultraviolet (EUV) emission, and X-rays (Pesnell et al. 2012).They are particularly well observed in the WL coronagraphs (e.g., Boe et al. 2020) and possibly extended to the outer heliosphere (McComas et al. 1996;Reisenfeld et al. 1999).Wang & Sheeley (1995) found that locations of plume base areas seen in the EUV image are near the mixed magnetic polarity regions, suggesting that the plume forms by magnetic reconnection between small bipoles within a coronal hole and unipolar flux concentrations.Wang et al. (1997) showed that base locations of diffuse plume emission in Fe IX 171 Å line roughly coincide with the patterns of network brightening in He II 304 Å band, which supports that the plume formation involves magnetic reconnection between unipolar flux concentrations and nearby bipoles.Based on high-resolution EUV images and magnetograms from the Solar Dynamics Observatory (SDO; Pesnell et al. 2012), it was found that plumes form where unipolar network elements inside coronal holes converge to form dense clumps, whose core region almost invariably show loop-like features (Wang et al. 2016).Pucci et al. (2014) studied a plume having a coronal bright point at its base, together with propagating intensity disturbances, and found that the plume started ∼2 hr after the coronal bright point first appeared and became undetectable ∼1 hr after the bright point disappeared, suggesting that the plume brightness varies with the density that might be supplied by transient magnetic activity (e.g., Raouafi & Stenborg 2014).It was found that a plume was composed of numerous time-evolving filamentary structures that account for most of the plume emission (Uritsky et al. 2021).It was also found that the filamentary structures involve quasi-periodic, tiny jets associated with transient brightening, flow, and plasma heating at the chromospheric foot points (Kumar et al. 2022).
When the solar limb at whole latitude is displayed in the polar coordinate, one would see long-lived intensity features so called the helmet streamer which typically appears at low-and mid-latitudes, but the features are repeatedly cross the poles due to the solar rotation (Li et al. 2000).It has been found that locations of helmet streamers observed from the altitude averaged intensity images along time and azimuth angle are associated with strong magnetic field active region outflow (Liewer et al. 2001).These helmet streamers, together with pseudostreamers, can be observed as corona rays (Wang et al. 2007).Streamer blobs of outwardly moving density inhomogeneity were frequently observed in helmet streamers (Wang et al. 1997(Wang et al. , 1998;;Song et al. 2009;López-Portela et al. 2018;Lee et al. 2021).Helmet streamers at high altitudes could be projected on the solar polar region, especially when it crosses the central part of the solar disk, as a ray-like structure and/or associated intensity propagation (e.g., Wang & Hess 2018).An helmet streamer lies at low latitudes in the solar minimum 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.periods, while it covers almost whole latitudes in the solar maximum periods (Boe et al. 2020), but they appear to cover almost whole longitudes of the Sun.Hence, the projections may happen very frequently.In other words, a portion of polar coronal rays are indeed projected helmet streamers.
In our study, we identify recurrently propagating intensity disturbances along polar coronal rays seen in the WL coronagraph on 2020 July, which are coherent with the EUV plumes rooted at 78°. 8 and 81°.4 solar latitudes.The positions of the WL coronal rays change with time, due to the solar rotation, and they also change with altitude, due to inclined coronal rays (e.g., Tlatov 2010.However, they remain coherent with the sinusoidal path on the azimuth-time image where EUV plume brightness is enhanced.The following section provides descriptions of the EUV and WL data we analyzed.In Section 3, we present how the location of WL coronal rays is determined based on the location of EUV plumes, and we also present the analysis results for the WL coronal rays and EUV plumes.Finally, we summarize our results.

Data
To study an intensity variation of coronal rays rooted on the polar coronal hole, we draw sinograms from EUV images at the altitude of 1.15 solar radii and WL images at higher altitudes.The sinogram indicates I'(r 0 , α, t), when the series of images, I(x, y, t) was transformed into the polar coordinate, I'(r, α, t), where r and α are the distance and azimuth angle of a position (x, y).Here, r 0 indicates a specific altitude.The azimuth angle starts from the west equator of the Sun and goes counterclockwise.The sinogram represents a temporal evolution of intensity as a function of azimuth angle at a specific altitude, and was used to describe an intensity variation along a radial direction as a vertical one (e.g., Lamy et al. 1997;Llebaria et al. 1998;DeForest et al. 2001).For this, we analyze the coronagraph image from the We also analyzed the 171 Å EUV filtergram images observed by the Atmospheric Imaging Assembly (AIA; Lemen et al. 2012) on board the SDO, whose observation epochs are closer to those of C2 images by 6 s, hence the analyzed EUV images are roughly synchronized to the WL images.The data are normalized by the exposure times.Each AIA image is normalized as in the WL image.

Association between EUV Plumes and WL Coronal Rays
In our study, the horizontal and vertical axes of the sinogram are the azimuth angle (0°at west equator, counterclockwise) and time, respectively.In Figure 1(a), we concentrate on the two long-lasting EUV intensity-enhanced regions starting from the azimuth angle of ∼80°and ∼93°, which we called tracks A and B (solid curves).Track A is considered to consist of plume activation places or birthplaces that appear recurrently.It moves from the northwest hemisphere to the northeast hemisphere, hence it is on the solar backside.Track B moves from the northeast hemisphere to the northwest hemisphere (solar frontside).A low-altitude plume is typically well observed with the EUV emission, but its intensity rapidly decreases along altitude.Hence, an intensity of the projected low-or mid-latitude plume onto the polar region would be faint.It is likely that the observed bright tracks are rooted at the high-latitude coronal hole.
To check whether the EUV plumes are really rooted at the high latitude, we try to fit the observed EUV tracks with the theoretically derived projected azimuth angle, which changes with the solar rotation (e.g., Lamy et al. 1997;Llebaria et al. 1998;Li et al. 2000).For example, Llebaria et al. (1998) analyzed temporal evolution of EUV and WL plumes on the sinograms, and found that they follow dotted sinusoidal tracks suggesting that they are enduring, recurrent structures in rigidbody rotation that are transiently active.Those authors also found that their lifetimes are different and therefore show no correlation between the EUV and WL intensities along the tracks.In their study, the sinusoidal tracks were described by three parameters: the maximum deviation of azimuth angle from the pole, the solar rotation period, and the longitudinal phase angle, which could be derived by applying the Radon transform.On the other hand, Li et al. (2000) analyzed temporal evolution of the polar rays on the EUV sinogram from 1996 January to 1998 June, and found that the rays were extended, hot plasma structures formed in the active regions projected onto the plane of the sky above the polar coronal holes.In their study, the sinusoidal track of the azimuth angle was modeled with , where Ψ is the azimuth angle from the north pole, θ 0 is the heliocentric latitude, and α is the longitude from east limb.It should be noted that both approaches can give positional information on the root of plumes, but the latter case would directly incorporate them.
In our study, we define the azimuth angle of plumes that is projected onto the sky plane, , where θ and f represent colatitude (90°-latitude(λ)) and longitude (from central meridian), respectively.We assume the low corona rotates as a rigid body, neglect an effect from when the solar B 0 angle is nonzero, and also neglect an effect from an inclination of the plume because the altitude range in the EUV image is close to the Sun.Our approach is basically the same as that of Li et al. (2000), but we use θ = 90°− λ and f starting from the central meridian of the solar disk.This approach is consistent with the convention of the spherical coordinate system if the Sun-Earth line is set to be the x-axis and the direction from the solar disk center to the west (north pole) is set to be the y(z)-axis.In this case, the projected azimuth angle is [ ] a q q f = = z y tan cos sin sin .Indeed, our f is actually f Synodic , which is calculated from f Synodic = f 0 + Δf Synodic considering the synodic rotation of the Sun.We note that Δf Synodic = 360°/P Synodic × (t − t 0 ), where P Synodic = 1/(1/P − 1/365) and ´t t 14.712 2.396 sin 1.787 sin 2 4 0 , applying the rotation rate given by Snodgrass & Ulrich (1990), where λ is the latitude.From this formula, we try to find f 0 and λ by manually checking a correspondence between α (dashed in Figure 1(a)) and the EUV tracks (solid in Figure 1(a)).Our approach differs slightly from the method proposed by Llebaria et al. (1998), where the unknown parameters were the maximum azimuth angle from the pole, the solar rotation period at high latitude, and the longitudinal phase angle.We find that λ is 78°.8 for track A and 81°.4 for track B. Here, the values of f 0 for tracks A and B are 114°.5 and −5°, respectively.We would like to note that the longitude of 114°.5 is westward at the backside, while −5°is eastward at the frontside viewed from Earth.
For the two EUV tracks, we test how their intensity features are different from those at a different view angle.Figure 2 shows the sinogram of the 171 Å channel images obtained from the Extreme Ultraviolet Imagers (EUVI) of the Sun Earth Connection Coronal and Heliospheric Investigation (SECCHI; Howard et al. 2008) on board the Solar TErrestrial RElations Observatory (STEREO; Kaiser et al. 2008) A spacecraft.The STEREO A spacecraft orbits the Sun in 347 days and is located ∼65°behind the Earth at the time.Two white dashed lines indicate the EUV tracks determined by using the same value of λ and f 0 , but using the revolution period of 347 days.It seems that two bright tracks similar to those from the SDO can be identified close to the white dashed lines.Therefore, the two EUV tracks are likely rooted at around 78°. 8 and 81°. 4 latitudes, rather than a superposition of plumes at different locations.The slight differences might originate from the difference in the B 0 angles at the two spacecraft (8°.1) and/or an inclination effect of the plumes.Formulating f Synodic as a function of B 0 angle and an inclination angle of plumes together with λ and f 0 is beyond the scope of our study.
We expect that a part of the EUV plume could be observed in a coronal ray.The coronal rays are typically inclined from their radial direction in the sky plane (e.g., Tlatov 2010).Hence, in our study, the WL track for a given heliospheric distance is scaled as , 1.15 90 , where a¢, α, and f are the azimuth angles of WL tracks, azimuth angle of the EUV track and scaling factor, respectively.In this formula, if α is larger (smaller) than 90°, a¢ is inclined to the left (right) relative to α by the amount |α − 90°| × f in the solar northern hemisphere, and hence, considering that the inclination is proportional to how far the plume is away from the pole, (|α − 90°|).If f = 0, then a a ¢ = , indicating a radial ray.Actually, one may use simply a a a ¢ = + D by changing Δα, but our approach is basically the same.The scaling factors were tested from 0 to 3 with a sampling interval 0.05, for a given distance.The WL intensity along each track is interpolated from the WL sinogram for a given distance.The set of WL intensities with different scale factors is compared with the intensity along the EUV track to find which WL track gives the maximum cross-correlation with the EUV intensity.
Figures 3(a) and (c) show the maximum correlations among lagged cross-correlations between I(α(t, 1.15R e )) and ( ( )) a¢ I t for tracks A and B for a given distance.Here, the intensities are high-pass filtered with a cutoff period of 4 days.Although the overall correlation is very low, there are relatively regions of relatively high correlation compared to the surroundings, which are continually varying with distance (dashed lines).The scale factors of the maximum correlations slowly increase with distance and become constant at ∼6 solar radii, indicating that the coronal rays are initially nonradial but eventually become radial at ∼6 solar radii.The right two panels (Figures 3(b If we choose the central distance for the LASCO/C2 field of view (FOV) to be 4 solar radii, the projected mean propagation speeds are calculated to be ∼42 km s −1 and ∼28 km s −1 .Figure 4 shows example snapshots of the EUV plumes (black box) and WL coronal rays (white dashed).It is shown that the WL intensity is enhanced within the white dashed lines, which are delayed by 13 hr from the EUV images.
We would like to note that the intensities along WL tracks are correlated with the long-lasting plume sites observed in the EUV emission, hence the WL tracks are likely connected with the EUV plumes at the low altitude.The positive delay times from the cross-correlation imply that the plumes and coronal rays are likely propagating structures within the timescales of a few days.The projected propagation speeds are found to be ∼42 and ∼28 km s −1 in the altitude range 1.15-4 solar radii.Based on the ground-based eclipse observations, Bělík et al. (2012) estimated the speed of brightness propagations within plumes to be 30-100 km s −1 .Hanaoka et al. (2018) reported much high speeds of ∼450 km s −1 from coronal jets in polar plumes.Our speed is also lower than the typical sound speed of 1 MK corona (∼152 km s −1 ).Moreover, the timescales appearing in our study are much longer than those of the above jets, and they are also longer than the timescales of EUV intensity disturbances (e.g., Cho et al. 2021).

Time-Distance Image along WL Plumes
From the determined WL tracks ¢ A and ¢ B in the distance range from 2.3 to 6 solar radii, we construct time-distance images (Figure 5).One may see many inclined and enhanced intensities in the time-distance images on a daily timescale, representing that the intensity disturbances are propagating.To calculate the speed of propagation, the lagged cross-correlations between intensities for an arbitrary distance with the intensity at 3.5 solar radii (Figures 6(a) and (c)) were obtained.A maximum correlation with positive lags above the reference height indicates that the correlated intensity pattern is delayed in comparison to the intensity pattern at the lower height.A maximum correlation with negative lags below the reference height indicates the intensity pattern leads the intensity pattern at the higher height.These imply that the intensity disturbances are upwardly propagating.The slopes of distances with respect to the lag times of the maximum correlations give the propagation speeds, which were calculated to be 159 ± 8 km s −1 for track ¢ A and 300 ± 24 km s −1 for track B'.We also perform the spectral analysis for the WL intensity at 3.5 solar radii and the EUV intensity at 1.15 solar radii (Figures 6(b) and (d)).The red and orange curves represent the Fourier powers for the WL intensity and EUV intensity,  respectively.The dashed lines are 99.9% significance levels, assuming red noise.It is found that significant powers at 1-2 days appear in both the WL intensity (red) of coronal rays as well as in the EUV intensity (orange) of plumes.Hence, the intensity variation of coronal rays observed in the WL coronagraph is likely related to the intensity variation of EUV plumes below.).In our study, the intensity along EUV tracks was enhanced repeatedly over 1-2 days, which is consistent with the above results.The recurrent propagating disturbances for tracks A′ and B′ are found to be accelerated from 42 to 159 km s −1 and 28 to 300 km s −1 .We interpret that plumes form recurrently along the EUV track, which may involve frequent reconnection in their initial phases, would repeatedly supply materials into the atmosphere.In our study, higher speeds were observed at higher latitudes.The uncertainty of the projection effect of coronal rays may obscure such a difference.For example, if the difference between coronal rays along the two tracks is 20°, this only gives a speed difference less than 10%.The energy flux density is more effectively transferred along a magnetic flux tube with a smaller expansion (e.g., Sheeley 2017), characterized by a lower number density according to the magnetic pressure balance.The flux tube with a large curvature can inhibit energy transfer, and hence it reduces the energy flux density (Li et al. 2011).Thus, the supplied materials might be accelerated according to different coronal expansions and curvatures at different latitudes.On the other hand, the density fluctuation was observed in the coronal hole up to 1.35 solar radii (e.g., Hahn et al. 2018), which may indicate a significant enhencement of the gradient of the Alfvén speed (van Ballegooijen & Asgari-Targhi 2016).Outward-propagating   In panel (b), two blue curves represent the 5 minute median intensity (lower blue) and the threshold intensity (upper blue).The threshold intensity is defined as the median absolute deviation between the original and 5 minute median intensity, plus the median intensity.The spike intensity event is defined as being when the original intensity is higher than the threshold.

Property of Foot-point Region Intensity
To explore whether any dynamic activity is related with the enhanced EUV intensity, we analyze the intensity time series for the frontside foot-point region of track B with 12 s cadence.Figure 7 shows the example snapshots of the AIA 171 Å channels, which include the foot-point region of B. The small box in each panel is a ±10″ region centered at −5°longitude and 81°.8 latitude on 2020 July 5 20:00 UT, which seems to repeatedly include bright intensity patches.From the intensities inside the box region, we obtained the mean intensity time series for the foot-point region (Figure 8(a)).In Figure 8(b), we plot the mean intensity time series during 1 hr together with the 5 minute median smoothed intensity (lower blue curve) as well as the threshold intensity (upper blue curve), where the difference between the threshold and smoothed one is defined by the median absolute deviation between the original mean intensity and the smoothed one.The red cross is the original intensity that exceeds the threshold intensity, which we define the spike event.In Figure 8(c), we plot the 1 hr mode intensity (black curve) and the number of spike events during 1 hr (red).It is found that the mode intensity is correlated with the number of spike events (CC = 0.71), which may imply that burst events are responsible for the enhanced coronal EUV emission.We note that the original intensity is the (mean) within ±10″, and hence the photon noise would be sufficiently suppressed.It should also be noted that the hourly sampled intensity is the mode value and hence not likely to be associated with the spiky intensity itself.
Figure 9 shows the waiting time histogram of the intensity spikes.It is found that the histogram is well fitted with the Poisson function in the range of waiting times shorter than 15 minutes, with an occurrence rate of 0.4 min −1 .We would like to note that the histogram around τ = 1 minutes is overpopulated, which is typically observed in the Poisson distributions of major flares on timescales of ∼1 hr (e.g., Moon et al. 2002) and flare X-ray bursts on timescales from 10 seconds to 10 minutes (Wheatland et al. 1998).The timescale of the overpopulation in our study is ∼1 minute and hence similar to the flare X-ray bursts.Therefore, the EUV intensity spikes might be a flare-like activity.

Summary
The recurrently propagating intensity disturbances along polar coronal rays in the LASCO/C2 FOV are observed.The locations of WL coronal rays change with time and altitude, and their intensities are associated with the variation of the EUV plumes over two weeks.The WL time-azimuth track is determined based on the lagged cross-correlation between the intensity along the EUV track and the intensities along differently scaled WL tracks, for a given distance.Although the maximum correlation is weak, the scaling factor of the maximum correlation is continually connected with altitude, which could be interpreted as meaning that the EUV intensity variations propagate to at least 6 solar radii and could be observed as WL intensity variations.Along the determined WL tracks, the time-distance images are obtained.The averaged propagation speed is 159 ± 8 km s −1 in the altitude range from 2.3 to 6 solar radii when rooted at 78°. 8 latitude, while it is 300 ± 24 km s −1 when rooted at 81°.8 latitude.The recurrent periods of WL intensity are 1-2 days that are also observed in the EUV plumes.
It is well known that plumes and pseudostreamers in coronal holes, which typically overlay a bipole or small arcade loops at their bases, cannot maintain the blob-like propagation along helmet streamers, because of strong magnetic fields at their cusps (Wang et al. 2007(Wang et al. , 2012;;Wang & Hess 2018).On the other hand, the average propagation speeds between 1.15 solar radii and 4 solar radii were 42 and 28 km s −1 , i.e., much slower than typical jets (e.g., Hanaoka et al. 2018).Raouafi et al. (2023) suggested that the physical mechanism that heats and drives the solar wind and its source is ubiquitous magnetic reconnections.It was found that these reconnection flows have power-law distributions in their volume and energy (Uritsky et al. 2023).On the other hand, it was found that the fleeting small-scale photospheric magnetic fields are responsible for jetlike eruptive activities in the quiet region (Chitta et al. 2023).We observe that the enhanced EUV emission is likely related to the number of intensity spikes, whose waiting time histogram is the flare-like Poisson distribution, therefore suggesting that the spike events are repeatedly enhanced at the plume foot point and may supply material into the corona.These materials could be observed in plumes and coronal rays.We interpret that the long timescale (1-2 days) is not indicative of intermittency, but rather may be understood in the context of background solar winds.
Large Angle Solar COronagraph (LASCO; Brueckner et al. 1995) C2 instrument on board the Solar and Heliospheric Observatory (SOHO, Domingo et al. 1995) from 2020 June 22 2020 to 2020 July 17 that covers the altitude range from 2 to 6 solar radii.The cadence is approximately 12 minutes.The level 0.5 images are normalized by the exposure times.From each WL image, we subtract the 3 day median image, and then divide the result by the image of the median absolute deviation for the subtracted image.Intensities of stars and planets are replaced by the median intensity within 7 × 7 pixels.

Figure 1 .
Figure 1.Sinograms of the AIA 171 Å channel intensity at 1.15 solar radii (a) and the LASCO/C2 intensity at 3.5 solar radii (b) from 2020 June 22 to 2020 July 17.The azimuth angle of 90°indicates the north pole starting from the solar west equator.The black solid curves in panel (a) are the azimuth angles of the intensityenhanced region as a function of time, which we defined as EUV tracks.The black dashed curves are the fitted azimuth angles with a = tan 1 ( q f 1 tan sin Synodic ), where α, θ, and f Synodic represent the azimuth angle, colatitude, and longitude, respectively.The gray solid curves in panel (b) are the scaled azimuth angles at 3.5 solar radii (see Figure 3).

Figure 2 .
Figure 2. The sinogram for the STEREO A 171 Å channel images at 1.15 solar radii.The two white dashed lines are the EUV tracks determined in Figure 1.
) and (d)) show the maximum correlations (black) along the distance and the corresponding delay times (blue open circle).The median delay time is 13 hr for track A' and 20 hr for track B'.

Figure 3 .
Figure 3. Lagged cross-correlations between the intensity along the EUV track at 1.15 solar radii, I(α(t, 1.15R e )) and intensities along the WL tracks, ( ( )) a¢ I t , for a given distance, where ( ) ( ) [ ( ) ]   a a a ¢ = + - t t R t R f , 1.15 , 1.15 90 (a, c) and corresponding maximum correlations and delay times (b, d) along dashed lines indicated in the left panels.

Figure 4 .
Figure 4. Example snapshots of the LASCO/C2 images overlaid with the SDO/AIA 171 Å filtergram.The black box indicates the position

Figure 5 .
Figure 5. Time-distance images along tracks ¢ A and ¢ B .
Telloni et al. (2013) have found intensity fluctuations a period of ∼10 hr in a ray-like structure in the polar region, and interpreted that the periodic fluctuations are signatures of intermittent, quasi-periodic magnetic reconnection due to continuously emerging flux tubes or the oscillatory transverse displacements of the coronal ray itself.The lifetime of the plume is closely tied to the evolutionary timescale of the supergranular network, approximately 1 day.This network involves interchange reconnection between open and closed magnetic fields within converging flows, which may play a crucial role in the emission of the plume(Wang et al. 2016).De Rosa & Toomre (2004) studied the life histories of over 3000 supergranules and found that most supergranules have lifetimes of less than 24 hr, coexisting among many longlived (several days) supergranules, and 7% of supergranules are recognizable for time periods of 48 hr or more.It was found that the typical duration of plumes ranges from 0.5 to 2 days(DeForest et al. 2001

Figure 6 .
Figure 6.Lagged cross-correlations between WL intensity at 3.5 solar radii and WL intensities at different altitudes (a, c), and the Fourier powers of the EUV and WL intensities ((b), (d)).In panels (a) and (c), solid lines represent manually determined slopes for the high-correlation region, whose average speeds are 159 ± 8 km s −1 and 300 ± 24 km s −1 , respectively.In panels (b) and (d), the orange and red curves are the Fourier powers for the EUV intensity and WL intensity at 3 solar radii with 99.9% significance levels, respectively.

Figure 7 .
Figure 7.An example of local snapshots of AIA 171 Å images.The black box indicates the ± 10′ region whose center is the root of track B.

Figure 8 .
Figure 8. Box-averaged intensity during 6 days (a), the spike intensities (red cross) during the first 1 hr (b), and the hourly mode intensity overplotted with the number of spike intensity events (c).In panel (b), two blue curves represent the 5 minute median intensity (lower blue) and the threshold intensity (upper blue).The threshold intensity is defined as the median absolute deviation between the original and 5 minute median intensity, plus the median intensity.The spike intensity event is defined as being when the original intensity is higher than the threshold.

Figure 9 .
Figure 9. Histogram of the waiting times for the consecutive spike intensity.The solid line is the least-squares fitting curve of the Poisson function.