Effects of flares on solar high-degree helioseismic acoustic mode amplitudes
M. Cristina Rabello Soares, Frédéric Baudin, Vanessa G. Teixeira
MMNRAS , 1–10 (2021) Preprint 1 March 2021 Compiled using MNRAS L A TEX style file v3.0
Effects of flares on solar high-degree helioseismic acoustic modeamplitudes
M. Cristina Rabello Soares, ★ Frederic Baudin, and Vanessa G. Teixeira Physics Department, Universidade Federal de Minas Gerais, Belo Horizonte MG 31270-901, Brazil Institut d’Astrophysique Spatiale, Universite Paris-Saclay Faculte des Sciences d’Orsay, F-91405 Orsay, France
Accepted XXX. Received YYY; in original form ZZZ
ABSTRACT
Several attempts have been made to observe whether solar flares excite acoustic modes since Wolff (1972) suggested thispossibility. Moreover, the rapid progress of asteroseismology and the study of stellar flares makes the study of these phenomenain the Sun important to inform our study of the influence of the more energetic stellar flares on asteroseismic acoustic modes.We look for the impact of flares on the amplitude of solar acoustic modes and other effects that are also affecting the modeamplitude. Solar acoustic mode amplitudes are known to be sensitive to magnetic fields. As flares usually occur in the presenceof strong magnetic fields and most likely are the by-product of magnetic reconnection, we show how the magnetic field in andaround the flaring region affects the mode amplitude. The mode amplitudes were obtained using ring-diagram analysis, whichwas first applied to a single event, the largest flare in the space age (the ‘Halloween Flare’, SOL2003-10-28T11:00), using MDIdata. Then, using HMI data, the analysis was applied to the regions corresponding to the flares observed during the high activityphase of cycle 24 and that fall into two groups. These two groups consist of small (10-60 erg cm − s − ) and large ( > − s − ) peak-flux flares, based on the Heliophysics Event Knowledgebase (HEK).After applying several corrections in order to take into account several sources of bias, we did not find any amplification inthe inferred mode amplitude due to flaring activity, within a 10 % uncertainty. Key words:
Sun: helioseismology – Sun: flares – Sun: activity
Although we now know that the acoustic modes of the quiet Sun areexcited by convection, the discussion by Wolff (1972) of the possibleexcitation of normal modes of solar oscillation ( 𝑝 -modes) by solarflares stimulated attempts to detect this excitation (Haber et al. 1988).Possible correlations with CMEs were investigated (Foglizzo 1998)as well as correlations between low- ℓ oscillations and soft X-rays(Karoff & Kjeldsen 2008), and even more recently by Kumar et al.(2017).Oscillations of small spatial scales were also investigated after theillustration of the effects of a flare on the photosphere (Kosovichev &Zharkova 1998) and the work of Donea et al. (1999). Changes in theenergy in high- ℓ 𝑝 -modes following flares were observed by Mauryaet al. (2009). Maurya et al. (2014) performed a statistical study on 53events and found a different behaviour of 𝑝 -mode parameters (am-plitude, width) in flaring regions compared to active but non-flaringregions. However, identifying correlations between the temporal be-haviour of 𝑝 -modes and flares (or other violent events) indicators hasled to contradictory results;for example, Richardson et al. (2012) didnot find a correlation between high-frequency 𝑝 -modes and flares.Indeed, mode amplitudes are very sensitive to observational biasesor problems, such as gaps in the data, which may may alter the re-sult. First, mode amplitudes decrease approximately linearly with ★ E-mail: cristina@fisica.ufmg.br (MCRS) the mean magnetic field in the region where the waves are observed(Komm et al. 2000a; Rajaguru et al. 2001; Howe et al. 2004; Rabello-Soares et al. 2008). Then, when analysing a solar region before andafter a flare, one needs to be aware of changes in the overall magneticfield of the sunspot in the region, which in general has a large area andstrong magnetic fields. These changes make the amplitude behaviourof the modes more complex to interpret. Other biases also alter theobserved amplitudes, such as the effect of the line of sight and gapsin the data. We list the main pitfalls that could be encountered inthis analysis in Section 2. In Section 3, we analyse a single event, the"Halloween" flare. Then, we analyse all flares that occurred duringthe four years of the highest activity during cycle 24 and fell in oneof two groups: those with peak-flux between 10–60 erg cm − s − andthose larger than 1200 erg cm − s − (including GOES classes M andX). The conclusions are summarised in Section 4.We focus here on the case of intermediate or high-degree modes; thecase of low degree modes will be investigated in a future article. We review here the main sources of bias when observing mode am-plitude variation in time, which can interfere with intrinsic amplitudevariation due to a possible excitation by flares. © a r X i v : . [ a s t r o - ph . S R ] F e b M. C. Rabello Soares et al.
Figure 1.
Variation of mean mode amplitude with distance from disc centrefor two acoustic modes with radial order 𝑛 = 𝜈 = 𝜇 Hz(left) and 4485 𝜇 Hz (right). The error bars are errors of the mean of 20 regionsat each disc position. Mode amplitudes obtained from the HMI Ring Analysispipeline for five-degree tiles from August 2015 to August 2016 and used inSection 3.2. The red line is the square of the cosine of the distance from disccentre (i.e., the l.o.s.), considering that the y axis is the amplitude of the powerspectra. The mode at higher frequency shows a stronger decrease with thedistance from disc centre.
The observed flaring region is carried by rotation across the Sunand is thus observed at a varying angle (for a given latitude). Themodes observed in ring diagrams are not purely radial, so a simplecorrection taking into account the projection on the light-of-sight(l.o.s.) by dividing by the cosine of the angle between this l.o.s.and the radial direction is not sufficient. This effect on helioseismicanalysis has been known for sometime (e.g., Basu et al. 2004) andresearch on this subject has been done by Zhao et al. (2012); Baldner& Schou (2012). The effect of the position on the disc can be clearlyseen when considering the mode amplitudes at all frequencies acrossall of the positions on the disc when ring diagrams are calculatedduring a magnetically quiet day. At a given centre-to-limb distance,the observed amplitude varies with frequency, 𝜈 , and radial order 𝑛 . Figure 1 shows the variation of the mean mode amplitude withthe distance of the observed region from the disc centre (averagedover 20 regions at each disc position) with a 100 % duty cycle fortwo different modes. The mode amplitude decreases by nearly 50 %with distance from disc centre on the right panel. It also varies withlatitude and central meridian distance (CMD), not only distance.Figure 2 shows the variation of mode amplitudes with frequency forfive different 16-degree regions with different CMD (squares: quietregions) at a given latitude, where we can see a significant change inthe mode amplitude.To take into account this effect, one can use a reference region, atthe same position on the disc but observed when no activity at allis seen (as in Basu et al. 2004). Using the amplitudes of the modesderived from this quiet region at the same location, it is possibleto estimate the amplitude variation in the observed active region bydividing them by those of the quiet region, both amplitudes beingaffected in the same way by l.o.s. effects. This method was adoptedin this paper as described in Section 3. The reduction of the amplitude of acoustic modes in active regions,approximately linearly with increase in the mean unsigned magneticfield, is a well-known phenomena ( e.g.
Komm et al. 2000a; Rajaguruet al. 2001; Howe et al. 2004; Rabello-Soares et al. 2008). If an in-crease in the mode amplitudes as a signature of a flare is investigated,the variation due to magnetic damping could be an important factor
Figure 2.
Top. Example of mode amplitude variation with frequency formodes with 𝑛 =1 obtained at 16-degree MDI regions at latitude 22.5 ◦ Southand at five different CMD: 3.5 (red), 7 (green), 10.5 (light blue), 14 (darkblue) and 18 ◦ (black), named Q1 – 5. As the Sun rotates, a region wouldmove from 18 ◦ to 3.5 ◦ East. The squares are for quiet regions (MAI ∼
20 G)obtained during 25 – 26 October 2003. The full circles are for these quietregions corrected for low data coverage, ‘DC’ (Section 2.3). The stars areactive regions (MAI ∼
270 G) obtained during 27 – 28 October 2003, and theyare corrected for reduced data coverage. The amplitude fitting uncertaintiesare smaller than 0.03 and approximately 5 % of the amplitude. Bottom. Rel-ative mode amplitude in relation to those for one of the disc positions (Q1,CMD=18 ◦ East) for the quiet regions with (full circles) and without (squares)the correction for the reduced data coverage. of variation, in particular in the case of a decrease of the magneticfield in the observed region, due, for example, to sunspot evolutionand the magnetic reconnection during the flare.In Figure 2 (top panel), we show active regions (stars) at differ-ent disc positions that have their amplitude strongly reduced by thestrong magnetic fields present, in comparison to quiet regions at thesame disc position but a few days apart. The magnetic activity index(MAI) is calculated by the HMI pipeline, by averaging all pixels inthe MDI magnetogram with a flux greater than 50 G over the trackinginterval (Basu et al. 2004; Bogart et al. 2011a). In the Figure, theMAI varies, on average, from ∼
12 G to ∼
270 G from quiet to activeregions. The active regions in the figure corresponds to the archety-pal Halloween flare which will be analysed in Section 3.1 and namedregions R1 – 5. The MAI varied only a few percent during the entiresequence R1 – 5. As seen in Figure 2, amplitudes in the Halloweenflare region are decreased by almost a factor of three, as initiallyobserved by Braun et al. (1987). A small change in the magneticfield strength, inclination or even a change in the active region mag-netic configuration will change the mode amplitude, which could beconfused as an effect of a flare.Rajaguru et al. (2001) found a change of mode amplitude around-0.004 G − , and Howe et al. (2004) reported -0.003 G − for frequen-cies below 4500 𝜇 Hz. A decrease in a region’s MAI, as large asthe Halloween Flare, of 10 % would imply an increase of 11 % in the
MNRAS000
MNRAS000 , 1–10 (2021) ffects of flares on solar 𝑝 -mode amplitudes Figure 3.
Variation of mode amplitude with MAI for four different modes(clockwise): ( 𝑛 = 𝜈 = 2054 𝜇 Hz), ( 𝑛 = 𝜈 = 3096 𝜇 Hz), ( 𝑛 = 𝜈 = 5324 𝜇 Hz), and ( 𝑛 = 𝜈 = 4659 𝜇 Hz). Mode amplitudes wereobtained from the HMI Ring Analysis pipeline for five-degree tiles for 20quiet regions (MAI < 1 G) at the same disc position, so that there was noeffect of a changing line of sight. The increase of mode amplitude at highfrequency (known as the acoustic halo effect) is seen in the bottom-rightpanel. The red line corresponds to coefficient of 0.003 G − given by Howeet al. (2004) averaging all modes with frequency smaller than 4500 𝜇 Hz. mode amplitude. Figure 3 shows the variation with MAI of mode am-plitude corrected for the line-of-sight effect for four different modes.For comparison, a line indicates a coefficient of -0.003 G − to em-phasize the mode dependence. The mode amplitude can vary by asmuch as 90 % in the presence of active regions. For high-frequencymodes ( 𝜈 > 5200 𝜇 Hz), there is an enhancement of the mode ampli-tude rather than an absorption in active regions: this is known as theacoustic halo effect (Brown et al. 1992), as seen in the bottom rightpanel.
The effect of gaps in the time series is apparently straightforward: theobserved spectrum is simply the convolution of the intrinsic spectrumwith the spectrum of the observing window: mode amplitude will de-crease and mode width will increase. This effect has been studied byKomm et al. (2000b) and Burtseva et al. (2013). An illustration of thecorrection of this bias is shown in Figure 2 for quiet regions observedby MDI, where one can compare its effect in comparison to the lineof sight effect.One should not forget that gaps not only decrease the observed am-plitude of the signal: dispersion of the measured amplitude is alsoaffected. We show here that some variance is to be expected whendealing with real cases, in particular when the duty cycle is lessthan 80 %. In order to quantify the effect of the gaps, a 1664-minutelong “ring-day” of data from the Global Oscillation Network Group(GONG) with no missing data was analysed after gaps were artifi-cially created (for example using a real window from another ring-day) leading to various values of the duty cycle, from 98 % down to70 %. The top panel of Figure 4 shows the distribution of the ratioof the fitted mode amplitudes from gapped series with a duty cycleof 98 % to those from ungapped series. They clearly peak at a value
Figure 4.
Histogram of the ratio of fitted amplitudes of 98 % (upper) and72 % (lower) filled time series to those from an ungapped series. The dottedline indicates the value of the duty cycle. The width of the distribution for72 % fill is to be noted, as well as its extension towards high values.
Figure 5.
Dispersion of the ratio of fitted amplitudes from gapped series tothose of ungapped series versus the duty cycle. The solid line represents themedian of fitted amplitudes, and the different dotted and dashed lines 1, 2 and3 𝜎 . The red line is the expected value (amplitudes varying linearly with theduty cycle). corresponding to the duty cycle, with a mild dispersion around thisvalue. Bottom of Figure 4 shows the same ratio for a duty cycle of72 %. Even if the distribution still peaks at the value of the duty cycle,the dispersion is much higher with in this particular case, values ashigh as 1.2 in extreme cases (compared to the expected value of 0.72).The overall variation of the dispersion for different values of the dutycycle is shown in Figure 5, confirming that fitted amplitudes whenthe duty cycle is too low have to be taken with caution. This is evenmore relevant for modes at frequencies where the signal-to-noiseratio (SNR) is low (typically below 2 mHz or above 4 mHz). MNRAS , 1–10 (2021)
M. C. Rabello Soares et al.
One of the most powerful flares observed in the last decades wasthe so-called Halloween flare. It was the largest solar flare everrecorded by the GOES system. It is also an archetypal case for theapparent signature of flares affecting the amplitudes of 𝑝 -modes (ofhigh – greater than 200 – spherical harmonic degree [ ℓ ]) as reportedby Maurya et al. (2009), later extended by Maurya et al. (2014).The former work is focused on the analysis of this ‘Halloween’intense flaring active region (October – November 2003) duringCycle 23. Using ring-diagram analysis of five observing periods(ending just before, starting just after and intermediate timings) themost intense flare on 28 October 2003, Maurya et al. (2009) showsa clear increase (sometimes more than 100 %) of 𝑝 -mode amplitudeas fitted in ring diagrams derived from GONG data. However, itshould be noted that the highest relative increases are observed athigh frequency, where absolute amplitudes are low. It can also benoted that this flare did not show a sunquake-type event despite itsobserved strength (in X-ray flux).They analysed five data sets with 16 ◦ in radius and 1664 minutesduration each with different starting times, such that the flare onsetwas placed at the very end of Region R1, at three-fourth of R2, centre(R3), one-fourth (R4) and at the beginning (R5). For the five regionsthe central meridian distance equal to -18 ◦ to -3.5 ◦ (respectively),with a constant latitude of -22.5 ◦ while the Sun had a B angle of4.8 ◦ . The mode amplitudes, obtained using MDI data, for regionsR1 – 5 and for quiet regions at the same disc position (Q1 – 5) butat a different time are shown in Fig. 2. The l.o.s. variation of theseregions, if not corrected, could lead to an artificial increase of modeamplitudes, by as much as 60 % as shown in the lower panel forQ1 – 5. The regions have a large MAI: [R1 – 5] have MAI equal to260, 266, 273, 279, and 283 G, respectively. At these large values,the decrease in mode amplitude with MAI is approximately constant.We perform here a re-analysis of this event. However, we prefernot to use GONG data since they present duty-cycle values as low as0.72 during the relevant period of observation, considering the effectof gaps in the data described in Section 2.3. Since Helioseismic andMagnetic Imager (HMI, the latest instrument launched) observationsstarted in 2010, we use here data from the Michelson DopplerImager (MDI) on board SOHO (HMI predecessor, see Scherreret al. 1995) to analyse this strong flare, despite some gaps in thedata: the duty cycle is 0.97 for all regions, except for R5 which is 0.81.We applied the algorithms from the HMI ring diagram pipeline(Bogart et al. 2011a,b) to the MDI data at position of the observa-tions on the disc identical to those used by Maurya et al. (2009) forthe GONG data (Fig. 2). MDI data have the same cadence 1-minuteand same spatial resolution (128 ×
128 pixels) as GONG data used byMaurya et al. (2009). Although, it has the same tracking time, MDIimage data was mapped using Postel’s azimuthal equidistant projec-tion, while the GONG pipeline uses transverse cylindrical projection.After remapping, the MDI data was tracked at the Carrington rotationrate whereas the GONG pipeline tracks with a differential rotationrate of the Sun (Snodgrass 1984). The power spectra were fitted usingthe peak-fitting method (called rdfitc , see Bogart et al. 2011a), whichis different than the one used in the GONG pipeline and was chosenbecause it fits more modes and fits an asymmetric Lorentzian. It iscorrected considering a strict proportionality of amplitudes with theduty cycle (Figure 5). Their mode amplitudes are shown in Figure 2as stars. The influence of the position on the disc is treated by using
Figure 6.
Relative amplitude of regions R1 – 5 in relation to a quiet regionat the corresponding region 𝑅 𝑖 disk position. Regions R1 – 5 are in black,blue, light blue, green, and red, respectively (using the same colour code as inFigure 2). The strong mode reduction due to very large MAI of these regionsis clearly seen. The coverage correction was applied. No clear increase ofamplitudes from R1 to R5 is seen for these four values of 𝑛 , as well as for 𝑛 =4 and 5 (not shown here). The error bars are shown only for R5 and forevery 10 points. The errors are smaller than ∼ ∼ quiet observations on another date but at the exact same positions(that we call regions Q1—5). We used quiet regions obtained daysbefore the large active region associated with the Halloween flareappeared and that have MAI ∼
12 G, which is considered quiet for a16 ◦ tile. Their mode amplitudes are shown in Figure 2 (full circles).Then, the amplitudes fitted during the Halloween sequence (R1 –5) are divided by the amplitudes of the quiet sequence. Results areshown in Figure 6.We did not find any significant variation in the mode amplitudebefore or during the Halloween flare. Very different results, a modeamplitude increase by as much as 150 %, were found by Mauryaet al. (2009), who did correct for the small duty cycle using a methoddescribed in Komm et al. (2000a), but the data were not correctedfor line-of-sight variations between Regions 1 to 5. Since solid conclusions cannot be drawn from one event, a largenumber of events have to be taken into account. The HeliophysicsEvent Knowledgebase (HEK, see Hurlburt et al. 2012), which isone the largest catalogs of solar events and features (SunPy Projectet al. 2020), has several automated solar feature-detection methodsapplied to solar observations. We use three automated detection rou-tines on the HEK database:
SolarSoft , SWPC , and
Feature FindingTeam (FFT) . These methods give the flare occurrence times (begin-ning, end, and peak times) and its location on the solar disc. Thefirst two return the GOES class (e.g. Phillips & Feldman 1995) andthe last one gives the peak flux.
SolarSoft and
FFT use data fromthe Atmospheric Imaging Assembly (AIA, see Lemen et al. 2012),onboard the Solar Dynamics Observatory (SDO), while
SWPC usesGeostationary Operational Environmental Satellite (GOES) X-RaySensor (XRS) data (Garcia 1994). We analysed flares that occurredduring high solar activity during Cycle 24, from June 2012 to August
MNRAS000
MNRAS000 , 1–10 (2021) ffects of flares on solar 𝑝 -mode amplitudes Figure 7.
Number of flares in the HEK database detected by
FFT during fouryears of highest solar activity during Cycle 24 within ± ◦ in solar latitudeand ± ◦ in CMD of disc centre. The bottom panel shows the large numberof flares with small peak flux. FFT ) that occurred within ± ◦ in solar latitude and central meridian distance (CMD) of disccentre, to avoid large line-of-sight effects.We analysed the acoustic-mode parameters obtained using ring-diagram analysis applied to five-degree regions of HMI Doppler-grams (Schou et al. 2012) and provided by the HMI pipeline (fordetails see Bogart et al. 2011a,b). The selected regions have 128 × − s − and/orGOES class M or X, (ii) ‘Weak Flares’: with peak flux between 10and 60 erg cm − s − , and (iii) ‘Without Flares’: where no flare wasdetected. Table 1 shows the number of flares detected, the numberof HMI data cubes, and the number of cubes that were used in ouranalysis. The same solar flare could have been detected and be presentmore than once in the HEK database. For the Strong and Weak Flaresets, we included only data cubes where the flare occurred within80 % of its radius and within the central 90 % of its duration.Besides, in the case of the Weak Flares, only regions where thereare no flares stronger than 60 erg cm − s − within 1.5 times theregion’s radius from its centre were considered. The Without Flareset includes only data cubes without any flares detected by HEKwithin 1.5 times the tile’s radius and within 1.2 times the durationof the data cube. Figure 8 shows the distribution of MAI values foreach data set in Table 1 at 10 G intervals. Most of the Strong Flaresregions (75 %) have an MAI smaller than 200 G and only 10 % larger Table 1.
Three sets of HMI data analysed.Data set Flares HMI regions Selected Data CoverageWithout Flares 0 11886 4143 1.00Weak Flares 9905 5081 2790 1.00Strong Flares 2117 2007 2007 0.98 – 1.00
Figure 8.
Number of HMI data cubes for each data set as a function of MAI.The Without Flares in black circles, Weak Flares in green stars and StrongFlares in red circles, used in our analysis. The total number for the WeakFlare set is shown as blue triangles. A smaller number of HMI regions for theWeak Flare and Without Flare sets were selected, with MAI values evenlydistributed, to a number closer to the Strong Flare set.
Figure 9.
Flare peak flux as a function of the MAI for the Strong and WeakFlare set. than 290 G. We selected a smaller number of HMI regions with MAIvalues evenly distributed and with high data coverage, for Weak Flareand Without Flare sets due to their large number. Figure 9 presentsthe flare peak flux as a function of the MAI of the region whereit was detected. Most flares are in tiles with MAI = 26 −
103 G and64 −
190 G for the Weak and Strong Flares set, given by the first andthird quartiles. We do not find any correlation between flare peakflux and the MAI of the corresponding HMI tile for the Strong Flareset. For tiles with MAI larger than ∼
20 G, the smallest peak fluxincreases with MAI for the Weak Flare set.As discussed in Section 2.1, even a small change in the disc positioncould be erroneously interpreted as an effect of a flare. Thus, for eachselected region in the three sets (Table 1), the line-of-sight effect on
MNRAS , 1–10 (2021)
M. C. Rabello Soares et al. the mode amplitude due to the observed position on the solar dischas to be removed. In order to make this correction, we divided theamplitude of each mode ( 𝑛 , 𝜈 ) of each region 𝑖 by an average of thequiet mode amplitude for the same region’s disc position (given byits solar latitude and CMD): Δ 𝐴 / 𝐴 𝑄 ( 𝑛, 𝜈, MAI ) = 𝐴 𝑖 ( 𝑛, 𝜈, latitude , CMD , MAI ) 𝐴 𝑄 ( 𝑛, 𝜈, latitude , CMD ) − 𝑛 is the mode radial order and 𝜈 its frequency. We used twentymagnetically quiet regions (MAI < 1 G), with no flare activity de-tected, at each solar disc position with 100 % data coverage to calcu-late the quiet mode amplitude average 𝐴 𝑄 (Figure 1).To look for an effect of a flare on the mode amplitude, we com-pared the relative mode amplitude, Δ 𝐴 / 𝐴 𝑄 ( 𝑛, 𝜈, MAI ) , obtained inthe Strong and Weak Flares set with those in the Without Flare set.However, to take into account the effect of strong magnetic fieldson the mode amplitude (discussed in Section 2.2), we need to com-pare regions with similar MAI. Figure 10 shows the average relativeamplitude for two MAI intervals: (8 ±
4) G and (45 ±
8) G for regionsWithout Flares and regions with Strong Flares. The well-known de-crease of mode amplitude with an increase in MAI is clearly seenwhen comparing the top and bottom panels. In both cases, there is aclear difference between regions with and without flares. The flaringregions have a smaller amplitude for modes with frequency smallerthan ∼ 𝜇 Hz and the opposite behaviour at higher frequencies.The left and centre columns in Figure 11 show the difference be-tween the mean relative amplitude for flaring and non-flaring regionsat five different MAI intervals. The mean relative amplitude for eachMAI interval, < Δ 𝐴 / 𝐴 𝑄 >, was calculated using between 30 to 220regions. The smallest number is in the bottom panel, since there arefewer HMI regions with MAI larger than ∼
220 G (Figure 8). Thefirst two lines in the centre column correspond to the MAI intervalsshown in Figure 10. To estimate systematic and random errors inour results, the Without Flares set was divided into three separatesets. The mean mode amplitude difference between them is shownas small black symbols in Figure 11 for the five MAI intervals. InFigure 11, the differences of relative amplitude should be small sincethese amplitudes are observed in regions with similar MAI. Howeverthis is not the case, especially for regions with low MAI. In regionswith Strong Flares (centre column), the mode absorption is evenlarger than for Weak Flares (left column). A possible explanation forthe mode amplitude decrease observed in these flaring regions couldbe due to the strong magnetic fields usually present in and around aflare. Rabello-Soares et al. (2016) calculated mode amplitude vari-ation for five-degree quiet regions when there was an active region(with MAI > 100 G) in their vicinity, at eight degrees or less centre-to-centre, in comparison with quiet regions at the same solar disclocation for which there were no neighbouring active regions (i.e.,no region with MAI larger than 5 G). They found a mode reductionas large as 0.1 around 3000 𝜇 Hz followed by an enhancement at highfrequencies of ∼ 𝜈 > 𝜇 Hz (as shown in the top leftpanel in their Figure 1). Their results can be directly compared withours in Fig. 11. Looking for a similar effect in our data, we showthe median MAI in the neighbourhood (within 14 ◦ ) of the regionsanalysed as a function of distance to its centre (rightmost column inFigure 11). As one might expect, the vicinity of flaring regions istypically very magnetically active and has large values of MAI, moreso for the Strong Flare set. The smaller the MAI, the larger is themagnetic field in their surroundings (right column), and the largerthe mean relative amplitude difference (left and centre columns).To check the hypothesis that the nearby active regions are affectingthe mean relative amplitude differences, we selected the regions in the Figure 10.
Relative amplitude averaged over HMI regions with MAI in twointervals: (8 ±
4) G (top panel) and (45 ±
8) G (bottom), for Strong Flares (fullcircles) and Without Flares (triangles) regions. The different colours representdifferent mode order 𝑛 : 0 (red), 1 (blue), 2 (green), 3 (orange). The error ofthe mean is of the order of 0.01 and smaller. Without Flares set with the largest mean MAI in their vicinity, thosein the 90 th percentile, and recalculated the mean relative amplitudedifference. Figure 12 compares the difference shown in Figure 11 (di-amonds) with the new difference (full circles) which are considerablysmaller in absolute value, confirming the effect of the surroundingson our results. The medians MAI in their neighbourhood are nowvery similar to each other (bottom panel).To take into account this additional influence on the mode ampli-tude, for each region in the Weak and Strong Flares sets, we lookedfor a region in the Without Flare set with not only similar MAI butalso with a similar MAI in its vicinity. Since the effect of a nearbyactive region varies with its distance to the analysed region, it isnecessary to quantify this effect. This was done by Rabello-Soareset al. (2018) that extended their previous work (Rabello-Soares et al.2016) and analysed how the effect of an active region on a quietregion varied with their separation. Figure 13, adapted from Figure 2in Rabello-Soares et al. (2018), shows the variation for six differentmodes and Figure 14 shows the slope of a linear fit for each mode.The decrease in the influence of the nearby active region with itsdistance, given by the exponential coefficient (Figure 14), varies foreach mode. We adopted an average value of -0.3 for the exponentialcoefficient.Then, to calculate the relative amplitude difference between a flaringand a non-flaring region, we chose a non-flaring region with a neigh-bourhood most similar to each region in the Weak and Strong Flaresset, as the one that minimises the function: 𝜒 = (cid:205) 𝑖 (cid:8)(cid:2) MAI flaring ( 𝑑 𝑖 ) − MAI non-flaring ( 𝑑 𝑖 ) (cid:3) × e − . 𝑑 𝑖 (cid:9) (cid:205) 𝑖 (cid:2) 𝑒 − . 𝑑 𝑖 (cid:3) (2)where 𝑑 𝑖 is the distance of the nearby active region and varies from0 to 8 degrees. MNRAS000
8) G (bottom), for Strong Flares (fullcircles) and Without Flares (triangles) regions. The different colours representdifferent mode order 𝑛 : 0 (red), 1 (blue), 2 (green), 3 (orange). The error ofthe mean is of the order of 0.01 and smaller. Without Flares set with the largest mean MAI in their vicinity, thosein the 90 th percentile, and recalculated the mean relative amplitudedifference. Figure 12 compares the difference shown in Figure 11 (di-amonds) with the new difference (full circles) which are considerablysmaller in absolute value, confirming the effect of the surroundingson our results. The medians MAI in their neighbourhood are nowvery similar to each other (bottom panel).To take into account this additional influence on the mode ampli-tude, for each region in the Weak and Strong Flares sets, we lookedfor a region in the Without Flare set with not only similar MAI butalso with a similar MAI in its vicinity. Since the effect of a nearbyactive region varies with its distance to the analysed region, it isnecessary to quantify this effect. This was done by Rabello-Soareset al. (2018) that extended their previous work (Rabello-Soares et al.2016) and analysed how the effect of an active region on a quietregion varied with their separation. Figure 13, adapted from Figure 2in Rabello-Soares et al. (2018), shows the variation for six differentmodes and Figure 14 shows the slope of a linear fit for each mode.The decrease in the influence of the nearby active region with itsdistance, given by the exponential coefficient (Figure 14), varies foreach mode. We adopted an average value of -0.3 for the exponentialcoefficient.Then, to calculate the relative amplitude difference between a flaringand a non-flaring region, we chose a non-flaring region with a neigh-bourhood most similar to each region in the Weak and Strong Flaresset, as the one that minimises the function: 𝜒 = (cid:205) 𝑖 (cid:8)(cid:2) MAI flaring ( 𝑑 𝑖 ) − MAI non-flaring ( 𝑑 𝑖 ) (cid:3) × e − . 𝑑 𝑖 (cid:9) (cid:205) 𝑖 (cid:2) 𝑒 − . 𝑑 𝑖 (cid:3) (2)where 𝑑 𝑖 is the distance of the nearby active region and varies from0 to 8 degrees. MNRAS000 , 1–10 (2021) ffects of flares on solar 𝑝 -mode amplitudes Figure 11.
Mean relative amplitude difference between Weak ("WF": left column) and Strong ("SF": centre column) compared to Without Flares ("WO") set.Each row shows the difference for distinct MAI intervals: MAI ± Δ MAI = 8 ± ± ±
13 G, 216 ±
17 G, and 243 ±
18 G from top to bottom. Thedifferent colours represent different mode order 𝑛 : 0 (red), 1 (blue), 2 (green), and 3 (orange). The Without Flare set was divided into three sets and the meanrelative amplitude difference between them was calculated as an indication of systematic variation in our analysis (crosses, diamonds and squares). At the topleft of each plot is shown the smallest and largest error bars. Right column: The median of the MAI in the neighbourhood of the analysed regions, divided bythe MAI of the target, MAI , as a function of distance from the target represented by full circles: Without Flares in black, Strong Flares in red, and Weak Flaresset in blue. The small crosses and diamonds are the first and third quartiles, respectively. MNRAS , 1–10 (2021) M. C. Rabello Soares et al.
Figure 12.
Top Panel: Mean relative amplitude difference between StrongFlares (SF) and Without Flares (WO) sets for regions with MAI = 45 ± th percentile(see text). The different colours represent different mode order 𝑛 : 0 (red), 1(blue), 2 (green), and 3 (orange). Bottom panel: The median, first, and thirdquartiles of the MAI in the neighbourhood of the analysed regions dividedby the MAI of the target (i.e. 45 G) as a function of the distance shown asfull circles, crosses, and diamonds respectively. Those for the Strong Flaresregions are in red and are the same as in Figure 11. Those for the selectedregions in the Without Flares set are in black. Taking into account all the corrections listed above, it becomespossible to reliably estimate the potential impact of flares on theamplitude of acoustic modes. In Fig. 15, we show the average of therelative-amplitude difference for each mode between all pairs with 𝜒 in the 40 th percentile, which corresponds to √︁ 𝜒 ≤
12 G and16 G for the Weak and Strong Flares set, respectively. The differencein the maximum 𝜒 between Strong and Weak Flare sets indicatesthat the vicinity of the Without Flare set is, in general, different fromthe Strong Flare set (as shown in the right column in Figure 11).For each mode, in Fig. 15, the number of averaged regions in theWeak (Strong) Flares set varies from 25 to 834 (554) and the mediannumber of regions is equal to 660 (405). Once again, to estimateerrors in our results, we divided the Without Flares set into two sepa-rate groups and calculated the average relative-amplitude differencebetween them for √︁ 𝜒 ≤
16 G (shown as small black symbols inFigure 15). Our results show an average close to zero for both sets(Weak and Strong Flares) indicating that our minimisation (Equa-tion 2) is a reasonable approximation. Using a different exponentialcoefficient to describe the effect of neighbour magnetic regions onobserved amplitudes, -0.2 or -0.5, does not change the results sig-nificantly. Figure 16 indicates, for each mode, the dispersion of therelative-amplitude difference of the pairs of regions analysed. Foreach mode, the skewness of the relative-amplitude difference is closeto zero. A negative skewness (i.e., a median larger than the aver-age) would imply that more than half of the regions have an positiverelative-amplitude difference, indicating an increase in the mode am-
Figure 13.
Examples of the logarithm of relative amplitude variation absolutevalue with distance for six different modes (adapted from Rabello-Soareset al. 2018). Top panels: 𝑛 =0 and 𝜈 =2460 (left) and 3009 𝜇 Hz (right). Middlepanels: 𝑛 =1 and 𝜈 =3704 and 4253 𝜇 Hz. Bottom panels: 𝑛 =2 and 𝜈 =4138and 5208 𝜇 Hz. The dashed line shows the linear fit. The small red symbolsshow the results for a control set (described in Rabello-Soares et al. 2018),that gives an indication of the noise level of the analysis.
Figure 14.
The slope of the linear fit as a function of mode frequency(Rabello-Soares et al. 2018). Modes with 𝑛 =0, 1, 2, and 3 are in red, blue,green, and orange respectively. The large variation seen in the linear-fit pa-rameters around approximately 4100 – 4500 𝜇 Hz corresponds to relative am-plitudes very close to zero shown in Figure 13 (and, in more detail, Fig.1 in Rabello-Soares et al. 2016). Hence the fitting is not meaningful. Thehorizontal dotted line corresponds to the mean and is equal to -0.3 degree − . plitude during a flare. The kurtosis is slightly positive, suggesting asmall tail in the distribution. As shown in Fig. 16, there is a sharpincrease in the dispersion of the relative-amplitude difference formodes with frequency larger than 4700 𝜇 Hz. The acoustic-modeamplitudes are an order of magnitude smaller (or even less) for thesehigh-frequency modes (see Fig. 2). Another issue that could con-tribute to the increase in variability is that Rabello-Soares et al.(2016) observed that the mode amplification due to nearby activeregions starts at a lower frequency (see Fig. 10), which will compete
MNRAS000
MNRAS000 , 1–10 (2021) ffects of flares on solar 𝑝 -mode amplitudes Figure 15.
Mean relative-amplitude difference between all pairs of flaringand non-flaring regions (WO) with similar MAI in and around each region.The Weak Flares (WF) set is shown in the left panel and the Strong Flares(SF) on the right. Modes with 𝑛 from zero to three are given by red, blue,green, and orange symbols. The error bars are the error of the mean for eachmode. The mean relative-amplitude difference between pairs of two distinctgroups of the Without Flare set is shown as black diamonds. Figure 16.
The interquartile range of the relative-amplitude pair difference:( Δ 𝐴 / 𝐴 𝑄 ) WF or SF - ( Δ 𝐴 / 𝐴 𝑄 ) WO for each mode, where the Weak Flares aregiven by diamonds and the Strong Flares by full circles. The different coloursare for the different order 𝑛 . with attenuation for the magnetic field present in the target tile. Inconclusion, based on Fig. 15 which summarize the results of hun-dreds of regions, we did not find any overall amplitude variationfor any mode between a flaring and a non-flaring region larger than ∼
10 %. However, if there is a smaller increase, we are not able todetect with our analysis.As first proposed by Wolff (1972), and more recently by Kumaret al. (2017), only some flares would increase the mode amplitude,and not necessarily the ones with largest peak X-ray flux. We look forthis in our data. In the Weak and Strong Flares set, there are a dozenor more flaring regions with a relative amplitude difference from itspaired region, ( Δ 𝐴 / 𝐴 𝑄 ) WF or SF - ( Δ 𝐴 / 𝐴 𝑄 ) WO , larger than 0.2 for atleast 60 % of modes, but there are a similar number of flaring regionsthat have a difference < ∼ -0.2. This variation in the differences isexpected for a normal distribution with a standard deviation equal to 0.1. Thus, we did not convincingly find an influence of any flare in ourdata set on the mode amplitude. Given the diversity of magnetic con-figurations in and around the flaring or its comparison (non-flaring)region, the MAI gives a useful but incomplete characterisation. We analysed several factors that affect the observed amplitude ofhigh-degree solar 𝑝 -modes, namely, line-of-sight, strong magneticfields and gaps in the observations. If not taken into account, theapparent changes in the observed mode amplitude could be misinter-preted as an effect of a flare. Care is required not only in analysingthe flaring region but also in the comparison one that is used as thequiescent state to infer the change in the mode amplitude due to theflare in an ever-changing Sun.We analysed the most intense flare observed in the space age, theso-called, Halloween flare, applying ring-diagram analysis to MDIdata. Contrary to the results obtained by Maurya et al. (2009), we didnot find any amplification (larger than ∼ − s − and larger than 1200 cm − s − .Although we observed that the Strong Flares are associated with HMItiles whose MAI has a median of 120 G (twice the median for tileswith Weak Flares), 10 % of regions with Strong Flares have an MAIless than 30 G (and 10 G for Weak Flares). Since the flares are aproduct of magnetic reconnection, they most often happen on, orin the vicinity of, strong magnetic fields. In fact, we observed thatthe HMI tiles with small MAI associated with Strong Flares have intheir vicinity (less than 8 ◦ away) regions with MAI ∼
12 times largerthan its MAI. The mode amplitude in a magnetically quiet tile isaffected by a nearby active region by as much as 20 % in its observedamplitude, as shown by Rabello-Soares et al. (2016, 2018). We seethe effect of nearby active regions in the results of our analysis. Thisis another effect that must be taken into account when looking foran effect of a flare in the mode amplitudes. The influence of nearbyactive regions complicated matters further since the increase in modeamplitude, known as the acoustic halo, occurs at frequencies smallerthan the acoustic cutoff frequency, at 𝜈 > 4.2 mHz (Rabello-Soareset al. 2016).Taking all these effects into account, we found that the modeamplitudes do not vary on average more than 10 % of their amplitudebetween flaring and non-flaring regions. Thus, we conclude that ifthere were a change in the solar acoustic mode amplitudes due tothe large energy released during a flare, the change would be small.We did not find any individual flaring region that has an increase inits mode amplitude outside the uncertainties in our analysis (i.e., 2.5sigma = 25 % variation). MNRAS , 1–10 (2021) M. C. Rabello Soares et al.
ACKNOWLEDGEMENTS
We thank J. Leibacher for a detailed reading of the originalmanuscript and several comments that have greatly improved it.This work was carried out with the support of Fundação de Am-paro à Pesquisa de Minas Gerais (FAPEMIG). V.G.T. would liketo acknowledge that: "This study was financed in part by the Coor-denação de Aperfeiçoamento de Pessoal de Nível Superior - Brasil(CAPES) - Finance Code 001".The automated detection routines on the HEK database:
SolarSoft , SWPC , and
Feature Finding Team (FFT) are provided by the Harvard-Smithsonian Center for Astrophysics (CfA/SAO), Space WeatherPrediction Center (SWPC/NOAA), and Lockheed Martin Solar andAstrophysics Laboratory (LMSAL), respectively. This research hasmade use of SunPy, an open-source and free community-developedsolar data analysis package written in Python (HEK module). MDIdata is provided by the SOHO/MDI consortium. SOHO is a projectof international cooperation between ESA and NASA. HMI data isprovided by NASA/SDO and HMI science team. This work utilizesdata obtained by the Global Oscillation Network Group (GONG) pro-gram, managed by the National Solar Observatory, which is operatedby AURA, Inc. under a cooperative agreement with the NationalScience Foundation. The data were acquired by instruments oper-ated by the Big Bear Solar Observatory, High Altitude Observatory,Learmonth Solar Observatory, Udaipur Solar Observatory, Institutode Astrofíısica de Canarias, and Cerro Tololo Interamerican Obser-vatory.
DATA AVAILABILITY
The data underlying this article are available from the Joint ScienceOperations Center (http://jsoc.stanford.edu) and from the GONGData Archive (https://gong.nso.edu).
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