AcceptedforpublicationinSolar Physics,waitingfortheauthoritativeversionandaDOI, whichwillbeavailableathttp://www.springerlink.com/content/0038-0938 Statistical Analysis of Small Ellerman Bomb Events C.J. Nelson1,2 · J.G. Doyle1 · R. Erd´elyi2 · Z. Huang1 · M.S. Madjarska1,3 · M. Mathioudakis4 · S.J. Mumford2 · K. Reardon4,5,6 Received: 1August2012 /Accepted: 22December2012 /Publishedonline: ••••••••••• 3 1 Abstract The properties of Ellerman bombs (EBs), small-scale brightenings in 0 the Hα line wings, have proved difficult to establish due to their size being close 2 to the spatial resolution of even the most advanced telescopes. Here, we aim n to infer the size and lifetime of EBs using high-resolution data of an emerging a active region collected using the Interferometric BIdimensional Spectrometer J (IBIS) and Rapid Oscillations of the Solar Atmosphere (ROSA) instruments 7 as well as the Helioseismic and Magnetic Imager (HMI) onboard the Solar ] Dynamics Observatory (SDO). We develop an algorithm to track EBs through R their evolution, finding that EBs can often be much smaller (around 0.3(cid:48)(cid:48)) and S shorterlived(lessthan1minute)thanpreviousestimates.Acorrelationbetween . h G-band magnetic bright points and EBs is also found. Combining SDO/HMI p and G-band data gives a good proxy of the polarity for the vertical magnetic - o field. It is found that EBs often occur both over regions of opposite polarity r t flux and strong unipolar fields, possibly hinting at magnetic reconnection as a s a driveroftheseevents.TheenergeticsofEBeventsisfoundtofollowapower-law [ distribution in the range of “nano-flare” (1022−25 ergs). 1 Keywords: Active Regions, Magnetic Fields- Magnetic fields, Photosphere- v Sunspots, Penumbra 1 5 3 1 1 ArmaghObservatory,CollegeHill,Armagh,UK,BT61 . 1 9DG 0 2 SolarPhysicsandSpacePlasmaResearchCentre, 3 UniversityofSheffield,HicksBuilding,HounsfieldRoad, 1 Sheffield,UK,S37RH 3 UCL-MullardSpaceScienceLaboratory,HolmburySt : v Mary,Dorking,Surrey,UK,RH56NT i 4 AstrophysicsResearchCentre,SchoolofMathematicsand X Physics,Queen’sUniversity,Belfast,UK,BT71NN r 5 INAF OsservatorioAstrofisicodiArcetri,I-50125Firenze, a Italy 6 NationalSolarObservatory/SacramentoPeak,P.O.Box 62,Sunspot,NM88349,U.S.A. email:c.j.nelson@sheffield.ac.uk 2 C.J.Nelsonet al. 1. Introduction Emerging active regions are some of the most diverse and abundant regions to study within the photosphere. Active regions possess a wide range of both large-scale (e.g. sunspots and pores) and small-scale (e.g. Ellerman bombs, also known as EBs) structures which, in a way that is yet to be fully understood, interacttoformthecomplexoverlyingchromosphere.HerewestudyEBs,small- scale brightenings in the wings of the Balmer Hα line profile, which occur in regions of high magnetic activity especially near opposite-polarity regions (see e.g. Georgoulis et al., 2002, Pariat et al., 2004). Small-scale structures in the solar atmosphere have proved difficult to study due to their size being close to the spatial resolution of current observational instruments. EBs, possible magnetic reconnection events in the lower atmo- sphere due to emerging flux, are one such example. First reported by Ellerman (1917) and originally named “solar hydrogen bombs”, EBs have been reported to have a size of the order of one arcsecond (see e.g. Kurokawa et al., 1982) and lifetime of around 10−15 minutes on average (see e.g. Vorpahl and Pope, 1972, Roy and Leparskas, 1973 and more recently Watanabe et al., 2011). The energeticsofEBshavebeenestimatedbyGeorgoulisetal.(2002)andFangetal. (2006), finding that each EB has a total lifetime energy of around 1027 ergs, a value typically associated with “micro-flares”. It has been widely acknowledged (e.g.Georgoulisetal.,2002)thattheseestimatesareupperboundswhichwillbe revisedoccasionallybyhigherresolution,highercadencedatasuchaswepresent here. The majority of investigations of EBs have been taken place the Hα line wings. EB events, however, are also seen in other wavelengths such as the 1600 ˚AcontinuumandtheCaiiwings(see,forexample,HerlenderandBerlicki,2011). Recently, Qiu et al. (2000) suggested that over 50 % of EBs show a correlation to UV emissions in the 1600 ˚A continuum; a similar result was also found by Pariatet al.(2007),providingevidencethatEBsareupper-photospheric,lower- chromospheric events. Recently,alinkhasbeensuggestedbetweenEBsandG-bandmagneticbright points (MBPs) (for a discussion of MBPs see Jess et al., 2010a), which are ubiquitousinthesolarphotosphere.MBPsarethelocationswherethemagnetic flux clumps together to form small magnetic concentrations with field strengths of the order of a kiloGauss (Stenflo, 1985). Their increased brightness is due to the reduced pressure and opacity within the flux tube allowing the observer to view a deeper, hotter region of the photosphere as well as heating of the plasma within the flux tube by material surrounding its walls. The increased temperature reduces the abundance of the CH molecule, thus making MBPs appear brighter in G-band imaging (Shelyag et al., 2004). Jess et al. (2010b) has recently suggested that the interaction of neighbouring MBPs can lead to multiple EBs as a consequence of forced reconnection, thus hinting at a link between EBs and MBPs. Therehavebeenanumberofrecentstudiesbothonobservations(Georgoulis etal.,2002,Pariatetal.,2007,Watanabeetal.,2011)andmodelling(Isobe,Tri- pathi, and Archontis, 2007, Archontis and Hood, 2009) of EBs. The main focus SOLA: Ellerman_Bomb_Statistics.tex; 11 December 2013; 22:09; p. 2 Small-Scale Ellerman Bomb Events 3 Figure1. ImagesofActiveRegionNOAA11126(takenat15:02:49)(a)attheHαlinecentre aswellas(b)-(c)at±0.7˚A,observedwithDST/IBIS.ThreeEBsareshownwitharrows.The sameregionisshownin(d),detectedbytheSDO/HMIinstrument(usingathresholdof±400 Gauss),whichhasbeenspatiallyandtemporallyalignedwith(a-c). ofmanyofthesestudieshasbeentoprovideevidenceformagneticreconnection as the possible formation mechanism of EBs. A good cartoon was presented by Georgoulis et al. (2002), which depicts the possible magnetic topologies that could lead to magnetic reconnection in the lower-atmosphere either through emerging flux in bipolar regions or topologically complex unipolar fields. In this work,wefindevidencethatEBsareformedoverregionsofstrongmagneticfield, shown in both SDO/HMI data and the G-band continuum. Magnetic reconnection is largely associated with high-energy events in the corona such as coronal mass ejections (CMEs) and large flares; however, in the past two decades, the applicability of the idea of magnetic reconnection to the lower-atmosphere has also been discussed. The process was described in Litvinenko (1999), who suggested that reconnection was likely to occur mainly around the temperature minimum region at z ≈ 600 km; this value does not appreciably disagree with the initial height of z ≈ 400 km found by Harvey (1963). In Litvinenko, Chae, and Park (2007) it was suggested that lower- atmosphericmagneticreconnectionisanimportantprecursorthatcouldleadto SOLA: Ellerman_Bomb_Statistics.tex; 11 December 2013; 22:09; p. 3 4 C.J.Nelsonet al. larger events in the corona as well as mass supply into the chromosphere and coronathroughtheejectionofcoolphotosphericplasmaintheformoffilaments. EBs were originally thought to be precursors for flares; however, McMath, Mohler, and Dodson (1960) found this not to be the case through an analysis of alargearrayofdatacollectedusingamultitudeofinstrumentsinthepreceding years.Theydidfind,however,thatEBsaremainlyobservedaroundthepenum- bra of active region sunspots; this has been discussed more recently by Pariat et al. (2004) who found that the majority of EBs occur in the trailing plage region. In this article we shall discuss the positioning of EBs identified in our dataset, finding formation to be common in both the unipolar penumbra and bipolar regions, in the surrounding active region close to the spot, suggesting both regions may have the required background conditions to form EBs. Mad- jarska,Doyle,andDePontieu(2009)studiedanHαsurge,findingthattheevent was triggered by EBs forming in a similar spatial position. This is important as it could possibly suggest a coupling between the photospheric EB events and chromospheric Hα surges. Westructureourstudyasfollows:inSection2wediscussourobservationsand data reduction methods; Section 3 presents our results along with the definition we have used to calculate our statistics. Section 4 contains our conclusions and poses some questions that should be answered through further study. 2. Observations In this article, we make use of high-resolution data collected by the Interfero- metric BIdimensional Spectrometer (IBIS) and Rapid Oscillations of the Solar Atmosphere(ROSA)instrumentsatthe DunnSolarTelescope(DST), National SolarObservatory,SacramentoPeak,NM,between15:02UTand17:04UTon18 November2010.Welimitouranalysistothefirst90minutesofobservationsdue tothedeteriorationoftheseeinginthesubsequentimages(i.e.leaving200IBIS frames).IBISdatahaveapixelsizeof0.096(cid:48)(cid:48) and,duetotheexcellentseeing,an approximatespatialresolutionof0.192(cid:48)(cid:48).IBISwassettoproducea15-point Hα line scan (between ±1.4 ˚A from the line centre in unequal steps) and 50 images in the line centre and both line wings at ±0.7 ˚A before repeating this routine (i.e.atotalof165imagespercycle),samplingatotalFOVof96(cid:48)(cid:48)×96(cid:48)(cid:48).G-band images from the ROSA instrument were collected during the same period with a cadence of 0.64 seconds (by combining 32 images, each with an intergration time of 0.02 seconds), a pixel size of 0.059(cid:48)(cid:48) and a spatial resolution of 0.118(cid:48)(cid:48), covering a FOV of 58(cid:48)(cid:48)×58(cid:48)(cid:48) (situated entirely within the IBIS FOV). We also usethe Helioseismic and Magnetic Imager(HMI)onboardthe Solar Dynamics Observatory(SDO)spacecraft,whichhasapixelsizeof0.5(cid:48)(cid:48) aspatialresolution of 1(cid:48)(cid:48) and a cadence of 45 seconds (whilst observing the whole disc). In Figure 1, we show context images with a field-of-view of 29(cid:48)(cid:48)×29(cid:48)(cid:48) (to illustrate the complex region surrounding the sunspot) of the emerging active region NOAA 11126 at 31S latitude 00 longitude with co-aligned HMI and IBIS images. The DSTtrackedtheleadingspot,whichevolvedslowlythroughthetimeseries.This spot was linked, by a coronal-loop arcade, to two small opposite-polarity spots situated in the trailing plage region. SOLA: Ellerman_Bomb_Statistics.tex; 11 December 2013; 22:09; p. 4 Small-Scale Ellerman Bomb Events 5 Dataanalysiswasconductedaftertwokeysteps:thespeckle-imagingprocess and the alignment of the datasets. The speckle-imaging technique (W¨oger, von der Lu¨he, and Reardon, 2008) was used for the IBIS line centre and wing data with each repetition of the IBIS routine contributing one final image with a cadence of 26.9 seconds. This process was applied to counteract the changes in seeingoverthecourseofasinglecyclebycombining50short-burstimagesintoa lower-cadence, higher-resolution image. For the ROSA G-band data, 32 images were used giving a final cadence of 0.64 seconds. Each Hα speckle image was alignedtothepreviousimagetoeliminatejitter.Next,alignmentofthedatasets fromseparateinstrumentswascarriedoutbyco-aligningthreespecificreference points on each image and then rotating the images accordingly. Contour plots of the region as observed by DST/IBIS were then overlaid on SDO/HMI and DST/ROSA images with large features, such as the sunspot, used to validate the alignment. Our Hα observations have two main limitations that should be considered before future studies in this area are undertaken. Firstly, there is a cadence of 26.9secondswhichislargeincomparisontotheoveralllifetimeofnetworkbright points(NBPs)aspredictedbyWatanabeetal.(2011)whonotethatthefunction y ∝exp(−x/C) fits the lifetimes and occurrence rates of NBPs well (where y is the number of NBPs for each lifetime, x). Therefore, our analysis is limited to events of lifetime longer than 54 seconds (or two consecutive frames) and could miss events that form and disappear within this time limit (brightenings that occur in one time frame are included in the histogram of lifetimes but are not includedelsewhere).InSection3.1,wediscusstheseshorter-livedeventsandhow they link to EBs. Secondly, the spatial resolution of our data is potentially too large, at 0.192(cid:48)(cid:48), to capture all EBs. EBs may form in much smaller areas than this.WedoacknowledgethatduetothespecklingoftheIBISimages,short-lived EBsmaybemissed;however,withthecurrentobservationaltechniquesandthe small scales of the events studied in this research, the compromise between high cadence and high spatial resolution is important. 3. Statistical Analysis 3.1. Identification of Ellerman Bombs The definition of an Ellerman bomb (and its relationship to network bright points) varies widely within the literature on the topic. Here, we shall discuss, and justify, what we have found appropriate and used as the definition of an Ellermanbombeventandhowthisdiffersfromthoseusedbyotherauthors.We suggest that, in essence, an Ellerman bomb is a brightening in the line wings of theHαopticalline(anexampleisshowninFigure2),whichisalsovisibleinthe wingsofotherchromosphericlinessuchasCaiiaswellasthe1600˚Acontinuum (Qiu et al., 2000). In his original article studying the Hα line profile, Ellerman (1917), suggested that the brightenings were “a very brilliant and very narrow bandextendingfourorfive˚Aoneithersideoftheline,butnotcrossingit.”This definition still holds, suggesting that EBs are features of the upper photosphere SOLA: Ellerman_Bomb_Statistics.tex; 11 December 2013; 22:09; p. 5 6 C.J.Nelsonet al. Figure 2. (a) Hα line-profile showing an Ellerman bomb stretching out into the line wings. ThesolidlineisfromaquietregionandthedashedlineistheprofilefortheEBindicatedby the arrow in the blue wing image shown at 15:14:01 by (b). This EB is not taken from the sameframeasFigure1. andlowerchromospherethatarecoveredbythehighlyopaquenetworkoffibrils andmottlesthatformthecomplexchromosphere,whichitispossibletoobserve using the Hα line centre. The threshold at which an Ellerman bomb is no longer classified as a net- work bright point is also a point of interest. Recently, Watanabe et al. (2011) suggested that the difference between EBs and network bright points was both their brightness (EBs are more intense events) and their tendency to flare (both in intensity and size). This definition may, however, cause confusion, as smaller events that possess brightenings may not be observed flaring due to the “flare” being within the spatial resolution of the data. Here, we define an Ellerman bombonlyintermsofbrighteningandsetourthresholdat130%oftheaverage intensity of the image (this value is the upper limit of thresholds discussed in Georgoulis et al., 2002). This value was chosen as it incorporated all major EB events selected by eye within this dataset as well as limiting the effect of the sunspot on the average FOV intensity. Overall, we suggest and use the following as parameters for an automated method for the detection of EBs that can be implemented to follow their evolu- tion through time: • The region is over 130 % of the FOV average brightness in both the red and blue wings of the Hα line-profile. • It has an initial spatial overlap in the red and blue wings. • Its area is greater than or equal to two pixels. • If there is a spatial overlap in both the red and blue wings between frames then the EB is deemed to have lived into the next frame. After the initial frame, no overlap is required between the wings as small-scale events may separate within their lifetime. • If there are multiple events with spatial overlap the one with the largest spatial correlation is taken; the others are neglected. SOLA: Ellerman_Bomb_Statistics.tex; 11 December 2013; 22:09; p. 6 Small-Scale Ellerman Bomb Events 7 • Any EBs that occur in the first or last frame are removed from the sample so that only EBs with a complete lifetime are included. Note that one of the main differences in the definition above from that by Watanabe et al. (2011) is that we do not set a lower time limit for the lifetimes ofEBs(240secondsisusedinbyWatanabeet al.,2011).Wediscussthischange in Section 3.3. Any analysis on EB events should also take into account the original description by Ellerman (1917), in that EBs are not visible in the line centre. In this dataset there are no brightening events observed in the Hα line centre during our time series, this was not included in the algorithm; however, this would potentially need to be revised for future studies. EBs have been predicted to occur at a rate of 1.5 per minute in an 18(cid:48)(cid:48)×24(cid:48)(cid:48) region by Zachariadis, Alissandrakis, and Banos (1987). Interpolating this to ourFOV,wewouldexpectaround30EBstooccurperminute.Thereforeinour 90-minutedatasetweshouldexpecttosee2690EBs.Zachariadis,Alissandrakis, andBanos(1987)suggestthatEBscanform,fadeandrecurinthesameposition meaningthat2690couldbeextremelyconservative.Byclassifyinganeventthat rises above the 130 % threshold, fades and then rises above the threshold again as two separate events, we present 3570 EBs in this time range (133 % of the predicted value presented by Zachariadis, Alissandrakis, and Banos, 1987). 3.2. Spatial Occurrence of Ellerman Bombs EBs form in highly magnetic regions, for example, in bipolar regions within emerging active regions or over complex unipolar topologies such as the penum- brae of sunspots (Georgoulis et al., 2002). Figure 3 shows contours of the EBs from the same image at different brightness threshold values as well as an HMI image of the same region. The temporal alignment between the Hα and HMI dataislessthan10secondsandweestimatethatthespatialalignmentisbetter thananarcsecondthereforewithinthespatialresolutionoftheHMIinstrument. TheoccurrenceofEBsinemergingactiveregionssuchasNOAA11126,which we study, has been used as evidence that they are magnetic reconnection events inthe lower-atmosphereduetoemergingflux(e.g.Georgoulisetal.,2002).They have, previously, been predominantly observed between the leading spot and the following plage region; however, they have also been reported as occurring within complex penumbrae, where complex unipolar magnetic fields dominate (for flux emergence see Pariat et al., 2004; for a good review of photospheric magnetic reconnection see Litvinenko, 1999). Both of these regions show strong and complex magnetic fields in photospheric magnetograms, therefore implying that magnetic fields are, in some way, responsible for the formation of EBs. The FOV that we are observing is extremely complex in terms of magnetic field structuring. For example, we see from Figure 1(d) that there is a region of bothpositiveandnegativemagneticfieldindicatedbythearrowtotheleft(51(cid:48)(cid:48), −530(cid:48)(cid:48)) of the spot, which leads an intense brightening indicated by an arrow in Figures 1(b) and (c). Also, around the spot sits a large, penumbral structure as well as both small and large fibril structures (easily seen in Figure 1(c)). We notice in Figure 3 that brighter EBs tend to form nearer to the strong magnetic fields within the penumbra of the leading spot. With a threshold of SOLA: Ellerman_Bomb_Statistics.tex; 11 December 2013; 22:09; p. 7 8 C.J.Nelsonet al. −510 −510 −520 −520 s] s] c c se−530 se−530 c c ar ar Y [−540 Y [−540 −550 −550 −560 −560 30 40 50 60 70 80 30 40 50 60 70 80 X [arcsecs] X [arcsecs] −510 −510 −520 −520 s] s] c c se−530 se−530 c c ar ar Y [−540 Y [−540 −550 −550 −560 −560 30 40 50 60 70 80 30 40 50 60 70 80 X [arcsecs] X [arcsecs] Figure3. IBISredwingimageswithcontoursofseveralbrightnessthresholdvaluesoverplot- tedwith:(a)120%,(b)130%and(c)140%,respectively.AtemporallyalignedHMIimage (±400G)isincludedin(d)with130%and140%contoursoverplotted. 120 % we find a near-ubiquitous covering of EBs in the FOV, especially trailing the spot (to the left). As has been discussed previously, many of these events appear to be small, localised changes in the background intensity, which are selected by the algorithm due to the decreasing of the average FOV intensity causedbythesunspot.Byincreasingtheinternsitythresholdto130%,manyof thecontourscreatedat120%disappearandleavewhat,byeye,appearstobeall majorEBevents.Athresholdof140%focusesthebrighteningsaroundthespot at the regions of highest magnetism (Figure 3(c)); however, several examples of large, flaring brightenings are not selected with this threshold, implying that it may be too high. The spatial correlation between EBs and strong vertical magnetic field, as showninFigure3(d),isanotherhintthatEBsareinfactmagneticeventswhose intensityisdominatedbythestrengthofthemagneticfield. BycontouringEBs identifiedwiththresholdsof130%and140%onatemporallyalignedSDO/HMI magnetogram, it is easy to see the correlation between Hα brightenings and strong magnetic fields. At approximately (55(cid:48)(cid:48), −543(cid:48)(cid:48)), one can pick out a line of negative polarity magnetic field that is mirrored exactly by EBs. An example SOLA: Ellerman_Bomb_Statistics.tex; 11 December 2013; 22:09; p. 8 Small-Scale Ellerman Bomb Events 9 at a region of positive polarity can be seen at (80(cid:48)(cid:48), −519(cid:48)(cid:48)). The cadence and, moreimportantly,thespatialresolutionoftheHMIimagesare,however,toolow topickoutfine-scalestructuringwithinthemagneticfieldmeaningnothingmore thanacorrelationbetweenEBsandstrong,verticalphotosphericmagneticfields is supported by this analysis. Higher-resolution magnetograms are required to fullyanalysewhetherEBsare associatedwithseparatrixofmagneticstructures as suggested by Georgoulis et al. (2002). 3.3. Lifetime of Ellerman Bombs PreviousstudiesofEBshavebeenlimitedbyrelativelylong-cadenceobservations (theFlareGenensisExperimentusedbyGeorgoulisetal.,2002,andPariatetal., 2004,forexample,hadacadenceof≈3.5minutes)exceptforasmallnumberof keystudies(e.g.Watanabeet al.,2011),whichcouldmisstheformationofEBs. Here, we present an analysis of EB lifetimes using high-resolution, relatively high-cadence observations. The speckle reconstruction technique we applied has improved the spatial resolution of these data, meaning that even brightenings of around 0.14(cid:48)(cid:48) are observable with a temporal cadence of 26.9 seconds. The resolution of our data in both spatial and temporal coordinates allows us to detectEBsbothoccurringand,moreimportantly,recurring(seee.g.Georgoulis et al., 2002), which influences previous lifetime estimates. In Figure 4(a), we show a histogram of the lifetimes of EBs for our dataset. We find that the function y ∝exp(−x/C) (where y and x are the total number and lifetime of EBs respectively and C = 2.7±0.16) proposed by Watanabe et al. (2011) fits our histogram for lifetimes less than 20 minutes, implying the possibility that EBs could be formed and disappear on timescales shorter than the temporal resolution presented here. Even higher cadence is required to fully answer this question. Although the fit of this curve appears to have a long tail, it should be noted that only seven events do not match the the exponential function, meaning that 5402 events do fit this curve. We suggest that EBs can be much shorter-lived than previous estimates and thatinfacttheycanbe shorterthanourcadence. Byconsideringonlythe3570 EBs with lifetimes over one frame, we find an average lifetime of approximately three minutes which is considerably less than previous estimates of five to ten minutes.Wefindthatfor5409EBs(includingthoseEBeventsonlyobservedin one frame), the average lifetime drops to approximately two minutes suggesting that this research may only present an upper limit on lifetime. To check the reliability of the algorithm, large events (over the 0.8(cid:48)(cid:48) spatial-resolution pre- sented by Georgoulis et al., 2002) are also analysed (histogram plotted in blue inFigure4(a))givinganaveragelifetimefortheseeventsofapproximatelyeight minutes. A continued trend, as seen in Figure 4(a), coupled with Figure 4(b) could suggest that small magnetic reconnection events are extremely common in emerging active regions especially at the outer penumbra (see Figure 3) as well as the surrounding quiet Sun. We suggest that a higher cadence dataset would find even shorter-lived EB events than presented here as well as better accounting for their recurrence. SOLA: Ellerman_Bomb_Statistics.tex; 11 December 2013; 22:09; p. 9 10 C.J.Nelsonet al. 104 s b m103 o B n a m er102 Ell of er b m101 u N 100 0 5 10 15 20 25 30 35 Lifetime [Minutes] 5000 4800 nits]4600 U e 4400 ut ol bs4200 A sity [4000 n e nt3800 I 3600 3400 0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4 Area [arcsecond2] 104 α= 0.07 0.003 − ± s b m103 o B n a m er102 Ell of er b m101 u N 100 0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 Average Area [arcsecs2] Figure 4. (a)Ellermanbomblifetimefrequencyplot. EBswitharealargerthan0.8(cid:48)(cid:48)×0.8(cid:48)(cid:48) (circular diameter of approximately 0.45(cid:48)(cid:48)) are shown using blue to compare estimates with previous researches. (b) Intensity by area plot. Again, blue indicates larger events and red showssmallerevents.(c)Ahistogramofareaagainstlog(frequency). SOLA: Ellerman_Bomb_Statistics.tex; 11 December 2013; 22:09; p. 10