In this paper the longitudinal and latitudinal spatial

distribution of macrospicules is examined. We found a statistical

relationship between the active longitude determined by

sunspot groups and the longitudinal distribution of macrospicules.

This distribution of macrospicules shows an inhomogeneity and

non-axysimmetrical behaviour in the time interval from June

2010 until December 2012 covered by observations of the Solar

Dynamic Observatory (SDO) satellite. The enhanced positions

of the activity and its time variation has been calculated. The

migration of the longitudinal distribution of macrospicules shows

a similar behaviour as that of the sunspot groups

A Chidambara

E Benevolenskaya

H Balthasar

H Wang

IG Usoskin

JD Bohlin

JR Lemen

K Murawski

K Mursula

K Wilhelm

L Győri

L Heggland

L Jing

LK Wilkinson

LY Zhang

N Gyenge

N. Gyenge

P Kayshap

Pike C. D.

R. Erdélyi

S Parenti

S. Bennett

Scullion

T Zaqarashvili

V Bumba

Journal of Astrophysics and Astronomy

arXiv

Gyenge, N.

Bennett, S.

Erdelyi, R.

White Rose Research Online

Non-homogeneous Behaviour of the Spatial Distribution of Macrospicules

J. Astrophys. Astr. (2015) 36, 103–109 c© Indian Academy of SciencesNon-homogeneous Behaviour of the Spatial Distributionof MacrospiculesN. Gyenge1,2,∗, S. Bennett2 & R. Erdélyi1,21Debrecen Heliophysical Observatory, Research Centre for Astronomy and Earth Sciences,Hungarian Academy of Sciences, Debrecen, P.O. Box 30, H-4010, Hungary.2Solar Physics and Space Plasmas Research Centre (SP2RC), University of Sheffield,Hounsfield Road, Hicks Building, Sheffield S3 7RH, UK.∗e-mail: gyenge.norbert@csfk.mta.huReceived 17 December 2014; accepted 30 January 2015Abstract. In this paper the longitudinal and latitudinal spatial distribu-tion of macrospicules is examined. We found a statistical relationshipbetween the active longitude (determined by sunspot groups) and the lon-gitudinal distribution of macrospicules. This distribution of macrospiculesshows an inhomogeneity and non-axisymmetrical behaviour in the timeinterval between June 2010 and December 2012, covered by observa-tions of the Solar Dynamic Observatory (SDO) satellite. The enhancedpositions of the activity and its time variation have been calculated.The migration of the longitudinal distribution of macrospicules shows asimilar behaviour to that of the sunspot groups.Key words. Active longitude—macrospicules.1. IntroductionThe behaviour of solar non-axisymmetric activity has been studied since the begin-ning of the last century (Chidambara 1932). It has been recognised that the distribu-tion of sunspot groups is not uniform, they tend to cluster to a certain heliographiclongitude (Bumba et al. 1965; Balthasar et al. 1984; Wilkinson et al. 1991). Theseearly studies of the active longitudes focused mainly on the distribution of sunspotgroups or sunspot relative numbers. From the middle of the 20th century it has beensuggested that it is not just the sunspot groups that have a non-homogeneous longi-tudinal distribution. This inhomogeneity has been found in the case of solar flares(Zhang et al. 2007), surface magnetic fields (Benevolenskaya et al. 1999), helio-spheric magnetic field (Mursula & Hiltula 2004) and, recently, active longitudes havebeen observed in coronal streamers (Jing 2011).Macrospicules (hereafter ‘MS’) are chromospheric objects observed in Hα andHe 30.4 nm (Bohlin et al. 1975; Wang et al. 1998; Murawski et al. 2011; Scullionet al. 2011). They are explosive jet-like features extending up to, on average, 29 Mmand velocities up to approximately 110 km/s (Zaqarashvili & Erdélyi 2009). Theirstructure reflects the solar atmosphere they move through; they are proposed to have103104 N. Gyenge et al.a cool core, surrounded by a hot sheath (Parenti et al. 2002). They are of particularuse in this study, as they are observed from the solar equator to the poles.In this paper, we study the longitudinal and latitudinal spatial distributions ofMS. Furthermore, we will explore the relationship between the sunspot groups,non-axisymmetric behaviour or Active Longitude (hereafter ‘AL’) and longitudinaldistributions of MS.2. Observations and databasesThe MS were observed using the 30.4 nm spectral window AIA on-board SDO(Solar Dynamic Observatory) (Lemen et al. 2012). This takes a 4096 × 4096 pixel,full disc, image of the Sun at a cadence of 12 s. We took typical samples of twohours, twice a month, from June 2010 until December 2012. For each image the solarlimb was flattened out, making it easier to identify and measure the MS. They areextremely difficult to measure on disk and as such, this study concentrates on thoseoccurring at the limb. We record the time at the moment they become visible at thelimb and their angular displacement from solar due east. Measuring MS this waywe identified 101 examples of MS. The physical dimensions and the heliographiccoordinates have been estimated.The source of sunspot data that we use to calculate the most enhanced longi-tude of sunspot groups (AL) is the Debrecen Photoheliographic Data (DPD) sunspotcatalogue (Győri et al. 2011). This database is the continuation of the classic Green-wich Photoheliographic Results (GPR), the source of numerous works in this field.The sunspot catalogue has been used, providing a time sample from 1974. This datasample contains information about area and position for each sunspot.3. Statistical study of the latitudinal distribution of MSTo study the latitudinal spatial behaviour of MS, as a first step, we determine theheliographical latitudes (B). For further analysis, the Carrington latitudes, B, havebeen transformed into the following system:φ = −(B + 90◦)/90◦, B < 0φ = −(B − 90◦)/90◦, B > 0 (1)The domain of interest of the quantity φ is [−1; 1]. The φ = 0 point containsthe northern and southern poles. The [0; 1] sub-domain of φ represents the northernhemisphere, the ascending φ values from 0 to 1 show the descending latitudes from90◦ to 0◦. The southern hemispheres have been considered in the same way.Figure 1 shows the result of the statistics above. The histogram depicts a normaldistribution. The mean of the distribution is φ̄ = 0.043, suggesting that most of theMS tend to cluster to the poles. We also found that the northern hemisphere wasslightly more active in this time period. The standard deviation 1σ = 0.3507 and2σ = 0.7014. Hence, 68% of the data tend to cluster in a 31.5◦ wide belt from thepoles. That is to say: 68% of MS are between the ±58.5◦ and ±90◦ heliographic lat-itude, and, 95% of MS are in a 63◦ degrees belt from the poles or between the ±27◦and ±90◦ in heliographic latitude. Therefore, MS are able to exercise longitudinalinhomogeneity at higher latitudes.Spatial Distribution of Macrospicules 105Figure 1. The grey area shows the probability density function of the parameter φ. The solidblack line is the fitted Gaussian distribution. The values of standard deviation 1σ and 2σ of thenormal distribution have been indicated in the top right corner.4. Statistical study of longitudinal distribution of MS4.1 Activity maps of active longitudes based on sunspotsAccording to our previous study (Gyenge et al. 2014) the active longitudes’ iden-tification method was considered and the active longitude was found to be distinctin each hemisphere. The present investigation started with a similar method asdescribed in our preceding paper (Gyenge et al. 2012). The areas and positions ofall sunspot groups are considered. The solar surface is divided into longitudinal binsof 20◦ and the areas of all groups were summed up in each bin: Ai in certain Car-rington Rotation (CR) between 2097 and 2128, which is the time interval of the MSsample. Next, the longitudinal activity concentration is represented by the quantityW defined by,Wi,CR = Ai,CR∑Nj=1Aj,CR, (2)where N is the number of bins,∑Nj=1Aj,CR is the sum of all sunspot groups in agiven CR and Ai,CR is the total area of sunspot groups in a CR and at a specificlongitudinal bin.In each CR, we omitted all of the Wi,CR values which are lower than the 3σ signifi-cance limit. The highest peak, ALCR, has been selected from this decayed sample(which contains only the significant peaks) caused by the significance test. For fur-ther analysis, the Carrington longitudes, λ, will now be transformed, into Carringtonphase period:ψ = λ/360◦. (3)Hence, the values of the phases are always smaller or equal (which is the entirecircumference) to one.106 N. Gyenge et al.Figure 2. The migration of the active longitudes in the time interval of CR 2097 to 2128based on sunspot groups. The left panel shows the northern hemisphere. The right panel is thesouthern hemisphere.The time-variation of the parameter ALCR is plotted in Figure 2. The verticalaxis is the phase parameter, which has been repeated three times. The northern(left-hand side) and the southern (right-hand side) cases are considered separately.Both figures unveil a clear increasing migration pattern. Usoskin et al. (2005) andGyenge et al. (2014) found similar patterns at a different time intervals. Most ofthe migration follows a parabola shape (which has been fitted by the least-squaresmethod).4.2 Relationship between the AL and MS longitudinal distributionThe parameter δψ is now introduced to study the relationship between the activelongitude ALCR defined by sunspot groups, and the longitudinal position of MS, LCRin CRδψ = |ALCR − LCR| . (4)The parameter δψ has been reduced by a unit phase if it is larger than 0.5, whichmeans, this quantity represents the shortest phase difference between the longitudinalposition of a given MS and the position of active longitudes in both hemispheres. Forfurther analysis, the δψ samples of the northern and southern hemispheres are nowcombined.The probability density function (PDF) of the quantity δψ is shown in Figure 3.On the x-axis, the meaning of the lower values reflect the smallest longitudinaldifference in phase; the value 0.5 phase jumps to the opposite side of the Sun.The MS tend to cluster near the active longitudes, which is shown by the firstand second peaks: δψ < 0.2 (<±36◦) 61% of the candidates. However, there is asignificant peak around 0.5, which is the signature of the appearance of secondarylongitudinal belts. The secondary belt always exists at the same time as the primary.Note that the latter is always stronger than the secondary belt, and the phase shift isaround 0.5. The MS show a similar behaviour. A secondary belt appears for 22% ofthe events and δψ < 0.1 (< ±18◦).Spatial Distribution of Macrospicules 107Figure 3. The probability density function (PDF) of the δψ parameter.5. Results and discussionWe investigated the distribution of macrospicules detected at the solar surface as afunction of their longitudinal and latitudinal coordinates in Carrington coordinates.A non-homogeneous latitudinal macrospicule distribution has been found. Mostof the events tend to cluster to the higher latitudes (95% of MS are within the±27◦ to ±90◦ heliographical latitude). The number of events is found to be growingexponentially from the equator to the pole in both hemispheres.A slightly asymmetrical behaviour has been found between the two hemi-spheres in the studied time interval, where the northern hemisphere was marginallymore active than the southern. In the studied time period other phenomena shownorthern–southern asymmetry. The northern hemisphere was significantly moreactive in terms of the averaged maximum sunspot area (northern hemisphere: 203,southern hemisphere: 183) and the international sunspot number (northern hemi-sphere: 29, southern hemisphere: 18). For this reason we assume that the locationof the MS might be connected to the solar dynamo processes, however, cau-tion must be exercised as this conclusion is based on a rather limited statisticalsample.The longitudinal spatial distribution of MS is not uniform either. A large propor-tion of the MS (83 from the 101 in our sample) tend to cluster to the AL. In the caseof the primary active longitude belt, the macrospicules are within ±36◦ of the activelongitude. The second belt has a ±18◦ wide range where the macrospicule is foundto be concentrated. This supports the existence of an active longitude at higher lat-itudes. MS instances extend up to 50 Mm in the solar atmosphere. Therefore, theyhave been proposed as a viable candidate for solar wind acceleration and coronalheating (see e.g. Pike & Harrison 1997).The origin of such MS is either due to wave modes (e.g., Zaqarashvili & Erdélyi2009; Scullion et al. 2011) or by magnetic reconnection (Wilhelm 2000; Hegglandet al. 2009; Murawski et al. 2011). However, how these triggering mechanisms of108 N. Gyenge et al.MS are related with magnetic flux transport processes is not yet known. Recently,Kayshap et al. (2013) reported the evolution of a small-scale bipolar flux tube inquiet-Sun and its internal reconnection to produce MS. This provides some clue tothe connection of localized generation of macrospicule with small-scale magneticfield evolution. However, more statistics in terms of the observations and stringentmodelling are needed to explore this aspect of MS origin.The temporal variation of the number of MS has been investigated, but the corre-lation between the temporal density of MS and the increasing trend of Solar Cycle25 has not yet been found. A reason for the lack of finding such correlation could bethe limited time period and sample size of the data investigated.A large sample and more comprehensive statistical study is now in preparationfor a more detailed search for further identifiable non-homogenous longitudinal dis-tributions of MS in the entire time period covered by observations of the SDOsatellite.AcknowledgementsThe authors would like to thank the Hungarian Academy of Sciences (under theirDistinguished Guest Scientists Fellowship Programme ref. no. 1751/44/2014/KIF)for the invitation, support and hospitality that has allowed the third author, RE, to stayfor three months at the Debrecen Heliophysical Observatory (DHO) of the ResearchCentre for Astronomy and Earth Sciences, Hungarian Academy of Sciences, duringwhich this research was undertaken. SB acknowledges the warm hospitality receivedfrom DHO while visiting there and carrying out this research. The research leadingto these results has also received funding from the European Community’s SeventhFramework Programme (FP7/2007-2013) under grant agreement eHEROES (ProjectNo. 284461) and from Science and Technology Facilities Council (STFC), UK. Thisresearch has made use of SunPy, an open-source and free community-developedPython solar data analysis package (Mumford et al. 2013).ReferencesBalthasar, H. et al. 1984, Solar Phys., 93, 177–179.Benevolenskaya, E. et al. 1999, Solar Phys., 190, 145–151.Bohlin, J. D. et al. 1975, The Astrophys. J. Lett., 197, 133–135.Bumba, V. et al. 1965, The Astrophys. J., 141, 1492–1517.Chidambara, A. 1932, Mon. Not. R. Astron. Soc., 93, 150–152.Gyenge, N. et al. 2012, Central European Astrophysical Bulletin, 36, 9–16.Gyenge, N. et al. 2014, Solar Phys., 289, 579–591.Győri, L. et al. 2011, IAU Symp., 273, 403–407.Heggland, L. et al. 2009, The Astrophys. J., 770, 1–18.Jing, Li 2011, Astrophys. J., 735, 130.Kayshap, P. et al. 2013, The Astrophys. J. Lett., 770, L3.Lemen, J. R. et al. 2012, Solar Phys., 275, 17–40.Mumford, S. et al. 2013, SunPy: Python for Solar Physicists, Proceedings of the 12th Pythonin Science Conference, 74–77.Murawski, K. et al. 2011, Astron. Astrophys., 535, 58.Mursula, K., Hiltula, T. 2004, Solar Phys., 224, 133.Parenti, S. et al. 2002, Astron. Astrophys., 384, 303–316.Spatial Distribution of Macrospicules 109Pike C. D., Harrison R. A. 1997, Solar Phys., 175, 457–465.Scullion et al. 2011, Astrophys. J., 743, 1–19.Usoskin, I. G. et al. 2005, Astron. Astrophys., 441, 347–352.Wang, H. et al. 1998, The Astrophys. J. Lett., 509, 461–470.Wilhelm, K. 2000, Astron. Astrophys., 360, 351–362.Wilkinson, L. K. et al. 1991, Am. Astron. Soc., 23, 1030–1031.Zhang, L. Y. et al. 2007, Astron. Astrophys., 471, 711–716.Zaqarashvili, T., Erdélyi, R. 2009, Space Sci. Rev., 149, 355–388.

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