Variation of Chromospheric Features as a Function of Latitude and Time using Ca-K Spectroheliograms for Solar Cycles 15-23: Implications for Meridional Flow
Pooja Devi, Jagdev Singh, Ramesh Chandra, Muthu Priyal, Reetika Joshi
SSolar PhysicsDOI: 10.1007/ ••••• - ••• - ••• - •••• - • Variation of Chromospheric Features as a Function ofLatitude and Time using Ca-K Spectroheliograms forSolar Cycles 15 – 23: Implications for MeridionalFlow
Pooja Devi · Jagdev Singh · Ramesh Chandra · Muthu Priyal · Reetika Joshi © Springer ••••
Abstract
We have analysed the Ca-K images obtained at Kodaikanal Obser-vatory as a function of latitude and time for the period of 1913 – 2004 coveringthe Solar Cycle 15 to 23. We have classified the chromospheric activity intoplage, Enhanced Network (EN), Active Network (AN), and Quiet Network (QN)areas to differentiate between large strong active and small weak active regions.The strong active regions represent toroidal and weak active regions poloidalcomponent of the magnetic field. We find that plages areas mostly up to 50 ◦ latitude belt vary with about 11-year Solar Cycle. We also find that weak activ-ity represented by EN, AN and QN varies with about 11-year with significantamplitude up to about 50 ◦ latitude in both the hemispheres. The amplitude ofvariation is minimum around 50 ◦ latitude and again increases by small amountin the polar region. In addition, the plots of plages, EN, AN and QN as afunction of time indicate the maximum of activity at different latitude occur atdifferent epoch. To determine the phase difference for the different latitude belts,we have computed the cross-correlation coefficients of other latitude belts with35 ◦ latitude belt. We find that activity shifts from mid-latitude belts towardsequatorial belts at fast speed at the beginning of Solar Cycle and at slowerspeed as the cycle progresses. The speed of shift varies between ≈
19 and 3 ms − considering all the data for the observed period. This speed can be linkedwith speed of meridional flows those believed to occur between convection zoneand the surface of the Sun. (cid:66) Pooja Devi [email protected] Department of Physics, DSB Campus, Kumaun University, Nainital 263 002, India Indian Institute of Astrophysics, Bangalore- 560 0034, India
SOLA: MS_rev2_0902.tex; 10 February 2021; 1:38; p. 1 a r X i v : . [ a s t r o - ph . S R ] F e b . Devi et al. Keywords:
Sun - activity: Sun - solar cycle: Sun - meridional flow: Sun -magnetic fields
1. Introduction
Solar surface depicts various activity features that vary on short and long timescales. The continuum images of the Sun show sunspots and white light faculae.Sun’s images in X-rays and EUV wavelength domain show bright points loopstructures in emission. The historic images of the Sun obtained in H α and Ca-Klines show plages, filaments and networks. The magnetograms of the Sun showhigh magnetic field at the location of sunspots and plage regions. These alsoindicate weak magnetic field spread over the whole visible surface of the Sun. Allthese features are related to each other and their occurrence varies with time. TheCa-K images show plages, enhanced network (EN), Active network (AN) andquiet network (QN). These represent magnetic field regions of different strengthand their brightness varies accordingly. Leighton (1959) found that the Ca-Kplage regions have magnetic fields in the range of 100 – 200 Gauss. Simon andLeighton (1964) showed a strong correlation between the boundaries of the largeconvective cells known as super-granules and Ca-K network. These magneticfeatures have cyclic variations (Oliver, Ballester, and Baudin, 1998; Gopalswamy,2008 and references cited therein). From the spectroscopic observations of theCa-K profiles, Sindhuja, Singh, and Ravindra (2014) reported that variationsin the Ca-K line parameters can be used to study the meridional flows. Themovement of solar activity towards lower latitudes has been studied by usingsunspots and related high magnetic field indices. During the later part of the 20 th century observations were made to make magnetic field images of the Sun. Usingthese images pole and equator ward shift in the activity, thereby the meridionalflows have been studied. The magnetic images of the Sun for the earlier times arenot available but other type such as Ca-K, H α are available since the beginning of20 th century (Oliver, Ballester, and Baudin, 1998; Gopalswamy, 2008; Sindhuja,Singh, and Ravindra, 2014; Priyal et al. , 2019 and references cited therein). Thecyclic variations of these features are known as Solar Cycle. The Solar Cycle isknown to us since one and half century and discovered by Schwabe (1843) at first.After that, Hale (1908) showed that sunspots are strongly magnetized. Hale’sobservations revealed that the complete magnetic cycle spans two Solar Cycles i.e.
22 years, before returning to its original state, called solar magnetic cycle.This cyclic variation of the solar magnetic cycle is due to the cycle continuouslychanging from toroidal to poloidal magnetic field then again from poloidal totoroidal magnetic field. They can interchange from one another as follows: Thepoloidal field is stretched by the solar differential rotation and as result of thisthe toroidal field is generated. Again it converts to a poloidal field by the helicalturbulence.The flow of plasma material towards or from the equator is known as merid-ional flow. It is believed that the polar magnetic field is generated by themovement of weak magnetic field towards the poles from the decaying activeregions (Howard and Labonte, 1981). Babcock (1961) first speculated that the
SOLA: MS_rev2_0902.tex; 10 February 2021; 1:38; p. 2 eridional Flow During Solar Cycles 15 – 23 meridional flows is a main transport process to explain the observed pole-wardmotion of flux from the sunspot belts. In addition to this the meridional flowtowards the equator plays an important role for the transportation of the toroidalcomponent of the magnetic field. The meridional flow is one of the importantand crucial results of the dynamo models and can be studied from the shift in theoccurrence of the active regions on the Sun (Choudhuri, Schussler, and Dikpati,1995; Schrijver, De Rosa, and Title, 2002; Hathaway et al. , 2003; Baumann,Schmitt, and Sch¨ussler, 2006; Jiang et al. , 2009; Jin and Wang, 2012). Jiang et al. (2009) found in their model, the decrease in polar field and they explainedit as a result of equatorial meridional flow. They reported the speed is of theorder of few m s − .There are observational evidences of meridional flow since long time and it isof great importance for the advancement of solar dynamo models. The pole-wardtransportation of magnetic flux was first confirmed by Howard (1974). Lateronit is confirmed in more observational studies (Svalgaard, Duvall, and Scherrer,1978; Wang and Sheeley, 1988; Cameron and Hopkins, 1998; Durrant, Turner,and Wilson, 2004). Using the vector spectromagnetograph data of Synoptic Op-tical Long-term Investigations of the Sun (SOLIS) in chromospheric line Raoufi et al. (2007) explored the distribution of magnetic flux elements as a functionof latitude in polar solar caps during minimum of Solar Cycle 23. Their resultsshows the flux transport towards pole and also reported that the meridionalcirculation responsible for the flux transport slows down before reaching to pole.The equatorial and pole-ward transport of the flux is recently presented in thestudy of Sindhuja, Singh, and Ravindra (2014). They have used the KodaikanalCa-K line spectra data for the Solar Cycle 22 – 23. They found the Ca-K widthattains maximum amplitudes at different latitude belts at different phases ofSolar Cycle.Since there is a strong correlation between the magnetic field and the Ca-Kemission (Skumanich, Smythe, and Frazier, 1975; Nindos and Zirin, 1998), theCa-K line observations can be taken as the proxy for the magnetic field to studythe meridional flow. With this background, we have studied the variations inplage, EN, AN and QN areas representing large scale and small scale magneticactivity on the Sun, as a function of time and latitude. The plages represent largescale magnetic activity and mostly can be seen from equator to mid-latitudes.Whereas networks represent small scale activity and can be seen over the wholeof visible surface. The period of the study is for the Solar Cycle 15 – 23. Thepaper is organised as follows: In section 2, we present the observational datasets and data reduction technique. The results about their implications on themeridional flows are discussed in Section 3. Finally, the summary is presentedin Section 4.
2. Data and Analysis
The details of the data and its digitization are described in a paper by Priyal et al. (2014) and results of investigation of variations in the intensity of above
SOLA: MS_rev2_0902.tex; 10 February 2021; 1:38; p. 3 . Devi et al. mentioned features are reported by Priyal et al. (2017). The high spatial resolu-tion (0.86 arcsec pixel − ) and 16-bit read out with high photometric accuracy ofdigitized data permits to identify the network elements and study their variationwith time. They found some scatter in the results and careful analysis of the dataindicated short and long term variations in the quality of Ca-K obtained over acentury. Singh et al. (2018) shorted out the data in two-time series termed as“Good” consisting of uniform images and other as “Okay” having the remainingimages. The “Good” series has relatively uniform images in terms of contrast andwithout any defects due to developments or passing clouds during observations,obtained at Kodaikanal observatory on daily basis for the period of 1907 – 2004.About two-third of the total images come under the category of “Good” time-series. Priyal et al. (2019) determined the threshold value of intensity and areato determine different features mentioned above. But the threshold values forthe study of variations as a function of latitude are different than those forthe whole image, since some part of plages and networks are likely to fall intwo latitude belts. We found that intensity > for the plages, intensity > forthe EN, intensity < > for theAN and intensity < > for QNare suitable to identify these features. The limiting value of 4 arcsec has beenchosen to avoid the noise in the data due to 1 or 2 pixels having values > ◦ interval up to 70 ◦ north andsouth latitudes considering the date of observations and size of the image and 70 ◦ to solar limb is considered as one latitude zone, which has seasonal variations.Then we determine the fractional area and average intensities of plage, EN, ANand QN for each latitude zone as defined above on daily basis.With an aim to determine the long-term variations in these features andto reduce the scatter in the data, we have taken monthly averages. Then therunning average of this monthly averaged data over one year upto 40 ◦ latitudeand three years for latitude belts > ◦ is taken. Further, we have computed thecross-correlation function between data of different latitudes to determine thephase differences between activity at various latitudes.
3. Results and Discussion
The study of long-term variations in solar surface features is important to under-stand the solar dynamo process. We have segregated the Ca-K active features in
SOLA: MS_rev2_0902.tex; 10 February 2021; 1:38; p. 4 eridional Flow During Solar Cycles 15 – 23
Figure 1.
SOLA: plage_north_south.tex; 25 November 2020; 15:37; p. 1
Figure 1.
Plots of averaged fractional plage area as a function of time for the period of1913 – 2004 for different latitude belts in northern (red) and southern (blue) hemisphere.The latitude belt is written on top right of each panel. The vertical dashed and solid linescorresponds to approximate beginning of large activity at 30 – 40 ◦ latitude belt for each SolarCycle in northern and southern hemispheres, respectively. four types as classified by Worden, White, and Woods (1998). The Ca-K plagesare the relatively bright and large regions generally occur around the sunspotregions. It is believed that decaying Ca-K plages fragments into small regionstermed as EN and then decay. The AN is probably related with the small-scaleactive regions, also known as Ca-K bright points. The QN generally represents SOLA: MS_rev2_0902.tex; 10 February 2021; 1:38; p. 5 . Devi et al. the boundaries of the Ca-K network (super-granular network). Leighton, Noyes,and Simon (1962) and Simon and Leighton (1964) have shown a strong corre-lation between large convective cells and Ca-K network. Thus, plages representtoroidal and networks represent poloidal fields on the Sun. The plages, EN, ANand QN represent different physical characteristics of the chromosphere and thusmay show different behaviour. Some features may show variations related withthe phase of the Solar Cycle and some may not show. There may be a phase-lag in the variations of different features. With this view, we have studied theirvariation with time. Thus, the variations in the chromospheric features such asplage, EN, AN, and QN areas with time provide a valuable tool to study theshift in activity from one latitude to other latitude and thereby the meridionalflows. In principle, butterfly diagram, generally made using the occurrence ofplages with time provide such information but up to middle latitudes only. Todetermine velocity of shift one needs the detailed analysis of the data. Thedetection of these features has been shown in Figure 8 of the paper by Priyal et al. (2014). Here, we determine the fractional areas of these chromosphericfeatures at different latitude belts at an interval of 10 ◦ for the northern andsouthern hemispheres. Fractional areas are defined as the areas occupied by theselected feature in pixels divided by the total number of pixels in consideredlatitude belt. Ca-K plages regions are large areas around the sunspots with magnetic fieldin the range of 100 – 200 Gauss. The variations in the plage areas indicatethe variation in the toroidial magnetic field on the Sun. In Figure 1 (upper sixpanels), we plot the monthly averaged fractional plage areas for latitude belts upto 60 ◦ at an interval of 10 ◦ for the northern and southern hemispheres. The redand blue curves indicate the variation of plage areas in the northern and southernhemispheres, respectively. The area of the latitude belts greater than 60 ◦ is smalldue to projection effect. Therefore, in the bottom most panel of the figure weshow the monthly averaged plage area as a function of time for the latitude belt of60 ◦ – limb (visible part). The polar region covered varies depending on B ◦ angleof the image of the Sun. The figure indicate activity due to plages at 30 – 40 ◦ beltremain for short duration as compared to lower latitude belts between equatorto 30 ◦ in both the hemispheres. A look at the figures indicate that fractionalplage areas mostly occur up to 40 ◦ latitude belt in both the hemispheres. Thefractional plage areas at higher latitude belts appear to be negligible as expected.The figure also indicate that the plages occur more in latitude belt of 10 – 20 ◦ both in the northern and southern hemispheres as compared to other latitudebelts. This is consistent with the findings of Priyal et al. (2017). The Figure 6 oftheir paper indicate that the number of plages peaks around 10 – 20 ◦ latitudesfor each Solar Cycle from 14 – 23. The figure also shows that on an average plagesvary with 11-year period. The Solar Cycle begins around middle latitude beltsand active regions occur at lower and lower latitudes as the cycle progresses.We, therefore, have found the approximate epoch of the large scale occurrenceof plages at the latitude belt of 30 – 40 ◦ for each Solar Cycle and shown by SOLA: MS_rev2_0902.tex; 10 February 2021; 1:38; p. 6 eridional Flow During Solar Cycles 15 – 23
Figure 1.
SOLA: en_north_south.tex; 25 November 2020; 15:29; p. 1
Figure 2.
Same as Figure 1 but for EN area. dotted black line in the figures. The epoch of maximum activity represented byfraction plage area at other latitude belts does not coincide with the peak of 30– 40 ◦ latitude belt in both the hemispheres. Using the cross-correlation functionwe have computed the phase differences between the occurrence of maximumactivity at various latitude belts with respect to 30 – 40 ◦ latitude belt whichwill be discussed in this paper later. SOLA: MS_rev2_0902.tex; 10 February 2021; 1:38; p. 7 . Devi et al.
The Ca-K plages fragments into smaller regions when decay after magnetic fieldof the region weakens. The EN represents the decaying plages with averageintensity less than that of plage regions (Priyal et al. , 2017). To identify theEN, the threshold intensity is the same as that for plages but area limit is muchsmaller than that for plages. Six upper panels of Figure 2 show the variation ofmonthly averaged fractional EN areas for latitude belts up to 60 ◦ at an intervalof 10 ◦ and the bottom panel indicates the monthly averaged EN area for thelatitude belt of 60 ◦ – limb for the both the hemispheres by red (north) and blue(south) curves. The fractional EN areas are less as compared to fractional plagesareas for each latitude belt. The values of fractional areas around maximumphase of each cycle are more for 10 – 20 ◦ latitude belt as compared to otherequatorial latitude belts. The average value of fractional EN area decreasesfrom mid-latitude towards polar regions becomes minimum around 60 ◦ latitudebelts. The figure indicates that EN fractional areas are more in the northernhemisphere as compared to those in the southern hemisphere after 60 ◦ latitude.It is not clear why it is so? It may be some instrumental effect but long termvariations do exist. It may be noted that occurrence of EN areas is significant inthe polar region whereas in the plage areas, it is very less. Further, the variationin EN areas as function of time in polar regions indicate cyclic variation withperiod of about 11-year and out of phase with the variations at 30 – 40 ◦ latitudebelt. It will be verified using cross-correlation function. The AN areas are less bright than the EN areas and probably represent magneticelements in the lanes between granulation. These can also be associated withdecaying plages or some magnetic elements seen at the photospheric layer. Thedescription of Figure 3 is similar to that of Figure 2 but for AN region. Thevariations of AN fractional area are similar to those EN fractional areas. Thefractional areas of AN are more than that of EN fractional area, by about afactor of 2. The Solar Cycle variations in the AN fractional area are clearlyvisible in Figure 3, up to 40 ◦ latitude belts throughout the period of SolarCycles 15 – 23 in both the hemispheres. But, the cyclic variations are seenup to 1974 only (Solar Cycle 15 – 20) in the higher latitude belts. This maybe because the data available for less number days year − with frequent gapsafter 1974. The amplitude variation in the fractional area of AN is similar forrespective latitude belts in northern and southern hemisphere up to the mid-latitudes. This variation becomes very small in the latitudes from 40 – 60 ◦ . Atthe poles ( > ◦ ), this variation in AN area is enhanced in northern hemispherewhereas, in southern hemisphere, this enhancement is not seen. There appearsanti-correlation between the variations in the mid-latitudes and those in thepolar latitude belts. This will be confirmed by computing the cross-correlationsfunctions between 30 – 40 ◦ latitude belt with other latitude belts. SOLA: MS_rev2_0902.tex; 10 February 2021; 1:38; p. 8 eridional Flow During Solar Cycles 15 – 23
Figure 1.
SOLA: an_north_south.tex; 25 November 2020; 15:29; p. 1
Figure 3.
Same as Figure 1 but for AN area.
The QN regions are generally found at the boundaries of the large convectivecells, known as super-granules. The horizontal flow from the center of the cellcaries the flux tube and deposit at the boundary of the cell creating the increasein magnetic field at the boundary. This causes the increase in brightness ofthose regions and appearance of QN. In Figure 4 we show the monthly averagedfractional QN areas as a function of time 0 – 60 ◦ latitudes at an interval of 10 ◦ for both the hemispheres in the upper six panels. The bottom panel of the figure SOLA: MS_rev2_0902.tex; 10 February 2021; 1:38; p. 9 . Devi et al.
Figure 1.
SOLA: qn_north_south.tex; 25 November 2020; 15:29; p. 1
Figure 4.
Same as Figure 1 but for QN area. shows the same for the 60 ◦ – limb. The figure indicate that QN fractional areavaries with 11-year Solar Cycle up to 40 ◦ latitude in both the hemispheres butat the higher latitude belts this cyclic variation is not seen clearly. Even thoughthe QN is not directly related with solar activity but it appears that it playssome role in increasing magnetic field at the boundaries of super-granules. Thiscauses increase in the fractional area of QN during the active phase of the Sun. SOLA: MS_rev2_0902.tex; 10 February 2021; 1:38; p. 10 eridional Flow During Solar Cycles 15 – 23
We have studied the variation of plage, EN, AN and QN areas as a function oflatitude and time for Solar Cycles 15 – 23. In Table 1, we list the average valuesof amplitude of variations for plages, EN, AN and QN areas for various latitudebelts. In case of fractional plage area the maximum amplitude of variation is0.021 for 10 – 20 ◦ latitude belt and minimum amplitude 0.0002 for 50 – 60 ◦ latitude belt for the northern hemisphere. The values of amplitude of fractionalplage area for the southern hemisphere also show the same trend as a functionof latitude. The amplitude values in the table indicate that the fractional areaof EN, AN and QN follows the similar trend as a function of latitude. Thus, itcan be said that variations in the fractional area of plage, EN, AN and QN withtime are maximum around 20 ◦ and minimum around 50 ◦ latitude belts whichagree the findings of Sindhuja, Singh, and Ravindra (2014). They reported thatthere is minimum variation in the Ca-K width around 50 ◦ latitude belt. Table 1.
Table showing the average amplitude variation of fractional areas of chromosphericfeatures (plage, EN, AN, and QN) in different latitude belts. “N” and “S” are used for northernand southern hemispheres, respectively.Latitude Belt Average Amplitude Variation of Chromospheric FeaturesPlage EN AN QN0 – 10 N 0.0101 0.0065 0.0162 0.040310 – 20 N 0.0210 0.0121 0.0279 0.054920 – 30 N 0.0114 0.0087 0.0204 0.046930 – 40 N 0.0024 0.0032 0.0092 0.031440 – 50 N 0.0004 0.0011 0.0050 0.023750 – 60 N 0.0002 0.0010 0.0054 0.025760 – limb N 0.0014 0.0064 0.0262 0.07410 – 10 S 0.0063 0.0047 0.0126 0.036110 – 20 S 0.0189 0.0108 0.0255 0.052920 – 30 S 0.0119 0.0094 0.0211 0.048230 – 40 S 0.0030 0.0039 0.0103 0.034540 – 50 S 0.0004 0.0009 0.0045 0.025450 – 60 S 0.0000 0.0003 0.0027 0.020660 – limb S 0.0001 0.0004 0.0030 0.0210
SOLA: MS_rev2_0902.tex; 10 February 2021; 1:38; p. 11 . Devi et al.
These findings do not support the Babcock (1961) model which says thattoroidal part of magnetic field moves towards the equator and poloidal com-ponent moves towards pole from mid-latitude belts. One can ask why there isminimum activity around 50 ◦ latitude belts as compared to mid latitude beltsand polar region if weak magnetic field moves towards polar regions from midlatitude belts? Further, Raouafi, Harvey, and Henney (2007) reported that themagnetic field elements remain approximately same between 55 ◦ and 75 ◦ andafterwards they decrease by more than 50% toward the pole. But, Jin and Wang(2012) restricted their analysis of the Solar Cycle variation of the magnetic fieldonly up to 60 ◦ because they found fewer magnetic elements and more noise whileapproaching the polar regions. The cross-correlation curves of EN and AN doindicate the significance existence of small scale magnetic elements at the polarregion. The activity diagram, popularly known as butterfly diagram indicates that thesunspots and related activity such as plages appear at middle latitudes around40 ◦ at the beginning of Solar Cycle. The sunspots and plages remain visiblefrom few days to few months and then decay by fragmentation as the relatedmagnetic field weakens. These appear at lower and lower latitudes as the SolarCycle progresses. The speed of movement can be determined from the phasedifferences between the two latitude belts considered. Therefore, to determinemovement of activity we have computed the cross-correlation function (CC) forvarious latitude belts with 30 – 40 ◦ latitude belt as the Solar Cycle activitybegins in this belt. Generally, it is advisable to investigate the meridional flowspeed for each cycle considering the data for about 20 years. But to begin with,we consider the data for the whole period of 1913 – 2004 to determine the phasedifference of the occurrence maximum activity at different latitude belts withrespect to the mean latitude of 35 ◦ . To compute the cross-correlation functionwe use monthly averages of plage, EN, AN and QN areas. As mentioned above, we have determined the plage, EN, AN and QN areas atan interval of 10 ◦ up to 60 ◦ latitude and from 60 ◦ to visible latitude in boththe hemispheres on daily basis. We refer each latitude belt by its mean latitude,for example 5n for 0 – 10 ◦ north latitude belt and 5s for 0 – 10 ◦ south latitudebelt. The computed values of cross-correlation function (CC) for various latitudebelts with respect to 35 ◦ latitude belt as a function of phase lag in months forplage areas are plotted in Figure 5. In the top left panel of the figure we plotCC values of 5 ◦ , 15 ◦ and 25 ◦ latitude belt with 35 ◦ belt up to a phase lag of100 months for the northern hemisphere shown in blue, red and yellow curves,respectively. The right top panel shows the same for the southern hemisphere.The CC values vary smoothly with the phase lag and maximum values of CCare very good indicating that accurate value of phase lag can be determined.Bottom row two panels show the CC curves for the higher latitudes of 45 ◦ , 55 ◦ SOLA: MS_rev2_0902.tex; 10 February 2021; 1:38; p. 12 eridional Flow During Solar Cycles 15 – 23
Figure 5.
Plots of cross-correlation coefficient of various latitude belts with 35 ◦ latitude beltas a function of phase lag in months for plage area considering the data for the period 1913 –2004, Solar Cycles 15 – 23. Panel (a) and (b) displays the plots for 5 ◦ (blue), 15 ◦ (red) and 25 ◦ (yellow) with 35 ◦ latitude belt for northern and southern hemisphere,respectively. Panel (c)and (d) shows the plots for 45 ◦ (blue), 55 ◦ (yellow), and 75 ◦ (red) for northern and southernhemisphere, respectively. and 75 ◦ with 35 ◦ belt (hereafter simply referred as 45, 55 75, etc.) for both thehemispheres by blue, yellow and red curves, respectively. The maximum valuesof CC (hereafter called CC-max) are very low as negligible number of plage occurat high latitude belts. The negative value of the phase difference between 35nwith 45n indicate that the activity began early at the higher than 35 ◦ latitudebelt. It may be due to coincidence as the plage activity in 45 ◦ belt is very low.On the other-hand the phase difference is positive for the 35s with 45s belt.This indicate that either some of the fragmented plages moved towards polarregion or coincidence because of less plage activity in 45 ◦ belt. This needs to beinvestigated further considering the data for one to two consecutive Solar Cycles.The values of CC-max and phase difference for plages for different latitude beltsare listed in Table 2. The CC curves for the 55 and 75 belts show negligiblecorrelation or anti-correlation for zero phase lag. The CC curves in northernhemisphere for 55 and 75 do not show phase lag clearly whereas 55 belt indicatein the southern hemisphere indicate a phase lag of about 14 months. And 75sbelt shows negligible correlation or anti-correlation at zero phase lag but twopeaks separated by about 11-years, one each side of the zero phase lag. This SOLA: MS_rev2_0902.tex; 10 February 2021; 1:38; p. 13 . Devi et al.
Figure 6.
Same as Figure 5, but for EN area. type of behaviour may be due to the reason that plages are rarely visible athigher latitudes.
In the top two panels of Figure 6 we plot the CC values for the 5, 15 and 25 lati-tude belts as a function of phase lag in months for the northern hemisphere (leftpanel) and southern hemisphere (right panel) for the EN. The CC curves andphase lags are similar to those for the plage areas. The curves for the northernhemisphere indicate a phase lag of about 3 months for occurrence of maximumactivity between 25 ◦ and 35 ◦ latitude belt. The phase becomes relatively largerabout 11 months for 15 ◦ and 35 ◦ belts. Then the phase lag increases at a fasterrate for 5 ◦ and 35 ◦ latitude belts. This behaviour indicates that activity does notshift from middle latitude belts towards equator at a uniform speed. It impliesthat at the beginning activity shift at a faster rate and later it moves at a lowerrate towards equator. Bottom two panels of Figure 6 show the CC curves for thehigher latitude belts, namely 45, 55 and 75 belts. The corresponding curves aresimilar to those for plage areas seen in Figure 5. Similarly, the Figures 7 and 8show the CC curves for the AN and QN, respectively.The Figures 5 – 8 indicate that CC curves are similar for the equatoriallatitude belts in case of plage, EN, AN and QN areas with similar phase differencebetween respective latitude belts. The values of phase difference for each pair of SOLA: MS_rev2_0902.tex; 10 February 2021; 1:38; p. 14 eridional Flow During Solar Cycles 15 – 23
Figure 7.
Same as Figure 5, but for AN area. latitude belt are given in Table 2. But, the CC curves differ for higher latitudebelts especially for 55 and 75 belts. The CC curves for 55 and 75 latitude beltsare similar for EN and AN. The CC curve for 55n shows double peak aroundthe zero phase lag whereas it is not seen in CC curve for 55s belt. But both the75n and 75s belts show double peak separated by about 11 years indicating anti-correlation in the occurrence maximum activity between equatorial and polarregions. The CC curves for 55n, 55s and 75s belts for QN show a single peakwith very small phase lag with corresponding 35 ◦ latitude belt. Whereas, the75n latitude belt shows double peak but of not significance separated by about11 years. The area of QN at the equatorial belts do vary with about 11-yearperiodicity, probably due to the effect of decaying active regions In general, wecan say that activity in the polar regions is anti-correlated with the activity atthe equatorial regions even though the values of CC-max are very low.
4. Summary
Most of the people believe that dynamo process operating at the base of convec-tion zone generates magnetic field. This leads to formation of sunspots, plages,filaments and other active features on the solar surface. The systematic varia-tions in these features with time have been used to study two components ofmagnetic field, namely toroidal and poloidal (Choudhuri, Schussler, and Dikpati,
SOLA: MS_rev2_0902.tex; 10 February 2021; 1:38; p. 15 . Devi et al.
Figure 8.
Same as Figure 5, but for QN area. et al. , 2003). The magneticfield data of the Sun has been used to study the variations of the magneticfield with the Solar Cycle (Jin and Wang, 2012). But the detailed magnetic fieldimages have been obtained from the last part of the 20 th century.The chromospheric such as Ca-K images of the Sun can be used as proxyto study the magnetic fields on the Sun which are available from the beginningof the 20 th century. The Ca-K plages represent strong toroidal component of SOLA: MS_rev2_0902.tex; 10 February 2021; 1:38; p. 16 eridional Flow During Solar Cycles 15 – 23 magnetic field whereas networks such as EN, AN and QN indicate weak poloidalfields.Hathaway and Rightmire (2011) found that the meridional flow is faster atminimum as compared to that at maximum phase. Further, the meridional flowspeed during the initial phase of Solar Cycle 23/24 minimum was substantiallyfaster than that at the Cycle 22/23 minimum. The average latitudinal profileis a sinusoidal that extends to the poles and peaks at about 35 ◦ latitude. Withthe progress in the Solar Cycle, a pattern of inflows toward the sunspot zonesdevelops and moves equator-ward as the sunspot zone shifts towards equator.They found a peak pole-ward meridional flow velocity of 11.2 m s − at a latitudeof 35 ◦ and an average meridional flow profile substantially different in the north-ern and southern hemispheres. The reported faster flow velocity in the southernhemisphere with peak at a higher latitude than in the northern hemisphere. Theirmeasurements indicated that flows almost vanish at the extreme northern limit(75 ◦ ) while the pole-ward flow with a speed of about 5 m s − at the southernlimit persists. Hathaway and Upton (2014) find that the systematic weakeningof the meridional flow on the pole-ward sides of the active (sunspot) latitudes.They interpreted this as an inflow toward the sunspot zones superimposed on ageneral pole-ward meridional flow profile. They also found that the meridionalflow varied from cycle to cycle. Models of the magnetic flux transport by avariable meridional flow suggest significant modulation on the size and timingof the following sunspot cycle through its impact on the Sun’s polar magneticfields.Imada and Fujiyama (2018) found that meridional circulation velocity peakedat ≈
12 m s − at a latitude of 45 ◦ . Their measurements showed that the magneticelements with stronger and weaker magnetic fields largely represent the charac-teristics of the active region remnants and solar magnetic networks, respectively.They found that magnetic elements with a strong (weak) magnetic field showa faster (slower) rotation speed. On the other hand, magnetic elements with astrong (weak) magnetic field show slower (faster) meridional circulation velocity.Imada et al. (2020) found that the average meridional flow profile peaked at ≈
15m s − at 45 ◦ . During the declining phase of the cycle, the meridional flow at themiddle latitude (30 ◦ ) accelerated from 10 to 17 m s − in both hemispheres. Allthese measurements indicate that meridional flows peaks around 40 ◦ latitude.The phase difference between different latitude belts may vary from cycle tocycle in both the hemispheres. Here we are considering average values of phasedifference for the period of 1915 – 2004. The values of phase differences for theplages, EN, AN and QN are similar for the northern hemisphere for differentlatitude belts. Table 2 indicates that it takes about 30 months for the toroidalfield to travel from mid-latitudes to equator in both the hemispheres but totaltime may be larger than 30 months as this period is for 35 ◦ to 5 ◦ latitudesonly. There may be overall symmetry in the northern and southern hemispheresbut not at shorter time scales as indicated by the values of phase lag betweendifferent latitude belts in the northern and southern hemispheres. The values ofphase lag for different latitude belts indicate that the variations in plage areas,EN, AN and QN are in-phase with each other with some differences. It is difficult SOLA: MS_rev2_0902.tex; 10 February 2021; 1:38; p. 17 . Devi et al.
Table 2.
Table of Maximum correlation coefficient with phase difference for different latitudeswith 35 ◦ latitude. The maximum correlation is for different features (plage, EN, AN, QN) fromSolar Cycle 15 – 23.Correlation Maximum Correlation Coefficient Phase Difference in MonthsBetween Plage EN AN QN Plage EN AN QNLatitude5n and 35n 0.57 0.64 0.68 0.66 30 32 29 26.515n and 35n 0.68 0.69 0.74 0.74 14.5 11 12 8.525n and 35n 0.84 0.89 0.92 0.92 3.5 2.5 2.5 1.535n and 35n 1 1 1 1 0 0 0 045n and 35n 0.59 0.54 0.60 0.79 -4.5 -0.5 -0.5 -0.555n and 35n 0.15, 0.02 0.09, 0.11 0.19, 0.22 0.43 -54, 76 -41,69 -41, 66 -0.575n and 35n 0.19, -0.06 0.07, 0.11 0.17, 0.26 0.17, 0.41 -38, 94 -45, 75 -44, 75.5 –5s and 35s 0.81 0.76 0.75 0.82 32 31.5 29 2715s and 35s 0.83 0.71 0.75 0.83 22.5 19.5 15 1725s and 35s 0.91 0.89 0.92 0.94 5.5 2.5 3 435s and 35s 1 1 1 1 0 0 0 045s and 35s 0.67 0.84 0.83 0.91 2 -3.5 -2 -155s and 35s 0.43 0.41 0.45 0.73 -14 -7 -8.5 -1.575s and 35s 0.33, 0.47 0.24, 0.26 0.31, 0.24 0.58, 0.33 -56, 86 -41.5, 74 -17, 61 – to comment on these differences without the detailed analysis on shorter timescales. The scatter and gaps in the data results significant variations in values ofphase lag on shorter time scales. The average phase difference is ≈ ≈ ◦ and 25 ◦ latitude belts in the northernhemisphere. This value of phase lag indicates a speed of the activity shift is ≈
19 m s − at the beginning Solar Cycle in these two belts, from higher to lowerlatitude in the northern hemisphere. Then speed slowed down to 5.4 m s − between 25 to 15 ◦ belts and further slowed to 2.7 m s − near the end phase ofcycle. But in the southern hemisphere these values are ≈ − for the corresponding latitude belts. These values imply that shift in activityfrom mid to lower latitude in northern and southern hemispheres is not exactlysymmetric. At the same time these values indicate that the activity shifts at afaster rate at the beginning of the Solar Cycle in higher to mid latitude belts SOLA: MS_rev2_0902.tex; 10 February 2021; 1:38; p. 18 eridional Flow During Solar Cycles 15 – 23 and then at a slower rate in lower latitude belts as the cycle progresses. Thesefindings of maximum speed occurring around 35 ◦ and an average amplitude ofabout 15 m s − agree with those of Hathaway and Rightmire (2011), Imada et al. (2020) and others. The differences in the shift of activity may be due tolatitude dependence of flux emergence, cycle variations, difference in meridionalflow velocities in north-south hemispheres.These findings need to be confirmed by using data of individual Solar Cycleand of better quality. Due to scatter in the data we had to take averages overlonger period of time. The shift of the poloidal field towards polar region isnot clear as the activity around 50 ◦ belt is very low and scatter in the data.But it is clear that activity near polar region around 75 ◦ is anti-correlated withthe activity at mid-latitudes. We have shown that it is possible to study themeridional flows using the Ca-K images and analysing the data as function oflatitude and time. The results of this study will be very useful to understanddynamics of the Sun. Disclosure of Potential Conflicts of Interest
The authors declare that theyhave no conflicts of interest.
Acknowledgments
We would like to thank the referee for the valuable comments. Wethank the numerous observers who has made the observations over a century and kept the datain good environment conditions. We acknowledge the enormous work done by the digitizationteam lead by Jagdev Singh. PD thanks the CSIR, New Delhi for their support. RJ acknowledgesthe Department of Science and Technology (DST), Government of India for the INSPIREfellowship.
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