Latitudinal profiles of the photospheric magnetic field for solar cycles 19-21

TL;DR

This study analyzes how the latitudinal distribution of photospheric magnetic fields varies with strength during solar cycles 19-21, revealing significant changes at specific field strengths and hemispheric asymmetries.

Contribution

It provides detailed latitudinal profiles of magnetic fields across different strengths and identifies key variations at specific thresholds, enhancing understanding of solar magnetic activity.

Findings

Magnetic field distribution changes notably at 5 G, 15 G, and 50 G.

Flux decreases monotonically with increasing field strength for B>5 G.

Weak fields (<5 G) are in antiphase with stronger fields in both location and timing.

Abstract

For groups of photospheric magnetic fields differing in strength the time averaged synoptic maps were obtained on the basis of the National Solar Observatory Kitt Peak data (1976-2003). The latitudinal profiles of magnetic field fluxes were considered separately for each 5 G interval of the field strength B. The changes both of the profile maxima and of the latitudinal localization of these maxima were studied. The obtained results show that the latitudinal distribution of magnetic fields considerably changes at certain values of the field strength: 5 G, 15 G, and 50 G. The magnetic flux for field groups differing in strength, monotonically decreases with increase of strength for all fields with strength B>5 G. For these fields the fluxes of the southern hemisphere exceed fluxes of the northern hemisphere. A very special group is represented by the weakest fields B<5 G, which are in antiphase both in localization and in time changes with stronger fields.

Full text

1 Introduction

The interest to the latitudinal distribution of solar activity is connected with such important problems as displacement of sunspot zones during 11-year solar cycle, periodic appearance of polar faculae in high latitudes, development of polar coronal holes, etc. (see review and references in (Hathaway, 2015). The most studied feature among these phenomena is the latitudinal distribution of sunspots and its change during 11-year solar cycle. According to Spörer’s law the mean latitude of sunspot groups gradually decreases from the beginning to the end of the solar activity cycle, i.e. sunspot zone moves from mean heliographic latitudes towards equator of the Sun. It was shown by Li, Yun, Gu (2001), that the latitude migration-velocity of sunspot groups is maximal at the beginning of a solar cycle, decreasing later in process of solar cycle development. The width of the sunspot zone and its connection to the solar cycle was studied in (Ivanov, Miletskii, Nagovitsyn, 2011; Miletsky, Ivanov, Nagovitsyn, 2015).

Another manifestation of solar activity concentrating around certain interval of heliolatitudes, are polar faculae (see, for example, Sheeley, 2008). Polar faculae appear at higher latitudes than sunspots and precede sunspots in their time development approximately by 6 years (Makarov, Makarova, 1996). Another research (Deng et al., 2013) has shown that polar faculae lead sunspot number by 52 months. Polar faculae measurements display good correlation with polar magnetic fields (Muñoz-Jaramillo et al., 2012).

All the wealth and diversity of the forms of solar activity phenomena are connected to the magnetic fields of the Sun differing both in strength and in localization on the Sun’s surface. The evolution of zonal distribution of the solar magnetic field was studied on the basis of Wilcox Solar Observatory (WSO) magnetograms (Hoeksema, 1991). It was shown, that the total magnetic flux is intimately connected to a level of activity and its distribution is similar to the Maunder butterfly diagram, presenting latitude of sunspot occurrence versus time. The variations of magnetic fields in time and latitude were considered in (Akhtemov et al., 2015). The strong difference of variations of a total magnetic flux at low and high latitudes is revealed. The analysis of development of latitudinal distributions for magnetic fields with different strengths in solar cycles 12–23 has shown, that the width of a sunspot zone is intimately connected with the total magnetic flux of sunspots (Miletsky, Ivanov, Nagovitsyn, 2015).

In our paper (Vernova, Tyasto, Baranov, 2016) the latitudinal distribution of magnetic fields was studied on the basis of synoptic maps of the photospheric magnetic field obtained by the Kitt Peak National Observatory (1976–2003). To consider the latitudinal distribution of magnetic fields we used the method of synoptic map superposition. As a result one average synoptic map of the magnetic field module for all period of 1976–2003 was constructed. Averaging magnetic field over the longitude, we received a latitudinal profile of magnetic flux of the Sun for three solar cycles. Thus, the stable features of the latitudinal distribution of magnetic field appear which are present during several solar cycles. In the averaged latitudinal profile two areas of magnetic field concentration were detected: one at the sunspot zone latitudes and the other at the polar faculae zone. The flux in the sunspot zone considerably exceeds that in the polar faculae zone. It is necessary to note, that the latitudinal profile in all range of latitudes has some lower threshold of the flux $~{}1.3\times 10^{21}Mx$. The maximum flux in the sunspot zone exceeds this threshold value approximately by 5 times. The results obtained by us display approximately symmetrical latitudinal distribution of the magnetic field module relative to helioequator. However the flux of the southern hemisphere, averaged for three solar cycles, proved to be somewhat higher than the flux of the northern hemisphere.

The main purpose of this research was to observe features of a latitudinal distribution of magnetic fluxes for different values of the magnetic field strength. Special attention was given to the distribution of weak magnetic fields ($B<50$ G). For these field strengths the most significant differences in latitudinal profiles of photospheric magnetic fields are observed.

2 Data and method

In this study synoptic maps of the photospheric magnetic field produced by the National Solar Observatory (NSO Kitt Peak) for 1976–2003 were used (http://nsokp.nso.edu/). Synoptic maps were obtained with the resolution of $1^{\circ}$ in longitude (360 steps) and 180 equal steps in the sine of the latitude. Thus, each map contained $360\times 180$ pixels of magnetic field strength in Gauss.

In order to underline the steady features of a latitudinal distribution, synoptic maps were averaged for three solar cycles. For this purpose we used the method of synoptic map superposition, which has allowed to receive one average synoptic map for all period of 1976–2003. Only absolute values of the magnetic fields were considered without taking into account their polarity.

To estimate the contribution of fields of different strength to the total magnetic flux, each synoptic map before summing was transformed in such a manner that only pixels in a chosen interval of field strength were left, while the remaining pixels were replaced by zeros. Thus, we obtain a summary map for three solar cycles for each particular interval of magnetic field strength. The number of pixels distinct from zero, displayed the ratio of particular group of fields in the total flux of the magnetic field.

Synoptic maps for different intervals of a field strength were constructed separately: from [math] G up to $5$ G, from $5$ G up to $10$ G, etc. By averaging these maps along the heliolongitude we obtained a latitudinal profile of magnetic field in a selected strength interval.

3 Results and discussion

In Figure 1a latitudinal profiles of the magnetic flux, averaged for solar cycles 21–23, are presented for three intervals of the field strength: $5-10$ G, $10-15$ G, and $20-25$ G. The latitudinal profile for fields of $5-10$ G differs significantly in its form from the profiles of stronger fields (Figure 1a): the flux is almost constant from $-60^{\circ}$ up to $+60^{\circ}$ and does not fall anywhere below $0.39\times 10^{21}Mx$. At high latitudes the magnetic flux increases more than twice as compared with the lowest limit. In spite of the approximate constancy of the magnetic flux at middle latitudes, some small increase of flux at the sunspot zone latitudes can be seen already in the latitudinal profile. With further increase of strength ($B>10$ G) the latitudinal profile starts gradually to change its form. At low latitudes the concentration of magnetic fields appears more distinctly in the sunspot zone. At high latitudes the maximum of the flux moves from poles to the polar faculae zone. While for the group of $10-15$ G the flux at high latitudes considerably exceeds the flux in the sunspot zone, with the increase of the field strength up to $20-25$ G the fluxes in the sunspot zone and in the polar faculae zone became nearly equal (Figure 1a).

Other feature of latitudinal profiles of weak fields is the presence of several regions of minimum field concentration, which appear more and more clearly with increase of the field strength. One of the flux minima is observed at near equatorial latitudes, others two - at latitudes $40^{\circ}-60^{\circ}$ in each of hemispheres. The position of the equatorial minimum is constant for all groups of fields, while in the range of latitudes $40^{\circ}-60^{\circ}$ the displacement of the minima occurs with the increase of the field strength (straight red lines in Figure 1a).

For groups of fields $25-30$ G, $35-40$ G and $45-50$ G (Figure 1b) all latitudinal profiles have nearly the same form with two maxima in each hemisphere: in the sunspot zone (sp) and in the polar faculae zone (pf) at latitude about $70^{\circ}$. The maximum of the flux in the sunspot zone considerably exceeds the flux in the polar faculae zone. For the strength interval $45-50$ G the flux in the polar faculae zone is practically equal to zero. Thus, the value of the field strength $50$ G can be considered as the boundary above which latitudinal profile displays only the sunspot zone. It should be noted, that in both zones with the increase of field strength the maximum of the flux will decrease monotonically.

In Figure 2 the relation of the flux maximum on the magnetic field strength is shown for northern and southern hemispheres. We consider separately: (a) low latitudes from $0^{\circ}$ up to $40^{\circ}$ and (b) high latitudes from $40^{\circ}$ up to a Sun’s pole.

Common features of the low latitude fields (Figure 2a) and of the high latitude fields (Figure 2b): the continuous decay of the flux maximum with increase of the magnetic field strength is seen in both cases, the flux of the southern hemisphere exceeding slightly the flux of the northern hemisphere. With the magnetic field strength increase the speed of the flux falling is slowed down. In comparison with fields of $5-10$ G the magnetic flux for fields of $45-50$ G decreases by 3 times (Figure 2a).

Difference between fluxes at low (Figure 2a) and at high latitudes (Figure 2b): the largest value of the high latitude flux, which corresponds to the group of fields $5-10$ G, is twice that of the low latitudes. While for the strongest fields at low latitudes (group of $45-50$ G) the flux falls only down to a level of $0.17\times 10^{21}Mx$, for high latitudes flux value drops almost down to zero with the increase of the field strength.

Latitude of localization of the profile maximum depending on magnetic field strength is shown in Figure 3 for northern and southern hemispheres. For low latitudes (Figure 3a) the position of maxima of two hemispheres coincide for the weak fields of $5-10$ G and $10-15$ G. Then northern and southern hemispheres develop differently, but the latitudes change insignificantly and vary between $15^{\circ}$ and $22^{\circ}$. Thus, the maxima of the flux for these fields are in sunspot zones. It can be seen for high latitudes (Figure 3b), that the weak fields $5-10$ G and $10-15$ G are localized at the highest latitudes and, apparently, are connected with coronal holes. Beginning from strengths of $15-20$ G both hemispheres display one dominating latitude around $70^{\circ}$ which is connected to localization of polar faculae at this latitude.

It is of interest to consider latitude regions, where the magnetic flux is minimal. The change of value and localization of the flux minimum is shown in Figure 4 depending on the field strength. The minimum of a latitudinal profile (Figure 4a) drops down with increase of the field strength in the same way as the value of a maximum (Figure 2a,b). The monotonic decrease of the flux with increase of the magnetic field strength is seen. For the whole strength range the flux of the southern hemisphere exceeds the flux of the northern hemisphere slightly. The displacement of latitudinal profile minimum in latitude range of $40^{\circ}-60^{\circ}$ (Figure 4b) is observed. The flux minimum for fields of $5-10$ G appears at the latitude $\sim 45^{\circ}$. As the field strength increases, the minimum is displaced to higher latitudes and for fields of $25-30$ G the minimum occurs at latitudes $56^{\circ}$ (southern hemisphere) and $58^{\circ}$ (northern hemisphere).

It is noteworthy, that latitudinal profiles for fields of $5-10$ G, $10-15$ G etc. form the set of similar curves, whose shapes gradually change in the course of the field strength increase, so that the curves do not intersect anywhere (Figure 1a,b). The weakest fields with strength $B<5$ G form a very special group, which is at the same time and the most numerous group. Pixels with a field strength of $0-5$ G for period 1976–2003 occupy more than 60 % of the solar surface, while strong fields ($B>50$ G) occupy only 3.3 % of the surface.

While studying the weakest magnetic fields ($B<5$ G) the influence of the instrumental noise becomes essential. The high-latitude measurements are less reliable because the magnetic field is radial in the photosphere and has only a small component in the line-of-sight direction where the instrument is sensitive. According to (Harvey, 1996), the instrumental noise level in the polar regions in NSO/KP maps is a function of latitude and is on the order of $2$ G per map element. The influence of these measurement errors is diminished by the data treatment we used here. To obtain latitudinal profiles, synoptic maps were averaged in longitude and then averaged as a function of time for nearly three cycles. With this averaging the noise level is reduced significantly.

In Figure 5a a comparison of the latitudinal profile of the weakest fields ($B<5$ G) with a profile of stronger fields is carried out (as an example the latitudinal profile of $15-20$ G fields is chosen). For the latitudinal profile of $15-20$ G, flux concentration in sunspot and polar faculae zones is observed, which is characteristic for all groups of fields with strength above $15$ G. The magnetic fields with strength $B<5$ G develop in antiphase and display minima of the flux both at latitudes of the sunspot zones and at latitudes of the polar faculae zones. These fields concentrate at latitudes from $40^{\circ}$ up to $60^{\circ}$ and in equatorial region $\pm 5^{\circ}$. The maxima of the weakest fields are located at latitudes $53^{\circ}$ and at the equator. Thus, two latitudinal profiles ($15-20$ G) and ($B<5$ G) are the reverse of each other, with correlation coefficient of two curves $R=-0.94$.

Not only the latitudinal profile for the weakest fields ($B<5$ G) is in antiphase to the profile of stronger fields, but also time course of these fields develops in antiphase with strong fields. In Figure 5b the time course of magnetic flux for fields with strength $B>5$ G is shown. The pronounced 11-year cycle is seen. The maximum of the flux coincides with the second Gnevyshev maximum.

In Figure 5c the time course for fields of $B<5$ G is shown. It can be seen, that weak fields develop in antiphase with stronger fields (coefficient of correlation $R=-0.96$), with the maximum values of flux approximately by the order lower, than for strong fields. This result is in agreement with results obtained on the basis of SOHO/MDI data for 1996–2011, which show that magnetic structures with a weak flux display anticorrelation with sunspots (Jin, Wang, 2014).

4 Conclusions

The form of the latitudinal profile changes as the magnetic field strength increases and these changes follow some regularity. The absolute flux value decreases both at maximum and at minimum of the profile along with the increase of the field strength. The localization of the profile extrema also depends on the field strength. While the latitude of the profile maximum does not change significantly, the minimum of the flux monotonically moves towards higher latitudes with increase of the magnetic field strength.

The obtained results show that the latitudinal distribution of magnetic fields considerably changes at certain values of the field strength: $5$ G, $15$ G, and $50$ G. The magnetic flux for field groups differing in strength, monotonically decreases with increase of strength, while the fluxes of the southern hemisphere exceed fluxes of the northern hemisphere. A very special group is represented by the weakest fields $B<5$ G, which are in antiphase both in localization and in time changes with stronger fields.

5 Acknowledgements

NSO/Kitt Peak magnetic data used here are produced cooperatively by NSF/NOAO, NASA/GSFC and NOAA/SEL.