Flux transport in solar hemispheres

For estimation of the flux transport between solar latitudes in time step of one Carrington rotation period, we have used net solar flux measurements, obtained for each Carrington rotations from the magnetic butterfly diagram, instead of the smoothed net solar flux measurements. The flux transport in both the northern and southern hemispheres is obtained for each 10^o solar latitude bin starting from latitude 0^o to 70^o.  The flux transport, thus estimated for different latitude bins, show how transport of the net flux occurs on the sun and since the flux transport on solar surface depends on meridional flow, surface diffusion and latitudinal emergence of the photospheric flux, one can infer about temporal variation in these parameters.

  

1. 0^o-10^o

 

Both the net solar flux and the flux transport in latitude bin, 0^o-10^o, are shown respectively below in Figures 15 and 16. In both Figures, the pink and blue solid lines respectively represent temporal variation of these measurements in the northern and southern solar hemispheres. The polarity of leading flux in the northern hemisphere is shown by + or - at top in pink (parameters in the north are represented in pink and the south in blue). The net solar flux in this latitude bin (Fig 15) is less in beginning because sunspots appear at latitude of ± 35^o during initial phase of solar cycle. Thereafter, the net solar flux rises up at a slower rate as the flux is transported from higher latitudes and at solar cycle maximum, the net flux attains the peak. Afterwards, in the declining phase of cycle, the net flux deepens down because of decline in emergence of active regions and rise in flux cancellation at the equator.

Fig 15.  Show the temporal variation in the net solar flux in latitude range, 0^o-10^o, in northern and southern hemispheres marked in pink and blue respectively for solar cycles 21-23. Also, the temporal variations in sunspot number are shown in grey solid line for corresponding periods. The polarity of leading flux in the northern hemisphere is marked by positive or negative at top in pink. The vertical lines demarcate solar minimum periods differentiating solar cycles.

Fig 16.  The temporal variation in the flux transport in latitude range, 0^o-10^o, is shown for the northern and southern hemispheres in pink and blue respectively. Also, the variation in sunspot numbers in time is shown in solid grey line indicating the solar activity in a solar cycle.

The flux transport in Figure 16 shows that the flux transport in latitude bin, 0^o-10^o, is less at the start. Then, it rises up slowly attending the peak at solar maximum. As the solar cycle enters into the declining phase, the flux transport slowly decreases until a fresh cycle starts which indicates that the flux cancellation at the equator is less in begin and then increases as solar cycle progresses. Afterwards, the flux cancellation decrease which is clearly followed up in the last three solar cycles viz. cycles 21, 22 and 23. The comparison between these three cycles reveals a comparatively weaker and longer flux cancellation at the end of cycle 23.

2. 10^o-20^o

 

The net solar flux and the flux transport in latitude range, 10^o-20^o, are shown respectively in Figures 17 and 18 for both northern and southern hemispheres.  The net solar flux in this case, unlike latitude bin 0^o-10^o, shows a faster rise and attains the peak near solar maximum. The increase in emergence of active regions in this latitude bin with time actually contributes for this behavior of the net solar flux. We also see a comparatively slower rate of decline in the net flux as the sun goes to the solar minimum phase. But the flux transport in this latitude range, as depicted in Figure 18, is found comparatively more to the previous latitude bin during whole period of time. The comparison between three cycles viz. cycles 21, 22 and 23 reveals about a continuous weaker flux transport in this regime towards solar minimum of cycle 23.

In both the latitude bins (0^o-10^o and 10^o-20^o), polarity of the net solar flux in both solar hemispheres is in accordance with polarity of the leading flux.

Fig 17.  Show the temporal variation in the net solar flux in latitude range, 0^o-10^o, for the northern and southern hemispheres marked in pink and blue respectively for solar cycles 21-23.

Fig 18.  The temporal variation in the flux transport in latitude range, 10^o-20^o, is shown for the northern and southern hemispheres in pink and blue respectively. Also, the variations in sunspot numbers in time is shown in solid grey line indicating the solar activity in a solar cycle.

3. 20^o-30^o

The temporal variation in the net solar flux and the flux transport in latitude bin 20^o-30^o are respectively shown in Figures 19 and 20 both in northern and southern hemispheres. The net solar flux as depicted in Figure 19 shows that it starts to increase at a medium rate in comparison to lower latitude bins and polarity of the net flux doesn’t follow polarity of the leading flux. It randomly changes to either positive or negative polarity without any certainty. We see new sunspots emerging in this regime at the beginning of solar cycle and the leading part of the sunspots move towards lower latitudes whiles the trailing ones move to higher. Simultaneously, as cycle progresses, trailing fluxes from latitudes below congregates in this latitude bin. So we see both polarity fluxes dominating at different instant of time that actually results in the random changes in polarity in this latitude range.

Fig 19.  Show the temporal variation in the net solar flux in latitude range, 20^o-30^o, in the northern and southern hemispheres marked in pink and blue for solar cycles 21-23.

Fig 20.  The temporal variation in the flux transport in latitude range, 20^o-30^o, is shown for northern and southern hemispheres in pink and blue respectively. Also, the variation in sunspot numbers in time is shown in solid grey line indicating the solar activity in a solar cycle.

As we move to the flux transport in Figure 20, we can see an early rise in the flux transport from the initial phase of solar cycle that shows the flux cancellation starts a little earlier comparing to lower latitude bins. But strength wise, the flux transport in this case is less. When we verify it in the last three solar cycles, it is almost comparative in each cycle. But we find the flux transport is more in beginning of the rising phase of cycle 22 and less in the declining phase of cycle 23.

4. 30^o-40^o

The net solar flux and the flux transport are shown respectively in Figures 21 and 22 for both the northern and southern hemispheres. The net solar flux, as depicted in Figure 21, shows that polarity of the net flux is now opposite to that of the leading flux. This is the accumulation of the trailing fluxes from regions below that actually changes polarity of the net flux in this regime. The Figure also reveals sudden change in polarity of the net flux around solar maximum. As we have seen in lower latitude bins, here also the flux transport changes abruptly with a faster rise to the peak and then decline. The fact to be noted that the flux transport is comparatively less and decline at a slower rate to that of lower latitude bins (10^o-20^o and 20^o-30^o).

Again, if we compare the flux transport between the three solar cycles, it reveals that the flux transport is declining for a longer duration in cycle 23.

Fig 21.  Show the temporal variation in the net solar flux in latitude range, 30^o-40^o, in the northern and southern hemispheres marked in pink and blue respectively for solar cycles 21-23.

Fig 22.  The temporal variation in the flux transport in latitude range, 30^o-40^o, is shown for the northern and southern hemispheres in pink and blue respectively. Also, the variation in sunspot numbers in time is shown in solid grey line indicating the solar activity in a solar cycle.

5. 40^o-50^o

The net flux and the flux transport are shown respectively in Figures 23 and 24 for both the north and south. Similar to latitude bin, 30^o-40^o, polarity of the net flux is opposite to that of leading flux (see in Figure 23) but sometimes random changes occur in polarity of the net flux. In particular, the net flux in solar cycle 22 shows more random changes around solar maximum with increase in its strength. In comparison to lower latitude bins, the strength of the net flux, in every solar cycle, is comparatively less. 

Fig 23.  Show the temporal variation in the net solar flux in latitude range, 40^o-50^o, for the northern and southern hemispheres marked in pink and blue respectively for solar cycles 21-23.

The flux transport (see Figure 24) is weakened at all time that shows much more flux cancellation in lower latitudes, so a less amount of the flux is transported to this regime. Also, the spikes during cycle 22, as seen in Figure 24, show transport of a large amount of flux compared to other two cycles viz. cycles 21 and 22.

Fig 24.  The temporal variation in the flux transport in latitude range , 40^o-50^o, is shown for the northern and southern hemispheres in pink and blue respectively. Also, the variation in sunspot numbers in time is shown in solid grey line indicating the solar activity in a solar cycle.

6. 50^o-60^o

Figures 25 and 26 represent the net solar flux and the flux transport respectively for both the northern and southern hemispheres. The net solar flux in this latitude bin, as depicted in Figure 25, actually represents the polar cap flux. At the initial phase, we see the polar cap flux of previous cycle having polarity same to that of the leading flux. As solar cycle progresses, the polar flux strength decreases down and around solar maximum, polarity of the net flux reverses. Actually, the trailing fluxes transport from latitudes below and on reach this regime; they cancel the old polar cap flux to produce the new flux with opposite polarity. If we compare the polar cap field strength in the three cycles, we clearly see a comparatively weaker polar cap flux towards the end of solar cycle 23.

We don’t see much flux transport (see Figure 26) in this regime since the rate of diffusion of flux elements is more to the rate of meridional flow speed. It eventually accumulates flux here. The comparison between the solar cycles reveals that in cycle 21, the flux transport shows a sharp peak in the northern hemisphere around solar maximum suggesting an increase in the rate of flux transport. Also, we see similar peak both in the north and south in cycle 22, but we don’t find such peaks in cycle 23.

Fig 25.  Show the temporal variation in the net solar flux in latitude range, 50^o-60^o, for the northern and southern hemispheres respectively marked in pink and blue for solar cycles 21-23.

Fig 26.  The temporal variation in the flux transport in latitude range, 50^o-60^o, is shown for northern and southern hemispheres in pink and blue respectively. Also, the variation in sunspot numbers in time is shown in solid grey line indicating the solar activity in a solar cycle.

7.      60^o-70^o

The net solar flux and the flux transport in latitude bin, 40^o-50^o, are respectively shown in Figures 27 and 28 for both the north and south. The temporal variation in net solar flux in this latitude bin, as depicted in Figure 27, show actually the polar flux variation in time. The temporal variation in the polar flux show that polarity of the polar flux reverses at around solar maximum causing polar reversal. Also, the strength of polar flux in cycle 23 is comparatively weaker than cycles 21 and 22. 

Fig 27.  Show the temporal variations in the net solar flux in latitude range, 60^o-70^o, in northern and southern hemispheres marked in pink and blue for solar cycles 21-23.

Fig 28.  The temporal variation in the flux transport in latitude range, 60^o-70^o, is shown for the northern and southern hemispheres in pink and blue respectively. Also, the variation in sunspot numbers in time is shown in solid grey line indicating the solar activity in a solar cycle.

The flux transport in Figure 28 show weaker flux transport in each cycle indicating almost no flux cancellation in this latitude range that reveals weaker meridional flow and strong diffusion. As we have seen spikes in the flux transport in latitude bin, 50^o-60^o, we could see a strong spike in cycle 21 during solar maximum but weak spikes in cycle 22 during declining phase of solar cycle. This suggests a large amount of flux transport in cycle 21 around maximum while random occurrence of strong flux transport during certain time periods in cycle 22.