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 10o solar latitude bin
starting from latitude 0o to
70o. 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. 0o-10o
Both the net solar flux and the flux transport in latitude bin, 0o-10o, 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 ± 35o 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, 0o-10o, 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, 0o-10o, 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, 0o-10o, 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. 10o-20o
The net solar flux and the flux
transport in latitude range, 10o-20o, are shown respectively in
Figures 17 and 18 for both northern and southern hemispheres. The net solar flux in this case, unlike
latitude bin 0o-10o, 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 (0o-10o and 10o-20o), 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, 0o-10o, 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, 10o-20o, 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. 20o-30o
The temporal variation in the net solar flux and the flux
transport in latitude bin 20o-30o
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, 20o-30o, 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, 20o-30o, 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. 30o-40o
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 (10o-20o and 20o-30o).
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, 30o-40o, 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, 30o-40o, 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. 40o-50o
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, 30o-40o, 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, 40o-50o, 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 , 40o-50o, 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. 50o-60o
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, 50o-60o, 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, 50o-60o, 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. 60o-70o
The net solar flux and the flux
transport in latitude bin, 40o-50o, 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, 60o-70o,
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, 60o-70o, 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, 50o-60o, 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.
