The flux transport on surface of the sun is
magnetic flux that is transported in successive time intervals between solar latitudes.
We have calculated the flux transport on the solar surface between latitudes
using the difference in net solar flux at successive time intervals.
If one wants to estimate the flux transport
between an initial and a final latitude, Li and Lf respectively,
in time intervals ∆t=tn-tn-1, then one needs to estimate
net solar flux between Li and Lf at tn-1and tn.
Thereafter, one has to find the difference in flux between these two time
intervals to calculate flux transport during that time. Repeating the procedure
for successive time intervals, in steps of 1 Carrington rotation covering the available
time span, will enable one to find the temporal variation in flux transport.
Here, magnetic flux values (in units of Maxwell) at different instants of time
have been estimated from the butterfly diagram using averaged magnetic field
values between desired ranges of latitudes and multiplied with corresponding
areas.
Test
We have first conducted a test to see how
temporal variations in flux transport look. We estimated both the net solar
flux and the flux transport for the same range of latitudes viz. 0o-10o, 0o-20o,
0o-30o, 0o-40o for the northern
hemisphere from the magnetic butterfly diagram that has been discussed
previously. Note that flux transport in this case is calculated from the net
solar flux which has been smoothed over 10 solar rotations. Figs. 3 and 4 show (in
pink) respectively, the net solar flux and flux transport in the latitude range
0o-10o. In Fig 3 the temporal variation in actual net
solar flux is shown in pink while the blue lines show temporal variation in
solar flux smoothed over 10 solar rotations. Smoothed sunspot numbers for solar
cycles 21, 22 and 23 are shown in grey indicating the level of solar activity. The
polarity of the leading flux in the northern hemisphere for each cycle is indicated
in the figure since the net flux is also expected to have the same
polarity. The dotted vertical lines
demarcate solar minimum periods.
Fig 3. Shows the temporal variation in the net
(signed) solar flux in the latitude range 00-100 for
solar cycles 21-23. The actual net solar flux for north hemisphere is estimated
from the magnetic butterfly diagram generated using data sets of NSO/Kitt-Peak
synoptic magnetograms is shown in pink, while the blue solid line represents the
magnetic flux value smoothed over 10 solar rotations. Also, the sunspot number
in time is shown, in grey, for corresponding periods for comparison in grey
solid line. The polarity of leading flux in northern hemisphere is indicated at
top. The vertical lines demarcate solar minimum periods
differentiating solar cycles.
In general, if net solar flux variation is
positive and smoothed (without much variation) in a solar cycle then flux
transport variation will be positive till solar flux variation attains a maximum
and afterwards it will be negative. This can be verified from comparing
temporal variation in net solar flux and flux transport (as shown in figures
below) for different latitudes bin.
Fig 4 shows variation of flux transport in
time in latitude range 0o-10o. The flux transport shown (in
pink) is estimated using smoothed net solar flux over 10 solar rotations (shown
in solid blue in Fig 3). The solid blue line in Fig 4 depicts the smoothed
value of flux transport after smoothing over 10 points of flux transport.
Fig 4. Show
temporal variation in flux transport in latitude range 00-100
for solar cycles 21-23 estimated from the smoothed net solar flux for solar northern
hemisphere (in pink). The blue solid line represents smoothed values of flux
transport after smoothing over 10 points. Also variation in sunspot number with
time is shown for solar cycles 21-23 in grey solid line. The polarity of
leading flux in northern hemisphere is shown in positive or negative at top and
the vertical lines demarcate solar minimum periods differentiating solar
cycles.
Similar to Fig 3 and 4, we have shown the same
for latitude ranges 0o-20o, 0o-30o and
0o-40o in Fig 5-10. From Figures 5-10, it is clear that
the temporal variation in flux transport is positive in the rising phase and negative
in the declining phase of smoothed net solar flux variation respectively.
Fig 5.
Show temporal variation in net solar flux in latitude range 0o-20o
for solar cycles 21-23.
Fig 6. Show
temporal variation in flux transport in latitude range 0o-20o
for solar cycles 21-23.
Fig 7.
Show temporal variation in net solar flux in latitude range 0o-30o
for solar cycles 21-23.
Fig 8.
Show temporal variation in flux transport in latitude range 0o-30o
for solar cycles 21-23.
Fig 9.
Show temporal variation in net solar flux in latitude range 0o-40o
for solar cycles 21-23.
Fig 10.
Show temporal variation in flux transport in latitude range 0o-40o
for solar cycles 21-23.
The results will be different, if we estimate the
flux transport from the actual net flux instead of the smoothed net flux. This
time, the flux transport is obtained from actual net solar flux in the same
latitude ranges 0o-10o, 0o-20o, 0o-30o,
0o-40o for the northern hemisphere and the results are
shown in Figures 11-14.
One can see difference in flux transport
comparing Fig 4 and 11 in latitude range 0o-10o. We can
find in Fig 11 that the flux transport is not behaving in the same way as we
have expected (as in Fig 4) rather it is much more fluctuating around zero axis
with variations both in positive and
negative much before the declining phase of net solar flux starts. Note that the
flux transport shown in pink are obtained from net flux that is shown in pink
in Fig 3 instead of deriving from smoothed net flux shown in blue. For a better
comparison, one can see Figures 6 and 12, 8 and 13, 10 and 14 estimated in
latitude ranges 0o-20o, 0o-30o and 0o-40o
respectively.
Fig 11. Show temporal variation in flux transport (in
pink) in latitude range 0o-20o for solar cycles 21-23.
Fig 12.
Show temporal variation in flux transport (in pink) in latitude range 0o-20o
for solar cycles 21-23.
Fig 13.
Show temporal variation in flux transport (in pink) in latitude range 0o-30o
for solar cycles 21-23.
Fig 14.
Show temporal variation in flux transport (in pink) in latitude range 0o-40o
for solar cycles 21-23.
