Flux transport

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, L_i and L_f respectively, in time intervals ∆t=t_n-t_n-1, then one needs to estimate net solar flux between L_i and L_f at t_n-1and t_n. 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. 0^o-10^o, 0^o-20^o, 0^o-30^o, 0^o-40^o 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 0^o-10^o. 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 0^o-10^o. 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 0^o-20^o, 0^o-30^o and 0^o-40^o 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 0^o-20^o for solar cycles 21-23.

Fig 6.  Show temporal variation in flux transport in latitude range 0^o-20^o for solar cycles 21-23.

Fig 7.  Show temporal variation in net solar flux in latitude range 0^o-30^o for solar cycles 21-23.

Fig 8.  Show temporal variation in flux transport in latitude range 0^o-30^o for solar cycles 21-23.

Fig 9.  Show temporal variation in net solar flux in latitude range 0^o-40^o for solar cycles 21-23.

 

Fig 10.  Show temporal variation in flux transport in latitude range 0^o-40^o 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 0^o-10^o, 0^o-20^o, 0^o-30^o, 0^o-40^o 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 0^o-10^o. 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 0^o-20^o, 0^o-30^o and 0^o-40^o respectively.

Fig 11.  Show temporal variation in flux transport (in pink) in latitude range 0^o-20^o for solar cycles 21-23.

Fig 12.  Show temporal variation in flux transport (in pink) in latitude range 0^o-20^o for solar cycles 21-23. 

Fig 13.  Show temporal variation in flux transport (in pink) in latitude range 0^o-30^o for solar cycles 21-23. 

  

Fig 14.  Show temporal variation in flux transport (in pink) in latitude range 0^o-40^o for solar cycles 21-23.