Source of a Prominent Poleward Surge During Solar Cycle 24

Abstract

As an observational case study, we consider the origin of a prominent poleward surge of leading polarity, visible in the magnetic butterfly diagram during Solar Cycle 24. A new technique is developed for assimilating individual regions of strong magnetic flux into a surface-flux transport model. By isolating the contribution of each of these regions, the model shows the surge to originate primarily in a single high-latitude activity group consisting of a bipolar active region present in Carrington Rotations 2104 – 05 (November 2010 – January 2011) and a multipolar active region in Rotations 2107 – 08 (February – April 2011). This group had a strong axial dipole moment opposed to Joy’s law. On the other hand, the modelling suggests that the transient influence of this group on the butterfly diagram will not be matched by a large long-term contribution to the polar field because it is located at high latitude. This is in accordance with previous flux-transport models.

Appendix: Assimilation Algorithm

To assimilate new magnetogram flux, we first process each individual synoptic magnetogram g(θ,ϕ) to determine a list of strong-flux regions, using the following procedure:

• i) Correct any overall net flux imbalance in g by subtracting an equal amount from each pixel.

• ii) Take the absolute value to obtain a new map f(θ,ϕ)=|g(θ,ϕ)|.

• iii) Smooth f with a Gaussian filter (standard deviation σ) to obtain $\bar{f}$. The purpose of this step is primarily to merge the positive and negative polarities of individual bipolar active regions.

• iv) Identify connected regions [R _i ] where $\bar{f}>B_{0}$. These are the new regions that will be inserted into the flux-transport model. (Note that these regions need not be simply connected and could have holes.)

Next, each strong flux region [R _i ] is incorporated into the flux-transport model as follows:

• i) Determine the centroid of R _i in Carrington longitude and choose to insert it on the corresponding day when this longitude crosses the central meridian.

• ii) Determine the net flux imbalance $\Phi_{i}=\int_{R_{i}}B_{r}\,\mathrm{d}\Omega$, where B _r (θ,ϕ) is the pre-existing simulated radial field.

• iii) Modify the observed field [$g|_{R_{i}}$] so that the net flux in R _i matches Φ _i , by subtracting an equal amount from each pixel. This prevents us from introducing a flux imbalance in the insertion step.

• iv) Replace the simulated B _r in R _i with the observed field [$g|_{R_{i}}$].

• v) Recompute the global vector potential [A _θ ,A _ϕ ] to match the modified B _r .

The process is designed to be fully automated, once the controlling parameters σ and B ₀ have been determined. For the GONG synoptic maps, we have found σ=3 pixels and B ₀=15 G to work well. The smoothing width σ should be large enough to merge the two opposite polarities of activity complexes while not merging too many neighbouring complexes. The threshold B ₀ needs to be large enough to include all significant new flux but be above the “noise” level of ephemeral regions (in the smoothed magnetogram), so that only flux at active latitudes is assimilated.

To preserve the field distribution, the net flux in each identified region R _i should be close to that existing beforehand in the simulation. For example, a region emerging in an empty area of the solar surface should have zero net flux. Otherwise, the flux correction will noticeably distort the observed field. This practical consideration requires σ to be sufficiently large and B ₀ to be sufficiently small.