Current Helicity Pattern in Large-scale Photospheric Magnetic Field Chuanyu Wang & Mei Zhang (National Astronomical observatories, Chinese Academy of Sciences)
Introduction: Hemispheric rule of helicity Magnetic fields are observed to emerge into each hemisphere with a preferred helicity sign: Positive in southern hemisphere Negative in northern hemisphere (Image credit: A. Pevtsov) However, most observations are made in active regions.
The same rule exists outside active regions? Pevtsov & Latushko (2000) were the first to study the current helicity of the global Sun outside active regions, by applying a reconstruction technique to full-disk longitudinal magnetograms. Pevtsov & Latushko., 2000, ApJ,528：999-1003 We use the same reconstruction technique, but apply different analysis method which strengthens the results.
Reconstruction of vector magnetic field Suppose that large-scale magnetic fields are evolving rather slowly and the variations of longitudinal magnetic fields within certain time duration are caused by the changing positions on the solar disk only.
Parameters used Differential rotation: Spatial resolution: △S=184’’ Time interval: △t=5 days Reference:Pevtsov & Latushko., 2000, ApJ,528：999-1003
Snapshot heliographic maps Roger K. Ulrich & John E. Boyden., 2006, Sol. phys.,235:17-29 We combine observations of the solar magnetic fields made at different times into a representation of the whole solar surface at a particular specified time which referred to as a “snapshot heliographic map’’ (different from tranditional Carrington map).
Obtained vector magnetic fields Constructed snapshot heliographic maps of Br, Bθ ,Bφfrom top to bottom panels respectively, of one solar rotation (~ CR1914). White background represents positive values of Br (pointing up), Bθ (pointing to the north) and Bφ(pointing to the left) respectively. Contours correspond to ± 2, 4, 8, 16, 32, 64G for Brand Bθ , and ±0.5, 1, 2G for Bφ .
The calculation of current helicity: Our method: calculating the hc map and then averaging along longitudinal direction to get hc profile √ Pevtsov & Latushko (2000) method: averaging along longitudinal direction before calculating hc profile √
Current helicity map The current helicity density hc map. White background represents positive values of hc. Contours correspond to hc= ±0.1,0.2, 0.4, 0.8 ×10-5G2m-1. It is interesting to see that the active region in the southern hemisphere shows a bulk area of negative hc values, which are opposite to that of surrounding regions. This seems to be consistent with the result of Zhang (2006) where strong and weak fields are found to have opposite helicity signs.
Hemispheric rule The profile of averaged hcwith the latitude, using our method. The profile of hcwith the latitude, using Pevtsov & Latushko’s approach. Our plot shows clearly the hemispheric rule, that is, positive helicity sign in the southern hemisphere and negative helicity sign in the northern hemisphere, for all latitudes, including the latitudes below 40 degrees.
A few notes: • We have used only one MDI magnetogram each day, having done none of smoothing between different magnetograms. The plot (right bottom) in Pevtsov & Latushko (2000) was obtained using a few months’ MDI data. • We estimate that our method gives a clearer tendency because: • First, there may be some very useful information of hc contained in the Bθ magnetogram that Pevtsov & Latushko (2000) ignored. We noticed that Bθ are usually larger than Bφand have a strong variation in longitudinal direction. This indicates that the second term may be a larger term in the equation. Pevtsov & Latushko.(2000) Second, our method gives each point on the synoptic map an equal weight whereas theirs are more heavily influenced by strong fields because they averaged the Br and Bφbefore calculating hc. Particularly, the difference may become more evident if the strong and weak fields show opposite helicity signs as reported in Zhang (2006) and also indicated in our hc figure.
Check the dependence of the result on different magnetograms used In the above figure we have used the first magnetogam of each day (solid line in this figure). Now we have used other magnetograms of each day and constructed other 14 different synoptic maps of vector magnetic field and hence get other 14 hcprofiles (dotted lines). They all clearly show the same hemispheric rule.
Check the dependence of the result ondifferent time interval & different sliding square window size The solid line shows the profile using △t=5 days, and the dotted and dashed lines show the profiles using △t=3 and 4 days respectively. The solid line shows the profile using △S=184”, and the dotted and dashed lines show the profiles using △S=90” and 224” respectively. We changed the △t and △S, and get similar profiles. This means that our result is also independent of the parameters we chose.
Conclusion: We concluded that the large-scale magnetic fields show clear and consistent current helicity pattern that follows the established hemispheric rule, that is, positive helicity sign in the southern hemisphere and negative helicity sign in the northern hemisphere. This hemispheric sign pattern is everywhere in the global magnetic field, including weak fields outside active regions, independent of the longitudinal magnetograms and the parameters we have used.