Principal Component Analysis of the Latitudinal and Longitudinal Structure of the Photospheric Magnetic Cycle

Details Principal Component Analysis of the Latitudinal and Longitudinal Structure of the Photospheric Magnetic Cycle Principal Component Analysis of the Latitudinal and Longitudinal Structure of the Photospheric Magnetic Cycle

May 2004

adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=2004aas...204.3708l&link_type=abstract

American Astronomical Society Meeting 204, #37.08; Bulletin of the American Astronomical Society, Vol. 36, p.710

Astronomy and Astrophysics

Astronomy

Scientific paper

We average magnetic fields in NSO synoptic maps over longitude and bin the result by sin(latitude). Also, we average over a band of latitudes and bin by longitude. A time stack of one-dimensional latitude "images" resembles the Maunder butterfly diagram. Time stacks of longitude "images" can be re-mapped to arbitrary rotation periods.
Principal component analysis recombines images in a stack into mutually orthogonal "empirical orthogonal functions" (EOFs). The EOFs are ordered by how well each correlates with the full set of images. The principal components (PCs) give the evolution of each EOF as a function of any ordering parameter, such as time. The original data can be wholly or partially reconstructed from subsets of the EOFs and their PCs.
Our latitudinal EOFs have a few leaders whose PCs show both the 11/22-year cycle and repeating substructure. Following are EOFs whose PCs show the cycle but no repeated substructure. Next are EOFs with small scale structure independent of the cycle. The least correlated EOFs contain high latitude, mostly unipolar fields. We suggest associating these four subsets of the EOFs with, respectively, global dynamo toroidal fields, turbulently disordered structures fed by the toroidal fields, a possible local surface dynamo process, and a global poloidal component.
We also studied a stack of longitudinal images of fields that were averaged over latitude between N25 and N35 degrees. Two especially active longitudes 180 degrees apart rotate with a period of 27.8 days. Structure at these longitudes dominates the leading EOFs. The corresponding PCs are active over the whole span of the data.
This work was supported by NASA Grant NAG5-10880. NSO/Kitt Peak data used here are produced cooperatively by NSF/NOAO, NASA/GSFC, and NOAA/SEL.

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