The Physical Content of the Leading Orders of Principal Component Analysis of Spectral Profiles

Details The Physical Content of the Leading Orders of Principal Component Analysis of Spectral Profiles The Physical Content of the Leading Orders of Principal Component Analysis of Spectral Profiles

May 2002

adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=2002apj...570..379s&link_type=abstract

The Astrophysical Journal, Volume 570, Issue 1, pp. 379-386.

Astronomy and Astrophysics

Astronomy

15

Methods: Statistical, Sun: Activity, Sun: Atmospheric Motions, Sun: Magnetic Fields, Sun: Sunspots

Scientific paper

We consider the principal component analysis (PCA) method of expanding Stokes intensity and net polarization profiles in terms of eigenfunctions (or principal components) of the spectral covariance matrix. The expansion is ordered by the magnitude of the relevant eigenvalue from largest to smallest. We find that the ordering represents a perturbation expansion. This allows us to examine the physical content of the first few orders of the basis set for 40,000 profiles for each Stokes parameter for a solar active region. For the intensity profile, we find that the expansion represents a Taylor series with the highest ranked, or first, eigenfunction being the zeroth order term, the second as the (scaled) first derivative of the zeroth term, and the third as the (scaled) second derivative term. Thus, we can derive a velocity from the coefficients of the first derivative term and a magnetic splitting parameter from those of the second using the standard velocity perturbation and weak-field expansion. For the net polarization profiles, we find that the zeroth order terms yield, using the weak-field expansion, the vector magnetic field. A comparison with a Stokes profile fitting inversion shows that the thus-estimated velocity and magnetic parameters are in good agreement with the more time-consuming profile fitting values, but do show a roll-off, or saturation, for sufficiently large values. We also find that the bright quiet-Sun points have an upflow signature, while the dark regions have a downflow-one in good agreement with that derived by traditional analysis.

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