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

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

May 2001

adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=2001aas...198.0303s&link_type=abstract

American Astronomical Society, 198th AAS Meeting, #03.03; Bulletin of the American Astronomical Society, Vol. 33, p.786

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We consider the PCA (Principle Component Analysis) method of profile analysis introduced by Ref (1). In this method one constructs a covariance matrix Cij given by the product of the profile amplitudes at wavelengths λ i and λ j averaged over all profile samples (either over space or time). The matrix is 'diagonalized' and ordered by Singular Value Decomposition. The resulting orthonormal eigenfunctions over wavelength space are then used as a basis for the expansion of the observed profiles at each space(time) point. The eigenvalue ordering is by magnitude of the mean square over space(time) of the expansion coefficients and is given by the product of the frequency of occurrence of the particular eigenfunction and its intrinsic mean square amplitude. An error based truncation scheme yields a coefficient set which is a compression of the original data set. We have applied the PCA method to the 40,000 profiles for each Stokes component for a Solar active region. In the case of the intensity profile we find that the expansion appears to be similar to a Taylor series with the 0th efunction being the zero order term, the 1st efunction as the first derivative of the zero term and the 2nd efunction as the second derivative term. Thus we derive a line-of-sight velocity from the coefficients of the first derivative term and a magnetic signature, using the weak field Milne-Eddington approximation, from the second. A comparison with a Stokes profile 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" for sufficiently large values. One also finds that the bright 'quiet' Sun points have an upflow while the dark have a downflow similar to that derived by other analysis. 1) Rees, D., López Ariste, A., Thatcher, J. & Semel, M. 2000, A & A, 355, 759 The National Center for Atmospheric Research is sponsored by the National Science Foundation.

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