Revisiting the Moment Method as a Mode Identification Technique
J. De Ridder, G. Molenberghs, C. Aerts
Institute of Astronomy, K.U.Leuven, B-3001 Heverlee, Belgium
Center for Statistics, L.U.C., B-3590 Diepenbeek, Belgium
The moment method is a well known technique, which uses a time series of
the first 3 moments of a spectral line, to estimate the (discrete) mode
parameters and . The method, contrary to Doppler imaging,
also yields other interesting
(continuous) parameters such as the inclination angle , or
sin during its identification procedure.
In this talk, we are not only interested in the estimation of these
continuous parameters themselves but also in
reliable estimates for their uncertainty.
We designed a statistical formalism for the moment method based on the
so-called generalized estimating equations (GEE). This formalism
attempts
to estimate the uncertainty of the continuous parameters taking into
account that the different moments of a line profile are correlated and -
more importantly - that the uncertainty of the observed moments depends on
the pulsation parameters. The latter property of the moment method makes
the least-squares technique a poor choice to estimate the uncertainty of
the continuous parameters. We implemented the GEE method in an attempt
to construct a statistically founded mode identification method
and did performance tests on artificial datasets and on a
high-resolution spectroscopic dataset of the star Cephei. We
report on our experiences with this method and outline our ideas for
improvements of spectroscopic mode identification.
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Last changed: 2002/Jun/04
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