Issue |
Astron. Astrophys. Suppl. Ser.
Volume 132, Number 1, October I 1998
|
|
---|---|---|
Page(s) | 107 - 119 | |
DOI | https://doi.org/10.1051/aas:1998441 | |
Published online | 15 October 1998 |
The art of fitting p-mode spectra
I. Maximum likelihood estimation
1
Space Science Department of ESA, ESTEC, NL-2200 AG Noordwijk, The Netherlands
2
W.W. Hansen Experimental Physics Laboratory, Center for Space Science and Astrophysics, Stanford University, Stanford, CA 94305-4085, U.S.A.
3
Teoretisk Astrofysik Center, Århus Universitet, DK-8000 Århus C, Denmark
Received:
17
October
1997
Accepted:
24
March
1998
In this article we present our state of the art of fitting
helioseismic p-mode spectra.
We give a step by step recipe for fitting the spectra: statistics of the
spectra both for spatially unresolved and resolved data, the use of Maximum
Likelihood estimates, the statistics of the p-mode parameters, the use
of Monte-Carlo simulation and the significance of fitted parameters.
The recipe is applied to synthetic low-resolution data, similar to
those of the LOI, using Monte-Carlo simulations. For such spatially resolved data,
the statistics of the Fourier spectrum is assumed to be a multi-normal
distribution; the statistics of the power spectrum is not a with
2 degrees of freedom. Results for
shows
that all parameters describing the p modes can be obtained with negligible bias
and with minimum variance provided that the leakage matrix is known.
Systematic errors due to an imperfect knowledge of the leakage matrix
are derived for all the p-mode parameters.
Key words: methods: analytical; data analysis; statistical / Sun: oscillations
© European Southern Observatory (ESO), 1998