The art of fitting p-mode spectra. I. Maximum likelihood estimation

T. Appourchaux, Laurent Gizon, M. C. Rabello-Soares

    Research output: Contribution to journalArticle

    Abstract

    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 χ2 with 2 degrees of freedom. Results for l = 1 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.

    Original languageEnglish (US)
    Pages (from-to)107-119
    Number of pages13
    JournalAstronomy and Astrophysics Supplement Series
    Volume132
    Issue number1
    DOIs
    StatePublished - Oct 1 1998

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    arts
    art
    statistics
    leakage
    maximum likelihood estimates
    matrices
    normal density functions
    matrix
    systematic errors
    power spectra
    simulation
    degrees of freedom
    parameter

    Keywords

    • Methods: analytical; data analysis; statistical
    • Sun: oscillations

    ASJC Scopus subject areas

    • Physics and Astronomy(all)

    Cite this

    The art of fitting p-mode spectra. I. Maximum likelihood estimation. / Appourchaux, T.; Gizon, Laurent; Rabello-Soares, M. C.

    In: Astronomy and Astrophysics Supplement Series, Vol. 132, No. 1, 01.10.1998, p. 107-119.

    Research output: Contribution to journalArticle

    Appourchaux, T. ; Gizon, Laurent ; Rabello-Soares, M. C. / The art of fitting p-mode spectra. I. Maximum likelihood estimation. In: Astronomy and Astrophysics Supplement Series. 1998 ; Vol. 132, No. 1. pp. 107-119.
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