Maximum likelihood estimators: AM application to the estimation of the precision of helioseismic measurements

Details Maximum likelihood estimators: AM application to the estimation of the precision of helioseismic measurements Maximum likelihood estimators: AM application to the estimation of the precision of helioseismic measurements

Sep 1994

adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1994a%26a...289..649t&link_type=abstract

Astronomy and Astrophysics (ISSN 0004-6361), vol. 289, no. 2, p. 649-658

Astronomy and Astrophysics

Astrophysics

73

Helioseismology, Maximum Likelihood Estimates, Parameter Identification, Power Spectra, Precision, Stellar Oscillations, Hessian Matrices, Monte Carlo Method, P Band, Signal To Noise Ratios, Simulation, Spectral Resolution

Scientific paper

In this paper we apply the theory of Maximum Likelihood estimators to determine the precision of parameters in fitting Lorentzian profiles to helioseismic power spectra. The precision of frequency, linewidth, amplitude and noise determination for a single p mode, and of the l = 1 splitting, are derived as a function of the signal-to-noise ratio and the spectral resolution of the spectrum, Libbrecht's formula (Libbrecht 1992) for frequency precision is derived in a more general case. For validating the approach, the theoretical precisions are compared with those obtained with Monte-Carlo simulations and with IPHIR observations. The robustness of the precisions obtained is ideal for predictive purposes. The method used to derive the precisions is general enough so that it can be used for other purposes.

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