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Astron. Astrophys. 333, 362-368 (1998)

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5. Conclusion

Our power spectrum model is based on normal noise added to some ideal function in the Fourier space, leading to a solar-like p-mode power spectrum. This process is intended to picture a stochastically driven oscillating system. We think that our simulation is realistic enough, and we have been able through it to verify numerically the corresponding theoretical predictions from Kumar. To use Monte Carlo simulation for the computation of error bars brings a few evidences:

  • The presence of daily sidelobes of the eigenmode peaks combined with a bad SNR and a blurred multiplet shape do decrease by a factor 1.5 to 2 the precision of the frequency measurements for [FORMULA] 2 and 3. [FORMULA] and [FORMULA] are better because of the smaller impact of the closest sidelobes and of the better SNR. The theoretical formula valid for [FORMULA] seems a good starting point in any circumstances.
  • Destructive interference between the real and imaginary parts of the noise in the Fourier transform are important for the p-modes parameters uncertainties. So are the interferences between different peaks with comparable values of frequencies, such as sidelobes of the [FORMULA] and [FORMULA] peak or between split components. On a single realization they can generate a dramatic variation of the spectral density shape, leading to absurd values for the p-modes parameters and/or error bars. Monte Carlo simulations cannot correct the initially biased estimation, but, as they do not rely on the values of the parameters to derive the error-bars, they will provide error bars that potentially allow the correct result to fall in the [FORMULA] interval.

As to the widths, the strategy of reducing the number of free parameters helps very much in reducing the error-bars by a factor of 2 in the best case. This is encouragingly in favor of the "iterative" fitting methods already designed for the collective splitting measurements (Toutain et al. 1992, Lazrek et al. 1996), in which some parameters of the vector [FORMULA] are in turn locked, then released, then locked again down to the entire convergence of all the set.

The IRIS network was funded and is supported by the French Institut National des Sciences de l'Univers (I.N.S.U.) and the Centre National de la Recherche Scientifique (C.N.R.S.).

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© European Southern Observatory (ESO) 1998

Online publication: April 15, 1998
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