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Astron. Astrophys. 330, 341-350 (1998)

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1. Introduction

The quality of GOLF data offers a unique opportunity to investigate the excitation mechanism of low degree p modes. In the region of 4-6 minutes, several modes can be extracted and analysed one by one with a short enough time resolution ([FORMULA] days) over one year, allowing an accurate statistical treatment of the data obtained.

Here we deal with the "superficial" energy per unit of mass [FORMULA], associated with the mode at the surface of the sun. We do not address the issue of the "global" energy of the mode, which is related to the superficial energy through the shape of the eigenfunction inside the sun.

Woodard (1984) first revealed the exponential nature of the distribution of spectral power in each frequency bin, using ACRIM data.

Goldreich & Keeley (1977) first considered the excitation of p modes by turbulent motions near the surface of the convection zone. Using the analogy of a damped oscillator excited stochastically, Kumar, Franklin & Goldreich (1988) described analytically how the theoretical distribution of energy, averaged over a given time-window, should depend on the damping time of the mode. Comparisons with real data were performed by Toutain & Fröhlich (1992) with 160 days of IPHIR data. They found in particular that the damping times deduced from the linewidths were compatible with those expected in the model of stochastic excitation.

Chang (1996) pointed out that strong localized peaks in the energy variations of a damped oscillator excited stochastically do not necessarily correspond to a strong excitation, but rather to an exceptional coherent addition of random phases.

This is true provided that the number of independent excitations per damping time of the mode is large enough, like in the case of excitation by solar granules. In this context, two different modes excited by exactly the same sources would have uncorrelated energies.

Different modes, however, would be correlated, if the timescale between two excitations from a common source were longer than their damping time.

The correlation between the modes energies is therefore directly related to the characteristics of their source of excitation.

Using 160 days of IPHIR data at the end of 1988 (just before the solar maximum, [FORMULA]), Baudin et al. (1996) concluded that the p modes were likely to be correlated. An anticorrelation between the mean solar magnetic field and the p-mode power was found by Gavryusev & Gavryuseva (1997) in IPHIR data, while no clear correlation has been detected yet in GOLF data (Baudin et al. 1997).

After checking in Sect.  2the exponential nature of the distribution of energy of p modes in GOLF data, we address the issue of their relative independence in Sect.  3, using statistical tests based on Montecarlo simulations.

These same tests are used to re-analyse IPHIR data in Sect.  4.

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© European Southern Observatory (ESO) 1998

Online publication: January 8, 1998