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Astron. Astrophys. 346, 626-632 (1999)

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6. Results of GOLF data analysis

As seen in the previous sections, we can obtain directly the longitudinal global component of the magnetic field as a function of the 8 GOLF observables and the magnetic modulation [FORMULA]. This quantity has a value of [FORMULA] G (Ulrich et al. 1999).

In Fig. 3, the resultant solar magnetic field is plotted as a function of time. A least square fitting of the form [FORMULA] gives a period of 13.8427 [FORMULA] [FORMULA] days with an amplitude [FORMULA] [FORMULA] 0.003 G and an offset [FORMULA] [FORMULA] 0.002 G (the errors come from the uncertainty in the determination of [FORMULA] G). This mean periodicity should be connected with the rotation period of the Sun. The Solar Wilcox Observatory observes every day the large scale solar magnetic field obtaining synoptic charts of every Carrington rotation. This information is available in the Web and also through the Solar Geophysical Data publication. This latter contains the large scale average called Source Surface Field. Looking at this magnitude, corresponding to the Carrington rotation 1905, a slightly quadrupolar distribution can be observed. In fact, the magnetic equator shows an undulation with the southern magnetic hemisphere dominating around Carrington longitudes 270 and 60 degrees. Due to the solar rotation, for an observer placed on the Earth or aboard SOHO, these longitudes were visible around January 24 and February 8, 1996. Therefore, an integrated magnetic field measurement should show a modulation with 2 maxima per solar rotation. These maxima are precisely observed by GOLF at the same dates.

[FIGURE] Fig. 3. Longitudinal global magnetic field of the Sun computed using Eq. (18) and a value of [FORMULA] G. The white line shows a least square sinusoidal fitting.

The C parameter of the fitting represents the SMMF during the period of the measurements. The value obtained is fully compatible with previous measurements of the same quantities at the minimum of solar magnetic activity (Sherrer et al. 1977b).

6.1. The SMMF power spectrum

By applying a Fourier transform over the whole magnetic signal sampled at its highest rate (40 seconds), the power spectrum can be calculated up to 12.5 mHz. Fig. 4 shows the resultant power spectrum ([FORMULA] µHz).

[FIGURE] Fig. 4. Power spectrum of the longitudinal global magnetic field of the Sun. No clear structures are visible.

We do not observe a mode-like structure like the p modes envelope (in velocity or intensity) in this power spectrum. On the contrary, a rather flat level of power is visible in the region above [FORMULA] µHz (see also Fig. 5). It is [FORMULA] 1.7- 2 mG from 50 µHz to 6 mHz which constitutes a new observational detection limit of magnetic signals in this frequency range.

[FIGURE] Fig. 5. Fraction of the power spectrum analyzed. The distribution is incompatible with an exponential noise above 5 times the level of noise, marked with a horizontal line. The peaks above this line are not compatible with an exponential noise with more than a [FORMULA] confidence level.

In order to check if magnetic signals could be present in the spectrum, we performed a statistical study in the region [FORMULA] mHz. The cumulative distribution shows a good agreement with an exponential distribution below [FORMULA] times the mean value (see Fig. 6). A Kolmogorov-Smirmov test applied straightforwardly to the full distribution using the estimated mean value does not reject the hypothesis of an exponential distribution. An exponential distribution is indeed the expected type for the power of a Gaussian noise.

[FIGURE] Fig. 6. Cumulative distribution of the power spectrum, normalized to its mean value, compared to an exponential distribution (straight line). The departure from the exponential distribution at [FORMULA] is clearly visible.

However, the departure of the exponential behaviour at high power in the distribution deserves attention: we exclude the possibility that it could be a random effect with more than a [FORMULA] confidence level. This number is deduced from the probability P that, in a sample of N independent points of an exponential distribution, less than k points exceed [FORMULA] times the mean value. This probability can be seen as the cumulative distribution of a Bernoulli law:

[EQUATION]

The level above which the power is significantly above an exponential distribution is shown in Fig. 5. We have verified that all these peaks do not match the different instrumental parameters being monitored (different subsystem temperatures, voltages...) and they do not correspond to the frequencies of any detectable p-mode in the velocity power spectrum. However, it is extremely difficult to say whether or not these peaks are artifacts coming from unknown instrumental effects due to the SOHO commissioning period where the measurements were taken or if they could really be considered as potentially magnetic signals. Longer data series available from another instrument will be necessary.

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© European Southern Observatory (ESO) 1999

Online publication: May 21, 1999
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