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Astron. Astrophys. 318, 970-974 (1997)

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4. Results and interpretation

The power spectra of each of the observational time series described already, and shown in Fig. 2, clearly show the five minute oscillations (only marginally for SLOT) at roughly the same level of power, plus some "noise". Such "noise" is the sum of instrumental noise, earth-atmospheric noise plus the solar atmospheric non-coherent signal which we have named "solar background" power. It is obvious that the two space instruments are free from earth-atmospheric noise and will hence yield a better estimate of the solar background. This is particularly true at high frequencies where the five-minute oscillation signal appears. IPHIR and LOI-T data are almost at the same level, while in the earth-bound SLOT this signal is barely visible. Between [FORMULA] 3500 and 6000 µHz, LOI-T observations of the solar background show even slightly less power than IPHIR. This maybe due to the method used (the radiance ratio) in the residual calculations and/or due to the extra noise in the IPHIR data due pointing effects.

For the frequency band from 200 to 2000 µHz, the spectrum seems to behave as a power law therefore allowing a linear fit in the log-log plot. The results of the fit give a slope of -1.46 [FORMULA] 0.05 - for the LOI-T power spectrum. The SLOT power spectrum has a somewhat similar slope: -1.72 [FORMULA] 0.05. In addition, the latter is always placed above the former by nearly an order of magnitude. As both are affected by the same earth-atmospheric noise this difference must be found in the method used to analyse the sets of data. Evidently the use of more information, in the case of LOI-T, allows to define a signal in which atmospheric noise has been effectively removed. In fact, the ACRIM power spectra, which are not contaminated by the earth-atmospheric noise, has a very similar slope to the LOI-T, -1.41 [FORMULA] 0.03 (see also Fisher et al. 1990). The fact that the ACRIM power spectra lie above LOI-T by about a factor 2 could be due to the difference in the spectral range (LOI-T at 500 nm and ACRIM total irradiance with 50 [FORMULA] cut at 700 nm) and/or instrumental noise (see Fröhlich et al. 1991). At intermediate frequencies, data from IPHIR cannot be used as explained above.

Below 10 µHz, the time variable components coming from active regions and the solar rotation dominate the spectra, but between 20 - 100 µHz approximately stationary components are dominant. At these frequencies, only ACRIM data can be used. Indeed, for the frequency band from 10 to 85 µHz, the ACRIM power spectra slope is -0.68 [FORMULA] 0.03 and -0.77 [FORMULA] 0.03 over periods of low and high solar activity phases, respectively; while for even lower frequencies (0.1 to 10 µHz), the slope is -1.99 [FORMULA] 0.06 and -2.69 [FORMULA] 0.06 over periods of low and high solar activity. These variations in the slope are attributed to active-region effects (Fröhlich et al. 1991).

When comparing with the solar velocity background spectrum, a similar behaviour is apparent. Pallé et al. (1995) found a slope of -1.53 [FORMULA] 0.01 in the frequency range from 100 to 1000 µHz, which resembles the one found here. However, for lower frequencies (0.1 to 10 µHz) the same authors infer a slope of -0.89 [FORMULA] 0.06 for both maximum and minimum solar activity which is different from the ACRIM results. Evidently, the contribution of active regions to both signals is of a fairly different nature.

The power level of the numerical simulation in the five-minute region is only a factor of two smaller than that observed by IPHIR and LOI-T. The kinks in the observed background power spectra shown around 3000 µHz are most probably due to a contamination from the p-modes caused by the limited spectral resolution of the averaged data. The kink in the model realization is caused by the choice of lifetime/intensity parameters of the granulation and mesogranulation. A further fine tuning of the input parameters of model maybe required to achieve a better fit for the observations. At higher frequencies, the differences diminish, in remarkable agreement around the acoustical cut-off frequency. At lower frequencies, from 200 to 1000 µHz, the spectrum slope of the model agrees with observations while its power level is a factor two lower than LOI-T. At even lower frequencies - from 10 to 100 µHz - the model output can only be compared to ACRIM results; again the model changes its slope at [FORMULA] 100 µHz and virtually reaches the power observed by ACRIM.

The reasonably good agreement in the overall shape of the power spectra of the model realization and the observations suggests that the former is reliable and that the input data chosen are adequate. The fact that the model output lies slightly lower than is observed can be interpreted as due to the presence of some instrumental noise in the observed spectra and/or to uncertainties in the input data of the model.

At the moment, the power spectra shown here are the best representation of the irradiance background continuum spectra, mainly at high frequencies. At intermediate frequencies, from 40 to 1200 µHz, where the g-mode and low order p-mode oscillations are predicted, the lack of good space data compel us to rely on earth-based data which can only constitute an upper limit to it. The slopes from the two different instruments (LOI-T, ACRIM), the model and even the velocity data agree reasonably well. It should be noted that the LOI-T data reductions presented here have removed a significant part of the earth-atmospheric noise. From these considerations, we believe that the solar background spectrum contributes significantly to the signal observed. At even lower frequencies, comparison of the model with ACRIM data turns out to be good enough to conclude that the model presented can be considered as a reasonable estimate of the solar non-oscillatory background signal. Obviously, reliable space data are needed at these frequencies and we look forward to the results from the VIRGO experiment on-board SOHO. Preliminary reductions of data from commisioning phase of VIRGO show a clear flattening of the power spectra at frequencies below 200 µHz. In addition no kink in the background spectra in the p-mode range is observed. These results are in accordance with our interpretation of the observations presented here.

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© European Southern Observatory (ESO) 1997

Online publication: July 3, 1998