Volume 528, April 2011
|Number of page(s)||9|
|Published online||22 February 2011|
This analysis presented in these appendices was motivated by the observation of an increase in the temporal evolution of the visibilities, mainly for the l = 1 mode, at the end of the year 1999, seen in the Sun-as-a-star GOLF and VIRGO/SPM instruments onboard the SoHO spacecraft. We wish here and in Appendix B to establish whether the origin of these variations might come from SoHO itself and not from the Sun. We decided then to perform the same analysis using two independent helioseismic datasets collected by the ground-based, multi-site BiSON, and GONG networks. The unresolved BiSON and spatially-resolved GONG networks are both composed of six stations located at selected longitudes around the world. The instruments at each BiSON2 site make Sun-as-a-star observations of the Doppler shift of the potassium Fraunhofer line at 770 nm (Elsworth et al. 1995), while the GONG2 cameras use Michelson Doppler interferometer-based instruments measuring in the absorption line Ni I at 676.8 nm (Harvey et al. 1996). In these appendices, we used the spatially-integrated GONG time series, which is analogous to the unresolved observations of GOLF, VIRGO/SPM, and BiSON, although the visibilities for the higher degree modes are different, with the relative strength falling off faster as a function of l in the GONG data. A total of 5339 days, starting on 1995 January 1, of BiSON observations, and of 5112 days, starting on 1995 May 7, of the GONG integrated data, with respective duty cycles of 81.0% and 85.4%, were analyzed in the same manner as described in Sect. 2. The daily temporal sidebands due to the diurnal gaps in ground-based observations were included in the fitting model (Sect. 2). The BiSON and GONG integrated l = 1, 2, and 3 mode visibilities, obtained as explained in Sect. 3, are represented as a function of frequency in Fig. A.1, and given in Table A.1 once averaged over frequency between 1800 and 3100 μHz. The l = 3 mode has a very small visibility in the GONG integrated data and was averaged from 2500 μHz only, due to its lower SNR at low frequency. The m-height ratios were also estimated and are given in Table A.2. Chaplin et al. (2001) calculated the m-height ratios in the BiSON data finding 0.55 ± 0.04 and 0.38 ± 0.02 for the l = 2 and l = 3 modes, respectively. Our analysis returns larger ratios than theirs, but are consistent within 1σ for l = 2 and 2σ for l = 3. These differences might be cause by differences in the total length of the datasets used, 8 years in Chaplin et al. (2001) compared to 14 years here, meaning a higher frequency resolution in the present case and different periods of time analyzed – indeed, variations with solar activity cannot be totally excluded. We calculated these height ratios over the same period of time as in Chaplin et al. (2001) and found 0.57 ± 0.04 and 0.40 ± 0.03 for l = 2 and 3, respectively, which agree with Chaplin et al. (2001) to 1σ. The remaining differences might be attributable to the peak-fitting itself, such as the size of the fitting windows, or the small multiplet frequency asymmetry at l = 2 and 3,
which is not taken into account in our analysis. In the case of the integrated GONG time series, no previously measured m-height ratios were found in the published litterature. We note that since the visibility of the l = 3 mode is close to being zero in the GONG integrated data, the m-height ratio for l = 3 could not be measured accurately.
Mode visibilities of l = 1 (blue dots), l = 2 (red squares), and l = 3 (black diamonds) relative to l = 0 as a function of frequency extracted from the analysis of the BiSON (left) and GONG integrated (right) observations.
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Temporal variations in the l = 1 mode visibilities extracted from the analysis of the non-independent 365-day (left column) and 91.25-day (right column) power spectra of the GOLF, VIRGO/SPM, GONG, and BiSON (from top to bottom) instruments. The vertical dashed lines correspond to 1999 October 10.
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Mode visibilities extracted from the analysis of the BiSON and integrated GONG time series.
Height ratios βl between the m-components of the l = 2 and l = 3 modes measured in the BiSON and integrated GONG time series.
Appendix B: Temporal evolution of the l = 1 mode visibility in several Sun-as-a-star helioseismic instruments
We compare the temporal evolution of the low-degree mode visibilities of the solar oscillations measured with the spaced-based GOLF and VIRGO/SPM instruments onboard the SoHO spacecraft, to the visibilities measured with the ground-based, multi-site BiSON, and GONG networks. The BiSON and GONG integrated time series were divided into contiguous 365-day and 91.25-day non-independent subseries (shifted by 1/4) and analyzed in the same manner as explained in Sect. 6. Figure A.2 shows the temporal evolution of the visibility of the l = 1 mode extracted from the analysis of the non-independent 365-day and 91.25-day GOLF, VIRGO/SPM, BiSON, and GONG integrated power spectra. The bump of the l = 1 mode visibility at the end of the year 1999 observed in the 365-day subseries (see Fig. 4) is present in all the analyzed independent datasets. As already mentioned in Sect. 6, this bump is most likely the result of a series of higher-than-average peaks between 1999 and 2001 observed in the 91.25-day visibilities. Moreover, similar short-term variations of about 6 months can be observed in the 91.25-days subseries of the GOLF, VIRGO/SPM, BiSON, and GONG instruments, some of them exhibiting significant and common increases. The same analysis performed using different lengths of subseries and overlapping factors confirms that this six-month periodicity is not an artifact of the methodology.
© ESO, 2011
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