Free Access
Volume 516, June-July 2010
Article Number L6
Number of page(s) 5
Section Letters
DOI https://doi.org/10.1051/0004-6361/201014789
Published online 22 June 2010

Online Material

Appendix A: Details on the CoRoT time series analysis and frequency extraction

We provide additional technical details about the data acquisition, light curve analysis, and frequency extraction.

KPD 0629-0016 was monitored with a sampling time of 32 s. At each measurement, a small image (also called ``imagette'') of the star was acquired, kept on board and transferred to the operation center. In the planet finding channel, the instrument is equipped with a small prism that produces a very low resolution spectrum on the CCD. When building photometric light curves, the pixel counts in the ``imagette'' are integrated into three separate time series corresponding to different colors (``red'', ``green'', and ``blue''). It is similar to broadband photometry, although with a limited wavelength coverage. Future exploitation of this color information needs to be investigated, but since our primary goal was to decrease as much as possible the noise level, we focused on the white light photometry produced by adding the counts of each color light curve at each time step.

For the analysis, we kept only data points that did not suffer from any reported perturbation (i.e., with flag set to zero). This excludes, most notably, measurements obtained during cyclic satellite transits across the South Atlantic Anomaly, which considerably degrades the accuracy and produces significant pollution in the data. The light curve was further de-trended for residual long term variations. Data points that significantly differ from the local standard deviation were removed by applying a running 3-$\sigma$ clipping filter. After all this filtering, the effective duty cycle dropped from $\sim$99.3% for the original data to $\sim$80.5%, but the periodograms are then vastly improved. The price to pay is the presence of side lobes in the window function, which, however, remain small and do not disturb the identification of true frequencies.

We applied the usual prewhitening technique to extract frequencies, one at time: at each step of the procedure, the Lomb-Scargle periodogram (LSP) is computed, the highest peak in the frequency domain is selected and a cosine wave is fitted for frequency, amplitude, and phase to the time series data using a Levenberg-Marquardt nonlinear least squares algorithm. The fitted cosine wave is then subtracted from the data, resulting in the removal of the corresponding peak in the LSP (as well as its associated side lobes due to the window). The procedure is repeated until no more signal emerges over a given detection threshold above the noise (see below). Repeatedly, and at the end of the procedure, all cosine waves are fitted simultaneously using the nonlinear least squares routine.

\end{figure} Figure A.1:

Lomb-Scargle periodograms (showing amplitude spectra in % of the mean brightness) and residuals after prewhitening of the identified frequencies in the CoRoT time series. The green (blue, red) dotted curves refer to a value equal to 4.0 (3.6, 3.0) times the local median noise level. Vertical dotted lines indicate the position of a peak previously removed.

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The prewhitening sequence is illustrated in Fig. A.1. The top panel shows the LSP of the light curve in the 90-400 $\mu $Hz range. The 5 dominant (in amplitude) frequencies are indicated and the result of their prewhitening is then plotted in the panel below. The procedure continues with 4 additional frequencies removed, leading to the LSP represented in the panel further down. The frequency selection and removal proceeds until peaks no longer emerge above the detection threshold. Various thresholds are shown in Fig. A.1 corresponding to 4 times (green), 3.6 times (blue), and 3 times (red) the median noise level, respectively. This noise level is estimated locally by computing the median amplitude value within a running box of width $\pm$1000 frequency bins in the LSP. It is re-evaluated after each frequency prewhitening, such that, at the end of the procedure, the value obtained is representative of the true local noise contribution separated from the signal window pattern, even in crowded frequency regions containing several close peaks.

It is usual to adopt the ``4-$\sigma$ criterion'' as a safe limit for the detection of frequencies, which roughly corresponds to the 99.9% statistical significance level. All the peaks indicated in the 3 successive panels from the top in Fig. A.1 conform to this criterion, leading to the detection of 17 frequencies, fn, given in Table 1. The 7 additional peaks, un, are identified in the fourth panel (from the top) in Fig. A.1. These have amplitudes between 3.6 and 4.0$\sigma$.

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