Inconsistencies in the application of harmonic analysis to pulsating stars

Using ultra-precise data from space instrumentation we found that the underlying functions of stellar light curves from some AF pul- sating stars are non-analytic, and consequently their Fourier expansion is not guaranteed. This result demonstrates that periodograms do not provide a mathematically consistent estimator of the frequency content for this kind of variable stars. More importantly, this constitutes the first counterexample against the current paradigm which considers that any physical process is described by a contin- uous (band-limited) function that is infinitely differentiable.Comment: 9 pages, 8 figure

MIARMA: An information preserving method for filling gaps in time series. Application to CoRoT light curves

The method here presented intends to minimize the effect of the gaps in the power spectra by gap-filling preserving the original information, that is, in the case of asteroseismology, the stellar oscillation frequency content. We make use of a forward-backward predictor based on autoregressive moving average modelling (ARMA) in the time domain. The method MIARMA is particularly suitable for replacing invalid data such as those present in the light curves of the CoRoT satellite due to the pass through the South Atlantic Anomaly, and eventually for the data gathered by the NASA planet hunter Kepler. We select a sample of stars from the ultra-precise photometry collected by the asteroseismic camera on board the CoRoT satellite: the {\delta} Scuti star HD 174966, showing periodic variations of the same order as the CoRoT observational window, the Be star HD 51193, showing longer time variations, and the solar-like HD 49933, with rapid time variations. We showed that in some cases linear interpolations are less reliable to what was believed. In particular: the power spectrum of HD 174966 is clearly aliased when this interpolation is used for filling the gaps; the light curve of HD 51193 presents a much more aliased spectrum than expected for a low frequency harmonic signal; and finally, although the linear interpolation does not affect noticeably the power spectrum of the CoRoT light curve of the solar-like star HD 49933, the ARMA interpolation showed rapid variations previously unidentified that ARMA interprets as a signal. In any case, the ARMA interpolation method provides a cleaner power spectrum, that is, less contaminated by spurious frequencies. In conclusion, MIARMA appears to be a suitable method for filling gaps in the light curves of pulsating stars observed by CoRoT since the method preserves their frequency content, which is a necessary condition for asteroseismic studies.Comment: 9 pages, 9 figures, submitted to A&

Impact of gaps in the asteroseismic characterization of pulsating stars. I. On the efficiency of pre-whitening

It is known that the observed distribution of frequencies in CoRoT and Kepler {\delta} Scuti stars has no parallelism with any theoretical model. Pre-whitening is a widespread technique in the analysis of time series with gaps from pulsating stars located in the classical instability strip such as {\delta} Scuti stars. However, some studies have pointed out that this technique might introduce biases in the results of the frequency analysis. This work aims at studying the biases that can result from pre-whitening in asteroseismology. The results will depend on the intrinsic range and distribution of frequencies of the stars. The periodic nature of the gaps in CoRoT observations, just in the range of the pulsational frequency content of the {\delta} Scuti stars, is shown to be crucial to determine their oscillation frequencies, the first step to perform asteroseismolgy of these objects. Hence, here we focus on the impact of pre-whitening on the asteroseismic characterization of {\delta} Scuti stars. We select a sample of 15 {\delta} Scuti stars observed by the CoRoT satellite, for which ultra-high quality photometric data have been obtained by its seismic channel. In order to study the impact on the asteroseismic characterization of {\delta} Scuti stars we perform the pre-whitening procedure on three datasets: gapped data, linearly interpolated data, and ARMA interpolated data. The different results obtained show that at least in some cases pre-whitening is not an efficient procedure for the deconvolution of the spectral window. therefore, in order to reduce the effect of the spectral window to the minimum it is necessary to interpolate with an algorithm that is aimed to preserve the original frequency content, and not only to perform a pre-whitening of the data.Comment: 27 pages, 47 figures Tables and typos fixe

Wild capuchin monkeys adjust stone tools according to changing nut properties

Animals foraging in their natural environments need to be proficient at recognizing and responding to changes in food targets that affect accessibility or pose a risk. Wild bearded capuchin monkeys (Sapajus libidinosus) use stone tools to access a variety of nut species, including otherwise inaccessible foods. This study tests whether wild capuchins from Serra da Capivara National Park in Brazil adjust their tool selection when processing cashew (Anacardium spp.) nuts. During the ripening process of cashew nuts, the amount of caustic defensive substance in the nut mesocarp decreases. We conducted field experiments to test whether capuchins adapt their stone hammer selection to changing properties of the target nut, using stones of different weights and two maturation stages of cashew nuts. The results show that although fresh nuts are easier to crack, capuchin monkeys used larger stone tools to open them, which may help the monkeys avoid contact with the caustic hazard in fresh nuts. We demonstrate that capuchin monkeys are actively able to distinguish between the maturation stages within one nut species, and to adapt their foraging behaviour accordingly