58 research outputs found
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&
Self-consistent method to extract non-linearities from pulsating stars light curves I. Combination frequencies
Combination frequencies are not solutions of the perturbed stellar structure
equations. In dense power spectra from a light curve of a given multi-periodic
pulsating star, they can compromise the mode identification in an asteroseismic
analysis, hence they must be treated as spurious frequencies and conveniently
removed. In this paper, a method based on fitting the set of frequencies that
best describe a general non-linear model, like the Volterra series, is
presented. The method allows to extract these frequencies from the power
spectrum, so helping to improve the frequency analysis enabling hidden
frequencies to emerge from the initially considered as noise. Moreover, the
method yields frequencies with uncertainties several orders of magnitude
smaller than the Rayleigh dispersion, usually taken as the present error in a
standard frequency analysis. Furthermore, it is compatible with the classical
counting cycles method, the so-called O-C method, which is valid only for
mono-periodic stars. The method opens the possibility to characterise the
non-linear behaviour of a given pulsating star by studying in detail the
complex generalised transfer functions.Comment: 10 pages, 4 figures. Submitted to MNRA
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
Searching for signatures of chaos in gamma-ray light curves of selected Fermi-LAT blazars
Blazar variability appears to be stochastic in nature. However, a possibility
of low-dimensional chaos was considered in the past, but with no unambiguous
detection so far. If present, it would constrain the emission mechanism by
suggesting an underlying dynamical system. We rigorously searched for
signatures of chaos in Fermi-Large Area Telescope light curves of 11 blazars.
The data were comprehensively investigated using the methods of nonlinear time
series analysis: phase-space reconstruction, fractal dimension, maximal
Lyapunov exponent (mLE). We tested several possible parameters affecting the
outcomes, in particular the mLE, in order to verify the spuriousness of the
outcomes. We found no signs of chaos in any of the analyzed blazars. Blazar
variability is either truly stochastic in nature, or governed by
high-dimensional chaos that can often resemble randomness.Comment: Pages : 7, figures: 5, accepted in MNRA
Fractal analysis applied to light curves of Scuti stars
Fractal behaviour, i.e. scale invariance in spatio-temporal dynamics, have
been found to describe and model many systems in nature, in particular fluid
mechanics and geophysical related geometrical objects, like the convective
boundary layer of cumulus cloud fields, topographic landscapes, solar
granulation patterns, and observational astrophysical time series, like light
curves of pulsating stars. The main interest in the study of fractal properties
in such physical phenomena lies in the close relationships they have with
chaotic and turbulent dynamic. In this work we introduce some statistical tools
for fractal analysis of light curves: Rescaled Range Analysis (R/S),
Multifractal Spectra Analysis, and Coarse Graining Spectral Analysis (CGSA), an
FFT based algorithm, which can discriminate in a time series the stochastic
fractal power spectra from the harmonic one. An interesting application of
fractal analysis in asteroseismology concerns the joint use of all these tools
in order to develop classification criteria and algorithms for {\delta}-Scuti
pulsating stars. In fact from the fractal and multi-fractal fingerprints in
background noise of light curves we could infer on different mechanism of
stellar dynamic, among them rotation, modes excitation and magnetic activity.Comment: 13 pages, 10 figure
Observational - relation for Sct stars using eclipsing binaries and space photometry
Delta Scuti ( Sct) stars are intermediate-mass pulsators, whose
intrinsic oscillations have been studied for decades. However, modelling their
pulsations remains a real theoretical challenge, thereby even hampering the
precise determination of global stellar parameters. In this work, we used space
photometry observations of eclipsing binaries with a Sct component to
obtain reliable physical parameters and oscillation frequencies. Using that
information, we derived an observational scaling relation between the stellar
mean density and a frequency pattern in the oscillation spectrum. This pattern
is analogous to the solar-like large separation but in the low order regime. We
also show that this relation is independent of the rotation rate. These
findings open the possibility of accurately characterizing this type of
pulsator and validate the frequency pattern as a new observable for
Sct stars.Comment: 11 pages, including 2 pages of appendix, 2 figures, 2 tables,
accepted for publication in ApJ
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