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

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

KIC 3440495: A Rapidly Rotating δ Scuti-γ Doradus Hybrid Pulsator in a Binary System

In this paper, we study the pulsation properties of KIC 3440495 using Kepler and TESS data. A Fourier analysis of the light curve reveals 24 pulsation modes as well as 29 frequencies associated with rotation. The rotation frequency is derived to be frot = 2.322909(2) day−1, and the rotational modulation is determined to be caused by starspots. A large frequency separation of Δν = 54.5 μHz is found by using a Fourier transform, the autocorrelation function, a histogram of frequency differences, and an échelle diagram. We use the large separation to estimate the refined stellar parameters of the star to be v = [239, 279] km s−1, M= [1.5, 1.65] Me, Requator = [2.03, 2.30] Re, Rpolar = [1.72, 1.78] Re, and ω = [0.61, 0.77]. The phase modulations of the pulsating frequencies show a long-term trend which may be attributed to an orbital effect of a binary system; hence, the star may be a fast rotating pulsator in a binary system. KIC 3440495 has an amplitude spectrum similar to Altair, and is identified as a potential sister of Altair. Based on studies of Altair, KIC 3330495 is presumably a young star at a similar evolutionary stage.National Natural Science Foundation of China (NSFC) 12003060 U2031209Natural Science Foundation of Xinjiang Uygur Autonomous Region 2020D01B59Chinese Academy of Sciences (CAS) "Light of West China" Program 2021-XBQNXZ-029"FEDER/Junta de Andalucia-Consejeria de Economia y Conocimiento" by Universidad de Granada E-FQM-041-UGR18"Programas Estatales de Generacion de Conocimiento y Fortalecimiento Cientifico y Tecnologico del Sistema de I+D+i y de I+D+i Orientada a los Retos de la Sociedad" from the Spanish Ministry of Science, Innovation and Universities (MCIU) PID2019-107061GB-C63State Agency for Research through the "Center of Excellence Severo Ochoa" award from the Spanish Ministry of Science, Innovation and Universities (MCIU) SEV-2017-070

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&

Asteroseismology of a Double-mode High-amplitude δ Scuti Star TIC 448892817

We thank the anonymous referee for the suggestive comments, which improved the manuscript. We would like to thank the TESS science team for providing such excellent data. J.P.G. acknowledges funding support from Spanish public funds for research from project PID2019-107061GB-C63 from the “Programas Estatales de Generación de Conocimiento y Fortalecimiento Científico y Tecnológico del Sistema de I+D +i y de I+D+i Orientada a los Retos de la Sociedad”, and from the State Agency for Research through the “Center of Excellence Severo Ochoa” award to the Instituto de Astrofísica de Andalucía (SEV-2017-0709), all from the Spanish Ministry of Science, Innovation and Universities (MCIU). A.G.H. acknowledges support from “FEDER/Junta de Andalucía- Consejería de Economía y Conocimiento” under project E-FQM-041-UGR18 by Universidad de Granada. The Large Sky Area Multi-Object Fiber Spectroscopic Telescope (LAMOST) is a National Major Scientific Project built by the Chinese Academy of Sciences. Funding for the project has been provided by the National Development and Reform Commission. LAMOST is operated and managed by the National Astronomical Observatories, Chinese Academy of Sciences.We propose that TIC 448892817 is a double-mode high-amplitude δ Scuti star. The radial modes detected in this star provide a unique opportunity to exploit asteroseismic techniques up to their limits. 30 significant frequencies are detected by frequency analysis, while two of them are independent frequencies, i.e., F0 = 13.43538(2) day−1 and F1 = 17.27007(4) day−1. The ratio of f1/f2 is measured to be 0.777957(2), suggesting that this target is a double-mode δ Scuti star. Nearly all the light variation is due to these two modes and their combination frequencies, but several other frequencies of very low amplitude are also present. The stellar evolutionary models were constructed with different mass M and metallicity Z using Modules for Experiments in Stellar Astrophysics (MESA). The frequency ratio f1/f2 obtained by the model is smaller than those obtained by observation. This might be caused by the rotation of the star pointing that rotational effects are more important than previously thought in HADS stars. This is something that deserves to be investigated in future works with models including rotational effects for moderate to intermediate rotators such as FILOU. On the other hand, the parameters obtained from MESA agree well with previous results as well as by observational spectra. The best-fitting model shows that TIC 448892817 is close to entering the first turnoff of the main sequence. In order to accurately determine the effective temperature and metallicities, thus further narrowing the parameter space of this star, we suggest high-resolution spectra is highly desired in the future.Center of Excellence Severo OchoaI+D+i y de I+D+i Orientada a los Retos de la SociedadJunta de Andalucía-Consejería de Economía y Conocimiento E-FQM-041-UGR18State Agency for ResearchMinisterio de Ciencia, Innovación y UniversidadesChinese Academy of SciencesUniversidad de GranadaEuropean Regional Development FundNational Development and Reform CommissionNational Astronomical Observatories, Chinese Academy of SciencesInstituto de Astrofísica de Andalucía SEV-2017-070

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

Ultra-precise analysis of the light curves of CoRoT and Kepler δ Scuti stars

It is well known that the residuals of the multifrequency analysis of δ Scuti stars are correlated, giving rise to challenging features such as a plateau (HD 50844, HD 50870, HD 49434, . . . ) of non-resolved frequencies with amplitude higher than the expected noise level. Several hypotheses have been advanced to explain these features: effective convection, rotation, non-linear interactions, etc. We have recently demonstrated that in some cases the underlying function describing the light variations of δ Scuti stars has not the property of being analytic. The strong consequence of this result is that the Fourier expansion on which the harmonic analysis is based could be not justified. In order to know the extension of this phenomenon among δ Scuti stars, we have used photometric data from CoRoT seismofield and a set of Kepler stars. The results show that this inconsistency in the application of harmonic analysis is almost ubiquitous to the δ Scuti pulsating stars

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