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Stellar pulsation is a common phenomenon and is sustained because of coherent driving mechanisms. When pulsations are driven by heat or convective mechanisms, it is usual to observe combination frequencies in the power spectra of the stellar light-curves. These combination frequencies are not solutions of the perturbed stellar structure equations. In dense power spectra from a light-curve of a given multiperiodic pulsating star, they can compromise the mode identification in asteroseismic analyses, and hence they must be treated as spurious frequencies and removed. In this paper, a method based on fitting the set of frequencies that best describes a general non-linear model, like the Volterra series, is presented. The method allows these frequencies to be extracted from the power spectrum, thereby improving the frequency analysis and enabling hidden frequencies to emerge from what was initially considered as noise. Moreover, the method yields frequencies with uncertainties several orders of magnitude smaller than the Rayleigh dispersion, which is sometimes used as if it were an error when identifying combination frequencies. 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 creates the possibility of characterizing the non-linear behaviour of a given pulsating star by studying in detail the complex generalized transfer functions on which the model is based. © 2020 The Author(s) Published by Oxford University Press on behalf of the Royal Astronomical Society, MLM, RGH and JPG acknowledge financial support from the State Agency for Research of the Spanish MCIU through the Center of Excellence Severo Ochoa' award to the Instituto de Astrofisica de Andalucía (SEV-2017-0709). The authors acknowledge funding support from Spanish public funds for research under project ESP201787676-C5-5-R.

Full list of authors: Castro-Tirado, A. J.; Østgaard, N.; Göǧüş, E.; Sánchez-Gil, C.; Pascual-Granado, J.; Reglero, V.; Mezentsev, A.; Gabler, M.; Marisaldi, M.; Neubert, T.; Budtz-Jørgensen, C.; Lindanger, A. Sarria, D.; Kuvvetli, I.; Cerdá-Durán, P.; Navarro-González, J.; Font, J. A.; Zhang, B. -B.; Lund, N.; Oxborrow, C. A.; Brandt, S.; Caballero-García, M. D.; Carrasco-García, I. M.; Castellón, A.; Castro Tirado, M. A.; Christiansen, F.; Eyles, C. J.; Fernández-García, E.; Genov, G.; Guziy, S.; Hu, Y. -D.; Nicuesa Guelbenzu, A.; Pandey, S. B.; Peng, Z. -K.; Pérez del Pulgar, C.; Reina Terol, A. J.; Rodríguez, E.; Sánchez-Ramírez, R.; Sun, T.; Ullaland, K.; Yang, S., Magnetars are strongly magnetized, isolated neutron stars1–3 with magnetic fields up to around 1015 gauss, luminosities of approximately 1031–1036 ergs per second and rotation periods of about 0.3–12.0 s. Very energetic giant flares from galactic magnetars (peak luminosities of 1044–1047 ergs per second, lasting approximately 0.1 s) have been detected in hard X-rays and soft γ-rays4, and only one has been detected from outside our galaxy5. During such giant flares, quasi-periodic oscillations (QPOs) with low (less than 150 hertz) and high (greater than 500 hertz) frequencies have been observed6–9, but their statistical significance has been questioned10. High-frequency QPOs have been seen only during the tail phase of the flare9. Here we report the observation of two broad QPOs at approximately 2,132 hertz and 4,250 hertz in the main peak of a giant γ-ray flare11 in the direction of the NGC 253 galaxy12–17, disappearing after 3.5 milliseconds. The flare was detected on 15 April 2020 by the Atmosphere–Space Interactions Monitor instrument18,19 aboard the International Space Station, which was the only instrument that recorded the main burst phase (0.8–3.2 milliseconds) in the full energy range (50 × 103 to 40 × 106 electronvolts) without suffering from saturation effects such as deadtime and pile-up. Along with sudden spectral variations, these extremely high-frequency oscillations in the burst peak are a crucial component that will aid our understanding of magnetar giant flares. © 2021, The Author(s), under exclusive licence to Springer Nature Limited., This work made use of data from ASIM. ASIM is an international experiment aboard the International Space Station. ASIM is a mission of the European Space Agency (ESA), funded by ESA and national grants from Denmark, Norway and Spain. ESA PRODEX contracts C 4000115884 (DTU) and 4000123438 (Bergen) support the ASIM Science Data Centre. The science analysis is supported by ESA Topical Team contract 4200019920/06/NL/VJ; European Research Council grant AdG-FP7/2007-2013: n 320839; Research Council of Norway contract 223252/F50 (CoE/BCSS); and Ministerio de Ciencia, Innovación y Universidades grants ESP 2017-86263-C4 and ESP2017-87676-C5-5-R. J.A.F. and P.C.-D. acknowledge support by the Spanish Agencia Estatal de Investigación (grant PGC2018-095984-B-I00) and by the Generalitat Valenciana (PROMETEO/2019/071). P.C.-D. acknowledges the Ramon y Cajal funding (RYC-2015-19074) for supporting his research. M.G. acknowledges support through the Generalitat Valenciana via the grant CIDEGENT/2019/031. A.J.C.-T., J.P.-G., M.D.C.-G. and E.R. acknowledge financial support from the State Agency for Research of the Spanish MCIU through the “Center of Excellence Severo Ochoa” award to the Instituto de Astrofísica de Andalucía (SEV-2017-0709). This work is partly based on observations made with the Gran Telescopio Canarias (GTC), installed at the Spanish Observatorio del Roque de los Muchachos of the Instituto de Astrofísica de Canarias, on the island of La Palma. We thank J. D. Scargle for his help with the preliminary time-series analysis and his comments. J.P.-G. also 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’ from the Spanish Ministry of Science, Innovation and Universities (MCIU).

Fractal fingerprints have been found recently in the light curves of several δ Scuti stars observed by Convection Rotation and planetary Transits(CoRoT) satellite. This sole fact might pose a problem for the detection of pulsation frequencies using classical pre-whitening techniques, but it is also a potentially rich source for information about physical mechanisms associated with stellar variability. Assuming that a light curve is composed of a superposition of oscillation modes with a fractal background noise, in this work we applied the Coarse Graining Spectral Analysis (CGSA), a fast Fourier transform (FFT)-based algorithm, which can discriminate in a time series the stochastic fractal power spectra from the harmonic one. We have found that the fractal background component is determining the frequency content extracted using classical pre-whitening techniques in the light curves of δ Scuti stars. This might be crucial to understand the amount of frequencies excited in these kinds of pulsating stars. Additionally, CGSA resulted to be relevant in order to extract the oscillation modes, this points to a new criterion to stop the pre-whitening cascade based on the percentage of fractal component in the residuals.

ARB, JPG, and RG acknowledge funding support from Spanish public funds for research from project ESP2017-87676-C5-5-R from the `Plan Estatal de Investigacion Cientifica y Tecnica y de Innovacion', from project PID2019-107061GB-C63 from the `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', and from the State Agency for Research through the `Center of Excellence Severo Ochoa' award to the Instituto de Astrofisica de Andalucia (SEV-2017-0709), all from the Spanish Ministry of Science, Innovation and Universities. ARB also acknowledges funding support from project PRE2018084322 from the `Programa Estatal de Promocion del Talento y su Empleabilidad del Plan Estatal de Investigacion Cientifica y Tecnica y de Innovacion 2013-2016' of the Spanish Ministry of Science, Innovation and Universities. AGHacknowledges funding support from Spanish public funds for research under projects ESP2017-87676-2-2 the SpanishMinistry of Science and Education, and from `European Regional Development Fund/Junta de Andalucia-Consejeria de Economia y Conocimiento' under project E-FQM-041-UGR18 by Universidad de Granada. JCS acknowledges funding support from Spanish public funds for research under projects PID2019-107061GB-C63 and ESP201787676-2-2, and from project RYC-2012-09913 under the `Ramon y Cajal' program of the Spanish Ministry of Science and Education., Detecting and understanding rotation in stellar interiors is nowadays one of the unsolved problems in stellar physics. Asteroseismology has been able to provide insights on rotation for the Sun, solar-like stars, and compact objects like white dwarfs. However, this is still very difficult for intermediate-mass stars. These stars are moderate-to-rapid rotators. Rotation splits and shifts the oscillation modes, which makes the oscillation spectrum more complex and harder to interpret. Here we study the oscillation patterns of a sample of benchmark delta Sct stars belonging to eclipsing binary systems with the objective of finding the frequency spacing related to the rotational splitting (delta r). For this task, we combine three techniques: the Fourier transform, the autocorrelation function, and the histogram of frequency differences. The last two showed a similar behaviour. For most of the stars, it was necessary to determine the large separation (Delta nu) prior to spot delta r. This is the first time we may clearly state that one of the periodicities present in the p modes oscillation spectra of delta Sct stars corresponds to the rotational splitting. This is true independent of the stellar rotation rate. These promising results pave the way to finding a robust methodology to determine rotational splittings from the oscillation spectra of delta Sct stars and, thus, understanding the rotational profile of intermediate-mass pulsating stars., Plan Estatal de Investigacion Cientifica y Tecnica y de Innovacion ESP2017-87676-C5-5-R, 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 PID2019-107061GB-C63, State Agency for Research through the `Center of Excellence Severo Ochoa' SEV-2017-0709, Spanish Ministry of Science, Innovation and Universities, Programa Estatal de Promocion del Talento y su Empleabilidad del Plan Estatal de Investigacion Cientifica y Tecnica y de Innovacion 2013-2016' of the Spanish Ministry of Science, Innovation and Universities PRE2018084322, Spanish Government ESP2017-87676-2-2, European Regional Development Fund/Junta de Andalucia-Consejeria de Economia y Conocimientoby Universidad de Granada E-FQM-041-UGR18, Spanish public funds for research PID2019-107061GB-C63 ESP201787676-2-2, Spanish Government RYC-2012-09913

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, and 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 analysed blazars. Blazar variability is either truly stochastic in nature or governed by high-dimensional chaos that can often resemble randomness. © 2021 The Author(s)., OO thanks the Astronomical Observatory of the Jagiellonian University for the summer internship during which this research began. MT acknowledges support by the Polish National Science Center through the OPUS grant No. 2017/25/B/ST9/01208. The work of N. Z is supported by the South African Research Chairs Initiative (grant no. 64789) of the Department of Science and Innovation and the National Research Foundation of South Africa. J.P.-G. acknowledges funding support from Spanish public funds for research under project ESP2017-87676-C5-5-R and financial support from the State Agency for Research of the Spanish MCIU through the `Center of Excellence Severo Ochoa' award to the Instituto de Astrof ' isica de Andaluc ' ia (SEV-2017-0709).

We thank the anonymous referee for a careful reading of the manuscript. DLH acknowledges financial support from the Science and Technology Facilities Council (STFC) via grant ST/M000877/1. MSC acknowledges the support by FCT/MCTES through the research grants UIDB/04434/2020, UIDP/04434/2020, and PTDC/FIS-AST/30389/2017, and by FEDER - Fundo Europeu de Desenvolvimento Regional through COMPETE2020 - Programa Operacional Competitividade e Internacionalizacao (grant: POCI01-0145-FEDER-030389). MSC is supported by national funds through FCT in the form of a work contract. VA was supported by a research grant (00028173) fromVILLUMFONDEN. Funding for the Stellar Astrophysics Centre is provided by The Danish National Research Foundation (Grant agreement no.: DNRF106). The research leading to these results has received funding from the Research Foundation Flanders (FWO) by means of a senior postdoctoral fellowship to DMB with grant agreement No. 1286521N. This project has been supported by the Lendulet Program of the Hungarian Academy of Sciences, project No. LP2018-7/2020 and by the EU's MW-Gaia COST Action (CA18104). ASG acknowledges financial support from the Max Planck Society under grant 'Preparations for PLATO science' and from ALMA-CONICYT under grant #31170029. ZsB acknowledges the support by the Janos Bolyai Research Scholarship of the Hungarian Academy of Sciences. LFM acknowledges the financial support from the UNAM under grant PAPIIT IN100918. CCL acknowledges the support of the Natural Sciences and Engineering Research Council of Canada (NSERC). DM acknowledges the support of the National Astronomical Research Institute of Thailand (NARIT). JPG acknowledges funding support from Spanish public funds for research from project PID2019-107061GB-C63 from the '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', and from the State Agency for Research through the Center of Excellence Severo Ochoa' award to the Instituto de Astrof ' isica de Andaluc ' ia (SEV2017-0709), all from the Spanish Ministry of Science, Innovation and Universities (MCIU). TRY acknowledges support from the NSF REU program, grant number PHY-1359195. The material is based upon work supported by NASA under award number 80GSFC21M0002. AD was supported by the UNKP-20-5 New National Excellence Program of the Ministry of Human Capacities and the J ' anos Bolyai Research Scholarship of the Hungarian Academy of Sciences. AD would like to thank the City of Szombathely for support under Agreement No. 67.177-21/2016. AGH acknowledges support from 'FEDER/Junta de Andalucia-Consejeria de Economia y Conocimiento' under project E-FQM-041-UGR18 by Universidad de Granada and from Spanish public funds (including FEDER funds) for research under project ESP2017-87676-C5-2-R. ARB acknowledges funding support from Spanish public funds for research through the research grant PRE2018-084322, through projects ESP2017-87676-C5-5-R and PID2019-107061GB-C63, and from the State Agency for Research through the `Center of Excellence Severo Ochoa' award to the Instituto de Astrof ' isica de Andaluc ' ia (SEV-2017-0709), all from the Spanish Ministry of Science, Innovation and Universities (MCIU). We are grateful to Sowgata Chowdhury, supported by Polish NCN grant 2015/18/A/ST9/00578, for conducting some spectroscopic observations that are reported in this work. This paper includes data collected by the TESS mission, which are publicly available from the Mikulski Archive for Space Telescopes (MAST). Funding for the TESS mission is provided by NASA's Science Mission directorate. Funding for the TESS Asteroseismic Science Operations Centre is provided by the Danish National Research Foundation (Grant agreement no.: DNRF106), ESA PRODEX (PEA 4000119301) and Stellar Astrophysics Centre (SAC) at Aarhus University. We thank the TESS team and staff and TASC/TASOC for their support of this work. This research has made use of the SIMBAD data base, operated at CDS, Strasbourg, France. This work has made use of data from the European Space Agency (ESA) mission Gaia (https://www.cosmos.esa.int/gaia), processed by the Gaia Data Processing and Analysis Consortium (DPAC, https://www.cosmos.esa.int/web/gaia/dpac/consortium).Funding for the DPAC has been provided by national institutions, in particular the institutions participating in the Gaia Multilateral Agreement., We present the results of a systematic search for new rapidly oscillating Ap (roAp) stars using the 2-min cadence data collected by the Transiting Exoplanet Survey Satellite (TESS) during its Cycle 1 observations. We identify 12 new roAp stars. Amongst these stars we discover the roAp star with the longest pulsation period, another with the shortest rotation period, and six with multiperiodic variability. In addition to these new roAp stars, we present an analysis of 44 known roAp stars observed by TESS during Cycle 1, providing the first high-precision and homogeneous sample of a significant fraction of the known roAp stars. The TESS observations have shown that almost 60 per cent (33) of our sample of stars are multiperiodic, providing excellent cases to test models of roAp pulsations, and from which the most rewarding asteroseismic results can be gleaned. We report four cases of the occurrence of rotationally split frequency multiplets that imply different mode geometries for the same degree modes in the same star. This provides a conundrum in applying the oblique pulsator model to the roAp stars. Finally, we report the discovery of non-linear mode interactions in α Cir (TIC 402546736, HD128898) around the harmonic of the principal mode – this is only the second case of such a phenomenon., UK Research & Innovation (UKRI), Science & Technology Facilities Council (STFC), Science and Technology Development Fund (STDF) ST/M000877/1, Portuguese Foundation for Science and Technology, European Commission UIDB/04434/2020 UIDP/04434/2020 PTDC/FIS-AST/30389/2017, FEDER - Fundo Europeu de Desenvolvimento Regional through COMPETE2020 - Programa Operacional Competitividade e Internacionalizacao POCI-01-0145-FEDER-030389, European Commission, VILLUMFONDEN 00028173, Danmarks Grundforskningsfond DNRF106 FWO 1286521N, Lendulet Program of the Hungarian Academy of Sciences LP2018-7/2020, EU's MW-Gaia COST Action CA18104, Max Planck Society, Foundation CELLEX, ALMA-CONICYT 31170029, Hungarian Academy of Sciences, UNAM under grant PAPIIT IN100918, Natural Sciences and Engineering Research Council of Canada (NSERC), National Astronomical Research Institute of Thailand (NARIT), Spanish public funds the Spanish Ministry of Science, Innovation and Universities (MCIU) PID2019-107061GB-C63 PRE2018-084322 ESP2017-87676-C5-5-R, '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), State Agency for Research through the 'Center of Excellence Severo Ochoa' award from the Spanish Ministry of Science, Innovation and Universities (MCIU) SEV-2017-0709, National Science Foundation (NSF), NSF - Office of the Director (OD) PHY-1359195, National Aeronautics & Space Administration (NASA) 80GSFC21M0002, New National Excellence Program of the Ministry of Human Capacities UNKP-20-5, City of Szombathely 67.177-21/2016, 'FEDER/Junta de Andalucia-Consejeria de Economia y Conocimiento' by Universidad de Granada E-FQM-041-UGR18, Spanish public funds (FEDER) ESP2017-87676-C5-2-R, Polish NCN 2015/18/A/ST9/00578, NASA's Science Mission directorate, European Space Agency PEA 4000119301, Stellar Astrophysics Centre (SAC) at Aarhus University

Full list of authors: Plachy, E.; Pál, A.; Bódi, A.; Szabó, P.; Molnár, L.; Szabados, L.; Benkő, J. M.; Anderson, R. I.; Bellinger, E. P.; Bhardwaj, A.; Ebadi, M.; Gazeas, K.; Hambsch, F. -J.; Hasanzadeh, A.; Jurkovic, M. I.; Kalaee, M. J.; Kervella, P.; Kolenberg, K.; Mikołajczyk, P.; Nardetto, N. Nemec, J. M.; Netzel, H.; Ngeow, C. -C.; Ozuyar, D.; Pascual-Granado, J.; Pilecki, B.; Ripepi, V.; Skarka, M.; Smolec, R.; Sódor, Á.; Szabó, R.; Christensen-Dalsgaard, J.; Jenkins, J. M.; Kjeldsen, H.; Ricker, G. R.; Vanderspek, R., We present the first analysis of Cepheid stars observed by the TESS space mission in Sectors 1–5. Our sample consists of 25 pulsators: ten fundamental mode, three overtone and two double-mode classical Cepheids, plus three type II and seven anomalous Cepheids. The targets were chosen from fields with different stellar densities, both from the Galactic field and from the Magellanic System. Three targets have 2 minutes cadence light curves available by the TESS Science Processing Operations Center: for the rest, we prepared custom light curves from the full-frame images with our own differential photometric FITSH pipeline. Our main goal was to explore the potential and the limitations of TESS concerning the various subtypes of Cepheids. We detected many low-amplitude features: weak modulation, period jitter, and timing variations due to light-time effect. We also report signs of nonradial modes and the first discovery of such a mode in an anomalous Cepheid, the overtone star XZ Cet, which we then confirmed with ground-based multicolor photometric measurements. We prepared a custom photometric solution to minimize saturation effects in the bright fundamental-mode classical Cepheid, β Dor with the lightkurve software, and we revealed strong evidence of cycle-to-cycle variations in the star. In several cases, however, fluctuations in the pulsation could not be distinguished from instrumental effects, such as contamination from nearby sources, which also varies between sectors. Finally, we discuss how precise light-curve shapes will be crucial not only for classification purposes but also to determine physical properties of these stars. © 2021. The American Astronomical Society. All rights reserved., The research leading to these results has been supported by the Hungarian National Research, Development and Innovation Office (NKFIH) grants KH_18 130405, K-125015, GINOP 2.3.2-15-2016-00033, and NN-129075, and the Lendulet LP2014-17 and LP2018-7/2020 grants of the Hungarian Academy of Sciences (HAS). The work reported on in this publication has been supported by the MW-Gaia COST Action (CA18104). Partial funding of the computational infrastructure and database servers were received from the grant KEP-7/2018 of the HAS. E.P. was supported by the Janos Bolyai Research Scholarship of the HAS. L.M. was supported by the Premium Postdoctoral Research Program of the HAS. C.C.N. thanks the funding from Ministry of Science and Technology (Taiwan) under the contract 107-2119-M-008014-MY2. Funding for the Stellar Astrophysics Centre is provided by The Danish National Research Foundation (grant agreement No. DNRF106). R.Sm. was supported by the National Science Center, Poland, Sonata BIS project 2018/30/E/ST9/00598. M.I.J. was supported by the Ministry of Education, Science and Technological Development (contract number 451-03-68/2020-14/200002) of Republic of Serbia. A.B. acknowledges a Gruber fellowship 2020 grant sponsored by the Gruber Foundation and the International Astronomical Union and is supported by the EACOA Fellowship Program under the umbrella of the East Asia Core Observatories Association, which consists of the Academia Sinica Institute of Astronomy and Astrophysics, the National Astronomical Observatory of Japan, the Korea Astronomy and Space Science Institute, and the National Astronomical Observatories of the Chinese Academy of Sciences. J.P.G. acknowledges financial support from the State Agency for Research of the Spanish MCIU through the "Center of Excellence Severo Ochoa" award to the Instituto de Astrofisica de Andalucia (SEV-2017-0709) and from Spanish public funds for research under project ESP2017-87676-C5-5-R. P.M. acknowledges support from the NCN grant No. 2016/21/B/ST9/01126. M.S. acknowledges the financial support of the Operational Program Research, Development and Education-Project Postdoc@MUNI(No.CZ.02.2.69/0.0/0.0/16_027/0008360) and the MSMT Inter Transfer program LTT20015. P.K. and N.N. acknowledge the support of the French Agence Nationale de la Recherche (ANR), under grant ANR-15-CE31-0012-01 (project UnlockCepheids). The research leading to these results has received funding from the European Research Council (ERC) under the European Union's Horizon 2020 research and innovation program (grant agreement No. 695099). This work has made use of data from the European Space Agency (ESA) mission Gaia (http://www.cosmos.esa.int/gaia), processed by the Gaia Data Processing and Analysis Consortium (DPAC, http://www.cosmos.esa.int/web/gaia/dpac/consortium).Funding for the DPAC has been provided by national institutions, in particular the institutions participating in the Gaia Multilateral Agreement. This paper includes data collected by the TESS mission. Funding for the TESS mission is provided by NASAs Science Mission directorate. Resources supporting this work were provided by the NASA High-End Computing (HEC) Program through the NASA Advanced Supercomputing (NAS) Division at Ames Research Center for the production of the SPOC data products.

We present the results of the Fermi-Large Area Telescope 10 yr long light curve (LC) modeling of selected blazars: six flat-spectrum radio quasars (FSRQs) and five BL Lacertae (BL Lacs), examined in 7, 10, and 14 day binning. The LCs and power spectral densities (PSDs) were investigated with various methods: Fourier transform, Lomb-Scargle periodogram (LSP), wavelet scalogram, autoregressive moving average (ARMA) process, continuous-time ARMA (CARMA), Hurst exponent (H), and the A-T plane. First, with extensive simulations we showed that parametric modeling returns unreliable parameters, with a high dispersion for different realizations of the same stochastic model. Hence, any such analysis should be supported with Monte Carlo simulations. For our blazar sample, we find that the power-law indices beta calculated from the Fourier and LSP modeling mostly fall in the range 1 less than or similar to beta less than or similar to 2. Using the wavelet scalograms, we confirm a quasi-periodic oscillation (QPO) in PKS 2155-304 at a 3 sigma significance level, but do not detect any QPOs in other objects. The ARMA fits reached higher orders for 7 day binned LCs and lower orders for 10 and 14 day binned LCs for the majority of blazars, suggesting there might exist a characteristic timescale for the perturbations in the jet and/or accretion disk to die out. ARMA and CARMA modeling revealed breaks in their PSDs at timescales of a few hundred days. The estimation ofHwas performed with several methods. We find that most blazars exhibit H > 0.5, indicating long-term memory. Finally, the FSRQ and BL Lac subclasses are clearly separated in the A-T plane. © 2020. The American Astronomical Society. All rights reserved., M.T. acknowledges support by the Polish National Science Center (NSC) through OPUS grant No. 2017/25/B/ST9/01208. The work of N.Z. is supported by the South African Research Chairs Initiative (grant No. 64789) of the Department of Science and Innovation and the National Research Foundation27 of South Africa. V.M. is supported by NSC grant No. 2016/22/E/ST9/00061. J.P.-G. acknowledges financial support from the State Agency for Research of the Spanish MCIU through the "Center of Excellence Severo Ochoa" award to the Instituto de Astrofisica de Andalucia (SEV-2017-0709) and from Spanish public funds for research under project ESP2017-87676-C5-5-R.

Open Access. Attribution 4.0 International (CC BY 4.0), This paper aims at being a provocative guide to the future of asteroseismology from the perspective of the analysis of time series, where the fundamentals of harmonic analysis are subjected to stress tests. In this context, we give an annotated summary of our research over the last decades on harmonic analysis of A-F stars. We discuss and explore the consequences of our findings, which may extend to any kind of pulsators. As well, we analyse the impact of this reconsideration on future asteroseismic studies, which would entail a paradigm shift. This includes a discussion on the presence of fractal behavior in delta Sct stars, and how this can be used to develop a stopping criterion of the pre-whitening process, as an alternative to SNR (or significance) criterion. Drilling a scientific paradigm has its natural resilience, hence the path described here is being arduous, although fruitful at the same time., SF, JP-G, JR, ML-M, and RG acknowledges financial support from the State Agency for Research of the Spanish MCIU through the Center of Excellence Severo Ochoa award for the Instituto de Astrofisica de Andalucia (SEV-2017-0709) and Spanish public funds for research under projects ESP2015-65712C5-5-R. JS and AG acknowledge funding support from Spanish public funds for research under projects ESP2017-87676-C5-2R. JS also acknowledges funding support from project RYC2012-09913 under the Ramon y Cajal program of the Spanish MINECO. AG acknowledges support from Universidad de Granada under project E-FQM-041-UGR18 from the Programa Operativo FEDER 2014-2020 programme by Junta de Andalucia regional Government.

The work reported here demonstrates that it is possible to accurately determine surface gravities of $\delta$ Sct stars using the frequency content from high precision photometry and a measurement of the parallax. Using a sample of 10 eclipsing binary systems with a $\delta$ Sct component and the unique $\delta$ Sct star discovered with a transiting planet, WASP-33, we were able to refine the $\Delta\nu-\bar\rho$ relation. Using this relation and parallaxes, we obtained independent values for the masses and radii, allowing us to calculate the surface gravities without any constraints from spectroscopic or binary analysis. A remarkably good agreement was found between our results and those published, extracted from the analysis of the radial velocities and light curves of the systems. This reinforces the potential of $\Delta\nu$ as a valuable observable for $\delta$ Sct stars and settles the degeneracy problem for the $\log g$ determination through spectroscopy., Comment: 5 pages, 2 figures, 1 table

We present the first results from the Transiting Exoplanet Survey Satellite (TESS) on the rotational and pulsational variability of magnetic chemically peculiar A-type stars. We analyse TESS 2-min cadence data from sectors 1 and 2 on a sample of 83 stars. Five new rapidly oscillating Ap (roAp) stars are announced. One of these pulsates with periods around 4.7 min, making it the shortest period roAp star known to date. Four out of the five new roAp stars are multiperiodic. Three of these and the singly periodic one show the presence of rotational mode splitting. Individual frequencies are provided in all cases. In addition, seven previously known roAp stars are analysed. Additional modes of oscillation are found in some stars, while in others we are able to distinguish the true pulsations from possible aliases present in the ground-based data. We find that the pulsation amplitude in the TESS filter is typically a factor of 6 smaller than that in the B filter, which is usually used for ground-based observations. For four roAp stars we set constraints on the inclination angle and magnetic obliquity, through the application of the oblique pulsator model. We also confirm the absence of roAp-type pulsations down to amplitude limits of 6 and 13 \mumag, respectively, in two of the best characterized non-oscillating Ap (noAp) stars. We announce 27 new rotational variables along with their rotation periods, and provide different rotation periods for seven other stars. Finally, we discuss how these results challenge state-of-the-art pulsation models for roAp stars.© 2019 The Author(s) Published by Oxford University Press on behalf of the Royal Astronomical Society., This work was supported by FCT - Fundacao para a Ciencia e a Tecnologia through national funds and by FEDER through COMPETE02020 - Programa Operacional Competitividade e Internacionalizacao by these grants: UID/FIS/04434/2019, PTDC/FIS-AST/30389/2017 & POCI-01-0145-FEDER-030389. MC is supported in the form of work contract funded by national funds through FCT. Funding for the Stellar Astrophysics Centre is provided by The Danish National Research Foundation (Grant agreement no.: DNRF106). DLH and DWK acknowledge financial support from the Science and Technology Facilities Council (STFC) via grant ST/M000877/1. This work has made use of data from the European Space Agency (ESA) mission Gaia (https://www.cosmos.esa.int/gaia), processed by the Gaia Data Processing and Analysis Consortium (DPAC, https://www.cosmos.esa.int/web/gaia/dpac/consortium).Funding for the DPAC has been provided by national institutions, in particular the institutions participating in the Gaia Multilateral Agreement. LFM acknowledges support from the UNAM by the way of DGAPA project PAPIIT IN100918. The research leading to these results has received funding from the European Research Council (ERC) under the European Union's Horizon 2020 research and innovation programme (grant agreement No670519: MAMSIE) and from the Fonds Wetenschappelijk Onderzoek -Vlaanderen (FWO) under the grant agreement G0H5416N (ERC Opvangproject). MS acknowledges the financial support of Postdoc@MUNI project CZ.02.2.69/0.0/0.0/16 027/0008360. EN acknowledges the Polish National Science Center grants no. 2014/13/B/ST9/00902. JCS acknowledges funding support from Spanish public funds for research under projects ESP2017-87676-2-2 and ESP2015-65712-C5-5-R, and from project RYC-2012-09913 under the 'Ramon y Cajal' program of the Spanish Ministry of Science and Education. AGH acknowledges funding support from Spanish public funds for research under projects ESP2017-87676-2-2 and ESP2015-65712-C5-5-R of the Spanish Ministry of Science and Education. AS, ZsB, and RSz acknowledge the financial support of the GINOP-2.3.2-15-2016-00003, K-115709, K-113117, K-119517, and PD-123910 grants of the Hungarian National Research, Development and Innovation Office (NKFIH), and the Lendulet Program of the Hungarian Academy of Sciences, project No. LP2018-7/2018. GH has been supported by the Polish NCN grant 2015/18/A/ST9/00578. MLM acknowledges funding support from Spanish public funds for research under project ESP2015-65712-C5-3-R. JPG acknowledges funding support from Spanish public funds for research under project ESP2017-87676-C5-5-R. MLM and JPG also acknowledges funding support from the State Agency for Research of the Spanish MCIU through the 'Center of Excellence Severo Ochoa' award for the Institute de Astrofisica de Andalucia (SEV-2017-0709). IS acknowledges funding support of NSF under projects DN 08-1/2016 and DN 18/13-12.12.2017. P. Kolaczek-Szymanski acknowledges support from the NCN grant no. 2016/21/B/ST9/01126. This paper includes data collected by the TESS mission. Funding for the TESS mission is provided by the NASA Explorer Program.

We report an analysis of the first known β Cep pulsator observed by the Transiting Exoplanet Survey Satellite (TESS) mission, the runaway star PHL 346 = HN Aqr. The star, previously known as a singly periodic pulsator, has at least 34 oscillation modes excited, 12 of those in the g-mode domain and 22 p modes. Analysis of archival data implies that the amplitude and frequency of the dominant mode and the stellar radial velocity were variable over time. A binary nature would be inconsistent with the inferred ejection velocity from the Galactic disk of 420 km s -1 , which is too large to be survivable by a runaway binary system. A kinematic analysis of the star results in an age constraint (23 +1 Myr) that can be imposed on asteroseismic modeling and that can be used to remove degeneracies in the modeling process. Our attempts to match the excitation of the observed frequency spectrum resulted in pulsation models that were too young. Hence, asteroseismic studies of runaway pulsators can become vital not only in tracing the evolutionary history of such objects, but to understand the interior structure of massive stars in general. TESS is now opening up these stars for detailed asteroseismic investigation. © 2019. The American Astronomical Society. All rights reserved.., This Letter includes data collected by the TESS mission. Funding for the TESS mission is provided by the NASA Explorer Program. Funding for the TESS Asteroseismic Science Operations Centre is provided by the Danish National Research Foundation (grant agreement No.: DNRF106), ESA PRODEX (PEA 4000119301) and Stellar Astrophysics Centre (SAC) at Aarhus University. We thank the TESS team and staff and TASC/TASOC for their support of the present work. This work is also based on observations collected at the European Southern Observatory under ESO programme 383.D-0909(A). Funding through the Polish NCN grants 2015/18/A/ST9/00578, 2016/21/B/ST9/01126, 2015/17/B/ST9/02082 and 2014/13/B/ST9/00902 is gratefully acknowledged. G.M.M. acknowledges funding by the STFC consolidated grant ST/R000603/1. The research leading to these results has received funding from the European Research Council (ERC) under the European Union's Horizon 2020 research and innovation programme (grant agreement No. 670519: MAMSIE). S.S.-D. acknowledges funding by the Spanish MCIU (projects AYA2015-68012-C2-1-P and SEV2015-0548) and the Gobierno de Canarias (project ProID2017010115).

Context. It is known that the observed distribution of frequencies in CoRoT and Kepler δ 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 δ Scuti stars. However, some studies have pointed out that this technique might introduce biases in the results of the frequency analysis. Aims. 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, only in the range of the pulsational frequency content of the δ Scuti stars, is shown to be crucial to determining their oscillation frequencies, the first step in performing asteroseismology of these objects. Hence, here we focus on the impact of pre-whitening on the asteroseismic characterization of δ Scuti stars. Methods. We select a sample of 15 δ 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 δ Scuti stars we perform the pre-whitening procedure on three datasets: gapped data, linearly interpolated data, and data with gaps interpolated using Autoregressive and Moving Average models (ARMA). Results. 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 a minimum, in addition to performing a pre-whitening of the data, it is necessary to interpolate with an algorithm that is aimed to preserve the original frequency content.© ESO 2018., JPG acknowledge support from the “Junta de Andalucía” local government under project 2012-P12-TIC-2469. JCS and AGH acknowledge funding support from Spanish public funds for research under project ESP2015-65712-C5-5-R (MINECO/FEDER), and from project RYC-2012-09913 under the “Ramón y Cajal” programme of the Spanish MINECO. JCS also acknowledge support by the European FP7 project “SPACEINN” (FP7-SPACE-2011-1). AM acknowledges support by the Spanish MINECO National Space Program through project ESP2015-65712-C5-1-R and “Ramon y Cajal” program RYC-2012-09913. This project has received funding from the European Union’s Horizon 2020 research and innovation programme under the Marie Sklodowska-Curie grant agreement No 749962.

Fractal behaviour, i.e. scale invariance in spatio-temporal dynamics, has 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 ¿ Scuti pulsating stars. In fact from the fractal and multifractal fingerprints in the background noise of the light curves we could infer properties of different mechanisms of stellar dynamic, among them rotation, modes excitation and magnetic activity. © 2018 The Author(s)., SdF, JPG and RG acknowledge funding support from Spanish public funds for research under projects ESP2015-65712-C5-3-R. JCS acknowledges funding support from Spanish public funds for research under projects ESP2017-87676-2-2 and ESP2015-65712-C5-5-R, and from project RYC-2012-09913 under the 'Ramon y Cajal' program of the Spanish MINECO. SdF, JPG and RG acknowledge support from the 'Junta de Andalucia' regional government under project 2012-P12-TIC-2469.

The power of asteroseismology relies on the ability to infer the stellar structure from the unambiguous frequency identification of the corresponding pulsation mode. Hence, the use of a Fourier transform is in the basis of asteroseismic studies. Nevertheless, the difficulties with the interpretation of the frequencies found in many stars lead us to reconsider whether Fourier analysis is the most appropriate technique to identify pulsation modes. We have found that the data, usually analyzed using Fourier techniques, present a non-analyticity originating from the lack of connectivity of the underlying function describing the physical phenomena. Therefore, the conditions for the Fourier series to converge are not fulfilled. In the light of these results, we examine in this talk some stellar light curves from different asteroseismology space missions (CoRoT, Kepler and SoHO) in which the interpretation of the data in terms of Fourier frequencies becomes difficult. We emphasize the necessity of a new interpretation of the stellar light curves in order to identify the correct frequencies of the pulsation modes., 5 pages, 5 figures, contributed talk for IAU Symposium No. 301 'Precision Asteroseismology', J.A. Guzik, W.J. Chaplin, G. Handler & A. Pigulski, eds

Delta Scuti ($\delta$ 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 $\delta$ 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 $\delta$ Sct stars., Comment: 11 pages, including 2 pages of appendix, 2 figures, 2 tables, accepted for publication in ApJL

Invalid flux measurements, caused mainly by the South Atlantic Anomaly crossing of the CoRoT satellite, introduce aliases in the periodogram and wrong amplitudes. It has been demonstrated that replacing such invalid data with a linear interpolation is not harmless. On the other side, using power spectrum estimators for unevenly sampled time series is not only less computationally efficient but it leads to difficulties in the interpretation of the results. Therefore, even when the gaps are rather small and the duty cycle is high enough the use of gap-filling methods is a gain in frequency analysis. However, the method must preserve the information contained in the time series. In this work we give a short description of an information preserving method (MIARMA) and show some results when applying it to CoRoT seismo light curves. The method is implemented as the second step of a pipeline for CoRoT data analysis.

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.

In this work, we present a new method to determine the surface gravity of δ Sct stars. We used a refined Δν=ρ̄ relation and the stellar parallaxes or luminosities to determine their masses and radii. A comparison with the data obtained from the binary analysis, has shown that the values found by both methods are equivalent, within the uncertainties. Moreover, thanks to the refined relation, the uncertainties in log g are of the order of those usually estimated with high-resolution spectroscopy. Because of that, this new method to determine the surface gravity is an important step forward to break the degeneracy problem in the spectroscopic analysis., AGH acknowledges support from Fundação para a Ciência e a Tecnologia (FCT,Portugal) through the fellowship SFRH/BPD/80619/2011 and from grant UID/FIS/04434/2013.AGH, MJPFGM and JCS acknowledge support from the EC Project SPACEINN (FP7-SPACE-2012-312844) .JCSalsoacknowledges funding support from the Spanish “Ministerio de Economía y Competitividad” under“Ramón y Cajal”subprogram. This research made use of the SIMBAD database and the VizieR catalogue access tool operated at CDS, Strasbourg, France, and the SAO/NASA Astrophysics Data System.

Using ultra-precise data from space instrumentation, we found that the underlying functions of stellar light curves from some AF pulsating 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 type of variable stars. More importantly, this constitutes the first counterexample against the current paradigm, which considers that any physical process is described by a continuous (band-limited) function that is infinitely differentiable.

Context. Gaps in time series cause spurious frequencies in the power spectra. In light curves of pulsating stars, this hampers identifying the theoretical oscillation modes. When these gaps are smaller than the total time span, the commonly used approach to overcome these difficulties involves linear interpolation. The original frequency content of the pulsating stars is not preserved in the resulting time series.Aims. The method presented here intends to minimize the effect of the gaps in the power spectra by gap-filling that preserves at best the original information, that is, the stellar oscillation frequency content for asteroseismology.Methods. We used a forward-backward predictor based on autoregressive moving-average modelling (ARMA) in the time domain. The algorithm 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 selected a sample of stars from the ultra-precise photometry collected by the asteroseismic camera on board the CoRoT satellite: the δ 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.Results. We show that in some cases linear interpolations are less reliable than previously believed. The ARMA interpolation method provides a cleaner power spectrum, that is, less contaminated by spurious frequencies. In summary, MIARMA appears to be a suitable method for filling gaps in the light curves of pulsating stars observed by CoRoT since the method aims to preserve their frequency content, which is a necessary condition for asteroseismic studies.

The need for a proper interpolation method for data coming from space missions like CoRoT is emphasized. A new gap-filling method is introduced which is based on auto-regressive moving average interpolation (ARMA) models. The method is tested on light curves from stars observed by the CoRoT satellite, filling the gaps caused by the South Atlantic Anomaly.