Phase-folded Light Curve Research Articles

New orbital periods of high-inclination dwarf novae based on Gaia Alerts photometry

The orbital period of a cataclysmic variable stands as a crucial parameter for investigating the structure and physics of these binary systems, as well as understanding their evolution. We use photometric Gaia data for dwarf novae (DNe) in the quiescent state ---which are available for a number of years--- to determine new orbital periods and improve or modify previously suggested period values. Two approaches are implemented for selecting high-inclination targets, either eclipsing or with ellipsoidal variations. We determine new orbital periods for 75 DNe and improve ephemerides for 27 more (three of which change significantly), contributing 9.4<!PCT!> of the known DNe periods of between 0.05 and 2.0 days, and doubling the number of known periods exceeding 0.44 days. Their phase-folded light curves are presented and arranged by orbital period, illustrating the transition from short-period systems, dominated by radiation from the accretion disc and the hot spot, to longer-period DNe, where the Roche-lobe-filling secondary star is the primary visual flux source. This transition ---which occurs around the well-known period gap (between sim 2 and 3 hours)--- is expected, as DNe with larger orbital periods typically harbour more massive donors, which contribute to the visible flux. However, this transition is not abrupt. Within the same range of periods, we observe systems dominated by ellipsoidal variations, where the companion star is clearly visible, as well as others dominated by the disc and the hot spot. The presence of some DNe with ellipsoidal variations near the lower edge of the period gap is striking, as the companions in these systems are expected to be cool low-mass M-dwarfs not visible in the light curve. This could indicate that we are observing systems where the donor star was originally much more massive and underwent significant nuclear evolution before mass-transfer began, as has been suggested previously for QZ Ser.

A Phase-resolved View of “Heartbeat”-like Variability in IGR J17091-3624 during the 2022 Outburst

IGR J17091–3624, in addition to GRS 1915 + 105, is the only black hole X-ray binary that displays “heartbeat”-like variability, characterized by structured flares with high amplitudes. In this study, we conduct a detailed phase-resolved analysis of the recently identified “heartbeat”-like Class X variability in IGR J17091–3624 during its 2022 outburst, utilizing data from NICER and NuSTAR observations. A shortage in the high-energy (>20 keV) X-ray flux is detected at peak phases of the soft-X-ray flare at a ∼15σ confidence level from the phase-folded light curves. Furthermore, our phase-resolved spectral analysis reveals variations in the spectral shape, particularly showing significant synchronous variations in the disk temperature and flux with the count rate. These findings imply that the flare is primarily driven by instabilities within the accretion disk, consistent with previous studies of the well-known Class ρ variability in GRS 1915+105. However, we also observe a positive correlation between the disk temperature and flux over the flare cycle, which differs from the loop relation between the two parameters found in the Class ρ variability. This could suggest differences in the underlying physical processes between the two variability classes. Variations in the Comptonization component during flares are also observed: the electron temperature and covering fraction show anticorrelations with the disk flux, revealing potential interactions between the accretion disk and the corona during these flares.

Application of Convolutional Neural Networks to time domain astrophysics. 2D image analysis of OGLE light curves

In recent years the amount of publicly available astronomical data has increased exponentially, with a remarkable example being large-scale multiepoch photometric surveys. This wealth of data poses challenges to the classical methodologies commonly employed in the study of variable objects. As a response, deep learning techniques are increasingly being explored to effectively classify, analyze, and interpret these large datasets. In this paper we use two-dimensional histograms to represent Optical Gravitational Lensing Experiment (OGLE) phasefolded light curves as images. We use a Convolutional Neural Network (CNN) to classify variable objects within eight different categories (from now on labels): Classical Cepheid (CEP), RR Lyrae (RR), Long Period Variable (LPV), Miras (M), Ellipsoidal Binary (ELL), Delta Scuti (DST), Eclipsing Binary (E), and spurious class with Incorrect Periods (Rndm). We set up different training sets to train the same CNN architecture in order to characterize the impact of the training. The training sets were built from the same source of labels but different filters and balancing techniques were applied. Namely: Undersampling (U), Data Augmentation (DA), and Batch Balancing (BB). The best performance was achieved with the BB approach and a training sample size of sim 370000 stars. Regarding computational performance, the image representation production rate is of sim 76 images per core per second, and the time to predict is sim 60$\ s $ per star. The accuracy of the classification improves from sim 92<!PCT!>, when based only on the CNN, to sim 98<!PCT!> when the results of the CNN are combined with the period and amplitude features in a two step approach. This methodology achieves comparable results with previous studies but with two main advantages: the identification of miscalculated periods and the improvement in computational time cost.

A False Positive Transit Candidate for EPIC 211101996 from K2 and TESS Data Identified as Background Eclipsing Binary Gaia DR3 66767847894609792

Transiting planets around young stars are hard to find due to the enhanced stellar activity. Only a few transiting planets have been detected around stars younger than 100 Myr. We initially detected a transit-like signal in the K2 light curve of a very cool M dwarf star (EPIC 211101996) in the Pleiades open cluster, with an estimated age of about 100 Myr. Our detailed analysis of the per-pixel light curves, detrending with the Wōtan software and transit search with the Transit Least Squares algorithm showed that the source of the signal is a contaminant source (Gaia DR3 66767847894609792) 20″ west of the target. The V-like shape of its phase-folded light curve and eclipse depth of ∼15% suggest that it is a grazing eclipsing binary. The contaminant has hitherto been listed as a single star, which we now identify as an eclipsing stellar binary with a period of about 6 days.

Secondary eclipse and day-night modulation of exoplanets observed by transiting exoplanet survey satellite

Astronomers have identified over five thousand extrasolar planets since the discovery of the first solar-like star in 1995. These systems exhibit greater diversity than our solar system, providing insights into their formation and evolution. To understand these exoplanets and their habitability, it is crucial to examine their atmosphere composition. The Transiting Exoplanet Survey Satellite (TESS) can detect reflected light from exoplanets with high accuracy, providing valuable insights into their formation and potential for life in the Universe. Planetary reflection can be detected by monitoring the light curve, which is the sum of stellar flux and planetary reflection. Orbiting planets may also reveal their presence by modulating reflected starlight, showing day-night variations in observers sight lines. However, these flux variations are extremely small, at a level of 0.01%, making detection difficult. This study developed an efficient Python program to search for secondary eclipse and day-night modulation on the TESS light curves of over four hundred known short-period transiting exoplanets. The program automatically identifies and rejects low-quality photometric data points in light curves, folding high-quality light curves in the orbital phase determined by primary transits. The phase-folded average light curves have high photometric precision, suitable for detecting secondary eclipse and day-night modulation. The program successfully identified planetary reflection in seventeen transiting exoplanetary systems, larger than the current TESS sample by twice. The program plans to upgrade to search for orbital phase modulation in non-transit exoplanets, taking advantage of the high precision of TESS photometry.

A Chandra search for periodic X-ray sources in the bulge of M31

ABSTRACT We present a systematic search for periodic X-ray sources in the bulge of M31, using ∼2 Ms of archival Chandra observations spanning a temporal baseline of 16 yr. Utilizing the Gregory–Loredo algorithm that is designed for photon-counting, phase-folded light curves, we detect seven periodic X-ray sources, among which four are newly discovered. Three of these sources are novae, the identified periods of which range between 1.3 and 2.0 h and are most likely the orbital period. The other four sources are low-mass X-ray binaries, the identified periods of which range between 0.13 and 19.3 h and are also likely orbital due to a clear eclipsing/dipping behaviour in the light curve. We address implications on the X-ray binaries population of the M31 bulge. Our study demonstrates the potential of using archival X-ray observations to systematically identify periodic X-ray sources in external galaxies, which would provide valuable information about the underlying exotic stellar populations.

Recovery of High-energy Low-frequency Quasiperiodic Oscillations from Black Hole X-Ray Binary MAXI J1535–571 with a Hilbert–Huang Transform Method

We propose a method based on the Hilbert–Huang transform (HHT) to recover the high-energy waveform of low-frequency quasiperiodic oscillations (QPOs). Based on the method, we successfully obtain the modulation of the phase-folded light curve above 170 keV using the QPO phase reconstructed at lower energies in MAXI J1535–571 with Insight-HXMT observations. A comprehensive simulation study is conducted to demonstrate that such modulation indeed originates from the QPO. Thus, the highest energies turn out to significantly exceed the upper limit of ∼100 keV for QPOs reported previously using the Fourier method, marking the first opportunity to study QPO properties above 100 keV in this source. Detailed analyses of these high-energy QPO profiles reveal different QPO properties between the 30–100 and 100–200 keV energy ranges: the phase lag remains relatively stable, and the amplitude slightly increases below ∼100 keV, whereas above this threshold, soft phase lags and a decrease in amplitude are observed. Given the reports of a hard-tail detection in broad spectroscopy, we propose that the newly discovered QPO properties above 100 keV are dominated by the hard-tail component, possibly stemming from a relativistic jet. Our findings also indicate a strong correlation between the QPOs originating from the jet and corona, supporting the scenario of jet–corona coupling precession. We emphasize that our proposed HHT-based method can serve as an efficient manner in expanding the high-energy band for studying QPOs, thereby enhancing our understanding of their origin.

Computing Transiting Exoplanet Parameters with 1D Convolutional Neural Networks

The transit method allows the detection and characterization of planetary systems by analyzing stellar light curves. Convolutional neural networks appear to offer a viable solution for automating these analyses. In this research, two 1D convolutional neural network models, which work with simulated light curves in which transit-like signals were injected, are presented. One model operates on complete light curves and estimates the orbital period, and the other one operates on phase-folded light curves and estimates the semimajor axis of the orbit and the square of the planet-to-star radius ratio. Both models were tested on real data from TESS light curves with confirmed planets to ensure that they are able to work with real data. The results obtained show that 1D CNNs are able to characterize transiting exoplanets from their host star’s detrended light curve and, furthermore, reducing both the required time and computational costs compared with the current detection and characterization algorithms.

The verification of periodicity with the use of recurrent neural networks

Abstract The ability to automatically and robustly self-verify periodicity present in time-series astronomical data is becoming more important as data sets rapidly increase in size. The age of large astronomical surveys has rendered manual inspection of time-series data less practical. Previous efforts in generating a false alarm probability to verify the periodicity of stars have been aimed towards the analysis of a constructed periodogram. However, these methods feature correlations with features that do not pertain to periodicity, such as light-curve shape, slow trends, and stochastic variability. The common assumption that photometric errors are Gaussian and well determined is also a limitation of analytic methods. We present a novel machine learning based technique which directly analyses the phase-folded light curve for its false alarm probability. We show that the results of this method are largely insensitive to the shape of the light curve, and we establish minimum values for the number of data points and the amplitude to noise ratio.

Soft X-ray and FUV observations of Nova Her 2021 (V1674 Her) with AstroSat

ABSTRACT Nova Her 2021 or V1674 Her was one of the fastest novae to be observed so far. We report here the results from our timing and spectral studies of the source observed at multiple epochs with AstroSat. We report the detection of a periodicity in the source in soft X-rays at a period of 501.4–501.5 s which was detected with high significance after the peak of the super-soft phase, but was not detected in the far ultraviolet (FUV) band of AstroSat. The shape of the phase-folded X-ray light curves has varied significantly as the nova evolved. The phase-resolved spectral studies reveal the likely presence of various absorption features in the soft X-ray band of 0.5–2 keV, and suggest that the optical depth of these absorption features may be marginally dependent on the pulse phase. Strong emission lines from Si, N, and O are detected in the FUV, and their strength declined continuously as the nova evolved and went through a bright X-ray state.

A candidate of binary black hole system in AGN with broad Balmer emission lines having quite different line widths

ABSTRACT In this paper, a candidate of sub-pc binary black hole (BBH) system is reported in SDSS J1257+2023 through different properties of broad Balmer emission lines. After subtractions of host galaxy contributions, Gaussian functions are applied to measure emission lines in SDSS J1257+2023, leading line width (second moment) 760 km s−1 of broad H β to be 0.69 times of line width 1100 km s−1 of broad H α, quite different from normal line width ratio 1.1 of broad H β to broad H α in quasars. The quite broader component in broad H α in SDSS J1257+2023 can be confirmed with confidence level higher than 5σ through F-test technique, through different model functions applied to measure emission lines. The broad Balmer emission lines having different line widths can be naturally explained by a BBH system with different obscurations on central two independent broad emission line regions. Meanwhile, through Zwicky Transient Facility (ZTF) light curves and corresponding phase folded light curves well described by sinusoidal function, BBH system expected optical quasi-periodic oscillations (QPOs) can be detected with periodicity about 1000 d, confirmed with confidence level higher than 3σ by generalized Lomb–Scargle periodogram. And through Continuous AutoRegressive process simulated light curves, confidence level higher than 2σ can be determined to support the optical QPOs in SDSS J1257+2023 not from intrinsic AGN activities, although the ZTF light curves have short time durations. Moreover, through oversimplified BBH system simulated results, studying different broad Balmer lines as signs of BBH systems in normal quasars with flux ratios around 4 of broad H α to broad H β could be done in near future.

The Detection of Possible γ-Ray Quasi-periodic Modulation with ∼600 days from the Blazar S2 0109+22

In this work, we analyzed the long-term γ-ray data by a Fermi Large Area Telescope of blazar S2 0109+22, ranging from 2008 to 2023. The quasi-periodic oscillations (QPOs) of blazars aided in investigating the physical properties of internal supermassive black holes, the nature of variability, and the underlying radiation mechanism. We employed four different methods—Weighted Wavelet Z-transform, Lomb–Scargle periodogram, REDFIT and phase folded light curve analysis, for searching QPO signals. Our analysis identified a possible QPO behavior with a periodicity of ∼600 days in 2013 November–2023 January at a significance level of ∼3.5σ. This QPO signal sustained ∼9 yr, corresponding to 5.6 cycles, which was in good agreement with the previously observed periodicity of ∼657 days in radio. We explained this phenomenon based on the accretion model and the lighthouse effect, in a binary black hole system.

A Systematic Search for Short-period Close White Dwarf Binary Candidates Based on Gaia EDR3 Catalog and Zwicky Transient Facility Data

Galactic short-period close white dwarf binaries (CWDBs) are important objects for space-borne gravitational-wave (GW) detectors in the millihertz frequency bands. Due to the intrinsically low luminosity, only about 25 identified CWDBs are detectable by the Laser Interferometer Space Antenna (LISA), which are also known as verification binaries (VBs). The Gaia Early Data Release 3 (EDR3) provids a catalog containing a large number of CWDB candidates, which also includes parallax and photometry measurements. We crossmatch the Gaia EDR3 and Zwicky Transient Facility public data release 8, and apply period-finding algorithms to obtain a sample of periodic variables. The phase-folded light curves are inspected, and finally we obtain a binary sample containing 429 CWDB candidates. We further classify the samples into eclipsing binaries (including 58 HW Vir-type binaries, 65 EA-type binaries, 56 EB-type binaries, and 41 EW-type binaries) and ellipsoidal variations (209 ELL-type binaries). We discovered four ultrashort period binary candidates with unique light-curve shapes. We estimate the GW amplitude of all of our binary candidates, and calculate the corresponding signal-to-noise ratio (S/N) for TianQin and LISA. We find two (six) potential GW candidates with S/Ns greater than 5 in the nominal mission time of TianQin (LISA), which increases the total number of candidate VBs for TianQin (LISA) to 18 (31).

Modeling photometric variations due to a global inhomogeneity on an obliquely rotating star: Application to light curves of white dwarfs

Abstract We develop a general framework to compute photometric variations induced by the oblique rotation of a star with an axisymmetric inhomogeneous surface. We apply the framework to compute light curves of white dwarfs adopting two simple models of their surface inhomogeneity. Depending on the surface model and the location of the observer, the resulting light curve exhibits a departure from a purely sinusoidal curve that is observed for a fraction of white dwarfs. As a specific example, we fit our model to the observed phase-folded light curve of a fast-spinning white dwarf ZTF J190132.9+145808.7 (with a rotation period of 419 s). We find that the size and obliquity angle of the spot responsible for the photometric variation are Δθs ≈ 60° and θ⋆ ≈ 60° or 90°, respectively, implying an interesting constraint on the surface distribution of the magnetic field on white dwarfs.

Variable Star Classification with a Multiple-input Neural Network

In this experiment, we created a Multiple-Input Neural Network, consisting of convolutional and multilayer neural networks. With this setup the selected highest-performing neural network was able to distinguish variable stars based on the visual characteristics of their light curves, while taking also into account additional numerical information (e.g., period, reddening-free brightness) to differentiate visually similar light curves. The network was trained and tested on Optical Gravitational Lensing Experiment-III (OGLE-III) data using all OGLE-III observation fields, phase-folded light curves, and period data. The neural network yielded accuracies of 89%–99% for most of the main classes (Cepheids, δ Scutis, eclipsing binaries, RR Lyrae stars, Type-II Cepheids), only the first-overtone anomalous Cepheids had an accuracy of 45%. To counteract the large confusion between the first-overtone anomalous Cepheids and the RRab stars we added the reddening-free brightness as a new input and only stars from the LMC field were retained to have a fixed distance. With this change we improved the neural network’s result for the first-overtone anomalous Cepheids to almost 80%. Overall, the Multiple-input Neural Network method developed by our team is a promising alternative to existing classification methods.

A 3.8 yr optical quasi-periodic oscillations in blue quasar SDSS J132144+033055 through combined light curves from CSS and ZTF

ABSTRACT In the manuscript, a 3.8 yr optical quasi-periodic oscillations (QPOs) is reported in blue quasar SDSS J132144+033055 (= SDSS J1321) at z = 0.269, based on 16.3yr-long light curve from both CSS and ZTF directly described by a sinusoidal function. The 3.8 yr QPOs can be confirmed through the Generalized Lomb–Scargle periodogram with confidence level higher than 5σ, through properties of the phase-folded light curve and the WWZ technique. Moreover, the collected Pan-STARRS light curves well follow the sinusoidal function described best fitting results to the Catalina Sky Survey (CSS) and Catalina Sky Survey (ZTF) light curves. The optical QPOs strongly indicate a central binary black hole (BBH) system in SDSS J1321, with expected space separation smaller than 0.018 pc, through the estimated upper limit of total BH mass 3.3 × 109 M⊙ through the correlation between BH mass and continuum luminosity. Meanwhile, we check disc precession applied to explain the optical QPOs. However, under the disc precession assumption, the determined optical emission regions from central BH have sizes about 37RG similar as the sizes 35RG of the expected NUV emission regions through the correlation between disc size and BH mass, indicating the disc precession is not preferred. And due to undetected radio emissions, jet precession can be ruled out. Furthermore, only 0.1 per cent probability can determined as the QPOs mis-detected through CAR process randomly created light curves related to intrinsic AGN activities, re-confirming the optical QPOs with significance level higher than 3σ. Therefore, combining long-term light curves from CSS and ZTF can lead to more QPOs candidates in the near future.

Searching for Anomalies in the ZTF Catalog of Periodic Variable Stars

Periodic variables illuminate the physical processes of stars throughout their lifetime. Wide-field surveys continue to increase our discovery rates of periodic variable stars. Automated approaches are essential to identify interesting periodic variable stars for multiwavelength and spectroscopic follow-up. Here we present a novel unsupervised machine-learning approach to hunt for anomalous periodic variables using phase-folded light curves presented in the Zwicky Transient Facility Catalogue of Periodic Variable Stars by Chen et al. We use a convolutional variational autoencoder to learn a low-dimensional latent representation, and we search for anomalies within this latent dimension via an isolation forest. We identify anomalies with irregular variability. Most of the top anomalies are likely highly variable red giants or asymptotic giant branch stars concentrated in the Milky Way galactic disk; a fraction of the identified anomalies are more consistent with young stellar objects. Detailed spectroscopic follow-up observations are encouraged to reveal the nature of these anomalies.

FBLS – a fast-folding BLS algorithm

ABSTRACTWe present fBLS – a novel fast-folding technique to search for transiting planets, based on the fast-folding algorithm (FFA), which is extensively used in pulsar astronomy. For a given light curve with N data points, fBLS simultaneously produces all the binned phase-folded light curves for an array of Np trial periods. For each folded light curve produced by fBLS, the algorithm generates the standard BLS periodogram and statistics. The number of performed arithmetic operations is $\mathcal {O}(N_p\cdot \log N_p)$, while regular BLS requires $\mathcal {O}(N_p\cdot N)$ operations. fBLS can be used to detect small rocky transiting planets, with periods shorter than one day, a period range for which the computation is extensive. We demonstrate the capabilities of the new algorithm by performing a preliminary fBLS search for planets with ultra-short periods in the Kepler main-sequence light curves. In addition, we developed a simplistic signal validation scheme for vetting the planet candidates. This two-stage preliminary search identified all-known ultra-short planet candidates and found three new ones.

Large-amplitude periodic outbursts and long-period variables in the VVV VIRAC2-β data base

ABSTRACT The VISTA Variables in the Via Lactea (VVV) survey obtained near-infrared photometry towards the Galactic bulge and the southern disc plane for a decade (2010–2019). We designed a modified Lomb–Scargle method to search for large-amplitude ($\Delta K_{s, 2-98{{\ \rm per\ cent}}}$ > 1.5 mag) mid to long-term periodic variables (P> 10 d) in the 2nd version of VVV Infrared Astrometric Catalogue (VIRAC2-β). In total, 1520 periodic sources were discovered, including 59 candidate periodic outbursting young stellar objects (YSOs), based on the unique morphology of the phase-folded light curves, proximity to Galactic H ii regions and mid-infrared colours. Five sources are spectroscopically confirmed as accreting YSOs. Both fast-rise/slow-decay and slow-rise/fast-decay periodic outbursts were found, but fast-rise/slow-decay outbursts predominate at the highest amplitudes. The multiwavelength colour variations are consistent with a variable mass accretion process, as opposed to variable extinction. The cycles are likely to be caused by dynamical perturbations from stellar or planetary companions within the circumstellar disc. An additional search for periodic variability amongst YSO candidates in published Spitzer-based catalogues yielded a further 71 candidate periodic accretors, mostly with lower amplitudes. These resemble cases of pulsed accretion but with unusually long periods and greater regularity. The majority of other long-period variables are pulsating dusty Miras with smooth and symmetric light curves. We find that some Miras have redder W3 − W4 colours than previously thought, most likely due to their surface chemical compositions.

The Impact of Observing Strategy on the Reliable Classification of Standard Candle Stars: Detection of Amplitude, Period, and Phase Modulation (Blazhko Effect) of RR Lyrae Stars with LSST

Abstract The Vera C. Rubin Observatory will carry out its Legacy Survey of Space and Time (LSST) with a single-exposure depth of r ∼ 24.7 and an anticipated baseline of 10 yr, allowing access to the Milky Way’s old halo not only deeper than, but also with a longer baseline and better cadence than, e.g., PS1 3π. This will make the LSST ideal to study populations of variable stars such as RR Lyrae stars (RRL). Here, we address the question of observing strategy optimization of LSST, as survey footprint definition, single-visit exposure time, as well as the cadence of repeat visits in different filters are yet to be finalized. We present metrics used to assess the impact of different observing strategies on the reliable detectability and classification of standard candle variable stars, including detection of amplitude, period, and phase modulation effects of RRL (the so-called Blazhko effect), by evaluating metrics for simulated potential survey designs. So far, due to the depths and cadences of typical all-sky surveys, it has been nearly impossible to study this effect on a larger sample. All-sky surveys with relatively few observations over a moderately long baseline allow only for fitting phase-folded RRL light curves, thus integrating over the complete survey length and hiding any information regarding possible period or phase modulation during the survey. On the other hand, surveys with cadences fit to detect slightly changing light curves usually have a relatively small footprint. LSST’s survey strategy, however, will allow for studying variable stars in a way that makes population studies possible.