Light Curves Of Variable Stars Research Articles

Automatic Detection of Plateau Phases in Light Curves of Variable Stars

Modern astronomical surveys produce millions of light curves of variable sources. These massive data sets challenge the community to create automatic light-curve processing methods for detection, classification, and characterization of variable stars. In this paper, we present a novel method for extracting the variable components of a light curve based on Otsu’s thresholding method. To validate the effectiveness of this method, we apply it to the light curves of detached eclipsing binaries and dwarf novae, sourced from Optical Gravitational Lensing Experiment catalogs.

Extending time-series models for irregular observational gaps with a moving average structure for astronomical sequences

ABSTRACT In this study, we introduce a novel moving-average model for analyzing stationary time-series observed irregularly in time. The process is strictly stationary and ergodic under normality and weakly stationary when normality is not assumed. Maximum likelihood (ML) estimation can be efficiently carried out through a Kalman algorithm obtained from the state-space representation of the model. The Kalman algorithm has order O(n) (where n is the number of observations in the sequence), from which it is possible to efficiently generate parameter estimators, linear predictors, and their mean-squared errors. Two procedures were developed for assessing parameter estimation errors: one based on the Hessian of the likelihood function and another one based on the bootstrap method. The behaviour of these estimators was assessed through Monte Carlo experiments. Both methods give accurate estimation performance, even with relatively small number of observations. Moreover, it is shown that for non-Gaussian data, specifically for the Student's t and generalized error distributions, the parameters of the model can be estimated precisely by ML. The proposed model is compared to the continuous autoregressive moving average (MA) models, showing better performance when the MA parameter is negative or close to one. We illustrate the implementation of the proposed model with light curves of variable stars from the OGLE and HIPPARCOS surveys and stochastic objects from Zwicky Transient Facility. The results suggest that the irregular MA model is a suitable alternative for modelling astronomical light curves, particularly when they have negative autocorrelation.

Classification of periodic variable stars with novel cyclic-permutation invariant neural networks

ABSTRACT We present Cyclic-Permutation Invariant Neural Networks, a novel class of neural networks (NNs) designed to be invariant to phase shifts of period-folded periodic sequences by means of ‘symmetry padding’. In the context of periodic variable star light curves, initial phases are exogenous to the physical origin of the variability and should thus be immaterial to the downstream inference application. Although previous work utilizing NNs commonly operated on period-folded light curves, no approach to date has taken advantage of such a symmetry. Across three different data sets of variable star light curves, we show that two implementations of Cyclic-Permutation Invariant Networks—iTCN and iResNet—consistently outperform state-of-the-art non-invariant baselines and reduce overall error rates by between 4 to 22 per cent. Over a 10-class OGLE-III sample, the iTCN/iResNet achieves an average per-class accuracy of 93.4 per cent/93.3 per cent, compared to recurrent NN/random forest accuracies of 70.5 per cent/89.5 per cent in a recent study using the same data. Finding improvement on a non-astronomy benchmark, we suggest that the methodology introduced here should also be applicable to a wide range of science domains where periodic data abounds.

Image-based Classification of Variable Stars: First Results from Optical Gravitational Lensing Experiment Data

Abstract Recently, machine learning methods have presented a viable solution for the automated classification of image-based data in various research fields and business applications. Scientists require a fast and reliable solution in order to handle increasingly large amounts of astronomical data. However, so far astronomers have been mainly classifying variable starlight curves based on various pre-computed statistics and light curve parameters. In this work we use an image-based Convolutional Neural Network to classify the different types of variable stars. We use images of phase-folded light curves from the Optical Gravitational Lensing Experiment (OGLE)-III survey for training, validating, and testing, and use OGLE-IV survey as an independent data set for testing. After the training phase, our neural network was able to classify the different types between 80% and 99%, and 77%–98%, accuracy for OGLE-III and OGLE-IV, respectively.

Towards a 1% measurement of the Hubble constant: accounting for time dilation in variable-star light curves

Assessing the significance and implications of the recently established Hubble tension requires the comprehensive identification, quantification, and mitigation of uncertainties and/or biases affecting H0 measurements. Here, we investigate the previously overlooked distance scale bias resulting from the interplay between redshift and Leavitt laws in an expanding Universe: Redshift-Leavitt bias (RLB). Redshift dilates oscillation periods of pulsating stars residing in supernova-host galaxies relative to periods of identical stars residing in nearby (anchor) galaxies. Multiplying dilated log P with Leavitt Law slopes leads to underestimated absolute magnitudes, overestimated distance moduli, and a systematic error on H0. Emulating the SH0ES distance ladder, we estimate an associated H0 bias of (0.27 ± 0.01)% and obtain a corrected H0 = 73.70 ± 1.40 km s−1 Mpc−1. RLB becomes increasingly relevant as distance ladder calibrations pursue greater numbers of ever more distant galaxies hosting both Cepheids (or Miras) and type-Ia supernovae. The measured periods of oscillating stars can readily be corrected for heliocentric redshift (e.g. of their host galaxies) in order to ensure H0 measurements free of RLB.

Weighted recurrence networks for the analysis of time-series data

Recurrence networks (RNs) have become very popular tools for the nonlinear analysis of time-series data. They are unweighted and undirected complex networks constructed with specific criteria from time series. In this work, we propose a method to construct a ‘weighted recurrence network’ from a time series and show that it can reveal useful information regarding the structure of a chaotic attractor which the usual unweighted RN cannot provide. Especially, a network measure, the node strength distribution, from every chaotic attractor follows a power law (with exponential cut off at the tail) with an index characteristic to the fractal structure of the attractor. This provides a new class among complex networks to which networks from all standard chaotic attractors are found to belong. Two other prominent network measures, clustering coefficient and characteristic path length, are generalized and their utility in discriminating chaotic dynamics from noise is highlighted. As an application of the proposed measure, we present an analysis of variable star light curves whose behaviour has been reported to be strange non-chaotic in a recent study. Our numerical results indicate that the weighted recurrence network and the associated measures can become potentially important tools for the analysis of short and noisy time series from the real world.

The Outer Halo of the Milky Way as Probed by RR Lyr Variables from the Palomar Transient Facility*

Abstract RR Lyrae stars are ideal massless tracers that can be used to study the total mass and dark matter content of the outer halo of the Milky Way (MW). This is because they are easy to find in the light-curve databases of large stellar surveys and their distances can be determined with only knowledge of the light curve. We present here a sample of 112 RR Lyr stars beyond 50 kpc in the outer halo of the MW, excluding the Sgr streams, for which we have obtained moderate-resolution spectra with Deimos on the Keck II Telescope. Four of these have distances exceeding 100 kpc. These were selected from a much larger set of 447 candidate RR Lyr stars that were data-mined using machine-learning techniques applied to the light curves of variable stars in the Palomar Transient Facility database. The observed radial velocities taken at the phase of the variable corresponding to the time of observation were converted to systemic radial velocities in the Galactic standard of rest. From our sample of 112 RR Lyr stars we determine the radial velocity dispersion in the outer halo of the MW to be ∼90 km s−1 at 50 kpc, falling to about 65 km s−1 near 100 kpc once a small number of major outliers are removed. With reasonable estimates of the completeness of our sample of 447 candidates and assuming a spherical halo, we find that the stellar density in the outer halo declines as .

Effect of data gaps on correlation dimension computed from light curves of variable stars

Observational data, especially astrophysical data, is often limited by gaps in data that arises due to lack of observations for a variety of reasons. Such inadvertent gaps are usually smoothed over using interpolation techniques. However the smoothing techniques can introduce artificial effects, especially when non-linear analysis is undertaken. We investigate how gaps can affect the computed values of correlation dimension of the system, without using any interpolation. For this we introduce gaps artificially in synthetic data derived from standard chaotic systems, like the R{\"o}ssler and Lorenz, with frequency of occurrence and size of missing data drawn from two Gaussian distributions. Then we study the changes in correlation dimension with change in the distributions of position and size of gaps. We find that for a considerable range of mean gap frequency and size, the value of correlation dimension is not significantly affected, indicating that in such specific cases, the calculated values can still be reliable and acceptable. Thus our study introduces a method of checking the reliability of computed correlation dimension values by calculating the distribution of gaps with respect to its size and position. This is illustrated for the data from light curves of three variable stars, R Scuti, U Monocerotis and SU Tauri. We also demonstrate how a cubic spline interpolation can cause a time series of Gaussian noise with missing data to be misinterpreted as being chaotic in origin. This is demonstrated for the non chaotic light curve of variable star SS Cygni, which gives a saturated D$_{2}$ value, when interpolated using a cubic spline. In addition we also find that a careful choice of binning, in addition to reducing noise, can help in shifting the gap distribution to the reliable range for D$_2$ values.

Multiperiodicity, modulations, and flip-flops in variable star light curves

We study LQ Hya photometry for 1982-2014 with the carrier fit (CF) -method and compare our results to earlier photometric analysis and recent Doppler imaging maps. We first utilize different types of statistical methods to estimate various candidates for the carrier period for the CF method. Secondly, a global fit to the whole data set and local fits to shorter segments are computed with the period that is found to be the optimal one. The harmonic least-squares analysis of all the available data reveals a short period close to 1.6 days as a limiting value for a set of significant frequencies. We interpret this as the rotation period of the spots near the equatorial region. In addition, the distribution of the significant periods is found to be bimodal, hinting of a longer-term modulating period, which we set out to study with a two-harmonic CF model. Weak modulation signal is, indeed retrieved, with a period of roughly 6.9 years. The phase dispersion analysis gives a clear symmetric minimum for coherence times lower than and around 100 days. We interpret this as the mean rotation period of the spots (1.60514 days), and this value is chosen to be used as the carrier period for the CF analysis. With the CF method we seek for any systematic trends in the spot distribution in the global time frame, and locally look for abrupt phase changes earlier reported in rapidly rotating objects. During 2005-2008 the global CF reveals a coherent structure rotating with a period of 1.6037 days, while during most other times the spot distribution appears rather random in phase. The evolution of the spot distribution of the object is found to be very chaotic, with no clear signs of an azimuthal dynamo wave that would persist over longer time scales, although the short-lived coherent structures observed occasionally do not rotate with the same speed as the mean spot distribution.

A comparison of period finding algorithms

This paper presents a comparison of popular period finding algorithms applied to the light curves of variable stars from the Catalina Real-time Transient Survey (CRTS), MACHO and ASAS data sets. We analyze the accuracy of the methods against magnitude, sampling rates, quoted period, quality measures (signal-to-noise and number of observations), variability, and object classes. We find that measure of dispersion-based techniques - analysis-of-variance with harmonics and conditional entropy - consistently give the best results but there are clear dependencies on object class and light curve quality. Period aliasing and identifying a period harmonic also remain significant issues. We consider the performance of the algorithms and show that a new conditional entropy-based algorithm is the most optimal in terms of completeness and speed. We also consider a simple ensemble approach and find that it performs no better than individual algorithms.

Estimating the parameters of globular cluster M 30 (NGC 7099) from time-series photometry

We present the analysis of 26 nights of V and I time-series observations from 2011 and 2012 of the globular cluster M 30 (NGC 7099). We used our data to search for variable stars in this cluster and refine the periods of known variables; we then used our variable star light curves to derive values for the cluster's parameters. We used difference image analysis to reduce our data to obtain high-precision light curves of variable stars. We then estimated the cluster parameters by performing a Fourier decomposition of the light curves of RR Lyrae stars for which a good period estimate was possible. We also derive an estimate for the age of the cluster by fitting theoretical isochrones to our colour-magnitude diagram (CMD). Out of 13 stars previously catalogued as variables, we find that only 4 are bona fide variables. We detect two new RR Lyrae variables, and confirm two additional RR Lyrae candidates from the literature. We also detect four other new variables, including an eclipsing blue straggler system, and an SX Phoenicis star. This amounts to a total number of confirmed variable stars in M 30 of 12. We perform Fourier decomposition of the light curves of the RR Lyrae stars to derive cluster parameters using empirical relations. We find a cluster metallicity [Fe/H]_ZW=-2.01 +- 0.04, or [Fe/H]_UVES=-2.11 +- 0.06, and a distance of 8.32 +- 0.20 kpc (using RR0 variables), 8.10 kpc (using one RR1 variable), and 8.35 +- 0.42 kpc (using our SX Phoenicis star detection in M 30). Fitting isochrones to the CMD, we estimate an age of 13.0 +- 1.0 Gyr for M 30.

Multiperiodicity, modulations and flip-flops in variable star light curves

The light curves of variable stars are commonly described using simple trigonometric models, that make use of the assumption that the model parameters are constant in time. This assumption, however, is often violated, and consequently, time series models with components that vary slowly in time are of great interest. In this paper we introduce a class of data analysis and visualization methods which can be applied in many different contexts of variable star research, for example spotted stars, variables showing the Blazhko effect, and the spin-down of rapid rotators. The methods proposed are of explorative type, and can be of significant aid when performing a more thorough data analysis and interpretation with a more conventional method.Our methods are based on a straightforward decomposition of the input time series into a fast "clocking" periodicity and smooth modulating curves. The fast frequency, referred to as the carrier frequency, can be obtained from earlier observations (for instance in the case of photometric data the period can be obtained from independently measured radial velocities), postulated using some simple physical principles (Keplerian rotation laws in accretion disks), or estimated from the data as a certain mean frequency. The smooth modulating curves are described by trigonometric polynomials or splines. The data approximation procedures are based on standard computational packages implementing simple or constrained least-squares fit-type algorithms.

Difference image photometry with bright variable backgrounds

Over the last two decades the Andromeda Galaxy (M31) has been something of a test-bed for methods aimed at obtaining accurate time-domain relative photometry within highly crowded fields. Difference imaging methods, originally pioneered towards M31, have evolved into sophisticated methods, such as the Optimal Image Subtraction (OIS) method of Alard & Lupton (1998), that today are most widely used to survey variable stars, transients and microlensing events in our own Galaxy. We show that modern difference image (DIA) algorithms such as OIS, whilst spectacularly successful towards the Milky Way bulge, may perform badly towards high surface brightness targets such as the M31 bulge. Poor results can occur in the presence of common systematics which add spurious flux contributions to images, such as internal reflections, scattered light or fringing. Using data from the Angstrom Project microlensing survey of the M31 bulge, we show that very good results are usually obtainable by first performing careful photometric alignment prior to using OIS to perform point-spread function (PSF) matching. This separation of background matching and PSF matching, a common feature of earlier M31 photometry techniques, allows us to take full advantage of the powerful PSF matching flexibility offered by OIS towards high surface brightness targets. We find that difference images produced this way have noise distributions close to Gaussian, showing significant improvement upon results achieved using OIS alone. We show that with this correction light-curves of variable stars and transients can be recovered to within ~10 arcseconds of the M31 nucleus. Our method is simple to implement and is quick enough to be incorporated within real-time DIA pipelines. (Abridged)

Mira variables in the OGLE bulge fields

The 222 000 I-band light curves of variable stars detected by the OGLE-II survey in the direction of the Galactic Bulge have been fitted and also correlated with the DENIS and 2MASS all-sky release databases and with lists of known objects. Lightcurves and the results of the lightcurve fitting (periods and amplitudes) and DENIS and 2MASS data are presented for 2691 objects with I-band semi-amplitude larger than 0.45 mag, corresponding to classical Mira variables. That the Mira period distribution of 6 fields at similar longitude but spanning latitudes from -1.2 to -5.8 are statistically indistinguishable indicates similar populations with initial masses of 1.5-2 M ○. , corresponding to ages of 1-3 Gyr. A field at similar longitude at b = -0.05 from Glass et al. (2001, MNRAS, 321, 77; erratum: 2002, MNRAS, 336, 1390) does show a significantly different period distribution, indicating the presence of a younger population of 2.5-3 M ○. and ages below 1 Gyr. The K-band period-luminosity relation is presented for the whole sample and for sub-fields. The zero point depends on Galactic longitude. Simulations are carried out to show that the observed dependence of the zero point with l, and the number of stars per field are naturally explained using the model of disk and bulge stars of Binney et al. (1997, MNRAS, 288, 365), for a viewing angle (major-axis Bar - axis perpendicular to the line-of-sight to the Galactic Centre) of 43 ± 17 degrees. The simulations also show that biases in the observed zero point are small, <0.02 mag. A comparison is made with similar objects in the Magellanic Clouds. The slope of the PL-relation in the Bulge and the MCs agree within the errorbars. Assuming the zero point does not depend on metallicity, distance modulus difference of 3.72 between Bulge and LMC is derived. This implies a LMC DM of 18.21 for an assumed distance to the Galactic Centre (GC) of 7.9 kpc, or, assuming a LMC DM of 18.50, a distance to the GC of 9.0 kpc. From the results in Groenewegen (2004, A&A, 425, 595) it is found for carbon-rich Miras that the PL-relation implies a relative SMC-LMC DM of 0.38, assuming no metallicity dependence. This is somewhat smaller than the often quoted value near 0.50. Following theoretical work by Wood (1990, in From Miras to Planetary Nebulae, ed. M. 0. Mennessier, & A. Omont (Gif-sur-Yvette: Editions Frontieres), 67) a metallicity term of the form M K ∼ log Z is introduced. If a relative SMC-LMC DM of 0.50 is imposed, β = 0.4 is required, and for that value the distance to the GC becomes 8.6 ± 0.7 kpc (for a LMC DM of 18.50), within the errorbar of the geometric determination of 7.9 ± 0.4 kpc. An independent estimate leads to a distance estimate to the GC of 8.8 ± 0.4 kpc.

Eclipsing binaries in the Galactic bulge: candidates for distance estimates

The 222~000 I-band light curves of variable stars detected by the OGLE-II survey in the direction of the Galactic Bulge have been searched for eclipsing binaries (EBs). A previously developed code to analyze lightcurve shapes and identify long period variables (LPVs) has been adapted to identify EBs. The parameters in the modified code have been optimised to recover a list of about 140 detached EBs in the Small Magellanic Cloud previously identified in the literature as particularly well suited for distance estimates (and wich have periods \more 0.85 days). The power of the code is demonstrated by identifying 16 and 178 previously uncatalogued EBs in the SMC and LMC, respectively. Among the 222~000 variable stars in the direction of the Galactic Bulge 3053 EBs have been identified. Periods and phased lightcurves are presented.

On the Nature of Stochastic Excited Oscillations: Subdwarf B Star PG 1605+072 as a Case Study

It is well known that the near discontinuities of the background state thermodynamic quantities, like those encountered in the upper layers of some stars, reflect acoustic-gravity waves and thereby partially contain them within the stellar interior. These reflections help to establish resonant cavities in which oscillations of discrete characteristic frequencies propagate. These oscillations, when excited, produce variations on the light curve. We present an investigation of the observed light curves of variable stars using a theoretical time series calculated on the assumption that the observed light curve is the superposition of sinusoidal waves of a given frequency, each one representing a stellar pulsation. By analyzing different simulated light curves, we show that the nature of the excitation of pulsating stars can be gathered from the time dependence of the observed mode's amplitudes, in spite of the limited information contained in some observational data. This analysis is based on the temporal variation of the oscillation amplitudes during several consecutive nights. It is expected that if an oscillation is excited and damped by a mechanism in stochastic equilibrium, the probability distribution of its amplitude, A, will be well defined. An interesting property is that the ratio of the standard deviation σA over the mean value μA is of the order of 0.52. Furthermore, we show from observational light curves that there is no stochastic mechanism exciting the oscillations in the subdwarf B star PG 1605+072. This new independent observational result solidifies the case that in subdwarf B stars, pulsations are originated by the excitation of intrinsically overstable modes.

Long Period Variables in the Magellanic Clouds: OGLE + 2 MASS + DENIS

The 68 000 I-band light curves of variable stars detected by the  survey in the Large and Small Magellanic Clouds (MCs) are fitted by Fourier series, and also correlated with the  and 2 all-sky release databases and with lists of spectroscopically confirmed M-, S- and C-stars. Lightcurves and the results of the lightcurve fitting (periods and amplitudes) and  and 2 magnitudes are presented for 2277 M-, S-, C-stars in the MCs. The following aspects are discussed: the K-band period-luminosity relations for the spectroscopically confirmed AGB stars, period changes over a timespan of about 17 years in a subset of about 400 LPVs, and candidate obscured AGB stars. The use of a sample of spectroscopically confirmed variables shows specifically that almost all carbon stars are brighter than the tip of the RGB, and occupy sequences A+, B+, C and D. It is shown (for the LMC where there is a sufficient number of spectroscopically identified M-stars) that for sequences A+ ,B +, C the M-stars are on average fainter than the C-stars, as expected from an evolutionary point of view and previously observed in MC clusters. However, this is not so for sequence D, suggesting that the origin of the so-called Long Secondary Periods is not related to an evolutionary effect. The fraction of objects that has a period in sequence D is also independent of chemical type. Three stars are identified that have been classified as oxygen-rich in the 1970s and carbon-rich in 1990s. Possibly they underwent a thermal pulse in the last 20 years, and dredged-up enough carbon to switch spectral type. The observations over almost two decades seem to suggest that up to 10% of AGB variables changed pulsation mode over that time span. More robust estimates will come from the ongoing and future (microlensing) photometric surveys. A sample of 570 variable red objects ((J − K) > 2.0 or (I − K) > 4.0) is presented in which most stars are expected to be dust-obscured AGB stars. Estimates are presented for cut-off si n (J −K) which should be applied to minimise dust obscuration in K, and based on this, C- and O-star K-band PL-relations for large amplitude variables in the SMC and LMC are presented.

The analyses of the light curves of magnetic CP stars by advanced PCA methods

We present a new method of phenomenologically modelling light curves of variable stars using Principal Component Analysis techniques that provide a realistic description of the variability with a minimum of free parameters. Examples of this method are demonstrated for the magnetic CP stars HD 90044 and HD 125248.To search for other articles by the author(s) go to: http://adsabs.harvard.edu/abstract_service.html

A Method for Optimal Image Subtraction

We present a new method designed for optimal subtraction of two images with different seeing. Using image subtraction appears to be essential for the full analysis of the microlensing survey images, however a perfect subtraction of two images is not easy as it requires the derivation of an extremely accurate convolution kernel. Some empirical attempts to find the kernel have used the Fourier transform of bright stars, but solving the statistical problem of finding the best kernel solution has never really been tackled. We demonstrate that it is possible to derive an optimal kernel solution from a simple least square analysis using all the pixels of both images, and also show that it is possible to fit the differential background variation at the same time. We also show that PSF variations can also be easily handled by the method. To demonstrate the practical efficiency of the method, we analyzed some images from a Galactic Bulge field monitored by the OGLE II project. We find that the residuals in the subtracted images are very close to the photon noise expectations. We also present some light curves of variable stars, and show that, despite high crowding levels, we get an error distribution close to that expected from photon noise alone. We thus demonstrate that nearly optimal differential photometry can be achieved even in very crowded fields. We suggest that this algorithm might be particularly important for microlensing surveys, where the photometric accuracy and completeness levels could be very significantly improved by using this method.

Light curves of variable stars: a pictorial atlas

Light curves of variable stars: a pictorial atlas