Analysis of pulsating variable stars using the visibility graph algorithm

We study the light curves of pulsating variable stars using a complex network approach to build visibility graphs. We consider various types of variables stars (e.g., Cepheids, δ Scuti, RR Lyrae), build two types of graphs (the normal visibility graph (VG) and the horizontal visibility graph (HVG)), and calculate various metrics for the resulting networks. We find that all networks have a power-law degree distribution for the VG and an exponential distribution for the HVG, suggesting that it is a universal feature, regardless of the pulsation features. Metrics such as the average degree, the clustering coefficient and the transitivity coefficient, can distinguish between some star types. We also observe that the results are not strongly affected by the presence of observation gaps in the light curves. These findings suggest that the visibility graph algorithm may be a useful technique to study variability in stars.

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Inference On Streamflow Predictability Using Horizontal Visibility Graph Based Networks

10.5194/egusphere-egu2020-3744 ◽

2020 ◽

Author(s):

Ganesh Ghimire ◽

Navid Jadidoleslam ◽

Witold Krajewski ◽

Anastasios Tsonis

Keyword(s):

Time Series ◽

Time Scale ◽

Temporal Trends ◽

Characteristic Exponent ◽

Visibility Graph ◽

Clustering Coefficient ◽

Series Data ◽

Dynamical Process ◽

Horizontal Visibility ◽

Horizontal Visibility Graph

<p>Streamflow is a dynamical process that integrates water movement in space and time within basin boundaries. The authors characterize the dynamics associated with streamflow time series data from about seventy-one U.S. Geological Survey (USGS) stream-gauge stations in the state of Iowa. They employ a novel approach called visibility graph (VG). It uses the concept of mapping time series into complex networks to investigate the time evolutionary behavior of dynamical system. The authors focus on a simple variant of VG algorithm called horizontal visibility graph (HVG). The tracking of dynamics and hence, the predictability of streamflow processes, are carried out by extracting two key pieces of information called characteristic exponent, &#955; of degree distribution and global clustering coefficient, GC pertaining to HVG derived network. The authors use these two measures to identify whether streamflow process has its origin in random or chaotic processes. They show that the characterization of streamflow dynamics is sensitive to data attributes. Through a systematic and comprehensive analysis, the authors illustrate that streamflow dynamics characterization is sensitive to the normalization, and the time-scale of streamflow time-series. At daily scale, streamflow at all stations used in the analysis, reveals randomness with strong spatial scale (basin size) dependence. This has implications for predictability of streamflow and floods. The authors demonstrate that dynamics transition through potentially chaotic to randomly correlated process as the averaging time-scale increases. Finally, the temporal trends of &#955; and GC are statistically significant at about 40% of the total number of stations analyzed. Attributing this trend to factors such as changing climate or land use requires further research.</p>

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Theoretical Study of Cepheid Light Curves

International Astronomical Union Colloquium ◽

10.1017/s0252921100109273 ◽

1985 ◽

Vol 82 ◽

pp. 153-156

Author(s):

C. G. Davis

Keyword(s):

Theoretical Study ◽

Heat Engine ◽

Variable Stars ◽

Light Curves ◽

Diffusion Equations ◽

Linear Features ◽

Radiation Diffusion ◽

Rr Lyrae ◽

Non Linear ◽

Linear Effects

Starting with the initial understanding that pulsation in variable stars is caused by the heat engine of Hydrogen and Helium ionization in their atmospheres (A.S. Eddington in Cox 1980) it was soon realized that non-linear effects were responsible for the detailed features on their light and velocity curves. With the advent of the computer we were able to solve the coupled set of hydrodynamics and radiation diffusion equations to model these non-linear features (Christy 1968, Cox et. al. 1966). Calculations including the effects of multi-frequency radiative transfer (Davis 1975) showed that grey diffusion was adequate for modeling Cepheids but not for the RR Lyrae or W Virginis type variables.

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Confirmation of monoperiodicity above 20 s for two blue large-amplitude pulsators

Monthly Notices of the Royal Astronomical Society ◽

10.1093/mnras/staa1560 ◽

2020 ◽

Vol 496 (2) ◽

pp. 1105-1114 ◽

Cited By ~ 1

Author(s):

Paul Ross McWhirter ◽

Marco C Lam ◽

Iain A Steele

Keyword(s):

Gravitational Lensing ◽

Large Amplitude ◽

Variable Stars ◽

Light Curves ◽

Driving Mechanism ◽

New Class ◽

Pulsating Variable Stars ◽

Short Period ◽

Filter Frequency ◽

High Cadence

ABSTRACT Blue large-amplitude pulsators (BLAPs) are a new class of pulsating variable stars. They are located close to the hot subdwarf branch in the Hertzsprung–Russell diagram and have spectral classes of late O or early B. Stellar evolution models indicate that these stars are likely radially pulsating, driven by iron group opacity in their interiors. A number of variable stars with a similar driving mechanism exist near the hot subdwarf branch with multiperiodic oscillations caused by either pressure (p) or gravity (g) modes. No multiperiodic signals were detected in the OGLE (Optical Gravitational Lensing Experiment) discovery light curves since it would be difficult to detect short-period signals associated with higher order p modes with the OGLE cadence. Using the RISE instrument on the Liverpool Telescope, we produced high-cadence light curves of two BLAPs, OGLE-BLAP-009 (mv = 15.65 mag) and OGLE-BLAP-014 (mv = 16.79 mag), using a 720 nm longpass filter. Frequency analysis of these light curves identifies a primary oscillation with a period of 31.935 ± 0.0098 min and an amplitude from a Fourier series fit of 0.236 mag for BLAP-009. The analysis of BLAP-014 identifies a period of 33.625 ± 0.0214 min and an amplitude of 0.225 mag. Analysis of the residual light curves reveals no additional short-period variability down to an amplitude of 15.20 ± 0.26 mmag for BLAP-009 and 58.60 ± 3.44 mmag for BLAP-014 for minimum periods of 20 and 60 s, respectively. These results further confirm that the BLAPs are monoperiodic.

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LSST Observations of RR Lyrae Stars for Mapping the Galactic Halo

Proceedings of the International Astronomical Union ◽

10.1017/s1743921311022988 ◽

2010 ◽

Vol 6 (S277) ◽

pp. 300-304

Author(s):

Hakeem M. Oluseyi ◽

Andrew C. Becker ◽

Christopher C. Culliton ◽

Muhammad Furqan ◽

Keri L. Hoadley ◽

...

Keyword(s):

Light Curve ◽

Local Group ◽

Galactic Halo ◽

Variable Stars ◽

Light Curves ◽

Chemical Compositions ◽

Galactic Halos ◽

Rr Lyrae Stars ◽

Rr Lyrae ◽

Lyrae Stars

AbstractThe Large Synoptic Survey Telescope (LSST) is an anticipated to undertake a 10–year, 3π steradian survey that promises to observe millions of new periodic variable stars. We report on a study to determine the efficiency of the LSST to recover the light curve properties of RR Lyrae stars. An LSST light curve simulation tool was used to sample input idealized light curves or RR Lyrae stars observed in SDSS Stripe 82 data, returning each as it would have been observed by LSST, including realistic photometric scatter, limiting magnitudes, and telescope downtime. Our results show that the LSST will be capable of mapping the spatial distributions and chemical compositions of halo stellar overdensities using RR Lyrae discovered across 3π steradians and out to nearly 1.5 Mpc. LSST will thus enable the mapping of halo merger streams, the discovery of new dwarf galaxies, and the mapping galactic halos throughout the Local Group galaxies.

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The Characteristics of the Field RR Lyrae Stars in the Magellanic Clouds

Symposium - International Astronomical Union ◽

10.1017/s0074180900237364 ◽

1974 ◽

Vol 59 ◽

pp. 107-108

Author(s):

J. A. Graham

Keyword(s):

Stellar Evolution ◽

Large Magellanic Cloud ◽

Variable Stars ◽

Magellanic Cloud ◽

Magellanic Clouds ◽

Light Curves ◽

Rr Lyrae Stars ◽

Rr Lyrae ◽

First Results ◽

Lyrae Stars

The Magellanic Clouds are well known as being very suitable for observing the various stages of stellar evolution. During the last few years, I have been studying the RR Lyrae variable stars in each of the two Clouds. Some first results were reported at IAU Colloquium No. 21 in 1972 (Graham, 1973). Here, I would like to update these results on the basis of more recent data and to comment on some of the characteristics of the field RR Lyrae stars in each system. Periods and light curves are now available for 63 RR Lyrae stars in a 1° x 1.3° field centered on the cluster NGC 1783 in the Large Magellanic Cloud (LMC) and for 62 stars in a 1° x 1.3° field centered on the cluster NGC 121 in the Small Magellanic Cloud (SMC). Both ab and c type variables are represented and, viewed individually, the Cloud RR Lyraes are identical in characteristics to those known in our Galaxy. Studied as groups, however, there are small but significant differences between the RR Lyrae stars in each system. The following four specific features seem to be emerging from the study.

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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

The Astrophysical Journal Supplement Series ◽

10.3847/1538-4365/ac3baf ◽

2021 ◽

Vol 258 (1) ◽

pp. 4

Author(s):

Nina Hernitschek ◽

Keivan G. Stassun

Keyword(s):

Phase Modulation ◽

Variable Stars ◽

Light Curves ◽

Rr Lyrae Stars ◽

Rr Lyrae ◽

Standard Candle ◽

Blazhko Effect ◽

The Impact ◽

Lyrae Stars

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.

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Gaia Data Release 2

Astronomy and Astrophysics ◽

10.1051/0004-6361/201833514 ◽

2018 ◽

Vol 620 ◽

pp. A127 ◽

Cited By ~ 8

Author(s):

László Molnár ◽

Emese Plachy ◽

Áron L. Juhász ◽

Lorenzo Rimoldini

Keyword(s):

Continuous Light ◽

Variable Stars ◽

Light Curves ◽

Case Scenario ◽

Worst Case ◽

Rr Lyrae ◽

Data Release ◽

Cepheid Variables ◽

Bulge Region ◽

Targeted Observations

Context. The second data release of the Gaia mission (DR2) includes an advance catalogue of variable stars. The classifications of these stars are based on sparse photometry from the first 22 months of the mission. Aims. We set out to investigate the purity and completeness of the all-sky Gaia classification results with the help of the continuous light curves of the observed targets from the Kepler and K2 missions, focusing specifically on RR Lyrae and Cepheid pulsators, outside the Galactic bulge region. Methods. We cross-matched the Gaia identifications with the observations collected by the Kepler space telescope. We inspected the light curves visually, then calculated the relative Fourier coefficients and period ratios for the single- and double-mode K2 RR Lyrae stars to further classify them. Results. We identified 1443 and 41 stars classified as RR Lyrae or Cepheid variables in Gaia DR2 in the targeted observations of the two missions and 263 more RR Lyre targets in the full-frame images (FFI) of the original mission. We provide the cross-match of these sources. We conclude that the RR Lyrae catalogue has a completeness between 70–78%, and provide a purity estimate of between 92 and 98% (targeted observations) with lower limits of 75% (FFI stars) and 51% (K2 worst-case scenario). The low number of Cepheids prevents us from drawing detailed conclusions, but the purity of the DR2 sample is estimated to be about 66%.

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The ASAS-SN catalogue of variable stars – IV. Periodic variables in the APOGEE survey

Monthly Notices of the Royal Astronomical Society ◽

10.1093/mnras/stz1681 ◽

2019 ◽

Vol 487 (4) ◽

pp. 5932-5945 ◽

Cited By ~ 9

Author(s):

Michał Pawlak ◽

O Pejcha ◽

P Jakubčík ◽

T Jayasinghe ◽

C S Kochanek ◽

...

Keyword(s):

Visual Inspection ◽

Variable Stars ◽

Eclipsing Binaries ◽

Spectral Lines ◽

Light Curves ◽

Machine Learning Techniques ◽

Red Giants ◽

Rr Lyrae ◽

Learning Techniques ◽

Evolution Experiment

ABSTRACT We explore the synergy between photometric and spectroscopic surveys by searching for periodic variable stars among the targets observed by the Apache Point Observatory Galactic Evolution Experiment (APOGEE) using photometry from the All-Sky Automated Survey for Supernovae (ASAS-SN). We identified 1924 periodic variables among more than $258\, 000$ APOGEE targets; 465 are new discoveries. We homogeneously classified 430 eclipsing and ellipsoidal binaries, 139 classical pulsators (Cepheids, RR Lyrae, and δ Scuti), 719 long-period variables (pulsating red giants), and 636 rotational variables. The search was performed using both visual inspection and machine learning techniques. The light curves were also modelled with the damped random walk stochastic process. We find that the median [Fe/H] of variable objects is lower by 0.3 dex than that of the overall APOGEE sample. Eclipsing binaries and ellipsoidal variables are shifted to a lower median [Fe/H] by 0.2 dex. Eclipsing binaries and rotational variables exhibit significantly broader spectral lines than the rest of the sample. We make ASAS-SN light curves for all the APOGEE stars publicly available and provide parameters for the variable objects.

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Statistical Investigation of Physical and Geometrical Parameters in Close Binaries using the ASAS Database

Proceedings of the International Astronomical Union ◽

10.1017/s1743921311026950 ◽

2011 ◽

Vol 7 (S282) ◽

pp. 73-74 ◽

Cited By ~ 1

Author(s):

J. Nedoroščik ◽

M. Vaňko ◽

Š. Parimucha

Keyword(s):

Light Curve ◽

Fourier Coefficients ◽

Variable Stars ◽

Statistical Investigation ◽

Eclipsing Binaries ◽

Light Curves ◽

Close Binaries ◽

Geometrical Parameters ◽

Statistical Research ◽

Pulsating Variable Stars

AbstractThe main goal of this work was to find dependencies between Fourier coefficients, which were developed by light curve fitting with Fourier polynomials. The light curves were acquired from the ASAS database (All Sky Automated Survey). In this statistical research it was necessary to sort and modify these data, because light curves of eclipsing binaries are just part of a bigger database, which contains the light curves of pulsating variable stars, novas etc. It was required to phase and normalize all of our light curves, that it could be possible to use a program to fit light curves with Fourier coefficients. Thereafter, we were looking for relations between Fourier coefficients.

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The Absolute Magnitudes of the RR Lyrae Stars

Highlights of Astronomy ◽

10.1017/s1539299600000897 ◽

1971 ◽

Vol 2 ◽

pp. 771-776

Author(s):

Richard Woolley

Keyword(s):

Classical Method ◽

Variable Stars ◽

Rr Lyrae Stars ◽

Rr Lyrae ◽

Pulsating Variable Stars ◽

Stellar Diameters ◽

Cepheid Variables ◽

The Absolute ◽

Absolute Magnitudes ◽

Lyrae Stars

The absolute magnitudes of pulsating variable stars, both RR Lyrae stars and Cepheid variables, may be assessed from observation in three ways: by the classical method of statistical parallaxes, by their occurrence in star clusters whose distance is otherwise known, particularly by ascertaining the position of the main sequence in the HR diagram, and by the Baade-Wesselink method of determining stellar diameters.As regards the first of these, the method of statistical parallaxes, the RR Lyrae stars lend themselves to this better than do the Cepheid variables, because the velocities relative to the Sun are so much larger. RR Lyrae radial velocities are frequently as high as 200 km/sec or even 300 km/sec, and as many of the stars lie at distances between 1000 and 1500 pc the proper motions of the transverse velocities may be expected to be as high as 0”.050 per annum. And, indeed, many investigations have been made recently, among which one may mention those by Plaut, by van Herk, and by the Royal Greenwich Observatory.

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