Variable classification in the LSST era: exploring a model for quasi-periodic light curves

LSST is expected to yield ~10^7 light curves over the course of its mission, which will require a concerted effort in automated classification. Stochastic processes provide one means of quantitatively describing variability with the potential advantage over simple light curve statistics that the parameters may be physically meaningful. Here, we survey a large sample of periodic, quasi-periodic, and stochastic OGLE-III variables using the damped random walk (DRW, CARMA(1,0)) and quasi-periodic oscillation (QPO, CARMA(2,1)) stochastic process models. The QPO model is described by an amplitude, a period, and a coherence time-scale, while the DRW has only an amplitude and a time-scale. We find that the periodic and quasi-periodic stellar variables are generally better described by a QPO than a DRW, while quasars are better described by the DRW model. There are ambiguities in interpreting the QPO coherence time due to non-sinusoidal light curve shapes, signal-to-noise, error mischaracterizations, and cadence. Higher-order implementations of the QPO model that better capture light curve shapes are necessary for the coherence time to have its implied physical meaning. Independent of physical meaning, the extra parameter of the QPO model successfully distinguishes most of the classes of periodic and quasi-periodic variables we consider.

[1]  R. Christy,et al.  A study of pulsation in RR Lyrae models. , 1966 .

[2]  Ciro Donalek,et al.  A novel variability-based method for quasar selection: evidence for a rest-frame ∼54 d characteristic time-scale , 2013, 1401.1785.

[3]  Ciro Donalek,et al.  A systematic search for close supermassive black hole binaries in the Catalina Real-time Transient Survey , 2015, 1507.07603.

[4]  C. Kochanek,et al.  A GLOBAL PHYSICAL MODEL FOR CEPHEIDS , 2011, 1112.3038.

[5]  Edwin A. Valentijn,et al.  Survey and other telescope technologies and discoveries , 2002 .

[6]  Chris Koen,et al.  The analysis of irregularly observed stochastic astronomical time-series—I. Basics of linear stochastic differential equations , 2005 .

[7]  M. Pinsonneault,et al.  Rotation and magnetism of Kepler pulsating solar-like stars : Towards asteroseismically calibrated age-rotation relations , 2014, 1403.7155.

[8]  C. Aerts,et al.  Automated supervised classification of variable stars II. Application to the OGLE database , 2008, 0806.3386.

[9]  Usa,et al.  QUANTIFYING QUASAR VARIABILITY AS PART OF A GENERAL APPROACH TO CLASSIFYING CONTINUOUSLY VARYING SOURCES , 2009, 0909.1326.

[10]  T. Bedding,et al.  Hipparcos Period-Luminosity Relations for Mira and Semiregular variables , 1998, astro-ph/9808173.

[11]  K. Biazzo,et al.  Magnetic activity and differential rotation in the very young star KIC 8429280 , 2011, 1106.4928.

[12]  R. C. Smith,et al.  The morphology of type ia supernovae light curves , 1996 .

[13]  E. O. Ofek,et al.  Automating Discovery and Classification of Transients and Variable Stars in the Synoptic Survey Era , 2011, 1106.5491.

[14]  E. Agol,et al.  QUASAR ACCRETION DISKS ARE STRONGLY INHOMOGENEOUS , 2010, 1012.3169.

[15]  Brandon C. Kelly,et al.  FLEXIBLE AND SCALABLE METHODS FOR QUANTIFYING STOCHASTIC VARIABILITY IN THE ERA OF MASSIVE TIME-DOMAIN ASTRONOMICAL DATA SETS , 2014, 1402.5978.

[16]  Richard Kessler,et al.  PHOTOMETRIC TYPE Ia SUPERNOVA CANDIDATES FROM THE THREE-YEAR SDSS-II SN SURVEY DATA , 2011, 1107.5106.

[17]  Howard Isaacson,et al.  Kepler Planet-Detection Mission: Introduction and First Results , 2010, Science.

[18]  A. J. Drake,et al.  FIRST RESULTS FROM THE CATALINA REAL-TIME TRANSIENT SURVEY , 2008, 0809.1394.

[19]  Daniel Foreman-Mackey,et al.  emcee: The MCMC Hammer , 2012, 1202.3665.

[20]  J. Scargle.  Studies in astronomical time series analysis. II - Statistical aspects of spectral analysis of unevenly spaced data , 1982 .

[21]  W. Press,et al.  Interpolation, realization, and reconstruction of noisy, irregularly sampled data , 1992 .

[22]  J. Pepper,et al.  KELT: The Kilodegree Extremely Little Telescope , 2004, astro-ph/0401220.

[23]  G. Basri,et al.  Rotation and differential rotation of active Kepler stars , 2013, 1308.1508.

[24]  Ray W. Klebesadel,et al.  Observations of Gamma-Ray Bursts of Cosmic Origin , 1973 .

[25]  Pavlos Protopapas,et al.  CLUSTERING-BASED FEATURE LEARNING ON VARIABLE STARS , 2016, ArXiv.

[26]  Jozsef Lazar,et al.  System Description and First Light Curves of the Hungarian Automated Telescope, an Autonomous Observatory for Variability Search , 2002, astro-ph/0206001.

[27]  Pavlos Protopapas,et al.  The EPOCH Project - I. Periodic variable stars in the EROS-2 LMC database , 2014, 1403.6131.

[28]  Canada.,et al.  Data Mining and Machine Learning in Astronomy , 2009, 0906.2173.

[29]  W. T. Vestrand,et al.  Identifying Red Variables in the Northern Sky Variability Survey , 2004 .

[30]  Nathaniel R. Butler,et al.  CONSTRUCTION OF A CALIBRATED PROBABILISTIC CLASSIFICATION CATALOG: APPLICATION TO 50k VARIABLE SOURCES IN THE ALL-SKY AUTOMATED SURVEY , 2012, 1204.4180.

[31]  T. Mazeh,et al.  Measuring the rotation period distribution of field M dwarfs with Kepler , 2013, 1303.6787.

[32]  S. Zoła,et al.  DETECTION OF POSSIBLE QUASI-PERIODIC OSCILLATIONS IN THE LONG-TERM OPTICAL LIGHT CURVE OF THE BL LAC OBJECT OJ 287 , 2016, 1609.02388.

[33]  A. Udalski,et al.  PULSATION MODES OF LONG-PERIOD VARIABLES IN THE PERIOD–LUMINOSITY PLANE , 2013, 1310.7630.

[34]  Sean Becketti,et al.  Introduction to Time Series Using Stata , 2013 .

[35]  L. Eyer,et al.  OGLE small-amplitude variables in the Galactic bar , 2003, astro-ph/0310578.

[36]  Ž. Ivezić,et al.  A DESCRIPTION OF QUASAR VARIABILITY MEASURED USING REPEATED SDSS AND POSS IMAGING , 2011, 1112.0679.

[37]  S. Aigrain,et al.  K2SC: flexible systematics correction and detrending of K2 light curves using Gaussian process regression , 2016, 1603.09167.

[38]  A. Sillanpää,et al.  OJ 287 - Binary pair of supermassive black holes , 1988 .

[39]  R. Zavala,et al.  BREAKING ALL THE RULES: THE COMPACT SYMMETRIC OBJECT 0402+379 , 2003, astro-ph/0310663.

[40]  J. Prieto,et al.  THE SLOAN DIGITAL SKY SURVEY-II SUPERNOVA SURVEY: SEARCH ALGORITHM AND FOLLOW-UP OBSERVATIONS , 2007, 0708.2750.

[41]  Z. Cano,et al.  The Observer's Guide to the Gamma-Ray Burst-Supernova Connection , 2016, 1604.03549.

[42]  L. Ho,et al.  SPECTROSCOPIC INDICATION OF A CENTI-PARSEC SUPERMASSIVE BLACK HOLE BINARY IN THE GALACTIC CENTER OF NGC 5548 , 2016, 1602.05005.

[43]  Eduardo Serrano,et al.  LSST: From Science Drivers to Reference Design and Anticipated Data Products , 2008, The Astrophysical Journal.

[44]  S. Kozłowski,et al.  Limitations on the recovery of the true AGN variability parameters using Damped Random Walk modeling , 2016, 1611.08248.

[45]  C. Koen.  Estimation of the coherence time of stochastic oscillations from modest samples , 2012 .

[46]  Richard A. Davis,et al.  Introduction to time series and forecasting , 1998 .

[47]  B. Enoch,et al.  The WASP Project and the SuperWASP Cameras , 2006, astro-ph/0608454.

[48]  L. M. Sarro,et al.  Automated supervised classification of variable stars - I. Methodology , 2007, 0711.0703.

[49]  S. Rappaport,et al.  Tracking the stellar longitudes of starspots in short-period Kepler binaries , 2014, 1412.8101.

[50]  V. Belokurov,et al.  The OGLE view of microlensing towards the Magellanic Clouds – I. A trickle of events in the OGLE‐II LMC data★ , 2009, 0905.2044.

[51]  Rick Edelson,et al.  KEPLER OBSERVATIONS OF RAPID OPTICAL VARIABILITY IN ACTIVE GALACTIC NUCLEI , 2011, 1111.0672.

[52]  N. Simon,et al.  The Light Curves Of RR Lyrae Field Stars , 1982 .

[53]  P. Wood.  Models of Asymptotic-Giant Stars , 1974 .

[54]  T. Bedding,et al.  The light curve of the semiregular variable L2 Puppis: II. Evidence for solar-like excitation of the oscillations , 2005, astro-ph/0507471.

[55]  E. Bullock,et al.  MODELING THE TIME VARIABILITY OF SDSS STRIPE 82 QUASARS AS A DAMPED RANDOM WALK , 2010, 1004.0276.

[56]  C. Kochanek,et al.  THE MAGELLANIC QUASARS SURVEY. III. SPECTROSCOPIC CONFIRMATION OF 758 ACTIVE GALACTIC NUCLEI BEHIND THE MAGELLANIC CLOUDS , 2013, 1305.6927.

[57]  Christopher Bebek,et al.  The Zwicky Transient Facility: Observing System , 2014, Astronomical Telescopes and Instrumentation.

[58]  Brandon C. Kelly,et al.  Are the Variations in Quasar Optical Flux Driven by Thermal Fluctuations , 2009 .

[59]  Bingqiu Chen,et al.  Analysis of a selected sample of RR Lyrae stars in the LMC from OGLE-III , 2012, 1208.4711.

[60]  T. Boroson,et al.  A Large Systematic Search for Recoiling and Close Supermassive Binary Black Holes , 2011, 1106.2952.

[61]  Richard Kessler,et al.  PHOTOMETRIC SN IA CANDIDATES FROM THE THREE-YEAR SDSS-II SN SURVEY DATA , 2022 .

[62]  S. Gezari,et al.  A PERIODICALLY VARYING LUMINOUS QUASAR AT z = 2 FROM THE PAN-STARRS1 MEDIUM DEEP SURVEY: A CANDIDATE SUPERMASSIVE BLACK HOLE BINARY IN THE GRAVITATIONAL WAVE-DRIVEN REGIME , 2015, Proceedings of the International Astronomical Union.

[63]  N. Simon,et al.  The Structural Properties Of Cepheid Light Curves , 1981 .

[64]  A. Udalski,et al.  The Optical Gravitational Lensing Experiment. Final Reductions of the OGLE-III Data , 2008, 0807.3884.

[65]  Leslie Greengard,et al.  Fast Direct Methods for Gaussian Processes , 2014, IEEE Transactions on Pattern Analysis and Machine Intelligence.

[66]  P. Uttley,et al.  False periodicities in quasar time-domain surveys , 2016, 1606.02620.

[67]  N. Lomb.  Least-squares frequency analysis of unequally spaced data , 1976 .

[68]  S. Woosley,et al.  The Evolution and Explosion of Massive Stars. II. Explosive Hydrodynamics and Nucleosynthesis , 1995 .

[69]  Mark Clampin,et al.  Transiting Exoplanet Survey Satellite (TESS) , 2014, Astronomical Telescopes and Instrumentation.

[70]  C. S. Kochanek,et al.  AN ALTERNATIVE APPROACH TO MEASURING REVERBERATION LAGS IN ACTIVE GALACTIC NUCLEI , 2010, 1008.0641.

[71]  Donald W. Sweeney,et al.  LSST Science Book, Version 2.0 , 2009, 0912.0201.

[72]  G. Richards,et al.  Are the variability properties of the Kepler AGN light curves consistent with a damped random walk , 2015, 1505.00360.

[73]  Linhua Jiang,et al.  SDSS J0159+0105: A RADIO-QUIET QUASAR WITH A CENTI-PARSEC SUPERMASSIVE BLACK HOLE BINARY CANDIDATE , 2015, 1512.08730.

[74]  Mark Clampin,et al.  Transiting Exoplanet Survey Satellite , 2014, 1406.0151.

[75]  E. al.,et al.  The Sloan Digital Sky Survey: Technical summary , 2000, astro-ph/0006396.

[76]  M. Graham,et al.  A Population of Short-Period Variable Quasars from PTF as Supermassive Black Hole Binary Candidates , 2016, 1604.01020.

[77]  Jianhua Z. Huang,et al.  Period estimation for sparsely-sampled quasi-periodic light curves applied to Miras , 2016, 1609.06680.

[78]  C. Kochanek,et al.  IS QUASAR OPTICAL VARIABILITY A DAMPED RANDOM WALK? , 2012, 1202.3783.

[79]  Ernest E. Croner,et al.  The Palomar Transient Factory: System Overview, Performance, and First Results , 2009, 0906.5350.

[80]  Dae-Won Kim,et al.  Assessment of stochastic and deterministic models of 6304 quasar lightcurves from SDSS Stripe 82 , 2013, 1304.2863.

[81]  E. L. Robinson.  The structure of cataclysmic variables. , 1976 .

[82]  Variable Star Network: World Center for Transient Object Astronomy and Variable Stars (Special Issue: Resent Results from VSNET) , 2003, astro-ph/0310209.

[83]  S. D’odorico.  Optical astronomical instrumentation : 26-28 March, 1998, Kona, Hawaii , 1998 .

[84]  M. Auvergne,et al.  The CoRoT satellite in flight : description and performance , 2009, 0901.2206.

[85]  Youjun Lu,et al.  A PROBABLE MILLI-PARSEC SUPERMASSIVE BINARY BLACK HOLE IN THE NEAREST QUASAR MRK 231 , 2015, 1508.06292.

[86]  National Radio Astronomy Observatory,et al.  A Compact Supermassive Binary Black Hole System , 2006, astro-ph/0604042.