A Bayesian test for periodic signals in red noise

Abstract

Many astrophysical sources, especially compact accreting sources, show strong, random brightness fluctuations with broad power spectra in addition to periodic or quasi-periodic oscillations (QPOs) that have narrower spectra. The random nature of the dominant source of variance greatly complicates the process of searching for possible weak periodic signals. We have addressed this problem using the tools of Bayesian statistics; in particular using Markov chain Monte Carlo techniques to approximate the posterior distribution of model parameters, and posterior predictive model checking to assess model fits and search for periodogram outliers that may represent periodic signals. The methods developed are applied to two example datasets, both long XMM-Newton observations of highly variable Seyfert 1 galaxies: RE J1034+396 and Mrk 766. In both cases a bend (or break) in the power spectrum is evident. In the case of RE J1034+396 the previously reported QPO is found but with somewhat weaker statistical significance than reported in previous analyses. The difference is due partly to the improved continuum modelling, better treatment of nuisance parameters, and partly to different data selection methods.

15 pages, 6 figures. Accepted for publication in MNRAS

References in corpus (2)

• Bayes in the sky: Bayesian inference and model selection in cosmology
• Searching for Narrow Emission Lines in X-ray Spectra: Computation and Methods

Cited by in corpus (124)

• Understanding the Lomb-Scargle Periodogram
• Stingray: A Modern Python Library For Spectral Timing
• Flexible and Scalable Methods for Quantifying Stochastic Variability in the Era of Massive Time-Domain Astronomical Data Sets
• X-ray variability of 104 active galactic nuclei. XMM-Newton power-spectrum density profiles
• A Stochastic Model for the Luminosity Fluctuations of Accreting Black Holes
• Long-term optical monitoring of TeV emitting Blazars
• Quasi-periodicities at year-like timescales in Blazars
• X-ray Quasi-periodic Eruptions driven by Star-Disc Collisions : Application to GSN069 and Probing the Spin of Massive Black Holes
• A 200-s Quasi-Periodicity Following the Tidal Disruption of a Star by a Dormant Black Hole
• Soft X-ray Pulsations in Solar Flares
• A large-scale search for evidence of quasi-periodic pulsations in solar flares
• Quasi-periodic pulsations in solar and stellar flares: re-evaluating their nature in the context of power-law flare Fourier spectra
• Discovery of a ~2 hr high frequency X-ray QPO and iron K alpha reverberation in the active galaxy MS 2254.9-3712
• Tormund's return: Hints of quasi-periodic eruption features from a recent optical tidal disruption event
• Discovery of a ~5 day characteristic timescale in the Kepler power spectrum of Zw 229-15
• A ~3.8 hour Periodicity from an Ultrasoft Active Galactic Nucleus Candidate
• Gamma-ray quasi-periodicities of blazars. A cautious approach
• Deciphering the extreme X-ray variability of the nuclear transient eRASSt J045650.3-203750: A likely repeating partial tidal disruption event
• Magnetic-Island Contraction and Particle Acceleration in Simulated Eruptive Solar Flares
• The remarkable X-ray variability of IRAS 13224-3809 I: The variability process
• Detection of a possible X-ray Quasi-periodic Oscillation in the Active Galactic Nucleus 1H~0707-495
• The rapid X-ray variability of NGC 4051
• Gamma-ray and Optical Oscillations of 0716+714, MRK 421, and BL Lac
• Quasi-Periodic Oscillations in Short Recurring Bursts of the Soft-Gamma Repeater J1550-5418
• Quasi-periodicities of BL Lac Objects
• Kepler observations of rapid optical variability in the BL Lac object W2R1926+42
• Detection of a QPO in 5 XMM-Newton observations of RE J1034+396
• XMM-Newton X-ray and UV observations of the fast nova V2491 Cyg during the supersoft source phase
• Quasi-Periodic Oscillations and broadband variability in short magnetar bursts
• Revisiting The Spectral and Timing Properties of NGC 4151
• Multi-color optical monitoring of the quasar 3C 273 from 2005 to 2016
• Quasi-Periodic Oscillations in Short Recurring Bursts of the magnetars SGR 1806-20 and SGR 1900+14 Observed With RXTE
• Oscillations in stellar superflares
• Black hole mass and spin measurements through the Relativistic Precession Model: XTE J1859+226
• The dual nature of blazar fast variability. Space and ground observations of S5 0716+714
• Coronal Fourier power spectra: implications for coronal seismology and coronal heating
• Individual power density spectra of Swift gamma-ray bursts
• A blueprint of state-of-the-art techniques for detecting quasi-periodic pulsations in solar and stellar flares
• Kilohertz quasiperiodic oscillations in short gamma-ray bursts
• Searching for the trigger of the AGN QPO: 8 years of RE J1034+396
• The phase lags of high-frequency quasi-periodic oscillations in four black-hole candidates
• Quasi-periodic oscillations of the X-ray burst from the magnetar SGR J1935+2154 and associated with the fast radio burst FRB 200428
• Looking at Blazar Light Curve Periodicities with Gaussian Processes
• An X-ray periodicity of $\sim$1.8 hours in a narrow-line Seyfert 1 galaxy Mrk 766
• Evaluating Quasi-Periodic Variations in the $\gamma$-ray Lightcurves of Fermi-LAT Blazars
• 25 Years of Self-Organized Criticality: Numerical Detection Methods
• The optical variability of Supermassive Black Hole Binary Candidate PG1302-102: Periodicity and perturbation in the light curve
• Multi-waveband quasi-periodic oscillations in the light curves of blazar CTA 102 during its 2016-2017 optical outburst
• Re-observing the NLS1 Galaxy RE J1034+396. I. the Long-term, Recurrent X-ray QPO with a High Significance
• Quasi-Periodic Oscillations in the long term radio light curves of the blazar AO 0235+164
• Bright X-ray flares from Sgr A*
• A search for pulsations in short gamma-ray bursts to constrain their progenitors
• Multiwavelength periodicity search in a sample of $\gamma$-ray bright blazars
• Bayesian timing analysis of giant flare of SGR 1806-20 by RXTE PCA
• X-ray timing analysis of the quasar PG 1211+143
• The model constraints from the observed trends for the quasi-periodic oscillation in RE J1034+396
• Possible ~0.4 hour X-ray quasi-periodicity from an ultrasoft active galactic nucleus
• Detectability of modulated X-rays from LISA's supermassive black hole mergers
• A deep X-ray view of the bare AGN Ark 120. III. X-ray timing analysis and multiwavelength variability
• The long-term centimeter variability of active galactic nuclei: A new relation between variability timescale and accretion rate
• Quasi-periodic dipping in the ultraluminous X-ray source, NGC 247 ULX-1
• Detection of Very Low-Frequency Quasi-Periodic Oscillations in the 2015 Outburst of V404 Cygni
• Multiple Wavelength Variability and Quasi-Periodic Oscillation of PMN J0948+0022
• Estimating red noise in quasi-periodic signals with MCMC-based Bayesian
• Pitfalls of periodograms: The non-stationarity bias in the analysis of quasi-periodic oscillations
• An XMM-Newton and NuSTAR study of IGR J18214-1318: a non-pulsating high-mass X-ray binary with a neutron star
• X-ray Intraday Variability of HBL Blazars with XMM-Newton
• Stochastic oscillations of general relativistic disks
• Correlation between peak energy and Fourier power density spectrum slope in gamma-ray bursts
• Variability In A Low-Mass AGN: Oscillation Or Eruption?
• A New Approach for Measuring Power Spectra and Reconstructing Time Series in Active Galactic Nuclei
• A possible 250-second X-ray quasi-periodicity in the fast blue optical transient AT2018cow
• Update on the X-ray variability plane for active galactic nuclei: The role of the obscuration
• On possible proxies of AGN light curves cadence selection in future time domain surveys
• Variability of Optical Counterparts in the Chandra Galactic Bulge Survey
• Generalized Langevin equation with colored noise description of the stochastic oscillations of accretion disks
• Search for Quasi-Periodical Oscillations in Precursors of Short and Long Gamma Ray Bursts
• Independent Black Hole Mass Estimation for the γ-ray Detected Archetypal Narrow-Line Seyfert 1 Galaxy 1H 0323+342 from X-ray Variability
• Quasi periodic oscillations in active galactic nuclei
• Flux and Spectral Variation Characteristics of 3C 454.3 at the GeV Band
• Detecting the periodicity of highly irregularly sampled light-curves with Gaussian processes: the case of SDSSJ025214.67-002813.7
• Searching for energy-resolved quasi-periodic oscillations in AGN
• On Detecting Transient Phenomena
• Minute-Cadence Observations of the LAMOST Fields with the TMTS: II. Catalogues of Short-Period Variable Stars from the First Two-Year Surveys
• X-ray variability analysis of a large series of XMM-Newton + NuSTAR observations of NGC 3227
• Using Leaked Power to Measure Intrinsic AGN Power Spectra of Red-Noise Time Series
• Searching for Quasi-periodic Oscillations in Active Galactic Nuclei of the Chandra Deep Field South
• The nature of the broadband X-ray variability in the dwarf Seyfert galaxy NGC 4395
• X-ray Intraday Variability and Power Spectral Density Profiles of the Blazar 3C 273 with XMM-Newton during 2000-2021
• Multi-wavelength Campaign on the Super-Eddington NLS1 RX J0134.2-4258 -- I. Peculiar X-ray Spectra and Variability
• Detection of a low frequency quasi-periodic oscillation in the soft state of Cygnus X-1 with Insight-HXMT
• Periodic X-ray sources in the Massive Globular Cluster 47 Tucanae: Evidence for Dynamically Formed Cataclysmic Variables
• Identifying a new intermediate-polar using XMM-Newton and INTEGRAL
• Exploring the Link between the X-ray Power Spectra and Energy Spectra of Active Galactic Nuclei
• Singular Spectrum Analysis for astronomical time series: constructing a parsimonious hypothesis test
• Analysis of the intra-night variability of BL Lacertae during its August 2020 flare
• Periodicity from X-ray sources within the inner Galactic disk
• Modelling variability power spectra of active galaxies from irregular time series
• Power Spectral Distribution of the BL Lacertae Object S5 0716+714
• Fractal dimension and thermodynamic fluctuation properties of IDV light curves
• X-ray and UV observations of V751 Cyg in an optical high state
• An 85-s X-ray quasi-periodicity after a stellar tidal disruption by a candidate intermediate-mass black hole
• The X-ray Transient 2XMMi J003833.3+402133: A Candidate Magnetar at High Galactic Latitude
• Characterising continuum variability in the radio-loud narrow-line Seyfert 1 galaxy IRAS 17020+4544
• Generalized Langevin equation description of the stochastic oscillations of general relativistic disks
• A Comprehensive Analysis of Insight-HXMT Gamma-Ray Burst Data. I. Power Density Spectrum
• Characterisation of the X-ray point source variability in the eROSITA south ecliptic pole field
• Appearance of an accretion disk perturbed by fractional Brownian Motion density
• GRB 201104A: A "Repetitive" Short Gamma-Ray Burst?
• Measuring interacting binary mass functions with X-ray fluorescence
• Fast Bayesian spectral analysis using Convolutional Neural Networks: Applications over GONG H$\alpha$ solar data
• Long-term Evolution of the Short-term X-ray Variability of the Jetted TDE Swift J1644+57
• Discovery and Identification of MAXI J1621-501 as a Type I X-ray Burster with a Super-Orbital Period
• Fourier Domain
• Properties of 2017-18 'failed' Outburst of GX 339-4
• Identifying massive black hole binaries via light curve variability in optical time-domain surveys
• Magnetar giant flare high-energy emission
• Searching for quasi-periodicities in short transients: the curious case of GRB 230307A
• A search for periodic activity in multi-peaked long gamma-ray bursts
• Variability Study and Searching for QPOs with day-like periods in the blazar S5 0716+714 with TESS
• Detection of Quasi-periodic Oscillations in SGR 150228213
• Quasi-Periodicities at Year Time Scales in Blazars
• Constraints on the magnetic field structure in accreting compact objects from aperiodic variability
• Quasi-Periodic Oscillations in magnetars: linking variability and emission