Understanding the Lomb-Scargle Periodogram

Abstract

The Lomb-Scargle periodogram is a well-known algorithm for detecting and characterizing periodic signals in unevenly-sampled data. This paper presents a conceptual introduction to the Lomb-Scargle periodogram and important practical considerations for its use. Rather than a rigorous mathematical treatment, the goal of this paper is to build intuition about what assumptions are implicit in the use of the Lomb-Scargle periodogram and related estimators of periodicity, so as to motivate important practical considerations required in its proper application and interpretation.

55 pages, 26 figures. Code available at https://github.com/jakevdp/PracticalLombScargle/

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• 21 cm Intensity Mapping with the DSA-2000
• TESS discovery of a super-Earth and two sub-Neptunes orbiting the bright, nearby, Sun-like star HD 22946
• Transit timing variation analysis of the low-mass brown dwarf KELT-1 b
• Exploring the potential of neural networks to predict statistics of solar wind turbulence
• A comprehensive search for Long and Short Periodic Features from an Extremely Active Cycle of FRB 20240114A
• Measuring the magnetic dipole moment and magnetospheric fluctuations of accretion-powered pulsars in the Small Magellanic Cloud with an unscented Kalman filter
• Search for dark matter annual modulation with DarkSide-50
• Study of periodic signals from blazars
• Decade-long periodicity study of 2FHL blazars with historical optical data
• The Sub-mm Variability of IRC+10216 and $o$ Ceti
• Detecting gravitational signatures of dark matter with atom gradiometers
• Fast Photometric Variability of Very Low Mass Stars in IC 348: Detection of Superflare in an M-dwarf
• Characterization of of (98943) 2001 CC${}_{21}$, the target of Hayabusa2$\#$
• SRGe J194401.8+284452 -- an X-ray Cataclysmic Variable in the Field of the Gamma-Ray Source 4FGL J1943.9+2841
• Identifying and characterising the population of hot sub-luminous stars with multi-colour MeerLICHT data
• TCP J07222683$+$6220548: a new AM CVn type system with infrequent outbursts
• Regular chains of star formation regions in spiral arms and rings of disk galaxies
• Characterising the short-orbital period X-ray transient Swift J1910.2-0546
• Revisiting the extremely long-period cataclysmic variables V479 Andromedae and V1082 Sagitarii
• Optimal frequency-domain analysis for spacecraft time series: Introducing the missing-data multitaper power spectrum estimator
• X-ray Activity Variations and Coronal Abundances of the Star-Planet Interaction candidate HD 179949
• PIPS, an advanced platform for period detection in time series -- I. Fourier-likelihood periodogram and application to RR Lyrae Stars
• SRGe2149+6736 -- the new candidate to AM~Her type variables discovered by eROSITA telescope on "Spectrum--Roentgen--Gamma" orbital observatory
• Infrared variability of young solar analogs in the Lagoon Nebula
• Observing Rayleigh-Taylor stable and unstable accretion through a Kalman filter analysis of X-ray pulsars in the Small Magellanic Cloud
• Bridging the Gap: OPTICAM Reveals the Hidden Spin of the WZ Sge Star GOTO 065054.49+593624.51
• Generalized Lomb-Scargle analysis of ${}^{90}\mathrm{Sr}{/}^{90}\mathrm{Y}$ decay rate measurements from the Physikalisch-Technische Bundesanstalt
• The flaring activity of blazar AO 0235+164 during year 2021
• New Photometry and Spectroscopy of DW Cnc
• Not so Swift: 20 years of multiwavelength observations of Mrk 421 and Mrk 501
• A solar rotation signature in cosmic dust: frequency analysis of dust particle impacts on the Wind spacecraft
• Generalized Lomb-Scargle analysis of ${}^{36}\mathrm{Cl}$ decay rate measurements at PTB and BNL
• New variable sources revealed by DECam toward the LMC: the first 15 deg2
• Discovery of a Proto-White Dwarf with a Massive Unseen Companion
• The Solar Neighborhood LII: M Dwarf Twin Binaries -- Presumed Identical Twins Appear Fraternal in Variability, Rotation, H$\alpha$, and X-rays
• Tracking X-ray Variability in Next Generation EHT LLAGN Targets
• A Supermassive Binary Black Hole Candidate in Mrk 501
• Exploring membership and variability in NGC 7419: An open cluster rich in super giants and Be type stars
• Fourier Domain
• Long-term temporal stability of the DarkSide-50 dark matter detector
• A NuSTAR study of quasi-periodic oscillations from the ultraluminous X-ray sources in M82
• Flare frequency in M dwarfs belonging to Young Moving Groups
• A circularly polarized low-frequency radio burst from the exoplanetary system HD 189733
• Multi-epoch spectro-photometric characterization of the minimoon 2024 PT${}_5$ in the visible and near-infrared
• Unsupervised learning for variability detection with Gaia DR3 photometry. The main sequence-white dwarf valley
• A Search For Pulsations in the Optical Light Curve of the Nova ASASSN-17hx
• Temperature Analysis of Flaring (AR11283) and non-Flaring (AR12194) Coronal Loops
• The time-variable ultraviolet sky: Active Galactic Nuclei, Stars and White Dwarfs
• Ytterbium atom interferometry for dark matter searches
• ANDICAM I and J band monitoring of bright inner Galactic late-type stars
• Doomed Worlds II: Reassessing Suggestions of Orbital Decay for TrES-5 b
• High-precision broadband linear polarimetry of early-type binaries IV. Binary system of DH Cephei in the open cluster of NGC 7380
• Precise radial velocities of giant stars -- XVII. Distinguishing planets from intrinsically induced radial velocity signals in evolved stars
• High-pass Filter Periodogram: An Improved Power Spectral Density Estimator for Unevenly Sampled Data
• Fast Bayesian spectral analysis using Convolutional Neural Networks: Applications over GONG H$\alpha$ solar data
• A QPO in NGC 4945 from Archival RXTE Data
• New cases of super-flares on slowly rotating solar-type stars and large amplitude super-flares in G- and M-type main-sequence stars
• Quantitative nanoscale MRI with a wide field of view
• GRAPE: Genetic Routine for Astronomical Period Estimation
• The JCMT Transient Survey: Four Year Summary of Monitoring the Submillimeter Variability of Protostars
• A Statistical Analysis of Crab Pulsar Giant Pulse Rates
• Direct Detection of Ultralight Dark Matter via Charged Lepton Flavor Violation
• Magnetic Reconnection as a Potential Driver of X-ray Variability in Active Galactic Nuclei
• High-precision broadband linear polarimetry of early-type binaries III. AO Cassiopeiae revisited
• About 300 days optical quasi-periodic oscillations in the long-term light curves of the blazar PKS 2155-304
• NGTS clusters survey IV. Search for Dipper stars in the Orion Nebular Cluster
• Cataclysmic Variable Candidates Identified in eROSITA-DE DR1,XMM-Newton, Swift, and ROSAT Catalogs
• Recurrent outbursts revealed in 3XMM J031820.8-663034
• Wideband Search for Axionlike Dark Matter Using Octupolar Nuclei in a Crystal
• Radial velocity analysis of stars with debris discs
• A search for photometric variability towards the globular cluster M3 with the TWenty Inch Survey Telescope
• Orbital Refinement and Stellar Properties for the HD 9446, HD 43691, and HD 179079 Planetary Systems
• A systematic search for orbital periods of polars with TESS. Methods, detection limits, and results
• Stacked Periodograms as a Probe of Exoplanetary Populations
• Taranga DR1: Analysis of TESS Short Cadence data for years 1 and 2
• Identifying massive black hole binaries via light curve variability in optical time-domain surveys
• Physical properties of the slow-rotating near-Earth asteroid (2059) Baboquivari from one apparition
• A Statistical Primer on Classical Period-Finding Techniques in Astronomy
• Far-ultraviolet investigation into the galactic globular cluster M30 (NGC 7099): II. Potential X-ray counterparts and variable sources
• Time series photometry and multi-wavelength characterisation of the young stellar cluster Mon R2
• Leveraging turbulence data from fusion experiments
• Apache Point Observatory follow-up of ACcelerating Candidate ExopLanet host Stars (APO ACCELS): Ages for 166 Accelerating Stars in the Northern Hemisphere
• Detection of a Millisecond Periodicity in BATSE Short Gamma-Ray Bursts
• Searching for unresolved massive black hole pairs through AGN photometric variability
• Spectral Hardening Revealed by Geometric De-boosting in the Masked Jet of PKS 2155$-$304
• A 4.5-s Quasiperiodic Spectral Oscillation in GRB 230307A: Evidence for Free Precession of a Post-Merger Magnetar?
• Transverse Oscillations and Wave Propagation in the Magnetically Dominated M87 Jet
• Variability Study and Searching for QPOs with day-like periods in the blazar S5 0716+714 with TESS
• Automated all-sky detection of γ Doradus / δ Scuti hybrids in TESS data from positive unlabelled (PU) learning
• Milliarcsecond astrometric oscillations in active galactic nuclei as a precursor of multi-messenger gravitational wave events
• An X-ray and Optical Study of the Dwarf Nova Candidate OGLE-BLG-DN-0064
• Optical and X-ray timing analysis of the 2018-2020 outburst and rebrightening of the black-hole transient MAXI J1820+070
• The VELOCE modulation zoo III. Detecting additional pulsation modes in optical spectra of classical Cepheids using semi-partial distance correlation periodograms
• Asteroseismology with TESS: Emergence of Dipole Mode Suppression From Subgiants?
• Generalized Lomb-Scargle analysis of ${}^{123}\mathrm{I}$ and ${}^{99m}\mathrm{Tc}$ decay rate measurements
• Catalog of variable stars in the WD 0009+501 and GRW +708247 fields based on photometric survey data on transiting exoplanets
• Periodic Astrometric Signal Recovery through Convolutional Autoencoders
• Double Mode Cepheids from the Zwicky Transient Facility Survey
• The Multivariate Extension of the Lomb-Scargle Method
• On The Unusual Variability of 2MASS J06195260-2903592: A Long-Lived Disk around a Young Ultracool Dwarf
• Optical Variability, Rotation Period and Inclination Angle of the M9.5 dwarf BRI 0021-0214
• Searching for white dwarf variables in TESS data
• Adaptation of the Phase Distance Correlation Periodogram to Account for Measurement Uncertainties
• EvryFlare IV: Detection of periodicity in flare occurrence from cool stars with TESS
• Clustering of Pain Dynamics in Sickle Cell Disease from Sparse, Uneven Samples
• New Insights into Time Series Analysis IV: Panchromatic and Flux Independent Period Finding Methods
• FINKER: Frequency Identification through Nonparametric KErnel Regression in astronomical time series
• Radar Classification of Vehicles Using a Ground-Reflection Model
• Optimization Applied to Selected Exoplanets
• Multiwavelength Characterization of a New Magnetic Cataclysmic Variable 2CXO J050740.7-091337
• VarStar Detect, a Python library dedicated to the semi-automatic detection of stellar variability
• SDSS J153231.80+420342.7: a triple black hole candidate with a close binary black hole
• VLTI-GRAVITY measurements of cool evolved stars: II. Pulsation properties and mass-loss process of the Mira star R Car and the red supergiant VX Sgr
• Variable Red Giants Exploration with MASTER Robotic Net: Main Algorithms and Study of Three Mira-type Targets
• Direct power spectral density estimation from structure functions without Fourier transforms
• High-precision broadband linear polarimetry of early-type binaries. V. The Binary System HD 165052 in Open Cluster NGC 6530
• GPU-Enabled Searches for Periodic Signals of Unknown Shape
• The SOL $\text{(Solar Origin and Life)}$ Project: Detailed characterization of candidates for the ZAMS and Subgiant stages
• Optimized cutting off transit algorithm to study stellar rotation from PLATO mission light curves
• Rotational Light-curve Recovery and Predictions of the LSST Yield of Hildas
• Predicting Stellar Parameters of Massive Stars from Light Curves with Machine Learning
• Activity and Rotation of Nearby Field M Dwarfs in the TESS Southern Continuous Viewing Zone
• Prospects for detecting proto-neutron star rotation and spindown using supernova neutrinos
• Demonstration of deuterium's enhanced sensitivity to symmetry violations governed by the Standard-Model Extension
• Exploring the operational limits of poloidal and helical arrays of Mirnov coils in stellarators by means of a synthetic diagnostic
• X-ray and Optical Analysis of the Prototype Polar AN UMa
• Intriguing nature of AM Her type candidate CXOU J204734.8+300105
• A magnetic field detection in the massive O-type bright giant 63 Oph
• A New Catalog of Asymptotic Giant Branch Stars in Our Galaxy
• LAMOST J2043+3413 -- a Fast Disk Precession SW Sextans Candidate in Period Gap
• Accelerometer-Based Gait Segmentation: Simultaneously User and Adversary Identification
• Windowing Artifacts Likely Account for Recent Claimed Detection of Oscillating Cosmic Scale Factor
• Analysing the flux stability of stellar calibrator candidates with TESS
• Exploring Young Stellar Variability with Gaia DR3 light curves
• iid2022: A Workshop on Statistical Methods for Event Data in Astronomy
• The possible long-term periodic variability of the extremely luminous quasar WISE J090924.01+000211.1
• Photometric Modulations on Intermediate Timescales in the Symbiotic Binaries
• Dynamic Photometric Variability in Three Young Brown Dwarfs in Taurus: Detection of Optical Flares with TESS data
• Estimating Unknown Cycles in Geophysical data
• Syntriod: A Robust Initial Parameter Estimator for Radial Velocity Curve Solutions Beyond Conventional Sampling Limits
• Photometric light curves analysis of SU UMa-type dwarf novae: the case of RZ LMi and KV Dra
• Harmonics as a Hidden Window into the Turbulent Convective Envelope of non-Blazhko RRab Stars
• Pushing the Limit of Asteroseismic Detection for Cool Dwarfs using TESS and Deep Learning
• When the horseshoe fits: Characterizing 2023 FY3 with the 10.4 m Gran Telescopio Canarias and the Two-meter Twin Telescope
• Magnetic geometry of M dwarfs in the southern PLATO field