Scargle (periodogram)

Scargle (periodogram)
Name	Jeffrey D. Scargle
Birth date	1948
Known for	Lomb–Scargle periodogram
Fields	Astronomy, Statistics
Workplaces	NASA, SETI Institute, University of California, Berkeley

Contents

Scargle (periodogram) is a method for detecting and characterizing periodic signals in unevenly sampled time series widely used in astronomy and geophysics. Developed in the late 20th century by Jeffrey D. Scargle building on earlier work by N. R. Lomb and influenced by methods from Joseph Fourier and Harold Jeffreys, the technique adapts classical power spectral analysis to irregular observations from facilities such as the Hubble Space Telescope, Kepler, and ground observatories like Mount Wilson Observatory. It intersects the practices of researchers at institutions including Harvard University, California Institute of Technology, Max Planck Institute for Astronomy, Princeton University, and Stanford University.

Introduction

The method originated in response to challenges faced by observers at Palomar Observatory, Arecibo Observatory, and Mauna Kea Observatories where irregular cadence impeded application of the Fourier transform as used by teams at Royal Observatory, Greenwich and Yerkes Observatory. Scargle synthesized statistical approaches from practitioners at Bell Labs and theoretical work by Andrey Kolmogorov and Norbert Wiener to create a periodogram suitable for astronomical projects like the Palomar Transient Factory, Sloan Digital Sky Survey, and surveys by the European Southern Observatory. Influential adopters include researchers associated with NASA Goddard Space Flight Center, European Space Agency, Jet Propulsion Laboratory, and projects such as Gaia (spacecraft) and TESS.

The Scargle formalism reframes power estimation in the context of irregular sampling by introducing a time-shift parameter analogous to phase used in Joseph Fourier's spectral synthesis and in methods developed at Cambridge University and Imperial College London. The formulation resembles least-squares fits of sinusoids familiar to analysts at Columbia University and University of Chicago, and connects to spectral estimation techniques advanced at Massachusetts Institute of Technology and Brown University. It computes normalized power from sums over data points, employing trigonometric terms that echo identities used by Leonhard Euler and Carl Friedrich Gauss; implementation often references linear algebra tools from Matrix Laboratory (MATLAB) and libraries maintained by NumPy and SciPy developers at Lawrence Berkeley National Laboratory.

Assessing whether a detected peak is real draws on statistical theory from figures like Ronald Fisher and Jerzy Neyman, and computational approaches used at Los Alamos National Laboratory and Sandia National Laboratories. The false alarm probability (FAP) in Scargle’s approach parallels hypothesis testing frameworks developed at University of Cambridge and University of Oxford and is often calibrated using Monte Carlo simulations practiced at CERN and Argonne National Laboratory. Astronomers working with teams at Space Telescope Science Institute and Max Planck Institute for Extraterrestrial Physics commonly employ bootstrap methods pioneered at Johns Hopkins University and significance corrections influenced by procedures created at Stanford University for multiple comparisons.

Extensions incorporate generalized Lomb–Scargle models including floating-mean variants used by groups at Princeton University and multiharmonic models applied in studies at Carnegie Institution for Science; Bayesian adaptations draw on concepts from Karl Pearson and modern probabilistic programming work at Google and Microsoft Research. Multiband and multivariate generalizations have been developed by collaborators at University of California, Santa Cruz and University of Michigan for surveys like Pan-STARRS and Zwicky Transient Facility. Robust and weighted implementations have origins in robust statistics from University of Chicago and computational optimizations influenced by algorithms from NVIDIA research teams and high-performance computing centers such as Oak Ridge National Laboratory.

Practical use spans detection tasks in exoplanet searches at Harvard–Smithsonian Center for Astrophysics and variability studies of active galactic nuclei by researchers at Max Planck Institute for Radio Astronomy and National Radio Astronomy Observatory. It is implemented in software ecosystems maintained by contributors at Astropy Project, SciPy, R Project for Statistical Computing, and proprietary platforms used at SpaceX and Ball Aerospace. Applications include pulsation analyses of stars investigated at Royal Astronomical Society meetings, rotation period studies of minor planets tracked by Minor Planet Center, and climate signal investigations by teams at National Oceanic and Atmospheric Administration and Intergovernmental Panel on Climate Change-affiliated groups.

Critics from communities at University of California, Los Angeles and Yale University note biases when sampling windows align with diurnal or yearly cadences typical of observatories like La Silla Observatory and Kitt Peak National Observatory, echoing concerns raised in methodological discussions at American Astronomical Society conferences and papers from Institute of Physics. The periodogram’s sensitivity to aliasing and window function effects links to classical sampling theorems by Claude Shannon and practical limitations highlighted by engineers at AT&T and Bell Labs. Alternative approaches advocated by researchers at Columbia University and Cornell University include wavelet transforms and Bayesian spectral synthesis, which have been promoted in workshops at Society for Industrial and Applied Mathematics and International Astronomical Union symposia.