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All sourcesNASA NTRSDOE OSTI
DOE OSTI2026

Red Noise–based False Alarm Thresholds for Astrophysical Periodograms via Whittle’s Approximation to the Likelihood

Astronomers who search for periodic signals using Lomb–Scargle periodograms rely on false alarm level (FAL) estimates to identify statistically significant peaks. Although FALs are often calculated from white noise models, many astronomical time series suffer from red noise. Prewhitening is a statistical technique in which a continuum model is subtracted from the log power spectrum estimate, after which the observer can proceed with a white-noise treatment. Here we present a prewhitening-based method of calculating frequency-dependent FALs. We fit power laws and autoregressive models of order 1 to each Lomb–Scargle periodogram by minimizing the Whittle approximation to the negative log-likelihood (NLL), then calculate FALs based on the best-fit model power spectrum. Our technique is a novel extension of the Whittle NLL to datasets with uneven time sampling. We demonstrate FAL calculations using observations of α Cen B, GJ 581, HD 192310, synthetic data from the radial velocity (RV) fitting challenge, and Kepler observations of a differential rotator. The Kepler data analysis shows that only true rotation signals are detected by red noise FALs, while white noise FALs suggest all spurious peaks in the low-frequency range are significant. A high-frequency sinusoid injected into α Cen B logR$'$ HK observations exceeds the 1% red noise FAL despite having only 8.9% of the power of the dominant rotation signal. In a periodogram of HD 192310 RVs, peaks associated with differential rotation and planets are detected against the 5% red noise FAL without iterative model fitting or subtraction. The software for calculating red noise–based FALs is available on GitHub.

Astrostatistics (1882)↗
DOE OSTI2019

Multipaper Spectral Estimation: An Alternative to the Welch Periodogram Approach

Dynamic structural systems either operational or under test require complex spectral analysis in order to characterize their modal responses. In some applications constant vigilance in terms of analysis or potential failures demand an accurate methodology to estimate both modal frequencies as well as mode shapes. Typically, classical periodogram spectra are windowed and averaged applying the well-known Welch periodogram methodology (WPM) for spectral estimation [1]. In this report we discuss an alternative technique—the Multitaper Method (MTM) that can be applied to solve this challenging problem especially in the case of noisy, uncertain accelerometer measurements [2]. This approach is based on the development of a set of orthogonal tapers or windows enabling a superior statistical performance alleviating the need to section/overlap the measured data. Therefore, the MTM is capable of producing reliable and accurate spectral estimates enabling the extraction of the structural modal vibration frequencies.

42 ENGINEERING↗
DOE OSTI2024

Periodicity significance testing with null-signal templates: reassessment of PTF’s SMBH binary candidates

Periodograms are widely employed for identifying periodicity in time series data, yet they often struggle to accurately quantify the statistical significance of detected periodic signals when the data complexity precludes reliable simulations. We develop a data-driven approach to address this challenge by introducing a null-signal template (NST). The NST is created by carefully randomizing the period of each cycle in the periodogram template, rendering it non-periodic. It has the same frequentist properties as a periodic signal template, and we show with simulations that the distribution of false positives is the same as with the original periodic template, regardless of the underlying data. Thus, performing a periodicity search with the NST acts as an effective simulation of the null (no-signal) hypothesis, without having to simulate the noise properties of the data. We apply the NST method to the supermassive black hole binaries (SMBHB) search in the Palomar Transient Factory (PTF), where Charisi et al. had previously proposed 33 high signal-to-noise candidates utilizing simulations to quantify their significance. Our approach reveals that these simulations do not capture the complexity of the real data. There are no statistically significant periodic signal detections above the non-periodic background. To improve the search sensitivity, we introduce a Gaussian quadrature based algorithm for the Bayes Factor with correlated noise as a test statistic. We show with simulations that this improves sensitivity to true signals by more than an order of magnitude. However, the Bayes Factor approach also results in no statistically significant detections in the PTF data.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2025

Investigation of oscillations above the acoustic cut-off frequency for a sample of Kepler stars. II. Identifying temporal frequency shifts

ABSTRACT Stellar oscillations with frequencies greater than the acoustic cut-off frequency are not trapped within the star’s interior. Geometric interference between these high-frequency waves produces a peak-like structure in the power spectrum of the star, known as the pseudo-modes. In this study, we aim to analyse 51 stars previously identified (from a sample of 91 Kepler stars) to contain statistically significant evidence for pseudo-modes, to determine if the pseudo-mode frequencies vary in time. We obtained these frequency variations and the uncertainty by the resampled periodogram approach, where periodogram realisations were created from successive, overlapping 90-d time segments, and a cross-correlation function was generated between them. The computed shifts were compared against temporal p-mode frequency shifts and a stellar magnetic activity proxy, $S_{\mathrm{ph}}$. We found that for 16 per cent of the stars pseudo-mode frequency shifts were significantly anticorrelated with p-mode shifts, as is the case for the Sun. However, we also found pseudo-mode and p-mode shifts to be significantly correlated in-phase in 8 per cent of our sample. The remainder showed no significant correlation. We also searched for trends between the maximum variation of pseudo-mode frequency shifts and stellar parameters. Whilst we found no correlation between the maximum variation and stellar photospheric and chromospheric proxies, we found frequency variations to have a greater amplitude for cooler and slower rotating stars, which is in opposition to p-mode frequency shift variation. Temporal changes to pseudo-mode frequencies may be attributable to variations in stellar magnetic activity, and therefore can contribute to our understanding of stellar activity cycles.

Millson, L. J. (ORCID:0009000342542676)↗
DOE OSTI2024

A Nonlinear Least Squares Phasor Estimation Algorithm with a Trust Metric

The paper presents a separable nonlinear least squares (NLLS)-based approach for estimation of fundamental-frequency phasors from sampled point-on-wave measurements. An analytical connection is established between the NLLS cost function and the discrete Fourier transform (DFT)-based periodogram of the input signal. This periodogram-based interpretation of the cost function offers an intuitive and easy-to-implement solution for the frequency estimate. Using the residual error of the NLLS-fit, the paper also presents an insightful measure for ascertaining the quality of the phasor estimates and their validity, especially for data windows containing signal transients.

Chatterjee, Kaustav↗
DOE OSTI2020

A Likely Magnetic Activity Cycle for the Exoplanet Host M Dwarf GJ 3512

Current radial velocity data from specialized instruments contain a large amount of information that may pass unnoticed if their analysis is not accurate. The joint use of Bayesian inference tools and frequency analysis has been shown as effective in revealing exoplanets but they have been used less frequently to investigate stellar activity. We intend to use radial velocity data of the exoplanet host star GJ 3512 to investigate its magnetic activity. Our study includes the analysis of the photometric data available. The main objectives of our work are to constrain the orbital parameters of the exoplanets in the system, to determine the current level of activity of the star and to derive an activity cycle length for it. An adaptive importance sampling method was used to determine the parameters of the exoplanets orbit. Generalized Lomb–Scargle periodograms were constructed with both radial velocity curve and photometric data. A careful analysis of the harmonic frequencies was conducted in each periodogram. Our fit to multiple Keplerian orbits constrained the orbital parameters of two giant gas planets orbiting the star GJ 3512. The host star showed an increase of its magnetic activity during the last observing campaign. The accurate fit of the radial velocity curve data to the multi-Keplerian orbit permitted to reveal the star rotation in the residuals of the best fit and estimate an activity cycle length of ~14 yr.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2023

Detecting Long-period Variability in the SDSS Stripe 82 Standards Catalog

We report the results of a search for long-period (100 < P < 600 days) periodic variability in the SDSS Stripe 82 standards catalog. The SDSS coverage of Stripe 82 enables such a search because there are on average 20 observations per band in ugriz bands for about one million sources, collected over about 6 yr, with a faint limit of r ~ 22 mag and precisely calibrated 1%–2% photometry. We calculated the periods of variable source candidates in this sample using the Lomb–Scargle periodogram and considered the three highest periodogram peaks in each of the gri filters as relevant. Only those sources with gri periods consistent within 0.1% were later studied. We use the Kuiper statistic to ensure uniform distribution of data points in phased light curves. We present five sources with the spectra consistent with quasar spectra and plausible periodic variability. This SDSS-based search bodes well for future sensitive large-area surveys, such as the Rubin Observatory Legacy Survey of Space and Time, which, due to its larger sky coverage (about a factor of 60) and improved sensitivity (~2 mag), will be more powerful for finding such sources.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2021

Self-calibrating the look-elsewhere effect: fast evaluation of the statistical significance using peak heights

In experiments where one searches a large parameter space for an anomaly, one often finds many spurious noise-induced peaks in the likelihood. This is known as the look-elsewhere effect, and must be corrected for when performing statistical analysis. Here, this paper introduces a method to calibrate the false alarm probability (FAP), or p-value, for a given dataset by considering the heights of the highest peaks in the likelihood. Specifically, we derive an equation relating the global p-value to the rank and height of local maxima. In the simplest form of self-calibration, the look-elsewhere-corrected $\chi^2$ of a physical peak is approximated by the $\chi^2$ of the peak minus the $\chi^2$ of the highest noise-induced peak, with accuracy improved by considering lower peaks. In contrast to alternative methods, this approach has negligible computational cost as peaks in the likelihood are a byproduct of every peak-search analysis. We apply to examples from astronomy, including planet detection, periodograms, and cosmology.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2021

Transient quasi-periodic oscillations at γ-rays in the TeV blazar PKS 1510-089

ABSTRACT We present periodicity search analyses on the γ-ray light curve of the TeV blazar PKS 1510-089 observed by the Fermi Large Area Telescope. We report the detection of two transient quasi-periodic oscillations: A 3.6-d QPO during the outburst in 2009 that lasted five cycles (MJD 54906–54923); and a periodicity of 92 d spanning over 650 d from 2018 to 2020 (MJD 58200–58850), which lasted for seven cycles. We employed the Lomb–Scargle periodogram, Weighted Wavelet Z-transform, redfit, and the Monte Carlo light-curve simulation techniques to find any periodicity and the corresponding significance. The 3.6-d QPO was detected at a moderate significance of ∼3.5σ, while the detection significance of the 92-d QPO was ∼7.0σ. We explore a few physical models for such transient QPOs including a binary black hole system, precession of the jet, a non-axisymmetric instability rotating around the central black hole near the innermost stable circular orbit, the presence of quasi-equidistant magnetic islands inside the jet, and a geometric model involving a plasma blob moving helically inside a curved jet.

Roy, Abhradeep (ORCID:0000000249984560)↗
DOE OSTI2023

Searching for quasar candidates with periodic variations from the Zwicky Transient Facility: results and implications

ABSTRACT We conduct a systematic search for quasars with periodic variations from the archival photometric data of the Zwicky Transient Facility by cross-matching with the quasar catalogues of the Sloan Digital Sky Survey and Véron-Cetty and Véron. We first select out 184 primitive periodic candidates using the generalized Lomb–Scargle periodogram and autocorrelation function and then estimate their statistical significance of periodicity based on two red-noise models, i.e. damped random walk (DRW) and single power-law (SPL) models. As such, we finally identify 106 (DRW) and 86 (SPL) candidates with the most significant periodic variations out of 143 700 quasars. We further compare DRW and SPL models using Bayes factors, which indicate a relative preference of the SPL model for our primitive sample. We thus adopt the candidates identified with SPL as the final sample and summarize its basic properties. We extend the light curves of the selected candidates by supplying other archival survey data to verify their periodicity. However, only three candidates (with 6–8 cycles of periods) meet the selection criteria. This result clearly implies that, instead of being strictly periodic, the variability must be quasi-periodic or caused by stochastic red-noise. This exerts a challenge to the existing search approaches and calls for developing new effective methods.

Chen, Yong-Jie (ORCID:0000000342807673)↗
DOE OSTI2020

Multichannel spectral estimation in acoustics: A state-space approach

Spectral estimation is a necessary methodology to analyze the frequency content of noisy data sets especially in acoustic applications. Many spectral techniques have evolved starting with the classical Fourier transform methods based on the well-known Wiener-Khintchine relationship relating the covariance-to-spectral density as a transform pair culminating with more elegant model-based parametric techniques that apply prior knowledge of the data to produce a high-resolution spectral estimate. Multichannel spectral representations are a class of both nonparametric, as well as parametric, estimators that provide improved spectral estimates. In any case, classical nonparametric multichannel techniques can provide reasonable estimates when coupled with peak-peaking methods as long as the signal levels are reasonably high. Furthermore, parametric multichannel methods can perform quite well in low signal level environments even when applying simple peak-picking techniques. In this paper, the performance of both nonparametric (periodogram) and parametric (state-space) multichannel spectral estimation methods are investigated when applied to both synthesized noisy structural vibration data as well as data obtained from a sounding rocket flight. It is demonstrated that for the multichannel problem, state-space techniques provide improved performance, offering a parametric alternative compared to classical methods.

42 ENGINEERING↗
DOE OSTI2022

Statistical Significance Testing for Mixed Priors: A Combined Bayesian and Frequentist Analysis

In many hypothesis testing applications, we have mixed priors, with well-motivated informative priors for some parameters but not for others. The Bayesian methodology uses the Bayes factor and is helpful for the informative priors, as it incorporates Occam’s razor via the multiplicity or trials factor in the look-elsewhere effect. However, if the prior is not known completely, the frequentist hypothesis test via the false-positive rate is a better approach, as it is less sensitive to the prior choice. We argue that when only partial prior information is available, it is best to combine the two methodologies by using the Bayes factor as a test statistic in the frequentist analysis. We show that the standard frequentist maximum likelihood-ratio test statistic corresponds to the Bayes factor with a non-informative Jeffrey’s prior. We also show that mixed priors increase the statistical power in frequentist analyses over the maximum likelihood test statistic. We develop an analytic formalism that does not require expensive simulations and generalize Wilks’ theorem beyond its usual regime of validity. In specific limits, the formalism reproduces existing expressions, such as the p-value of linear models and periodograms. We apply the formalism to an example of exoplanet transits, where multiplicity can be more than 10 7 . We show that our analytic expressions reproduce the $p$-values derived from numerical simulations. We offer an interpretation of our formalism based on the statistical mechanics. We introduce the counting of states in a continuous parameter space using the uncertainty volume as the quantum of the state. We show that both the $p$-value and Bayes factor can be expressed as an energy versus entropy competition.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2019

An Easy Algorithm to Generate Colored Noise Sequences

The need for accurate and efficient simulation of the noise background arises in statistical significance tests for periodic signals buried in colored noise. This paper discusses techniques for generating colored-noise sequences which simulate processes with a given spectral density. Matlab routines based on the fast fractional difference algorithm are presented. These routines can create various stochastic models (e.g., first-order autoregressive (AR(1)), power law (PL), autoregressive fractionally integrated moving average ((1, d, 0)), and generalized Gauss Markov (GGM)) that serve as possible candidate null hypotheses to test against in various scenarios. Allan variance and power spectral density (PSD) show that our algorithms are accurate and efficient, and can be easily implemented for stationary noise models and non-stationary PLs with spectral indices up to 2. Our algorithms can also be extended to produce a non-stationary PL with a range-limited steeper PSD (spectral indices up to about 4) using a GGM approximation with a proper break frequency. The red-noise leakage effect on the periodogram is further discussed. The result shows that our GGM approximation has a potential for alleviating the red-noise leakage in the PSD estimates. The Timmer and Koenig procedure is also included for comparison.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2019

Asteroseismic Determination of the Stellar Rotation Period of the Kepler Transiting Planetary Systems and its Implications for the Spin–Orbit Architecture

We measure the rotation periods of 19 stars in the Kepler transiting planetary systems, P {sub rot,astero} from asteroseismology and P {sub rot,phot} from the photometric variation of their light curves. Two stars exhibit two clear peaks in the Lomb–Scargle periodogram, neither of which agrees with the seismic rotation period. Other four systems do not show any clear peak, whose stellar rotation period is impossible to estimate reliably from the photometric variation; their stellar equators may be significantly inclined with respect to the planetary orbital plane. For the remaining 13 systems, P {sub rot,astero} and P{sub rot,phot} agree within 30%. Interestingly, 3 out of the 13 systems are in the spin–orbit resonant state in which P{sub orb,b}/P{sub rot,astero}≈1 with P {sub orb,b} being the orbital period of the innermost planet of each system. The corresponding chance probability is (0.2–4.7)% based on the photometric rotation period data for 464 Kepler transiting planetary systems. While further analysis of stars with reliable rotation periods is required to examine the statistical significance, the spin–orbit resonance between the star and planets, if confirmed, has important implications for the star–planet tidal interaction, in addition to the origin of the spin–orbit (mis-)alignment of transiting planetary systems.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2020

Photometry as a Proxy for Stellar Activity in Radial Velocity Analyses

Stellar activity remains a limiting factor in measuring precise planet parameters from radial velocity spectroscopy, not least in the search for Earth-mass planets orbiting in the habitable zones of Sun-like stars. One approach to mitigate stellar activity is to use combined analyses of both radial velocity and time-series photometry. We present an analysis of simultaneous disk-integrated photometry and radial velocity data of the Sun in order to determine the useful limits of a combined analysis. We find that simple periodogram or autocorrelation analysis of solar photometry give the correct rotation period <50% of the time. We therefore use a Gaussian process to investigate the time variability of solar photometry and to directly compare simultaneous photometry with radial velocity data. We find that the hyperparameter posteriors are relatively stable over 70 yr of solar photometry and the amplitude tracks the solar cycle. We observe good agreement between the hyperparameter posteriors for the simultaneous photometry and radial velocity data. Our primary conclusion is a recommendation to include an additional prior in Gaussian process fits to constrain the evolutionary timescale to be greater than the recurrence timescale (i.e., the rotation period) to recover more physically plausible and useful results. Our results indicate that such simultaneous monitoring may be a useful tool in enhancing the precision of radial velocity surveys.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2021

Variability in NGC 3201 Giant Stars and Its Impact on Their Spectroscopic [Fe/H] Determination

We present the analysis of 34 light curves in V and I of 17 giant stars in the globular cluster NGC 3201 to check if such stars are variable and if their variability has some kind of impact on the iron abundance as obtained from spectroscopic measurements. First, we computed the generalized Lomb–Scargle and phase dispersion minimization periodograms of the sample to check if the stars were variables. In this way, seven stars of the sample were found to be nonvariable, two stars are considered as possible variables, and eight stars were found to be variable, with periods ranging from 0.0881 ± 0.0001 to 0.5418 ± 0.0027 days. According to the literature, the variables have distinct values of [Fe I/H]: the three most metal-rich stars are in the red giant branch (RGB) stage, one has [Fe I/H] = −1.37 dex, while the other two have [Fe I/H] = −1.31 dex. The two most metal-poor variables have [Fe I/H] = −1.61 dex and [Fe I/H] = −1.62 dex, and are AGB stars; the remaining variables have [Fe I/H] = −1.44, −1.48, and −1.50 dex, the first two being RGB stars while the last is an AGB star. On the other hand, stars that appear to be nonvariable have −1.56 ≤ [Fe I/H] ≤ −1.40. We conclude that variability somehow affects the spectroscopic determination of the iron content of giant stars in NGC 3201, increasing the iron spread of the cluster. If variability is not taken into account, this spread could be incorrectly interpreted as due to an intrinsic iron spread affecting the stars of the cluster.

36 MATERIALS SCIENCE↗
DOE OSTI2021

Stellar Activity Manifesting at a One-year Alias Explains Barnard b as a False Positive

Barnard’s star is among the most studied stars given its proximity to the Sun. It is often considered the radial velocity (RV) standard for fully convective stars due to its RV stability and equatorial decl. Recently, an Msin i=3.3M{sub ⊕} super-Earth planet candidate with a 233 day orbital period was announced by Ribas et al. New observations from the near-infrared Habitable-zone Planet Finder (HPF) Doppler spectrometer do not show this planetary signal. We ran a suite of experiments on both the original data and a combined original + HPF data set. These experiments include model comparisons, periodogram analyses, and sampling sensitivity, all of which show the signal at the proposed period of 233 days is transitory in nature. The power in the signal is largely contained within 211 RVs that were taken within a 1000 day span of observing. Our preferred model of the system is one that features stellar activity without a planet. We propose that the candidate planetary signal is an alias of the 145 day rotation period. This result highlights the challenge of analyzing long-term, quasi-periodic activity signals over multiyear and multi-instrument observing campaigns.

47 OTHER INSTRUMENTATION↗
DOE OSTI2022

K2-79b and K2-222b: Mass Measurements of Two Small Exoplanets with Periods beyond 10 days that Overlap with Periodic Magnetic Activity Signals

We present mass and radius measurements of K2-79b and K2-222b, two transiting exoplanets orbiting active G-type stars observed with HARPS-N and K2. Their respective 10.99 day and 15.39 day orbital periods fall near periods of signals induced by stellar magnetic activity. The two signals might therefore interfere and lead to an inaccurate estimate of exoplanet mass. We present a method to mitigate these effects when radial velocity (RV) and activityindicator observations are available over multiple observing seasons and the orbital period of the exoplanet is known. We perform correlation and periodogram analyses on subsets composed of each target's two observing seasons, in addition to the full data sets. For both targets, these analyses reveal an optimal season with little to no interference at the orbital period of the known exoplanet. We make a confident mass detection of each exoplanet by confirming agreement between fits to the full RV set and the optimal season. For K2-79b, we measure a mass of 11.8 ± 3.6 M ⊕ and a radius of 4.09 ± 0.17 R ⊕ . For K2-222b, we measure a mass of 8.0 ± 1.8 M ⊕ and a radius of 2.35 ± 0.08 R ⊕ . According to model predictions, K2-79b is a highly irradiated Uranus analog and K2-222b hosts significant amounts of water ice. We also present a RV solution for a candidate second companion orbiting K2-222 at 147.5 days.

79 ASTRONOMY AND ASTROPHYSICS↗