Multiscale Time- and Frequency-domain Likelihood Analysis with Photon Weights

Abstract

We present an unbinned likelihood analysis formalism employing photon weights-the probabilities that events are associated with a particular source. This approach is applicable to any photon-resolving instrument, and thus well suited to high-energy observations; we focus here on GeV γ-ray data from the Fermi Large Area Telescope. Weights connect individual photons to the outputs of a detailed, expensive likelihood analysis of a much larger data set. The weighted events can be aggregated into arbitrary time spans ranging from microseconds to years. Such retrospective grouping permits timeand frequency-domain analysis over a wide range of scales and enables characterization of disparate phenomena like blazar flares, γ-ray bursts, pulsar pulses, novae, γ-ray binaries, and other variable sources. To demonstrate the formalism, we incorporate photon weights into the Bayesian blocks algorithm and perform a hierarchical time scale analysis of 3C 279 activity. We analyze pulsar pulse profiles and estimate the unpulsed emission level and the optimal division of the data into on-and offpulse intervals. We extend the formalism to Fourier analysis and derive estimators for power spectra, used to search for and characterize periodic sources. We show how the Fast Fourier transform can be used to probe orbital periods as short as a minute and we discuss mitigation of spurious signals. Our final example combines time-and frequency-domain analysis to jointly characterize the flares and orbital modulation of Cygnus X-3, yielding the strongest detection of the orbital signal (>13σ) to date. Finally, we discuss extensions of the work to other GeV sources and to X-ray and TeV observations.

The eROSITA Final Equatorial-Depth Survey (eFEDS)

“…To measure the source flux variability (instead of the observed count rate variability), the background and instrument sensitivity at any time needs to be incorporated. While the original count event formulation of Bayesian blocks can incorporate varying sensitivity, contributions from a potentially varying background deduced by an 'off' region go beyond the current work (but see Kerr 2019, for Bayesian blocks extensions) However, when the Gaussian approximation is used in a pre-binned light curve, we can infer the (background-corrected) source count rate at each time bin, (X i , σ i ). The Bayesian block formulation using the Gaussian error bars can then attempt to detect changes.…”

The observability of plasmoid-powered $γ$-ray flares with the Fermi Large Area Telescope

“…In order to draw firm conclusions in the future, magnetic reconnection simulations over longer time scales would be highly desirable. Additionally, a PSD analysis of unbinned Fermi data could help to probe frequencies below the chosen time binning (e.g., Kerr 2019). All models discussed so far were based on simulations of reconnection in plasmas with fixed magnetization σ = 10.…”

Gamma-ray Eclipses and Orbital Modulation Transitions in the Candidate Redback 4FGL J1702.7-5655

“…Thus, when a source is brighter than the model predicts, the probability of a photon coming from the source is underestimated, and, when the source is fainter than the model prediction, the probability is overestimated (e.g. Kerr 2019). This results in a reduction of the apparent amplitude of any variability.…”

“…The light curves were obtained using a variant of aperture photometry where we estimate the probability "p" that each photon comes from a source of interest and sum these probabilities (e.g. Kerr 2011;Fermi LAT Collaboration et al 2012;Kerr 2019). To facilitate this, model files were created for each source using make4FGLxml including sources from the 4FGL DR2 catalog within a 10 degree radius from the source.…”