The Non-homogeneous Poisson Process for Fast Radio Burst Rates

Abstract

This paper presents the non-homogeneous Poisson process (NHPP) for modeling the rate of fast radio bursts (FRBs) and other infrequently observed astronomical events. The NHPP, well-known in statistics, can model changes in the rate as a function of both astronomical features and the details of an observing campaign. This is particularly helpful for rare events like FRBs because the NHPP can combine information across surveys, making the most of all available information. The goal of the paper is two-fold. First, it is intended to be a tutorial on the use of the NHPP. Second, we build an NHPP model that incorporates beam patterns and a power law flux distribution for the rate of FRBs. Using information from 12 surveys including 15 detections, we find an all-sky FRB rate of 586.88 events per sky per day above a flux of 1 Jy (95\% CI: 271.86, 923.72) and a flux power-law index of 0.91 (95\% CI: 0.57, 1.25). Our rate is lower than other published rates, but consistent with the rate given in Champion et al. 2016.

19 pages, 2 figures

References in corpus (7)

• A bright millisecond radio burst of extragalactic origin
• Fast Radio Burst Discovered in the Arecibo Pulsar ALFA Survey
• Exoplanet population inference and the abundance of Earth analogs from noisy, incomplete catalogs
• A fast radio burst in the direction of the Carina dwarf spheroidal galaxy
• The Galactic Position Dependence of Fast Radio Bursts and the Discovery of FRB 011025
• An absence of fast radio bursts at intermediate galactic latitudes
• The Euclidean distribution of Fast Radio Bursts

Cited by in corpus (49)

• Fast Radio Bursts
• Fast Radio Bursts: An Extragalactic Enigma
• The First CHIME/FRB Fast Radio Burst Catalog
• A Living Theory Catalogue for Fast Radio Bursts
• Fast radio bursts as synchrotron maser emission from decelerating relativistic blast waves
• The CHIME Fast Radio Burst Project: System Overview
• Highest-frequency detection of FRB 121102 at 4-8 GHz using the Breakthrough Listen Digital Backend at the Green Bank Telescope
• A concordance picture of FRB 121102 as a flaring magnetar embedded in a magnetized ion-electron wind nebula
• A Multi-telescope Campaign on FRB 121102: Implications for the FRB Population
• Fast Radio Bursts from Magnetars Born in Binary Neutron Star Mergers and Accretion Induced Collapse
• The Physics of Fast Radio Bursts
• On the FRB luminosity function -- II. Event rate density
• Chromatic periodic activity down to 120 MHz in a Fast Radio Burst
• The z-DM distribution of fast radio bursts
• Fast Radio Bursts
• Constraints on the Engines of Fast Radio Bursts
• Unveiling the Engines of Fast Radio Bursts, Super-Luminous Supernovae, and Gamma-Ray Bursts
• A Distant Fast Radio Burst Associated to its Host Galaxy with the Very Large Array
• Realfast: Real-Time, Commensal Fast Transient Surveys with the Very Large Array
• Fast Radio Bursts
• The Slope of the Source-Count Distribution for Fast Radio Bursts
• Interpreting the distributions of FRB observables
• A Fast Radio Burst Occurs Every Second throughout the Observable Universe
• PALFA Single-Pulse Pipeline: New Pulsars, Rotating Radio Transients and a Candidate Fast Radio Burst
• Lensing of fast radio bursts: future constraints on primordial black hole density with an extended mass function and a new probe of exotic compact fermion and boson stars
• Compact Binary Mergers and The Event Rate of Fast Radio Bursts
• Initial results from a realtime FRB search with the GBT
• Cosmology with fast radio bursts in the era of SKA
• Fast radio bursts: do repeaters and non-repeaters originate in statistically similar ensembles
• Using negative-latency gravitational wave alerts to detect prompt radio bursts from binary neutron star mergers with the Murchison Widefield Array
• The Performance and Calibration of the CRAFT Fly's Eye Fast Radio Burst Survey
• Energy function, formation rate and low-metallicity environment of fast radio bursts
• Associating Fast Radio Bursts with Extragalactic Radio Sources: General Methodology and a Search for a Counterpart to FRB 170107
• Formation of periodic FRB in binary systems with eccentricity
• Multi-dimensional population modelling using frbpoppy: magnetars can produce the observed Fast Radio Burst sky
• GREENBURST: a commensal fast radio burst search back-end for the Green Bank Telescope
• A method for reconstructing the Galactic magnetic field using dispersion of fast radio bursts and Faraday rotation of radio galaxies
• The Statistical Similarity of Repeating and Non-Repeating Fast Radio Bursts
• Fast radio bursts: superpulsars, magnetars, or something else?
• GBTrans: A commensal search for radio pulses with the Green Bank twenty metre telescope
• Statistical properties of fast radio bursts elucidate their origins: magnetars are favoured over gamma-ray bursts
• Population modelling of FRBs from intrinsic properties
• A targeted search for repeating fast radio bursts associated with gamma-ray bursts
• Artificial Broadcasts as Galactic Populations: I. A Point Process Formalism for Extraterrestrial Intelligences and Their Broadcasts
• Fast Radio Bursts
• Detectability of radio afterglows from binary neutron star mergers and implications for fast radio bursts
• Diverse origins for non-repeating fast radio bursts: Rotational radio transient sources and cosmological compact binary merger remnants
• The variance of dispersion measure of high-redshift transient objects as a probe of ionized bubble size during reionization
• Apertif, Phased Array Feeds for the Westerbork Synthesis Radio Telescope