Inferring kilonova population properties with a hierarchical Bayesian framework I : Non-detection methodology and single-event analyses

TL;DR

This paper introduces a hierarchical Bayesian framework, Nimbus, that infers kilonova luminosity parameters from non-detections using GW data and survey limits, highlighting the importance of prior choices and model effects.

Contribution

The paper presents Nimbus, a novel Bayesian method for analyzing kilonova populations from non-detections, incorporating GW data, survey coverage, and model independence.

Findings

Methodology tested on GW190425 follow-up data

Uniform priors constrain parameter space effectively

Astrophysical priors yield less informative results

Abstract

We present ${\tt nimbus}$ : a hierarchical Bayesian framework to infer the intrinsic luminosity parameters of kilonovae (KNe) associated with gravitational-wave (GW) events, based purely on non-detections. This framework makes use of GW 3-D distance information and electromagnetic upper limits from multiple surveys for multiple events, and self-consistently accounts for finite sky-coverage and probability of astrophysical origin. The framework is agnostic to the brightness evolution assumed and can account for multiple electromagnetic passbands simultaneously. Our analyses highlight the importance of accounting for model selection effects, especially in the context of non-detections. We show our methodology using a simple, two-parameter linear brightness model, taking the follow-up of GW190425 with the Zwicky Transient Facility (ZTF) as a single-event test case for two different prior choices of model parameters -- (i) uniform/uninformative priors and (ii) astrophysical priors based on surrogate models of Monte Carlo radiative transfer simulations of KNe. We present results under the assumption that the KN is within the searched region to demonstrate functionality and the importance of prior choice. Our results show consistency with ${\tt simsurvey}$ -- an astronomical survey simulation tool used previously in the literature to constrain the population of KNe. While our results based on uniform priors strongly constrain the parameter space, those based on astrophysical priors are largely uninformative, highlighting the need for deeper constraints. Future studies with multiple events having electromagnetic follow-up from multiple surveys should make it possible to constrain the KN population further.