# From Blackbirds to Black Holes: Investigating Capture-Recapture Methods for Time Domain Astronomy

## TL;DR

This paper evaluates capture-recapture statistical methods for estimating transient populations in time domain astronomy, demonstrating their effectiveness through simulations of accreting binary star populations.

## Contribution

It introduces a new exponential model based on radioactive decay laws and compares classical and modern capture-recapture methods for astronomical applications.

## Key findings

- Capture-recapture methods accurately estimate populations at 95% confidence.
- The exponential decay model recovers population size and duty cycle efficiently.
- Methods require only 10-50% of the observations needed for full discovery.

## Abstract

In time domain astronomy, recurrent transients present a special problem: how to infer total populations from limited observations. Monitoring observations may give a biassed view of the underlying population due to limitations on observing time, visibility and instrumental sensitivity. A similar problem exists in the life sciences, where animal populations (such as migratory birds) or disease prevalence, must be estimated from sparse and incomplete data. The class of methods termed Capture-Recapture is used to reconstruct population estimates from time-series records of encounters with the study population. This paper investigates the performance of Capture-Recapture methods in astronomy via a series of numerical simulations. The Blackbirds code simulates monitoring of populations of transients, in this case accreting binary stars (neutron star or black hole accreting from a stellar companion) under a range of observing strategies. We first generate realistic light-curves for populations of binaries with contrasting orbital period distributions. These models are then randomly sampled at observing cadences typical of existing and planned monitoring surveys. The classical capture-recapture methods, Lincoln-Peterson, Schnabel estimators, related techniques, and newer methods implemented in the Rcapture package are compared. A general exponential model based on the radioactive decay law is introduced, and demonstrated to recover (at 95% confidence) the underlying population abundance and duty cycle, in a fraction of the observing visits (10-50%) required to discover all the sources in the simulation. Capture-Recapture is a promising addition to the toolbox of time domain astronomy, and methods implemented in R by the biostats community can be readily called from within Python.