# Constraining the duty cycle of transient low-mass X-ray binaries through simulations

## TL;DR

This study uses simulations to understand how survey strategies impact the measurement of duty cycles in transient low-mass X-ray binaries, highlighting biases and optimal observation practices.

## Contribution

It introduces a simulation-based analysis of survey biases affecting duty cycle estimates and proposes optimal monitoring strategies for transient X-ray sources.

## Key findings

- Fluctuations in outburst duration bias duty cycle estimates.
- Short, frequent surveys better detect short-duration outbursts.
- Long, regular surveys improve duty cycle accuracy.

## Abstract

We performed simulations of a large number of so-called very faint X-ray transient sources from surveys obtained using the X-ray telescope aboard the Neil Gehrels \emph{Swift} Observatory on two Galactic globular clusters, and the Galactic Center. We calculated the ratio between the duty cycle we input in our simulations and the one we measure after the simulations. We found that fluctuations in outburst duration and recurrence times affect our estimation of the duty cycle more than non detected outbursts. This biases our measures to overestimate the simulated duty cycle of sources. Moreover, we determined that compact surveys are necessary to detect outbursts with short duration because they could fall in gaps between observations, if such gaps are longer than their duration. On the other hand, long surveys are necessary to detect sources with low duty cycle because the smallest duty cycle a survey can observe is given by the ratio between the shortest outburst duration and the total length of the survey. If one has a limited amount of observing time, these two effects are competing, and a compromise is required which is set by the goals of the proposed survey. We have also performed simulations with several artificial survey strategies in order to evaluate the optimal observing campaign aimed at detecting transients as well as at having the most accurate estimates of the duty cycle. As expected, the best campaign would be a regular and dense monitoring that extends for a very long period. The closest real example of such a dataset is the monitoring of the Galactic Centre.