Structural Parameters of Star Clusters: Signal to Noise Effects

TL;DR

This study investigates how photometric signal-to-noise ratio affects the accuracy of structural parameters of unresolved star clusters, using simulations and MCMC fitting to determine the necessary SNR for reliable measurements.

Contribution

It introduces a method to assess the impact of SNR on parameter estimation of star clusters and identifies a threshold SNR of about 50 for accurate half-light radius determination.

Findings

A SNR of ~50 is needed for <20% accuracy in half-light radius.

Posterior distributions reveal parameter uncertainties and degeneracies.

The technique applies to synthetic images of extragalactic star clusters.

Abstract

We study the impact of photometric signal to noise on the accuracy of derived structural parameters of unresolved star clusters using MCMC model fitting techniques. Star cluster images were simulated as a smooth surface brightness distribution following a King profile convolved with a point spread function. The simulation grid was constructed by varying the levels of sky background and adjusting the cluster's flux to a specified signal to noise. Poisson noise was introduced to a set of cluster images with the same input parameters at each node of the grid. Model fitting was performed using emcee algorithm. The presented posterior distributions of the parameters illustrate their uncertainty and degeneracies as a function of signal to noise. By defining the photometric aperture containing 80% of the cluster's flux, we find that in all realistic sky background level conditions a signal to noise ratio of $\sim$50 is necessary to constrain the cluster's half-light radius to an accuracy better than $\sim$20%. The presented technique can be applied to synthetic images simulating various observations of extragalactic star clusters.