Utilizing Voronoi Tessellations to Determine Radial Density Profiles

TL;DR

This paper introduces a Voronoi tessellation-based method for determining 2D radial density profiles in astronomical systems, demonstrating its superior accuracy and lower uncertainties compared to traditional annulus-based methods through simulations and real data applications.

Contribution

The paper presents a novel Voronoi tessellation approach for radial density profiling, improving accuracy and reducing uncertainties over standard methods in astronomical data analysis.

Findings

Voronoi method yields lower uncertainties in density profile parameters.

The Voronoi approach provides more accurate total object counts, especially in larger systems.

Application to real globular cluster data confirms improved precision over traditional methods.

Abstract

We have developed a novel method of determining 2D radial density profiles for astronomical systems of discrete objects using Voronoi tessellations. This Voronoi-based method was tested against the standard annulus-based method on 5 simulated systems of objects, following known Hubble density profiles of varying parameters and sizes. It was found that the Voronoi-based method returned radial density fits with lower uncertainties on the fitting parameters across all 5 systems compared to the annulus-based method. The Voronoi-based method also consistently returned more accurate estimates of the total number of objects in each system than the annulus-based method, and this accuracy increased with increasing system size. Finally, the Voronoi-based method was applied to two observed globular cluster systems around brightest cluster galaxies ESO 444-G046 and 2MASX J13272961-3123237 and the results were compared to previous results for these galaxies obtained with the annulus-based method. Again, it was found that the Voronoi-based method returned fits with lower uncertainties on the fitting parameters, and the total number of globular clusters returned are within errors of the annulus-based method estimates, however also with lower uncertainties.