# Spatial Statistics in Star Forming Regions: Testing the Limits of Randomness

## TL;DR

This study evaluates the effectiveness of various spatial statistical tests in analyzing the distribution of young stars in star-forming regions, finding that O-ring and Ripley's K are most effective in detecting clustering against randomness.

## Contribution

The paper assesses and compares the performance of multiple spatial statistics tests on astrophysical data, highlighting the superior effectiveness of O-ring and Ripley's K in identifying star clustering.

## Key findings

- O-ring with logarithmic bins performs best in detecting clustering.
- Ripley's K closely follows O-ring in effectiveness.
- F and G functions require higher signal-to-noise to reject randomness.

## Abstract

Observational studies of star formation reveal spatial distributions of Young Stellar Objects (YSOs) that are `snapshots' of an ongoing star formation process. Using methods from spatial statistics it is possible to test the likelihood that a given distribution process could produce the observed patterns of YSOs. The aim of this paper is to determine the usefulness of the spatial statistics tests Diggle's G function (G), the `free-space' function (F), Ripley's K and O-ring for application to astrophysical data. The spatial statistics tests were applied to simulated data containing 2D Gaussian clusters projected on random distributions of stars. The number of stars within the Gaussian cluster and number of background stars were varied to determine the tests' ability to reject complete spatial randomness (CSR) with changing signal-to-noise. The best performing test was O-ring optimised with overlapping logarithmic bins, closely followed by Ripley's K. The O-ring test is equivalent to the 2-point correlation function. Both F and G (and the minimum spanning tree, of which G is a subset) performed significantly less well, requiring a cluster with a factor of two higher signal-to-noise in order to reject CSR consistently. We demonstrate the tests on example astrophysical datasets drawn from the Spitzer catalogue.