Structural Parameters of the Globular Cluster M 15

TL;DR

This study provides a detailed analysis of M 15's structural parameters, revealing a slight ellipticity variation and consistent position angle, using advanced photometric data and multiple analysis methods.

Contribution

It introduces a comprehensive approach combining ellipse fitting and MCMC sampling to accurately determine M 15's structural parameters, highlighting the importance of multi-method analysis.

Findings

Inner ellipticity $ar{ ext{epsilon}}=0.09 ext{--}0.02$

Outer ellipticity $ar{ ext{epsilon}}=0.04 ext{--}0.02$

Position angle $ m{PA} ext{~}=44.4^ ext{o} ext{--}46.6^ ext{o}$

Abstract

We present a detailed analysis of the structural parameters of the globular cluster M 15 using g- and i-band photometric data from Pan-STARRS1 DR2. The central coordinates ($X_{\rm{C}}, Y_{\rm{C}}$), ellipticity ($\epsilon$), and position angle (PA) are derived via two independent methods: ellipse fitting of the two-dimensional stellar number isodensity distribution and Markov Chain Monte Carlo (MCMC) sampling. Our analysis of 38 stellar density intervals reveals a cluster center offset by only $4\,.\!\!^{\prime\prime}1\pm9\,.\!\!^{\prime\prime}6$ from the commonly accepted in the literature value, a good agreement on the order of our map resolution. We find a radial variation in the ellipticity, with a mean value of $\epsilon=0.09\pm0.02$ for the inner region ($R\leq4\,.\!\!^{\prime}5$) and $\epsilon=0.04\pm0.02$ for the outer region ($R>4\,.\!\!^{\prime}5$), where the errors correspond to $1\sigma$. The MCMC analysis of 75 datasets yields a mean $\epsilon=0.022\pm0.005$ for the entire cluster. The PA remains constant with increasing distance from the cluster center, $\rm{PA}=44\,.\!\!{\rm{^\circ}}4\pm16\,.\!\!{\rm{^\circ}}2$, and the MCMC method providing a consistent value of $\rm{PA}=46\,.\!\!{\rm{^\circ}}6\pm7\,.\!\!{\rm{^\circ}}1$. Our results are in agreement with some recent studies but challenge others, suggesting that a single $\epsilon$ value may be insufficient to fully characterize the overall oblateness of M 15 due to incompleteness and crowding effects in its core.