Structural Parameters of the Globular Cluster M 15

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 ($ε$), 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 $ε=0.09\pm0.02$ for the inner region ($R\leq4\,.\!\!^{\prime}5$) and $ε=0.04\pm0.02$ for the outer region ($R>4\,.\!\!^{\prime}5$), where the errors correspond to $1σ$. The MCMC analysis of 75 datasets yields a mean $ε=0.022\pm0.005$ 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 $ε$ value may be insufficient to fully characterize the overall oblateness of M 15 due to incompleteness and crowding effects in its core.

Figures (11)

• Figure 1: Two-dimensional spatial distribution of the photometrically filtered stars of the GC M 15 in a $20^\prime$$\times$$20^\prime$ field. The first panel from left to right shows the 2D distribution of the unfiltered sources, the second shows their distribution after filtering, and the third panel displays the 2D distribution of the rejected sources, which in this case satisfy the condition for the removal of extended objects in the g- or i-band (f4). As expected, these objects are predominantly located in the cluster's center and around the brightest stars.
• Figure 2: CMDs of point-like sources (quality flag $<2^{24}=16777216$) in g- and i-bands within the 20$^\prime$$\times$20$^\prime$ field of M 15. The top-left diagram shows the unfiltered sample with all sources plotted in blue. Each subsequent diagram presents one filtering type: retained objects are marked in blue and rejected ones with red. As expected, f4 excludes the largest fraction of sources.
• Figure 3: Ellipse fitting over the 7--9 */px density interval for the 100$\times$100 array smoothed with a 5$\times$5 boxcar. The major and minor axes are indicated by a red dashed line and a blue dash-dotted line, respectively. The fitted ellipse is drawn in orange and the isodensities are marked with blue pixels.
• Figure 4: Ellipse fitting results for all considered 38 stellar density intervals within the 40$^\prime$$\times$40$^\prime$ field. From left to right the first row presents the 100$\times$100 array under the three conditions -- unsmoothed, 3$\times$3 boxcar and 5$\times$5 boxcar. The second row shows the same arrangement for the 200$\times$200 array. The color scale on the right of the panels represents the density */px.
• Figure 5: Example of M 15 structural parameters derived from MCMC for 50$^\prime$$\times$$50^\prime$ field using filtration f3 and background subtraction b2. The histograms show the distribution for each parameter, with vertical dashed lines marking the 0.25, 0.5, and 0.75 quantiles. The contour plots show the pairwise parameter correlations. The median values and corresponding errors are listed above each histogram.