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Unveiling Dynamics and Variability in Open Clusters: Insights from a Comprehensive Analysis of Six Galactic Clusters

Kuldeep Belwal, D. Bisht, Ing-Guey Jiang, R. K. S. Yadav, Ashish Raj, Geeta Rangwal, Arvind K. Dattatrey, Mohit Singh Bisht, Alok Durgapal

TL;DR

We analyze six intermediate-age Galactic open clusters with Gaia DR3 and TESS data to derive membership, structure, dynamics, and stellar content. By comparing Bayesian and Gaussian Mixture Model membership methods, we adopt GMM for clean member separation, then fit King models to radial density profiles and estimate distances via parallax with a Bailer-Jones prior. Isochrone fitting reveals ages $0.199$–$1.95$ Gyr and metallicities ranging near solar to subsolar, with MF slopes indicating dynamical mass segregation; orbits are near-circular in the thin disk, implying disk tidal shaping and low escape rates for low-mass members. Variable-star census from TESS identifies 12 variables across four clusters, including one $\ extgamma$ Dor and one SPB pulsator, plus two eclipsing binaries which are modeled with PHOEBE to yield mass ratios $q=1.37$ and $q=2.16$. This integrated approach, linking orbital dynamics with stellar variability, provides a comprehensive view of open-cluster evolution in the Galactic disk.

Abstract

We present a kinematic and dynamical analysis of six Galactic open clusters NGC~2204, NGC~2660, NGC~2262, Czernik~32, Pismis~18, and NGC~2437, using \textit{Gaia}~DR3. We used Bayesian and Gaussian Mixture Model (GMM) methods to identify cluster members, but chose GMM because it's more appropriate for low-mass stars. Estimated distances range from 1.76 to 4.20~kpc and ages from 0.199 to 1.95~Gyr, confirming their intermediate-age nature. King model fits indicate compact morphologies, with core radii of 1--10~arcmin and cluster radii of 5--24~arcmin. We identify 13 BSS and 3 YSS members, whose central concentrations suggest origins via mass transfer or stellar collisions. The mass function slopes (0.96--1.19) are flatter than the Salpeter value, which indicates that these clusters have undergone dynamical mass segregation. Orbit integration within a Galactic potential indicates nearly circular orbits (eccentricities 0.02--0.10), vertical excursions within $\pm$132~pc, and guiding radii near the solar circle, suggesting disk confinement. These clusters likely formed in the thin disk and are shaped by Galactic tidal perturbations, facilitating the rapid loss of low-mass members. Additionally, twelve variable stars were found across four clusters using \textit{TESS} light curves, including $γ$~Doradus and SPB pulsators, eclipsing binaries, and a yellow straggler candidate. Periods were derived via Lomb-Scargle analysis. Two eclipsing binaries (TIC~94229743 and TIC~318170024) were modeled using PHOEBE, yielding mass ratios of 1.37 and 2.16, respectively. Our findings demonstrate that integrating orbital dynamics and variable star studies presents valuable insights into the evolutionary pathways of open clusters.

Unveiling Dynamics and Variability in Open Clusters: Insights from a Comprehensive Analysis of Six Galactic Clusters

TL;DR

We analyze six intermediate-age Galactic open clusters with Gaia DR3 and TESS data to derive membership, structure, dynamics, and stellar content. By comparing Bayesian and Gaussian Mixture Model membership methods, we adopt GMM for clean member separation, then fit King models to radial density profiles and estimate distances via parallax with a Bailer-Jones prior. Isochrone fitting reveals ages – Gyr and metallicities ranging near solar to subsolar, with MF slopes indicating dynamical mass segregation; orbits are near-circular in the thin disk, implying disk tidal shaping and low escape rates for low-mass members. Variable-star census from TESS identifies 12 variables across four clusters, including one Dor and one SPB pulsator, plus two eclipsing binaries which are modeled with PHOEBE to yield mass ratios and . This integrated approach, linking orbital dynamics with stellar variability, provides a comprehensive view of open-cluster evolution in the Galactic disk.

Abstract

We present a kinematic and dynamical analysis of six Galactic open clusters NGC~2204, NGC~2660, NGC~2262, Czernik~32, Pismis~18, and NGC~2437, using \textit{Gaia}~DR3. We used Bayesian and Gaussian Mixture Model (GMM) methods to identify cluster members, but chose GMM because it's more appropriate for low-mass stars. Estimated distances range from 1.76 to 4.20~kpc and ages from 0.199 to 1.95~Gyr, confirming their intermediate-age nature. King model fits indicate compact morphologies, with core radii of 1--10~arcmin and cluster radii of 5--24~arcmin. We identify 13 BSS and 3 YSS members, whose central concentrations suggest origins via mass transfer or stellar collisions. The mass function slopes (0.96--1.19) are flatter than the Salpeter value, which indicates that these clusters have undergone dynamical mass segregation. Orbit integration within a Galactic potential indicates nearly circular orbits (eccentricities 0.02--0.10), vertical excursions within 132~pc, and guiding radii near the solar circle, suggesting disk confinement. These clusters likely formed in the thin disk and are shaped by Galactic tidal perturbations, facilitating the rapid loss of low-mass members. Additionally, twelve variable stars were found across four clusters using \textit{TESS} light curves, including ~Doradus and SPB pulsators, eclipsing binaries, and a yellow straggler candidate. Periods were derived via Lomb-Scargle analysis. Two eclipsing binaries (TIC~94229743 and TIC~318170024) were modeled using PHOEBE, yielding mass ratios of 1.37 and 2.16, respectively. Our findings demonstrate that integrating orbital dynamics and variable star studies presents valuable insights into the evolutionary pathways of open clusters.

Paper Structure

This paper contains 30 sections, 9 equations, 19 figures, 7 tables.

Table of Contents

  1. Introduction
  2. Data Sources and Selection Criteria
  3. Gaia DR3
  4. TESS Data
  5. Membership probability
  6. Bayesian Method
  7. Gaussian Mixture Model
  8. Source Extraction
  9. Normalisation and GMM Implementation
  10. Structural Analysis of Clusters
  11. Parallax-Based Distance Estimation
  12. Color-Magnitude Diagram Analysis and Cluster Characterization
  13. Dynamical Study
  14. Luminosity Function
  15. Mass Function
  16. ...and 15 more sections

Figures (19)

  • Figure 1: Identification chart of six OCs taken from the STScI Digitized Sky Survey, oriented in the northeast direction (north is up and east is left). The inner red circle represents the core radius, while the outer green ring denotes the cluster radius. The blue and yellow open circles represent the BSS and YSS, respectively.
  • Figure 2: Photometric uncertainties in the G, $G_{\mathrm{BP}}$, and $G_{\mathrm{RP}}$ bands plotted as a function of G magnitude for stars in the open cluster NGC 2204.
  • Figure 3: This figure illustrates the initial cluster member separation method based on Gaia's proper motions for the cluster. The top panel displays the VPDs, while the bottom panels show the Gaia CMDs for the total stars, cluster members, and field stars. In the top panel, a circle with a radius of 0.5 mas yr$^{-1}$ represents the member stars within the cluster field.
  • Figure 4: Membership analysis of the open cluster NGC 2204. Panel (a) shows the spatial distribution of stars in R.A. and Dec., panel (b) displays the proper motion distribution in the $\mu_{\alpha}\cos\delta$ vs. $\mu_{\delta}$ plane, and panel (c) presents the parallax distribution. The results from the GMM-based method and the Bayesian approach (ML-MOC) are compared, with red and blue dots indicating high probability members identified by each method, respectively, and grey points representing the full sample.
  • Figure 5: A comparison of the CMDs from both methods is shown on the left, displaying stars with a membership probability greater than 70$\%$. The Venn diagram for the cluster NGC 2204 is presented on the right.
  • ...and 14 more figures