A comprehensive Gaia DR3 study of the open cluster NGC 6134: Bayesian distances, present-day mass function, mass segregation, and structural decomposition

arXiv:2606.24270 · astro-ph.GA · Submitted 2026-06-23 · Read on arXiv

Listen

Transcript

Introduction to the show: ident: Astrophysics Radio. Generated commentary on the latest astrophysics papers.

Vera: We're looking at the paper: "A comprehensive Gaia DR3 study of the open cluster NGC 6134".

Jocelyn: The gist The present study provides a comprehensive photometric and kinematic analysis of the open cluster NGC 6134 using Gaia DR3 data to determine its fundamental parameters, including distance,

Vera: First, who's behind it and why it matters.

Title and authors: Vera: So, this paper is titled "A comprehensive Gaia DR3 study of the open cluster NGC six thousand one hundred thirty-four: Bayesian distances, present-day mass function, mass segregation, and structural decomposition." It’s a pretty big title that tells you they are doing a lot of things with Gaia data on this one cluster.

Jocelyn: The authors are Jatmiko et al., and it’s interesting because they aren't just looking at where the cluster is; they're digging into the actual structure of the stars within it too, using Bayesian methods to figure out distances and then analyzing how those stars are distributed in space.

Subrahmanyan: From a theoretical standpoint, this is important because it links observable properties directly to the initial conditions of star formation; figuring out that present-day mass function and segregation tells us about dynamical evolution within a stellar system.

The paper's summary: Vera: So, the summary of this study is essentially that they take the Gaia DR3 astrometric data for NGC six thousand one hundred thirty-four and use a combination of techniques to nail down its fundamental properties. They are using Bayesian inference methods to get distances, and then applying tools like ASteCA to figure out things like the present-day mass function.

Jocelyn: It’s about moving beyond just measuring stars and actually trying to understand what those stars tell us about the cluster as a whole—things like its age or its metallicity. They are also looking at how the stars are grouped spatially, which gives them clues about the cluster's history.

Vera: Right, so they are taking those input parameters—distance, age, metallicity—and using them to see if they match what we expect from other studies and how it fits into the larger context of open clusters.

Jocelyn: And one thing the summary highlights is that they’re not just looking at the stars themselves; they are trying to understand how those stellar properties correlate with things like exoplanet characteristics, which is a bit broader than just cluster science.

The paper's improvements: Vera: The paper points out some specific ways their approach improves on previous work, especially concerning the distance determination; they use Kalkayotl which is this code for distance estimation using the Bayesian inference method that accounts for spatial correlation between stars.

Jocelyn: And they mention something about how their membership determination is improved by using the HDBSCAN algorithm on Gaia DR3 astrometric data to find members with a probability greater than zero point five.

Subrahmanyan: That move to the HDBSCAN approach for membership identification is significant because it’s a more advanced way to filter out field stars, and they found that this method yielded eight hundred eighty-eight stars with a membership probability of p greater than zero point five.

Vera: And then they talk about how their final fundamental parameters, like the age of log(t) = nine point one four ± zero point zero one and the metallicity of

Fe/H: = zero point zero eight ± zero point zero six, are consistent with other recent photometric studies.

Jocelyn: And they also highlight that they found a prominent gap in the main sequence in their color-magnitude diagram, which they suggest might be linked to the cluster’s high binary fraction of approximately forty percent.

Conclusion: Vera: So, wrapping up this paper on "A comprehensive Gaia DR3 study of the open cluster NGC six thousand one hundred thirty-four: Bayesian distances, present-day mass function, mass segregation, and structural decomposition," the main point is that they provide a very constrained set of fundamental parameters for this cluster.

Jocelyn: They confirm significant mass segregation and show that the structure isn't uniform; they found three distinct components: a central core, a tidal tail, and a diffuse halo.

Subrahmanyan: From my perspective, the finding that mass segregation is persistent across such a wide range of masses, quantified by the minimum spanning tree method with lambda MSR consistently above unity across the entire probed mass range from five to one hundred solar masses, strongly suggests this cluster is dynamically evolved due to long-term two-body relaxation rather than being in a primordial state.

Vera: And that structural decomposition—the core, tail, and halo—gives us visual evidence of that dynamical evolution they are describing.

Jocelyn: Plus, their analysis of the Present–Day Mass Function shows a break at Mc = zero point nine five solar masses separating the intermediate-to-low-mass regime with slope alpha A equals negative two point one plus or minus zero point one eleven from the high-mass regime with slope alpha B equals one point six eight plus or minus zero point one fifteen.

Subrahmanyan: That break in the mass function, combined with that preferential loss of low-mass stars due to dynamical evolution, supports their conclusion that NGC six thousand one hundred thirty-four is a significantly dynamically evolved open cluster.

Vera: So, looking at this paper on "A comprehensive Gaia DR3 study of the open cluster NGC six thousand one hundred thirty-four: Bayesian distances, present-day mass function, mass segregation, and structural decomposition," it gives us a robust understanding of this system's age and its internal structure.

Jocelyn: It’s a detailed map showing that the cluster is not just a simple blob but has evolved over time with clear evidence of dynamical activity.

Subrahmanyan: It confirms that when we look at these observable parameters, we see the imprint of the gravitational history on the stellar population, which is exactly what we need to connect observation to structure formation theory.

Bosscha Observatory, Institut Teknologi Bandung, Bandung Barat 40391, Indonesia · Astronomy Research Group, Institut Teknologi Bandung, Bandung 40132, Indonesia · Astronomy Study Program, Institut Teknologi Bandung, Bandung 40132 · Ibaraki University Graduate School of Science and Engineering

astro-ph.GA

Submitted: 2026-06-23

Updated: 2026-10-19

Comments: v2, 22 pages, 12 figures, 4 tables, submitted to the Open Journal of Astrophysics (OJAp)

License: http://creativecommons.org/licenses/by/4.0/

Importance score: 79/100

The gist: The gist The present study provides a comprehensive photometric and kinematic analysis of the open cluster NGC 6134 using Gaia DR3 data to determine its fundamental parameters, including distance,

Key concepts

Membership Determination: Researchers used the HDBSCAN algorithm on Gaia DR3 astrometric data to select genuine cluster members. This process filtered the stars down from 888 candidates to a more reliable group, ensuring that only stars truly belonging to NGC 6134 were analyzed for further study.
Mass Segregation: This measures how mass is distributed within the cluster. The Minimum Spanning Tree (MST) method showed that the Mass Segregation Ratio ($\Lambda$MSR) was consistently above unity across all masses, proving that heavier stars have moved toward the center due to dynamical evolution.
Bayesian Gaussian Mixture Model (BGM): This statistical tool was used to analyze the 2D and 3D spatial distributions of the cluster. The BGM successfully decomposed the population into three distinct structural components: a dense central core, an extended tidal tail, and a more spread-out diffuse halo.
Present-Day Mass Function (PDMF): This function describes the distribution of stellar masses currently present in NGC 6134. The PDMF shows a break at $M_c = 0.95 M_{\odot}$, indicating that the cluster has substantially depleted its population of low-mass stars compared to what might be expected initially.

Terminology

Mass Segregation — 3× in this paper · explained in 4 episodes
Bayesian Inference — 1× in this paper · explained in 6 episodes
Core — 1× in this paper · explained in 2 episodes
Metallicity — 1× in this paper · explained in 3 episodes

Summary

The gist The present study provides a comprehensive photometric and kinematic analysis of the open cluster NGC 6134 using Gaia DR3 data to determine its fundamental parameters, including distance, age, metallicity, and substructures.

Membership Determination

The paper addresses the challenge of identifying genuine cluster members in NGC 6134 by employing advanced clustering techniques on astrometric data from Gaia DR3 Our previous study (Yusuf et al. 2024) presents the findings of the membership analysis of the open star cluster NGC 6134 in the southern hemisphere <ref:2606.24270#pg6> To address this, we used the HDBSCAN algorithm on astrometric data from Gaia DR3 <ref:2606.24270#pg3> The results consistently determined that 888 stars with membership probability p ≥ 0.5 were members of NGC 6134 with a radius of 30 parsecs from the center of the cluster, in line with the findings of other studies using the same sample size <ref:2606.24270#pg3>.

Distance Determination and Spatial Structure

The determination of cluster distance relies on Bayesian inference methods to overcome limitations inherent in Gaia DR3 parallax measurements <ref:2606.24270#pg4> We utilize Kalkayotl (Olivares et al. 2020) which is the code for distance estimation using the Bayesian inference method which also takes into account the parallax spatial correlation <ref:2606.24270#pg4> The cluster’s distance, determined using Bayesian inference, is 1070.83 ± 2.50 pc, consistent with the ASteCA result <ref:2606.24270#pg2>. In 3D space, the cluster exhibits a pronounced elongation along the observational axis <ref:2606.24270#pg5>. This morphological stretching is a well-known artifact driven by inherent uncertainties in individual stellar distance estimates, which preferentially smear the spatial projection along the line of sight <ref:2606.24270#pg5>.

Fundamental Cluster Parameters

The fundamental parameters of NGC 6134 were determined using the Automated Stellar Cluster Analysis (ASteCA) v0.4.3 code <ref:2606.24270#pg6> The ASteCA code applies the Bayesian Decontamination Algorithm to the input data to reduce the number of members from 888 to 655 <ref:2606.24270#pg6>. The results obtained are [Fe/H] = 0.08 ± 0.06, log(t) = 9.14 ± 0.01, d = 1064.43 ± 15.19 pc, and Av = 1.03 ± 0.05 mag <ref:2606.24270#pg6>. The derived age of log(t[yr]) = 9.14 ± 0.01 is in close agreement with the majority of recent photometric studies <ref:2606.24270#pg7>. Our metallicity of [Fe/H] = 0.08 ± 0.06 is consistent within uncertainties with Zeng et al. (2025) (0.091 ± 0.04), Dias et al. (2021) (0.11 ± 94), and with the spectroscopic value of Heiter et al. (2014) (– – 896 ± 3). The CMD reveals a prominent gap in the main sequence, which may be associated with the cluster’s high binary fraction of approximately 40% <ref:2606.24270#pg8>.

Mass Segregation and Substructure Analysis

The degree of mass segregation was quantified using the Minimum Spanning Tree (MST) method based on the Mass Segregation Ratio (ΛMSR) formalism <ref:2606.24270#pg9> The median ΛMSR (solid black line in Figure 6) remains consistently and significantly above unity across the entire probed mass range (NMST = 5 to 100) <ref:2606.24270#pg9>. The persistence of the signal across such a large subset of the cluster population indicates a pervasive, global mass segregation rather than primordial formation conditions <ref:2606.24270#pg9>. Furthermore, a Bayesian Gaussian Mixture Model (BGM) was applied to both the projected 2D and 3D spatial distributions to detect substructures <ref:2606.24270#pg13> This decomposition reveals three distinct components: a central core, a tidal tail, and a more diffuse halo <ref:2606.24270#pg13>.

Present-Day Mass Function

The Present–Day Mass Function (PDMF) of NGC 6134 was constructed by using the mass of members adopted from ASteCA output <ref:2606.24270#pg10> The PDMF exhibits a break at Mc = 0.95 ± 0.02 M⊙, separating the intermediate-to-low-mass regime with slope αA = −2.1 ± 0.11 from the high-mass regime with slope αB = 1.68 ± 0.15 <ref:2606.24270#pg10>. The observed PDMF slope in this regime is also shallower than the Salpeter IMF slope (α = 2.35), which may be attributed to the preferential loss of low-mass stars due to dynamical evolution and mass segregation <ref:2606.24270#pg10>.

Conclusion

Our results are broadly consistent with and complementary to the independent study of Zeng et al. (2025) <ref:2606.24270#pg14> Both studies confirm significant mass segregation and derive a well-constrained set of fundamental cluster parameters <ref:2606.24270#pg14>. Our larger and more spatially extended membership sample reveals additional structural complexity, including the presence of a core, a tidal tail, and a diffuse halo <ref:2606.24270#pg14>. The presence of this substructure is likely related to the cluster’s dynamical evolution <ref:2606.24270#pg14>. Our individual Bayesian distance estimates and relatively high binary fraction (fbin ≈ 0.42) provide a plausible explanation for the observed main-sequence gap <ref:2606.24270#pg14>. Our mass segregation analysis likewise supports a dynamical origin driven by long-term two-body relaxation and the preferential loss of low-mass stars, in agreement with the conclusions of Zeng et al. (2025) <ref:2606.24270#pg14>. The study concludes that NGC 6134 is a significantly dynamically evolved open cluster <ref:2606.24270#pg14>.

ACKNOWLEDGMENTS Our gratitude goes to the Faculty of Mathematics and Natural Sciences, Institut Teknologi Bandung (ITB) for the financial support provided through the PPMI 2023 funding program. We also acknowledge using data from the ESA mission Gaia (https://www.cosmos.esa.int/web/gaia) in this work.

REFERENCES Ahmed, N. M., Bendary, R., Samir, R., & Elhosseiny, E. 2024, Scientific Reports, 14, 23777 <ref:2606.24270#pg9> Ahumada, A. V., Cignoni, M., Bragaglia, A., et al. 2013, Monthly Notices of the Royal Astronomical Society, 430, 221 <ref:2606.24270#pg9> Ahumada, J. 2002, in Observed HR Diagrams and Stellar Evolution, Vol. 274, 307 <ref:2606.24270#pg9> Allison, R. J., Goodwin, S. P., Parker, R. J., et al. 2009, Monthly Notices of the Royal Astronomical Society, 395, 1449 <ref:2606.24270#pg9> Angelo, M., Santos Jr, J., Maia, F., & Corradi, W. 2023, Monthly Notices of the Royal Astronomical Society, 522, 956 <ref:2606.24270#pg9> Astraatmadja, T. L., & Bailer-Jones, C. A. L. 2016a, ApJ, 832, 137 <ref:2606.24270#pg9> Bailer-Jones, C. A. L. 2015, PASP, 127, 994 <ref:2606.24270#pg9> Bailer-Jones, C. A. L., Rybizki, J., & Fouesneau, M. 2021, AJ, 161, 147 <ref:2606.24270#pg9> Bastian, N. Covey, K. R., & Meyer, M. R. 2010, Annual Review of Astronomy and Astrophysics, 48, 339 <ref:2606.24270#pg9> Bayo, A., Rodrigo, C., Barrado Y Navascu´es, D., et al. 2008, A&A, 492, 277 <ref:2606.24270#pg9> Binney, J., & Merrifield, M. 1998, Galactic Astronomy (Princeton, NJ: Princeton University Press) Binney, J., & Tremaine, S. 2008, Galactic Dynamics: Second Edition Bossini, D., Vallenari, A., Bragaglia, A., et al. 2019, Astronomy & Astrophysics, 623, A108 <ref:2606.24270#pg9> Bressan, A., Marigo, P., Girardi, L., et al. 2012, Monthly Notices of the Royal Astronomical Society, 427, 127 <ref:2606.24270#pg9> Brunntt, H., Frandsen, S., Kjeldsen, H.

Improvements for AI systems

Bold Header: Robust Membership Determination via HDBSCAN

This improved AI system can perform high-precision membership determination by using the HDBSCAN algorithm on astrometric data from Gaia DR3 as described in Section 2, allowing it to identify members with a probability p ≥ 0.5, which is more spatially comprehensive than previous methods.

Bold Header: Self-Consistent Cluster Distance Estimation

The AI system can determine the cluster distance using a method that is consistent with the ASteCA result and provides an estimate of 1070.83 ± 2.50 pc, which is derived from the median of the individual member distance distribution, mitigating skewness.

Bold Header: Substructure Identification via Bayesian GMM

The system can apply a Bayesian Gaussian Mixture Model (BGM) with a Dirichlet Process prior to both projected 2D and 3D spatial distributions to successfully detect substructures within the 3D data of NGC 6134, revealing components such as a central core, a tidal tail, and a more diffuse halo.

Bold Header: Dynamical Evolution Assessment via Mass Segregation

The AI can quantify mass segregation using the Minimum Spanning Tree (MST) method and the formula ΛMSR = Median(lrandom)/lmassive, concluding that the observed segregation is driven by dynamical evolution rather than being primordial because the cluster’s age exceeds its relaxation timescale.

Bold Header: Initial Mass Function (IMF) Inference

The system can build a Present–Day Mass Function (PDMF) using the Hierarchical Binned Likelihood (HBL) framework to construct an Initial Mass Function (IMF), allowing it to infer that NGC 6134 shows a substantial depletion of sub-solar mass stars by observing the break at Mc = 0.95 M⊙.

Abstract

Open clusters are key laboratories for studying the formation and dynamical evolution of stellar populations. We present a comprehensive characterization of the intermediate-age open cluster NGC 6134 using Gaia DR3 astrometry and photometry. Adopting the 890-member Hierarchical Density-Based Spatial Clustering of Applications with Noise (HDBSCAN) membership catalog, we determine the cluster distance and individual member distances with the Bayesian hierarchical code Kalkayotl under a King spatial prior, derive the fundamental parameters with the automated isochrone-fitting code ASteCA, quantify mass segregation, and decompose the projected spatial distribution into structural components. We obtain a Bayesian cluster distance of 1070.8+21.0-19.0 pc (mode and 68% credible interval), consistent with the ASteCA value (d = 1064.4 plus or minus 15.2 pc), with member distances peaking at 1071.2 plus or minus 2.5 pc. ASteCA yields[Fe/H] = 0.08 plus or minus 0.06, (t) = 9.14 plus or minus 0.01, and A V = 1.03 plus or minus 0.05 mag. The present-day mass function (PDMF) follows a broken power law with slopes Γ A = -2.10+0.10-0.10 and Γ B = 1.59+0.14-0.14 and break mass M c = 0.95+0.02-0.02 M, with a negative low-mass slope and a high-mass slope steeper than the canonical Salpeter value (Γ= 1.35), consistent with the preferential loss of the most massive stars through stellar evolution rather than with dynamical depletion. The observed mass segregation is consistent with an origin in long-term dynamical evolution. The cluster comprises a core, a diffuse halo, and a coherent plane-of-sky elongated feature that is unlikely to arise from noise based on a size-matched isotropic null test, and that lies beyond the radius at which masses are available. The observed main-sequence gap is closely linked to the cluster's binary fraction.