Robust ellipticity measurements of 29 Galactic globular clusters

This paper addresses the biases in traditional ellipticity measurements of globular clusters by developing and validating a robust method using ground-based and space-based photometry, which reveals that rotation is the primary driver of flattening in ten specific Galactic clusters while also highlighting the roles of velocity anisotropy and tides.

The Gist

Imagine the night sky is filled with ancient, glowing snow globes. These are Globular Clusters (GCs): massive, tightly packed families of hundreds of thousands of stars that have been orbiting our galaxy for billions of years.

For a long time, astronomers thought these globes were perfectly round, like billiard balls. But this new paper suggests that's not quite right. Many of them are actually slightly squashed, like a beach ball that someone sat on. This "squashiness" is called ellipticity.

The authors of this paper wanted to answer two big questions:

1. How squashed are these clusters really?
2. Why are they squashed? Is it because they are spinning like a pizza dough being tossed in the air? Or is it because the Milky Way galaxy is stretching them like taffy?

Here is the story of how they figured it out, explained simply.

The Problem: The "Bad Ruler"

To measure how squashed a cluster is, astronomers usually use two common tools:

1. The Contour Map: Drawing lines around the stars to see the shape.
2. The Math Sort (PCA): A statistical method that finds the "long way" and "short way" of the star group.

The Catch: These tools are like using a ruler that stretches when it gets hot. If a cluster has very few stars, or if it's almost perfectly round, these tools get confused. They tend to say, "Oh, this round ball is actually an oval!" just because there wasn't enough data to be sure. They also get easily tricked by "outliers"—a few stray stars that don't belong to the group, which can make the whole shape look distorted.

The Solution: The "Smart Detective"

The team developed a new, super-robust method. Think of it as a smart detective that ignores the noise.

• It ignores the outliers: If a few stars are wandering off, the detective doesn't let them ruin the measurement of the main group.
• It corrects its own mistakes: The detective knows that when looking at a small group of stars, it tends to overestimate how squashed they are, so it automatically adjusts the answer to be more accurate.

They tested this new detective on fake, computer-generated star clusters first, and it passed with flying colors. Then, they used it on 29 real globular clusters in our Milky Way.

The Findings: Spinning vs. Stretching

Once they had accurate measurements, they looked at why the clusters were squashed. They used a special graph (the V/σ diagram) that acts like a "speedometer" for rotation.

Here is what they found:

1. The Spinners (The Pizza Dough):
   About 55% of the clusters they studied were noticeably squashed. For 10 specific clusters (including famous ones like NGC 104 and NGC 6205), the squashing matched perfectly with how fast they were spinning.

   • Analogy: Imagine spinning a ball of dough. The faster it spins, the flatter it gets. For these clusters, rotation is the main reason they are flat. The "short axis" of the squashed shape lines up perfectly with the axis they are spinning on.

2. The Stretchers (The Taffy):
   Some clusters were squashed more than their spin should explain.

   • NGC 6838: This cluster is very flat but barely spins. The authors suspect it was recently "shocked" by passing through the dense disk of our galaxy. The Milky Way's gravity stretched it out, like pulling on a piece of taffy.
   • NGC 2808: This one is a mix. It spins, but it also seems to have been stretched by the galaxy's gravity, leaving behind "tidal tails" (streams of stars) like a comet's tail.

3. The Rounders:
   Some clusters are almost perfectly round. This happens when they are very old and have had time to settle down, or if they aren't spinning fast enough to flatten out.

Why Does This Matter?

This paper is a big deal for two reasons:

• Better Tools: They gave astronomers a new, reliable way to measure shapes that works even when there aren't many stars to look at. This is crucial for studying multiple stellar populations (different generations of stars born inside the same cluster), which are often small groups of stars that previous tools couldn't measure accurately.
• Understanding the Galaxy: By knowing what shapes these clusters are and why, we can learn how the Milky Way has been moving and interacting with these clusters over billions of years. It's like looking at the dents in a car to figure out what kind of road it drove on.

The Bottom Line

The universe isn't just full of perfect spheres. Globular clusters are dynamic, squashed, and spinning objects. The authors built a better "ruler" to measure them, proving that for many clusters, spinning is the reason they are flat, while for others, the gravity of our galaxy is the sculptor. It's a reminder that even the oldest objects in the sky are still being shaped by the forces around them.

Technical Summary

Here is a detailed technical summary of the paper "Robust ellipticity measurements of 29 Galactic globular clusters" by Fréour et al.

1. Problem Statement

Globular clusters (GCs) are not perfectly spherical; they exhibit varying degrees of flattening (ellipticity) that provide insights into their internal dynamics (rotation, velocity anisotropy) and evolutionary history (tidal interactions). However, measuring this ellipticity accurately is challenging due to:

• Methodological Biases: Common techniques, such as ellipse fitting to density contours (Kernel Density Estimation - KDE) and Principal Component Analysis (PCA), suffer from systematic biases.
• Data Limitations: These methods tend to overestimate ellipticity when the number of observable stars is small or when the cluster is nearly round.
• Outlier Sensitivity: Both standard KDE and PCA are highly sensitive to outlier stars (non-members or field stars), which can significantly distort the recovered shape and position angle.
• Inconsistency: Previous studies using different datasets (optical vs. infrared) and methods have produced conflicting results regarding the shapes of specific clusters.

There is a critical need for a robust measurement technique that yields consistent results across diverse datasets, particularly for small samples (e.g., multiple stellar populations within GCs) and is resilient to outliers.

2. Methodology

Data Sources

The authors utilized a combination of two photometric catalogues to create a wide-field view of 29 Galactic GCs:

• Ground-based: The Stetson homogeneous catalogue (U, B, V, R, I filters).
• Space-based: The Hubble Space Telescope UV Globular Cluster Survey (HUGS) (F275W, F336W, F438W, F606W, F814W filters).
• Selection: Only Red Giant Branch (RGB) stars were used to ensure high and uniform photometric completeness, particularly in crowded cluster cores.
• Cleaning: Non-member stars were removed using Gaia DR3 proper motions (threshold $\chi^2 < 5$) and membership probabilities (>75%). Differential reddening corrections were applied.

Method Development & Testing

The authors tested and compared three approaches:

1. Standard KDE: Smoothing stellar distribution and fitting ellipses to isodensity contours.
2. Standard PCA: Analyzing the covariance matrix of stellar positions to find principal axes.
3. Robust PCA (Proposed Method):
   • Outlier Resistance: Instead of standard covariance, they employed the Minimum Covariance Determinant (MCD) method. This identifies a subset of data with the smallest covariance determinant, effectively down-weighting or excluding outliers.
   • Bias Correction: They identified that even the robust PCA overestimates ellipticity for small datasets ($N < 300$) and nearly round clusters. Using mock data (King profiles with known ellipticity), they derived a bias correction function to adjust the measured ellipticity based on the number of stars and the true ellipticity.

Validation

The methods were tested on 1,000 realizations of mock GCs with varying parameters ($N$, true ellipticity, position angle, and outlier presence). The Robust PCA with bias correction successfully recovered true parameters regardless of outlier direction or sample size, whereas standard methods failed significantly under these conditions.

3. Key Contributions

• Development of a Robust Algorithm: The creation of a bias-corrected, MCD-based PCA method that provides reliable ellipticity measurements even for small stellar samples and round clusters.
• Systematic Re-analysis: Application of this new method to 29 Galactic GCs, providing a consistent dataset that resolves discrepancies found in previous literature (e.g., White & Shawl 1987, Chen & Chen 2010).
• Dynamic Framework Application: Integration of the new ellipticity measurements with the $V/\sigma$ diagram (ratio of rotation velocity to velocity dispersion) to distinguish between rotation-driven flattening and other mechanisms (anisotropy, tides).

4. Key Results

General Findings

• Flattening Prevalence: 55% of the 29 clusters in the sample have an ellipticity $e > 0.05$.
• Agreement with Literature: The new measurements show better agreement with White & Shawl (1987) than with Chen & Chen (2010), though significant discrepancies remain for specific clusters (e.g., NGC 6838, NGC 6656). The authors attribute previous discrepancies to the sensitivity of older methods to bright stars and projection effects.

Drivers of Flattening ($V/\sigma$ Analysis)

The authors categorized the clusters based on their position in the $V/\sigma$ diagram and the alignment of their semi-minor axis with their rotation axis:

1. Rotation-Dominated (8 clusters):

   • Clusters: NGC 3201, NGC 5024, NGC 5286, NGC 5904, NGC 5986, NGC 6205, NGC 6341, NGC 7078.
   • Evidence: These clusters lie on the isotropic oblate rotator relation, and their semi-minor axes align closely with their rotation axes. Rotation is identified as the primary driver of their shape.
   • Note: NGC 104 and NGC 5904 show alignment but are less flattened than expected, suggesting counteracting mechanisms (e.g., radial anisotropy in NGC 104).

2. Tidal/External Influence (3 clusters):

   • Clusters: NGC 2808, NGC 6838, NGC 4833.
   • Evidence: These clusters are more flattened than their rotation signature predicts.
     • NGC 2808: Likely a combination of rotation and tidal stripping (evidenced by extra-tidal stars).
     • NGC 6838: Non-rotating but highly flattened; attributed to recent disk crossing (tidal shocking) ~31 Myr ago.
     • NGC 4833: Non-rotating and highly flattened; likely due to recent disk crossing.

3. Complex/Counteracting Mechanisms (6 clusters):

   • Clusters: NGC 104, NGC 1851, NGC 5904, NGC 6101, NGC 6656, NGC 7089.
   • Evidence: These are less flattened than expected given their rotation.
     • NGC 104: Radial anisotropy counteracts rotation-induced flattening.
     • NGC 6656: Recent disk crossing (2.7 Myr) and complex formation history (potential extragalactic origin) may explain deviations.
     • NGC 7089: Preferential stripping of stars on radial orbits may round the cluster despite high rotation.

Radial Coverage Impact

The authors tested the impact of inhomogeneous radial coverage (some clusters covered to $2r_h$, others to$20r_h$). Restricting analysis to$3r_h$ showed that inner regions are generally rounder (due to faster relaxation), while outer regions are more elliptical. However, the overall conclusions regarding the drivers of flattening remained robust.

5. Significance

• Theoretical Modeling: The study emphasizes that theoretical models and simulations of GCs must account for flattening and the specific mechanisms driving it (rotation vs. tides vs. anisotropy).
• Future Applications: The robust method is specifically designed to handle small datasets, making it ideal for future studies of Multiple Stellar Populations (MSPs) within GCs, where only a few stars are available for shape analysis.
• Dynamical Insight: The $V/\sigma$ diagram remains a powerful tool for disentangling the complex interplay of internal dynamics and external tidal forces in shaping GCs. The study confirms that while rotation is a dominant driver for many clusters, tidal interactions and anisotropy play crucial roles in specific cases.