[Paper Review] Deriving physical parameters of unresolved star clusters III. Application to M31 PHAT clusters

P. de Meulenaer, D. Narbutis+2 more|arXiv (Cornell University)|Feb 17, 2015

Stellar, planetary, and galactic studies26 references6 citations

TL;DR

This study applies stochastic star cluster models to WFC3+ACS photometry of 203 M31 star clusters from the PHAT survey, demonstrating accurate derivation of age, mass, extinction, and metallicity even when metallicity is free to vary. It confirms that the WFC3+ACS system enables robust photometric metallicity measurements, with results showing strong agreement (within 0.2 dex) with spectroscopic values for 36 massive clusters.

ABSTRACT

This study is the third of a series that investigates the degeneracy and stochasticity problems present in the determination of physical parameters such as age, mass, extinction, and metallicity of partially resolved or unresolved star cluster populations situated in external galaxies when using broad-band photometry. This work tests the derivation of parameters of artificial star clusters using models with fixed and free metallicity for the WFC3+ACS photometric system. Then the method is applied to derive parameters of a sample of 203 star clusters in the Andromeda galaxy observed with the HST. Following Papers I \& II, the star cluster parameters are derived using a large grid of stochastic models that are compared to the observed cluster broad-band integrated WFC3+ACS magnitudes. We derive the age, mass, and extinction of the sample of M31 star clusters with one fixed metallicity in agreement with previous studies. Using artificial tests we demonstrate the ability of the WFC3+ACS photometric system to derive the metallicity of star clusters. We show that the metallicity derived using photometry of 36 massive M31 star clusters is in a good agreement with the metallicity previously derived using spectroscopy taken from literature.

Motivation & Objective

• To test the accuracy of deriving physical parameters (age, mass, extinction, metallicity) for unresolved star clusters using stochastic models and the WFC3+ACS photometric system.
• To assess whether the WFC3+ACS system can reliably derive metallicity when it is not fixed a priori, especially in low signal-to-noise regimes.
• To validate the method on real clusters from the M31 PHAT survey, comparing photometric results with existing spectroscopic metallicities.
• To quantify the impact of photometric accuracy and cluster mass on metallicity derivation precision.
• To determine whether fixed-solar metallicity models remain a valid assumption for young M31 clusters, given the observed metallicity distribution.

Proposed method

• Constructed a 4D grid of stochastic star cluster models using the PADOVA isochrones (including TP-AGB phase) with random stellar mass sampling based on the Kroupa IMF.
• Used the WFC3+ACS photometric system (filters F275W, F336W, F475W, F606W, F814W, F110W, F160W) and applied a Milky Way extinction law (Cardelli et al. 1989) with E(B-V) from 0 to 1 in steps of 0.01.
• Computed likelihood for each model node using a Gaussian error model: $ L_{\text{model}} = \prod_{f=1}^{F} \frac{1}{\sqrt{2\pi}\sigma_f} \exp\left[-\frac{(\text{mag}_{f,\text{obs}} - \text{mag}_{f,\text{model}})^2}{2\sigma_f^2} \right] $.
• Permitted metallicity to vary freely in the model grid (from [M/H] = +0.2 to -2.2 in steps of 0.2) for the main analysis, and compared results with a fixed-solar metallicity case.
• Performed artificial cluster tests with known parameters and varying photometric errors (σ = 0.05 mag) to assess accuracy and degeneracy in parameter recovery.
• Used marginalized likelihood maps to identify best-fit parameters and confidence intervals (68%, 95%, 99%) for each cluster.

Experimental results

Research questions

• RQ1 Can the WFC3+ACS photometric system accurately derive the metallicity of unresolved star clusters when metallicity is not fixed in the model grid?
• RQ2 How does the photometric accuracy (e.g., σ = 0.05 mag) affect the precision of metallicity and other physical parameter recovery?
• RQ3 To what extent do photometrically derived metallicities agree with spectroscopic values for massive M31 star clusters?
• RQ4 Is the assumption of fixed solar metallicity valid for young M31 clusters, given the observed metallicity distribution?
• RQ5 How does cluster mass influence the reliability of photometric metallicity estimates?

Key findings

• The WFC3+ACS photometric system enables accurate derivation of age, mass, extinction, and metallicity for unresolved star clusters, even when metallicity is allowed to vary freely.
• Artificial cluster tests show that with photometric errors of 0.05 mag per filter, metallicity can be recovered with a typical accuracy of ±0.2 dex.
• For 36 massive M31 clusters in common with the spectroscopic study of Caldwell et al. (2011), photometric metallicities agree with spectroscopic values to within 0.2 dex on average.
• The metallicity distribution of young clusters (log(t/yr) < 9) is predominantly metal-rich, with most clusters having [M/H] > 0, supporting the use of solar or supersolar metallicity assumptions for young populations.
• The scatter in metallicity differences increases with decreasing cluster mass, indicating that signal-to-noise ratio limits the precision of metallicity derivation in low-mass clusters.
• Even with low photometric accuracy (σ = 0.1 mag), the method correctly identifies that young clusters are more likely metal-rich than metal-poor, demonstrating robustness in parameter degeneracy resolution.