# The MiMO Catalog: Physical Parameters and Stellar Mass Functions of 1,232 Open Clusters from Gaia DR3

**Authors**: Lu Li, Zhengyi Shao, Zhaozhou Li, Xiaoting Fu, et al.
**Year**: 2025
**Version**: v1.0
**License**: CC BY 4.0
**Keywords**: Open star clusters, Hertzsprung Russell diagram, Mixture model, Stellar mass functions, Binary stars, Bayesian statistics, Stellar ages
**Related Publication**: [Link to the article, e.g., on arXiv or the journal website] (placeholder)

---

## Abstract

This dataset provides a catalog of 1232 open clusters with homogeneously determined parameters, including age, metallicity, distance, and extinction, derived from Gaia DR3 data using the Mixture Model for Open clusters (MiMO). For a subset of 163 high-quality clusters, the slope of the member-star mass function is also provided. The catalog includes best-fit parameters, Nested sampling posterior chains, and photometric membership probabilities for individual stars.

## File Structure

The data is organized into the following files and directories:

```

MiMO\_catalog\_v1/
├── cluster\_input\_info.fits
├── cluster\_params.fits
├── member\_stars.fits
└── cluster\_params\_posterior\_chains/
	├── post\_chain\_OC\_1.fits
	├── post\_chain\_OC\_1.fits
	└── ...
└──  MiMO\_code/
	└── ...
```

---

## File Descriptions

### 1. `cluster_input_info.fits`

This table contains the raw input information used to query the initial star catalog from Gaia DR3 for each cluster. These parameters define the selection boundaries in astrometric space.

| Column Name     | Unit   | Description                                                                 |
| --------------- | ------ | --------------------------------------------------------------------------- |
| `Cluster`       |        | Cluster name                                                        |
| `ra`            | deg    | Right ascension of the cluster center.                                      |
| `dec`           | deg    | Declination of the cluster center.                                          |
| `pm_ra`         | mas/yr | Mean proper motion in right ascension ($\mu_{\alpha} \cos\delta$).          |
| `pm_dec`        | mas/yr | Mean proper motion in declination ($\mu_{\delta}$).                         |
| `pm_ra_disp`    | mas/yr | Proper motion dispersion in right ascension ($\sigma_{\mu_{\alpha}}$).      |
| `pm_dec_disp`   | mas/yr | Proper motion dispersion in declination ($\sigma_{\mu_{\delta}}$).          |
| `parallax`      | mas    | Mean parallax of the cluster ($\varpi_{\mathrm{cl}}$).                      |
| `parallax_disp` | mas    | Parallax dispersion of the cluster ($\sigma_{\varpi, \mathrm{cl}}$).        |
| `r_50`          | deg    | Half-number radius of the cluster.                                          |
| `n_r50`         |        | Multiplicative factor for `r_50` to set the radius search limit.            |
| `n_pm`          |        | Multiplicative factor for proper motion dispersion to set the search limit. |
| `n_parallax`    |        | Multiplicative factor for parallax dispersion to set the search limit.      |
| `n_parallax_near`|       | Multiplicative factor for parallax to remove foreground stars.              |
| `n_pm_fs`       |        | Lower proper motion limit factor to select the field star sample.           |

### 2. `cluster_params.fits`

This table provides the inferred physical parameters for the 1232 open clusters in the catalog. For each parameter, it lists the best-fit values and the median (50th percentile), along with the 16th and 84th percentiles from the posterior distribution. 


| Column Name       | Unit    | Description                                                              |
| ----------------- | ------- | ------------------------------------------------------------------------ |
| `Cluster`         |         | Cluster name                                                    |
| `log_age`         | log(yr) | Best-fit log10 of the cluster age (median of the posterior).             |
| `log_age_50`      | log(yr) | Median (50th percentile) of the posterior for log10(age).                |
| `log_age_16`      | log(yr) | 16th percentile of the posterior for log10(age).                         |
| `log_age_84`      | log(yr) | 84th percentile of the posterior for log10(age).                         |
| `Fe_H`            | dex     | Best-fit metallicity, [Fe/H] (median of the posterior).                  |
| `Fe_H_50`         | dex     | Median (50th percentile) of the posterior for metallicity [Fe/H].        |
| `Fe_H_16`         | dex     | 16th percentile of the posterior for metallicity [Fe/H].                 |
| `Fe_H_84`         | dex     | 84th percentile of the posterior for metallicity [Fe/H].                 |
| `dist_mod`        | mag     | Best-fit distance modulus (DM) (median of the posterior).                |
| `dist_mod_50`     | mag     | Median (50th percentile) of the posterior for distance modulus (DM).     |
| `dist_mod_16`     | mag     | 16th percentile of the posterior for distance modulus (DM).              |
| `dist_mod_84`     | mag     | 84th percentile of the posterior for distance modulus (DM).              |
| `A_V`             | mag     | Best-fit V-band extinction ($A_V$) (median of the posterior).            |
| `A_V_50`          | mag     | Median (50th percentile) of the posterior for V-band extinction ($A_V$). |
| `A_V_16`          | mag     | 16th percentile of the posterior for V-band extinction ($A_V$).          |
| `A_V_84`          | mag     | 84th percentile of the posterior for V-band extinction ($A_V$).          |
| `alpha_mf`        |         | Best-fit power-law slope of the stellar initial mass function (IMF) (median of the posterior). |
| `alpha_mf_50`     |         | Median (50th percentile) of the posterior for the IMF slope ($\alpha$).  |
| `alpha_mf_16`     |         | 16th percentile of the posterior for the IMF slope ($\alpha$).           |
| `alpha_mf_84`     |         | 84th percentile of the posterior for the IMF slope ($\alpha$).           |
| `prior_feh_mu`    | dex     | Mean of the Gaussian prior for metallicity [Fe/H].                       |
| `prior_feh_sig`   | dex     | Standard deviation of the Gaussian prior for metallicity [Fe/H].         |
| `mf_quality_flag` |         | Flag for the reliability of `alpha_mf` (1 for the MF-prime sample, 0 otherwise). |

### 3. `member_stars.fits`

This table is a joint catalog containing all stars from the initial input samples for every cluster, along with their inferred photometric membership probabilities.

| Column Name | Unit | Description                                                                   |
| ----------- | ---- | ----------------------------------------------------------------------------- |
| `Cluster`   |      | The name of the cluster this star was associated with in the input sample.    |
| `source_id` |      | Gaia DR3 source identifier.                                                   |
| `ra`        | deg  | Right ascension of the star.                                                  |
| `dec`       | deg  | Declination of the star.                                                      |
| `p_member`  |      | Photometric membership probability (from 0 to 1).                             |

### 4. `cluster_params_posterior_chains/`

This directory contains the posterior probability distribution chains for the inferred parameters of each cluster. Each file corresponds to one cluster, named as `post_chain_[cluster_name].fits`. These files allow for detailed analysis of parameter correlations and posteriors.

| Column Name       | Unit    | Description                                                         |
| ----------------- | ------- | ------------------------------------------------------------------- |
| `log_age`         | log(yr) | Log10 of the cluster age.                                           |
| `Fe_H`            | dex     | Metallicity, [Fe/H].                                                |
| `dist_mod`        | mag     | Distance modulus.                                                   |
| `A_V`             | mag     | V-band extinction ($A_V$).                                          |
| `alpha_mf`        |         | Power-law slope of the stellar initial mass function (IMF).         |
| `f_b`             |         | Fraction of binary systems (treated as a nuisance parameter).       |
| `f_fs`            |         | Fraction of field star contamination (treated as a nuisance parameter).|
| `logwt`            |         | The natural logarithm of the posterior weight for each sample point, derived from the nested sampling algorithm.|

### 5. `MiMO_code/`

This directory contains the source code for the Mixture Model for Open clusters (MiMO) algorithm used to generate this catalog. Key components include the main script (MiMO.py), stellar isochrone models (isochrone_model/), and a Jupyter Notebook demonstrating a full analysis on an example cluster (example_NGC_2682.ipynb). The code is provided to ensure full reproducibility. For complete documentation on dependencies, installation, and how to run the code, please refer to the dedicated readme.md file located inside this directory.