Using Neural Network Models to Estimate Stellar Ages from Lithium Equivalent Widths: An EAGLES Expansion

TL;DR

This study replaces the analytic LiEW–age relation of the EAGLES framework with a data-driven Artificial Neural Network trained on ~6200 stars in 52 Gaia-ESO open clusters, spanning ages from $2$ Myr to $6000$ Myr and $3000<T_{ m eff}<6500$ K. The ANN predicts LiEW and its intrinsic dispersion $\sigma_{ m LiEW}$ as functions of $T_{ m eff}$ and $\\log( ext{age}/ ext{yr})$, and infers Bayesian posterior ages for individual stars or coeval groups using Monte Carlo dropout to quantify epistemic uncertainty. Compared with the original analytic model, the ANN better captures the lithium dip and the dispersion pattern, but age discrimination remains poor for ages $ obreak> obreak 1$ Gyr, revealing unmodeled astrophysical factors such as rotation, accretion, and surface gravity. The authors provide EAGLES v2.0, discuss expansion pathways to include additional observables, and highlight the need for expanded training data to improve accuracy in young and intermediate-age regimes, underscoring the method’s potential for leveraging future large spectroscopic surveys.

Abstract

We present an Artificial Neural Network (ANN) model of photospheric lithium depletion in cool stars (3000 < Teff / K < 6500), producing estimates and probability distributions of age from Li I 6708A equivalent width (LiEW) and effective temperature data inputs. The model is trained on the same sample of 6200 stars from 52 open clusters, observed in the Gaia-ESO spectroscopic survey, and used to calibrate the previously published analytical EAGLES model, with ages 2 - 6000 Myr and -0.3 < [Fe/H] < 0.2. The additional flexibility of the ANN provides some improvements, including better modelling of the "lithium dip" at ages < 50 Myr and Teff ~ 3500K, and of the intrinsic dispersion in LiEW at all ages. Poor age discrimination is still an issue at ages > 1 Gyr, confirming that additional modelling flexibility is not sufficient to fully represent the LiEW - age - Teff relationship, and suggesting the involvement of further astrophysical parameters. Expansion to include such parameters - rotation, accretion, and surface gravity - is discussed, and the use of an ANN means these can be more easily included in future iterations, alongside more flexible functional forms for the LiEW dispersion. Our methods and ANN model are provided in an updated version 2.0 of the EAGLES software.

Figures (16)

• Figure 1: The structure of the ANN prediction model. The number of neurons in each hidden layer (i.e. not the input or output layers) is scaled down by a factor of 30 for this visualisation. The input layer takes scaled values of T$_{\text{eff}}$ and $\log$(age), and the output layer produces similarly scaled values of LiEW and the dispersion in LiEW. Neurons are connected to the subsequent and previous layers' neurons, with dropout layers between each hidden layer dropping 20% of the connections from the previous layer's neurons, as described in §\ref{['subsec:architecture']}.
• Figure 2: Isochrones of predicted LiEW from eagles (left) and the ANN model (right) on the LiEW - T$_{\text{eff}}$ plane.
• Figure 3: ANN model isochrones at the youngest ages (1-10 Myrs). For T$_{\text{eff}}$$<5500$ K the predicted LiEW increases before starting to decrease after about 5 Myr.
• Figure 4: Predicted dispersion in LiEW from the ANN model minus the eagles model on the $\log$ (age/yr) - T$_{\text{eff}}$ plane. The ANN dispersion is higher in the majority of the plane. It is noted that, at $\log$ (age/yr) $\gtrsim$ 8.5, the small differences in predicted dispersion shown on this plot do not take into account the low LiEW prediction at these ages. This means that the relative dispersion compared to predicted LiEW is often very high despite the low raw predicted dispersion value. The linear features at 4200K and 5200K, between 7.5 < $\log$ (age/yr) < 8.3, are due to the manually added dispersion in the eagles model.
• Figure 5: Centre Left: Differences in the median $\log$(age) estimates between the ANN and eagles models, colour-coded and in dex units. Red areas denote the ANN model estimating higher ages than eagles, and blue areas denote the opposite. A flat age prior is assumed in both cases. Centre Right: Differences in the most probable $\log$(age) estimates shown with the same colour scheme. Areas in white are regions of the LiEW/T$_{\text{eff}}$ plane where a significant probability peak is not found in one or both models (e.g., see the probability distributions for star A). Above/Below: The probability distributions of $\log$(age) for four hypothetical stars: A, B, C and D, with no observational LiEW error, at the positions labelled in the central plots.