Neural Network identification of Dark Star Candidates. II. Spectroscopy

TL;DR

This work develops a fast FFNN to identify spectroscopic Dark Star candidates in JWST/NIRSpec data by mapping 500-band spectra to the DM-powered stellar mass $M$ (in $10^5\,M_\odot$) and redshift $z$, trained on TLUSTY-based SMDS spectra for two formation channels. The model achieves near-perfect predictive accuracy on synthetic data ($R^2 \gtrsim 0.99$) and demonstrates a dramatic speed advantage over traditional Nelder–Mead fitting, yielding parameter estimates in milliseconds. Validation on four real SMDS candidates (JADES-GS-z11, z13-0, z14-0, z14-1) shows spectral fits consistent with observations and mass/redshift estimates in close agreement with prior analyses (within ~10%), underscoring the approach’s reliability and scalability. The results establish a foundation for Bayesian uncertainty analyses and automated pipelines to mine large JWST datasets for Dark Star signatures, potentially enabling rapid, archive-scale exploration of the early DM-powered stellar population.

Abstract

Some of the first stars in the Universe might be powered by Dark Matter (DM) annihilations, rather than nuclear fusion. Those objects, i.e. Dark stars (DS), offer a unique window into understanding DM via the observational study of the formation and evolution of the first stars and their Black Hole (BH) remnants. In \cite{NNSMDSPhot} (Paper~I) we introduced a feedforward neural network (FFNN) trained on synthetic DS photometry in order to detect and characterize dark star {\it photometric} candidates in the early universe based on data taken with the NIRCam instrument onboard the James Webb Space Telescope (JWST). In this work we develop a FFNN trained on synthetic DS spectra in order to identify {\it spectroscopic} dark star candidates in the data taken with JWST's NIRSpec instrument. In order to validate our FFNN model we apply it to real data for the four spectroscopic Supermassive Dark Star (SMDS) candidates recently identified in \cite{ilie2025spectroscopicsupermassivedarkstar} and reconfirm that indeed \JADESeleven, \JADESzthirteen, \JADESfz, and \JADESfo have spectra that are consistent with those of Supermassive Dark Stars. The main advantage of our FFNN model, in comparison to the Nedleaer-Mead Monte Carlo parameter estimator used in \cite{ilie2025spectroscopicsupermassivedarkstar}, is that the approach introduced here predicts parameters in milliseconds, over 10,000 times faster than the traditional method used in \cite{ilie2025spectroscopicsupermassivedarkstar}. With this in mind, the FFNN model we developed and validated in this work will be adapted for Bayesian uncertainty analyses and automatic analyses of NIRSpec publicly available data for high redshift objects. This study establishes a robust and efficient tool for probing Dark Stars and understanding their role in cosmic evolution.

Figures (4)

• Figure 1: Architecture of the feed-forward neural network (FFNN) used to predict stellar mass and redshift from input spectra. The input layer consists of 500 flux values sampled uniformly across the 1–5.2 $\mu$m range. The network includes three fully connected hidden layers (256, 128, and 64 neurons) with ReLU activations, followed by a two-neuron output layer corresponding to mass (in units of $\text{10}^5\,M_\odot$) and redshift ($z$).
• Figure 2: Training and validation loss curves for the Feedforward Neural Network (FFNN) during the training process for the two scenarios of SMDSS formation: DM capture (panel a) and Adiabatic Contraction (panel b). The loss is measured in terms of Mean Squared Error (MSE) and is plotted against the number of epochs. The close alignment of the training and validation loss curves indicates the model generalizes well to unseen data without overfitting.
• Figure 3: Predicted versus true values for mass and redshift on test data for dark stars forming via DM Capture (panel a) and Adiabatic Contraction (panel b). The $R^2$ values indicate the model's performance, demonstrating excellent agreement between predictions and true values. The dashed red line represents the ideal $y=x$ relationship.
• Figure 4: Comparison of FFNN model predictions with observed spectra for the four spectroscopic Supermassive Dark Stars (SMDS) candidates identified in ilie2025spectroscopicsupermassivedarkstar. Orange: FFNN model; blue: observed; gray: uncertainties. Residuals show (model–data)/$\sigma$ below each spectrum.