Inferring Asteroseismic Parameters from Short Observations Using Deep Learning: Application to TESS and K2 Red Giants

Technical Summary: Inferring Asteroseismic Parameters from Short Observations Using Deep Learning

Problem Statement
Asteroseismology provides precise determinations of stellar mass, radius, surface gravity, and age by analyzing resonant oscillations. While space-based missions like Kepler and K2 provided long-duration, high-precision data, the ongoing TESS mission offers nearly complete sky coverage with significantly shorter observation baselines (typically one to two months per sector). The TESS mission is estimated to have observed over 300,000 oscillating red giants. However, the short duration of these observations limits frequency resolution, making the inference of global seismic parameters—specifically the large frequency separation ($\Delta\nu$), the frequency at maximum power ($\nu_{\max}$), and the period spacing of dipolar gravity modes ($\Delta\Pi_1$)—challenging using traditional methods. There is a pressing need for fast, efficient, and robust methods to analyze this massive dataset to enable uniform galactic archaeology.

Methodology
The authors developed deep learning-based methods to infer asteroseismic parameters directly from Power Spectral Density (PSD) profiles without requiring background fitting or manual mode identification.

• Data Preparation:

  • TESS Data: Utilized detrended light curves from the TASOC pipeline for 30,720 red giants.
  • K2 Data: Used detrended light curves from the K2SFF pipeline for 18,560 red giants.
  • Training Sets:
    • TESS Model: Trained on one-month segments of Kepler and K2 light curves (simulating TESS duration) to predict $\nu_{\max}$ and $\Delta\nu$. This approach leverages empirical relationships between granulation and oscillation amplitudes found in real data, which outperformed synthetic data training for this specific task.
    • K2 Models: Trained on synthetic datasets generated using an asymptotic theory-based simulator (Benomar 2023) to predict $\nu_{\max}$, $\Delta\nu$, $\Delta\Pi_1$, and the coupling factor $q$. Two distinct models were created: Model-1 for the full $\Delta\nu$ range (1–19 $\mu$Hz) and Model-2 for a restricted range (9–19 $\mu$Hz) to better handle young red giants where $\Delta\Pi_1$ inference is more feasible.

• Architecture and Training:

  • The models utilize a Residual Network (ResNet) architecture, chosen for its ability to capture multi-scale features in PSDs and mitigate vanishing gradient problems.
  • The regression problem was reformulated as a classification task. Continuous parameter ranges were discretized into bins, and the networks output probability distributions over these bins. This allows for the recovery of Bayesian posterior approximations, providing uncertainty estimates and handling multimodal distributions (common in $\Delta\Pi_1$).
  • Hyperparameters, including kernel sizes and dropout rates, were fine-tuned to balance model complexity with overfitting risks, particularly for the data-scarce TESS domain.

Key Contributions

1. Development of Specialized Deep Learning Models: The creation of a TESS model for one-month data and K2 models for three-month data, capable of inferring $\nu_{\max}$, $\Delta\nu$, and $\Delta\Pi_1$ directly from PSDs.
2. Probabilistic Inference Framework: By treating the output as a probability distribution over binned parameters, the method provides not just point estimates but calibrated uncertainty measures and the ability to detect multimodal solutions.
3. Validation Against Classical Methods: Rigorous comparison of model outputs against reference values from Kepler (4-year data) and K2 GAP DR3, as well as MCMC posteriors, demonstrating that the ML approach can approximate Bayesian posteriors effectively.
4. New Catalog of Inferences: The application of these models to large observational datasets, resulting in a new catalog of reliable seismic parameters for TESS and K2 red giants.

Results

• TESS Model Performance:

  • On a test set of one-month Kepler/K2 segments, the model achieved reliable $\nu_{\max}$ predictions (uncertainty < 20%) for ~95% of samples and reliable $\Delta\nu$ predictions (uncertainty < 10%) for ~80% of samples.
  • Applied to 30,720 TESS red giants, the model yielded reliable $\nu_{\max}$ for ~55% (17,374 stars) and reliable $\Delta\nu$ for ~23% (7,001 stars). The lower yield for $\Delta\nu$ in TESS data is attributed to lower oscillation amplitudes in the TESS passband and spacecraft systematics not present in the training data.
  • The model demonstrated that $\Delta\nu$ is inferred based on underlying frequency spacing patterns rather than simply relying on the $\Delta\nu$–$\nu_{\max}$ scaling relation.

• K2 Model Performance:

  • Model-1 ($\nu_{\max}, \Delta\nu$): Showed strong agreement with K2 GAP DR3, with 92% of $\nu_{\max}$ and 95% of $\Delta\nu$ inferences falling within specified relative error bounds.
  • Model-2 ($\Delta\Pi_1$): Validated on three-month Kepler segments against 4-year Kepler results (Kuszlewicz et al. 2023). For a subset of 191 stars, 98% showed relative errors < 2%.
  • Applied to 2,176 K2 red giants with $\Delta\nu > 9$ $\mu$Hz, the model produced reliable $\Delta\Pi_1$ inferences for 217 stars. Of these, 209 stars follow the well-established $\Delta\nu$–$\Delta\Pi_1$ degenerate sequence.

• Uncertainty Calibration: The empirical 1$\sigma$ fractions for reliable subsets typically ranged from 0.63 to 0.80, indicating that the reported uncertainties are generally well-calibrated or slightly conservative.

Significance
The paper demonstrates that deep learning can effectively extract asteroseismic parameters from short-duration observations where traditional methods struggle due to limited frequency resolution. By successfully inferring $\Delta\Pi_1$ from three-month K2 data and $\Delta\nu$ from one-month TESS data, the work enables the study of stellar populations across the Milky Way with a uniformity previously unattainable. The authors note that while the yield for reliable parameters is lower for TESS compared to Kepler due to observational constraints, the method provides a robust, scalable pipeline for analyzing the hundreds of thousands of red giants observed by TESS. The resulting catalogs of $\nu_{\max}$, $\Delta\nu$, and $\Delta\Pi_1$ serve as a foundation for galactic archaeology and the study of stellar evolution, particularly for young red giants where mixed-mode period spacings are critical.