Radiative Transfer Modeling of Stripped-envelope Supernovae II: Neural Network Emulation of Light Curves

Technical Summary: Radiative Transfer Modeling of Stripped-envelope Supernovae II: Neural Network Emulation of Light Curves

Problem Statement
Stripped-envelope supernovae (SESNe) exhibit a wide range of luminosities and evolution timescales. Traditional methods for inferring physical parameters (such as ejecta mass $M_{ej}$, nickel mass $M_{Ni}$, and velocity profiles) from light curves rely on semianalytical models like the Arnett model. However, these models often rely on simplifying assumptions—such as uniform density and frequency-independent opacity—that fail to capture the complexities of real ejecta, including variable velocity profiles and $^{56}$Ni mixing. Consequently, they suffer from strong degeneracies between mass and velocity, leading to systematic biases in inferred parameters.

While radiative transfer (RT) codes like SEDONA provide more realistic simulations by tracking photon diffusion through complex ejecta structures, they are computationally expensive. A single simulation can take hours, making them infeasible for Bayesian inference pipelines which may require $\sim10^6$ forward model calls to sample posterior distributions. Performing such inference with direct RT simulations would take millennia on a single core.

Methodology
The authors present the first neural network-based emulator for SESN light curves, designed to approximate the output of the SEDONA RT code with orders-of-magnitude speed improvements.

• Training Data: The emulator is trained on a grid of 4,499 light curves simulated with SEDONA. This grid augments the original 1,000-point grid from a previous study (Yadavalli et al. 2026, hereafter Y26) with 3,499 additional points generated via random sampling and active learning.
• Physical Parameterization: The input space consists of nine physical parameters describing the ejecta profile: $M_{He}$, $M_{Ni}$, $M_{bulk}$, minimum velocity ($v_{min}$), velocity difference ($\Delta v$), and four latent variables ($\eta_{vel}, \eta_{He}, \eta_{Ni}, \eta_{bulk}$) that define the distribution of mass and velocity. The output is a downsampled spectrum (resolution $R \approx 30$) over 41 log-uniformly spaced wavelengths (3000–10000 Å) at specific timesteps (5 to 60 days post-explosion).
• Architecture: The emulator utilizes a Multilayer Perceptron (MLP) with five hidden layers and 2,000 neurons per layer. While a transformer architecture was tested and showed high accuracy in spectral reconstruction, the MLP was selected for its superior inference speed ($\sim$milliseconds per call vs. $\sim$100s of milliseconds for transformers).
• Uncertainty Quantification: The authors explicitly model two sources of systematic error in their Bayesian inference pipeline (implemented in MOSFiT):
  1. Emulator Uncertainty: The RMS difference between the emulator's prediction and the true SEDONA simulation.
  2. SEDONA Uncertainty: The systematic error introduced by SEDONA's assumption of Local Thermal Equilibrium (LTE), estimated by comparing SEDONA results to non-LTE CMFGEN simulations.
     These uncertainties are parameterized as functions of time since explosion and incorporated directly into the likelihood calculation.

Key Contributions and Results

1. Breakdown of Mass-Velocity Degeneracy:
   The primary finding is that the emulator successfully breaks the strong degeneracy between ejecta mass ($M_{ej}$) and ejecta velocity ($v_{ej}$) that plagues the Arnett model. In the Arnett model, these parameters are inherently coupled, often forcing the inference to rely on the degenerate combination $\sqrt{M_{ej}/v_{ej}}$. The emulator, by learning the full RT physics, can independently constrain $M_{ej}$ and the velocity profile.

2. Superior Parameter Recovery:
   The authors tested the emulator on simulated light curves resembling those from the Zwicky Transient Facility (ZTF) and the upcoming Vera C. Rubin Observatory (LSST).

   • $M_{Ni}$: The emulator achieves a Root Mean Square (RMS) error of 0.008 $M_{\odot}$ (LSST) and 0.007 $M_{\odot}$ (ZTF), compared to 0.33 and 0.70 $M_{\odot}$ for the Arnett model, respectively. The Arnett model systematically overpredicts $M_{Ni}$ by $\sim$80% (LSST) to a factor of three (ZTF).
   • $M_{ej}$: The emulator recovers ejecta mass with an RMS of 0.9 $M_{\odot}$ (LSST) and 1.2 $M_{\odot}$ (ZTF), whereas the Arnett model returns essentially prior draws with errors of 2.6 and 3.0 $M_{\odot}$.
   • Velocity: The emulator recovers velocity with an RMS of $\sim$1,340 km/s (LSST), significantly outperforming the Arnett model ($\sim$3,800 km/s).
   • Mixing: The emulator successfully constrains the degree of $^{56}$Ni mixing ($r_{95,Ni}$), a parameter the Arnett model cannot address.

3. Application to Real Observations:
   The pipeline was applied to three well-studied SESNe: SN 1994I (Type Ic), SN 2007gr (Type Ic), and iPTF13bvn (Type Ib).

   • SN 1994I: The inferred $M_{Ni}$ (0.048 $M_{\odot}$) matches tail-based measurements but is lower than peak-luminosity estimates. The model suggests high $^{56}$Ni mixing ($r_{95,Ni} \approx 0.35$), consistent with spectral studies, and implies that the discrepancy between peak and tail luminosity is due to mixing rather than an additional power source.
   • SN 2007gr: Results are consistent with literature values, indicating moderate $^{56}$Ni mixing.
   • iPTF13bvn: The model infers weak $^{56}$Ni mixing ($r_{95,Ni} \in [0.1, 0.2]$) and a flatter velocity profile compared to the Type Ic events, supporting spectropolarimetric constraints over 1D light curve models that require strong mixing.

Significance and Claims
The paper claims that this work establishes a computationally feasible framework for performing rigorous Bayesian inference on SESN light curves using full radiative transfer physics. By replacing expensive RT simulations with a fast neural network emulator, the authors enable the independent constraint of ejecta mass, velocity, and mixing—parameters that are traditionally degenerate in semianalytical approaches.

The authors emphasize that their method provides significantly more accurate physical parameter recovery than the classical Arnett model for both simulated and observed data. They note that while the emulator is trained on a specific grid of models (based on Woosley et al. 2021 progenitors), it successfully reproduces observed light curves and recovers physical parameters consistent with independent literature constraints. The work lays the groundwork for applying this inference pipeline to statistical samples of hundreds of SESNe in the LSST era to characterize the diversity of progenitor systems and explosion mechanisms.