HOLISMOKES XXI: Detecting strongly lensed type Ia supernovae from time series of multi-band LSST-like imaging data -- Part II

Technical Summary: HOLISMOKES XXI – Detecting Strongly Lensed Type Ia Supernovae from Multi-Band Time Series

Problem Statement
Strongly gravitationally lensed supernovae (LSNe), particularly Type Ia, are rare but critical probes for cosmology, specifically for time-delay cosmography (TDC) to measure the Hubble constant ($H_0$) and constrain dark energy. Upcoming time-domain surveys like the Vera C. Rubin Observatory's Legacy Survey of Space and Time (LSST) are expected to detect hundreds of LSNe. However, the sheer volume of alerts ($\sim 10^7$ per night) renders manual inspection impossible. Early identification is essential to enable timely follow-up for mass modeling and progenitor studies. Previous methods often rely on resolving multiple images or detecting host galaxy arcs, which is difficult for small-separation systems or during the early phases of an explosion. Furthermore, distinguishing LSNe from false positives—such as supernovae occurring in the foreground lens galaxy itself—is a significant challenge.

Methodology
This work extends the deep-learning framework introduced in HOLISMOKES XVII (Bag et al. 2026) to detect LSNe Ia directly from multi-band, multi-epoch image cutouts. The core methodology employs a Convolutional Long Short-Term Memory (ConvLSTM) architecture to simultaneously capture spatial and temporal correlations in time-series imaging data.

Key methodological advancements over the previous study include:

1. Enhanced Realism in Simulations: The training dataset was upgraded from Hyper Suprime-Cam (HSC) Public Data Release 2 (PDR2) to PDR3, increasing the sample size by $\sim 50\%$.
2. Incorporation of Lensing Features: The simulations now include realistic lensed host-galaxy arcs. Real galaxies from the Hubble Ultra Deep Field (HUDF) are used as host galaxies, ray-traced through lens models to generate lensed arcs on the image plane.
3. Dynamic Observational Conditions: Unlike the previous static approach, this work introduces epoch-to-epoch variations in the Point Spread Function (PSF) and Poisson noise. A self-consistent pipeline generates time series from single-epoch observations by varying the seeing and updating the variance maps to reflect injected flux and changing noise conditions.
4. Improved Transient Modeling: Light curves are modeled using the SALT2 spectral template (replacing the Hsiao template), incorporating intrinsic variations in stretch and color.
5. Challenging Negative Classes: A new negative class (Set N2) was introduced, consisting of Type Ia supernovae occurring in the foreground lens galaxy itself. These are astrophysically motivated false positives that are difficult to distinguish from genuine LSNe, especially when the background source is also lensed. The dataset also includes HSC variables and normal SNe in LRGs and spiral galaxies.

The model processes 59 $\times$ 59 pixel image cutouts ($\sim 10'' \times 10''$) across $g, r, i, z$ bands. It utilizes a dual-branch architecture: a ConvLSTM branch for image sequences and an LSTM branch for observation timestamps, with features concatenated for final classification.

Key Results
The model demonstrates robust performance under these more realistic conditions:

• Rapid Convergence: The Receiver Operating Characteristic (ROC) curves improve rapidly during the first few observations. By the 7th observation ($N_{obs, m-b} = 7$), the model achieves a True Positive Rate (TPR) of $\sim 60\%$ at a False Positive Rate (FPR) of $O(10^{-4})$. By the 10th observation, the TPR rises to $\sim 80\%$ at the same FPR.
• Robustness to Complexity: Despite the inclusion of time-varying PSFs, Poisson noise, and the challenging "SN in lens" negative class, the performance remains comparable to the previous study, indicating the method's resilience to observational complexities.
• False Positive Analysis: The primary sources of false positives are SNe in lenses (Set N2) and SNe in LRGs (Set N3). These subclasses dominate the FPR budget, particularly at early epochs. However, the model effectively suppresses these contaminants at conservative score thresholds (e.g., $P_{th} > 0.8$).
• Impact of Host Arcs and Offsets: Systems with detectable host-galaxy arcs show slightly better early performance due to additional spatial information, but this advantage diminishes as more temporal data accumulates. Similarly, the classification performance is largely insensitive to the offset between the SN and its host galaxy center, though systems with smaller offsets ($< 0.4''$) show a marginal improvement.
• Sibling Supernovae: The model was tested against a sample of "sibling SNe" (two SNe in the same galaxy). While a small fraction of these mimic lensed configurations (particularly those with large projected angles), the majority are correctly classified as unlensed.

Significance and Claims
The authors claim that the image-time-series approach remains robust when extended to more realistic observing conditions and astrophysical configurations. The study demonstrates that:

1. Early Identification is Feasible: The model can distinguish LSNe from other transients with high confidence using only a small number of early observations, which is critical for enabling follow-up before peak brightness.
2. Realism Does Not Degrade Performance: Incorporating dynamic PSFs, realistic noise, and difficult negative classes does not significantly hinder the model's ability to learn the necessary features.
3. Suitability for LSST: The framework is well-suited for real-time searches in LSST and other time-domain surveys. The authors note that the improved cadence of LSST compared to the HSC-based simulations used here is expected to further enhance early identification capabilities.

The paper concludes that while the current study uses HSC data as a proxy for LSST, the methodology is ready for transition to LSST data products and can be extended to other transient types (e.g., core-collapse SNe, TDEs) in future work.