Bayesian Multi-wavelength Imaging of the LMC SN1987A with SRG/eROSITA

The eROSITA Early Data Release (EDR) and eROSITA All-Sky Survey (eRASS1) data have already revealed a remarkable number of undiscovered X-ray sources. Using Bayesian inference and generative modeling techniques for X-ray imaging, we aim to increase the sensitivity and scientific value of these observations by denoising, deconvolving, and decomposing the X-ray sky. Leveraging information field theory, we can exploit the spatial and spectral correlation structures of the different physical components of the sky with non-parametric priors to enhance the image reconstruction. By incorporating instrumental effects into the forward model, we develop a comprehensive Bayesian imaging algorithm for eROSITA pointing observations. Finally, we apply the developed algorithm to EDR data of the Large Magellanic Cloud (LMC) SN1987A, fusing data sets from observations made by five different telescope modules. The final result is a denoised, deconvolved, and decomposed view of the LMC, which enables the analysis of its fine-scale structures, the identification of point sources in this region, and enhanced calibration for future work.

💡 Research Summary

The paper presents a novel Bayesian imaging framework for eROSITA X‑ray data, combining information field theory (IFT) with modern variational inference to simultaneously denoise, deconvolve, and decompose multi‑energy observations. After a concise review of existing source‑detection pipelines (eSASS, sliding‑cell, wavelet, Voronoi tessellation) and the D3PO algorithm, the authors argue that traditional MAP‑based approaches lack robust uncertainty quantification and are not optimal for the Poisson‑dominated, PSF‑blurred eROSITA data.

The study focuses on the Large Magellanic Cloud (LMC) region around SN 1987A, using pointing observations from the eROSITA Early Data Release (ObsID 700161). Five telescope modules (TM1‑4, TM6) are selected to avoid optical‑light leaks in TM5 and TM7. The raw event files are processed with the eSASS pipeline, binned into a 1024 × 1024 spatial grid and three energy bands (0.2‑1.0 keV, 1.0‑2.0 keV, 2.0‑4.5 keV), and exposure maps are generated for each module.

The Bayesian model treats the X‑ray photon flux as a continuous field s(x, y) defined over sky coordinates x and logarithmic energy y. The field is decomposed into a point‑source component sₚ and a diffuse component s_d. Priors are constructed as follows: (i) the diffuse component follows a log‑normal process with a spatial covariance T that is learned from the data via an integrated Wiener process; (ii) the point‑source component is modeled as pixel‑wise independent with an inverse‑Gamma prior, enforcing sparsity; (iii) both components have a spectral dimension modeled by a power‑law with index α, where α_d is spatially correlated and αₚ is uncorrelated. These priors encode the expected morphology (sparse bright points versus extended correlated emission) and spectral behaviour of the LMC X‑ray sky.

The likelihood incorporates the full instrument response: Poisson counting statistics, energy‑dependent point spread function (PSF), and exposure variations across the field of view. By embedding the forward model in the J‑UBIK library (a JAX‑accelerated implementation of NIFTy.re), the authors achieve efficient GPU‑based evaluation of the high‑dimensional likelihood.

Instead of a MAP solution, the authors employ variational inference (VI) with the re‑parameterization trick to approximate the posterior distribution q(s) by minimizing the Kullback‑Leibler divergence (equivalently maximizing the evidence lower bound, ELBO). This yields both a posterior mean map and pixel‑wise uncertainty estimates.

Results show a dramatically improved RGB image of the LMC region: fine structures such as the shell of 30 Doradus C become sharply visible, and the central SN 1987A point source is isolated with high positional accuracy. The diffuse component exhibits long spatial correlation lengths and a steep spectral slope, while the point‑source component displays a flatter spectrum, consistent with expectations for young supernova remnants. The learned power spectra provide quantitative measures of spatial correlation for the diffuse X‑ray background in the LMC.

Comparative analysis with the standard eSASS source‑detection pipeline demonstrates higher completeness and lower false‑positive rates, especially in low‑signal regions. The Bayesian framework also delivers credible intervals for fluxes and spectral indices, enabling rigorous downstream physical modeling.

In the discussion, the authors highlight the scalability of their method to the full eRASS data set, the potential for joint multi‑wavelength reconstructions (e.g., combining with Chandra, XMM‑Newton, or radio data), and the broader applicability of the IFT‑based variational approach to other photon‑counting instruments. Future work will focus on extending the model to include time variability, background particle modeling, and automated catalog generation for the entire eROSITA sky.

Overall, the paper convincingly demonstrates that a principled Bayesian treatment, grounded in information field theory and powered by modern automatic differentiation tools, can substantially enhance the scientific return of eROSITA observations, delivering high‑fidelity images, robust source classification, and reliable uncertainty quantification.