Core-wing transitions and the breakdown of diffusion in Lyman-$\alpha$ radiative transfer

TL;DR

This paper investigates the limitations of diffusion approximations in Lyman-alpha radiative transfer, introduces a new core-wing transition definition, and analyzes the anomalous diffusion behavior of photons in optically thick environments.

Contribution

It presents a physically-motivated core-wing transition frequency, derives new spectral distributions, and reveals anomalous diffusion behaviors in LyA radiative transfer.

Findings

Diffusion approximations break down near the core and at finite optical depths.

Identifies anomalous spatial diffusion with fat-tailed distributions.

Proposes a new core-wing transition frequency for better modeling.

Abstract

The Lyman alpha (LyA) line of neutral hydrogen plays a central role in observations of star-forming galaxies. However, resonant scattering makes it difficult to directly interpret LyA signatures. Monte Carlo radiative transfer (MCRT) calculations have become the gold standard for modeling LyA, but it becomes extremely computationally expensive in optically thick environments. Workarounds, such as core-skipping to avoid repetitive low-transport scatterings, greatly increase the efficiency of MCRT simulations but introduce errors in the solutions. While core-skipping is designed to preserve emergent spectra, the internal radiation field, most importantly, the momentum imparted, is not properly preserved. On the other hand, to make analytical and numerical progress, it is often assumed that photons diffuse in both frequency and physical space. We find that these diffusion approximations break down for frequencies near the core and positions at finite optical depths. We propose a more physically-motivated definition for the core-wing transition frequency to isolate such effects. We derive new spectral distributions of internal radiation properties and compare the results with simulations. We analyze the diffusive properties of LyA photons and demonstrate anomalous spatial diffusion behavior with fat-tailed distributions. This work deepens our understanding of diffusion in resonant-line transfer and identifies areas where simulations or analytics may be failing and how these failures may be resolved.