The Linear Perturbation Theory of Reionization in Position-Space: Cosmological Radiative Transfer Along the Light-Cone

TL;DR

This paper reformulates the linear perturbation theory of reionization in position space, clarifying its approximations, and compares it with existing models to enhance understanding and explore diverse reionization scenarios including X-ray contributions.

Contribution

It introduces a position-space formulation of the LPTR, improving interpretability and extending its applicability beyond previous Fourier space approaches.

Findings

Position-space LPTR clarifies radiative transfer approximations.

Comparison with ESMR highlights differences and extensions.

LPTR can explore X-ray reionization scenarios.

Abstract

The linear perturbation theory of inhomogeneous reionization (LPTR) has been developed as an analytical tool for predicting the global ionized fraction and large-scale power spectrum of ionized density fluctuations during reionization. In the original formulation of the LPTR, the ionization balance and radiative transfer equations are linearized and solved in Fourier space. However, the LPTR's approximation to the full solution of the radiative transfer equation is not straightforward to interpret, since the latter is most intuitively conceptualized in position space. To bridge the gap between the LPTR and the language of numerical radiative transfer, we present a new, equivalent, position-space formulation of the LPTR that clarifies the approximations it makes and facilitates its interpretation. We offer a comparison between the LPTR and the excursion-set model of reionization (ESMR), and demonstrate the built-in capability of the LPTR to explore a wide range of reionization scenarios, and to go beyond the ESMR in exploring scenarios involving X-rays.