We present a novel method to implement time-delayed propagation of radiation fields in cosmo- logical radiative transfer simulations. Time-delayed propagation of radiation fields requires construction of retarded-time fields by tracking the location and lifetime of radiation sources along the corresponding light-cones. Cosmological radiative transfer simulations have, until now, ignored this “light-cone effect” or implemented ray-tracing methods that are computationally demanding. We show that radiative trans- fer calculation of the time-delayed fields can be easily achieved in numerical simulations when periodic boundary conditions are used, by calculating the time-discretized retarded-time Green’s function using the Fast Fourier Transform (FFT) method and convolving it with the source distribution. We also present a direct application of this method to the long-range radiation field of Lyman-Werner band photons, which is important in the high-redshift astrophysics with first stars.

Abstract
1. INTRODUCTION
2. RETARDED RADIATION FIELD: FORMALISMAND NUMERICAL METHOD
    2.1. Green’s Function Formalism
    2.2. Numerical Method
3. APPLICATION: LYMAN-WERNER BACKGROUND
4. DISCUSSION
REFERENCES

• Kyungjin Ahn(Department of Earth Sciences, Chosun University) Corresponding author