Photon arrival time lags in 3D radiative transfer with SKIRT

Abstract

Reprocessed X-ray emission from cold material surrounding compact objects carries critical information about the geometry and physical state of the system. In particular, the Fe K$α$ fluorescence line provides a powerful diagnostic through its spectral and timing properties relative to the direct emission. Interpreting these observables requires self-consistent modelling of radiative transfer (RT) in three-dimensional (3D) space. We aim to implement photon arrival time lags in SKIRT, a Monte Carlo RT code, thereby enabling self-consistent modelling of both the spectral and timing properties of reprocessed emission in 3D space. We modified the code to accumulate photon path lengths over their lifetimes and convert them into arrival time lags relative to the direct emission. The implementation is validated using simple geometries and then applied to a realistic model of an active galactic nucleus (AGN), for which we compute the time-lag and energy distribution and the cross-correlation functions (CCFs) between the fluorescence line and broad bands. The simulations reproduce the expected time-lag distributions and their energy dependence for both free-electron scattering and the photoelectric absorption $+$ fluorescence. In the AGN application, the model naturally yields distinct lag components from the inner and outer structures, as well as energy-dependent time lags associated with the fluorescence line. The derived CCFs successfully recover both the peak time lag and its finite width, which arise from the extended geometry and intrinsic variability. In X-rays, this capability provides a robust framework for interpreting high-resolution spectroscopic data in conjunction with timing information from current and future missions such as XRISM and NewAthena. A wide range of applications is foreseen, including reverberation mapping studies of accreting systems.