OSIRIS: a new code for ray tracing around compact objects

Abstract

The radiation observed in quasars and active galactic nuclei is mainly produced by a relativistic plasma orbiting close to the black hole event horizon, where strong gravitational effects are relevant. The observational data of such systems can be compared with theoretical models to infer the black hole and plasma properties. In the comparison process, ray-tracing algorithms are essential to computing the trajectories followed by the photons from the source to our telescopes. In this paper, we present : a new stable FORTRAN code capable of efficiently computing null-geodesics around compact objects, including general relativistic effects such as gravitational lensing, redshift, and relativistic boosting. The algorithm is based on the Hamiltonian formulation and uses different integration schemes to evolve null-geodesics while tracking the error in the Hamiltonian constrain to ensure physical results. We found from an error analysis that the integration schemes are all stable, and the best one maintains an error below $$10^{-11}$$ 10 - 11 . Particularly, to test the robustness and ability of the code to evolve geodesics in curved space-time, we compute the shadow and Einstein rings of a Kerr black hole with different rotation parameters and obtain the image of a thin Keplerian accretion disk around a Schwarzschild black hole. Although is parallelized neither with MPI nor with CUDA, the computation times are of the same order as those reported by other codes with these types of parallel computing platforms.

All analytic solutions for geodesic motion in axially symmetric space-times

“…Now, it will be possible to build templates from exact General Relativistic analytical solutions, i.e. without any approximations for the orbits of stars [1][2][3], and the imaging of black holes [4,5,20]. The method shown here allows us to find solutions of the form f 1 (r, θ) = C 1 and f 2 (r, θ) = C 2 (equations (70) and (71)) which complement the standard elliptic integrals procedure handling in writing down the geodesics trajectories ( see for example references [21][22][23] ).…”

Blacklight: A General-relativistic Ray-tracing and Analysis Tool

“…In terms of robustness and ease of use, however, the recommended geodesic integrator is the "RK5(4)7M" method of Dormand & Prince (1980;DP), which is an adaptive fifthorder Runge-Kutta method that calculates RK4 values from the same set of function evaluations in order to estimate errors for each step. In comparing common integrators in the context of the computation of null geodesics around black holes, Velásquez-Cadavid et al (2022) find DP to be far more accurate. The step size is adjusted dynamically based on this error estimate, in order to take steps as large as possible given a user-prescribed tolerance (see Press et al 1997).…”

“…(see James et al 2015;Pu et al 2016;Kawashima et al 2021;Velásquez-Cadavid et al 2022). It also sometimes tracks proper distance along the ray via…”

Blacklight: A General-Relativistic Ray-Tracing and Analysis Tool

“…errors for each step. In comparing common integrators in the context of the computation of null geodesics around black holes, Velásquez-Cadavid et al (2022) find DP to be far more accurate. The step size is adjusted dynamically based on this error estimate, in order to take steps as large as possible given a user-prescribed tolerance (cf.…”

“…(cf. James et al 2015;Pu et al 2016;Kawashima et al 2021;Velásquez-Cadavid et al 2022). It also sometimes tracks proper distance along the ray via…”