Modeling the Thermal Low-Frequency Radio Sun with Ray Tracing

Incoherent radio emission at meter--decimeter wavelengths provides a key diagnostic of the coronal thermal plasma, but at frequencies below $\sim$\,1\,GHz coronal refraction can substantially bend ray paths and modify the apparent source size and brightness distribution. We develop a forward-modeling framework that combines refractive ray tracing through a global 3D coronal model with radiative transfer along each ray. The method tracks the ray-tube cross-sectional area $S(s)$ using a step-wise perturbation retracing approach and incorporates a geometric magnification term proportional to $d\ln S/ds$ to enforce flux conservation under focusing/defocusing. Thermal free--free emission and absorption are then computed with the \texttt{GRFF} radiative transfer code to produce synthetic radio maps over 40--800\,MHz. Applying the framework to Carrington rotation 2298, we find that including propagation effects allows the quiet-Sun background spectrum to be well reproduced. However, active region brightness is less accurately modeled, suggesting that additional physical factors should be considered in future work. These results establish a physics-based method for generating low-frequency quiet-Sun synthetic images suitable for quantitative comparison with interferometric observations and for assessing how propagation effects shape the observed morphology.