Investigating the Center-to-Limb Effects in Helioseismic Data Using 3D Radiative Hydrodynamic Simulations

Full-disk observations from missions such as the SDO and SOHO have enabled comprehensive studies of solar oscillations and dynamics. Interpreting helioseismic and photospheric data is complicated by systematic center-to-limb variations. To explore the physical origin of these variations, we perform local 3D radiative hydrodynamic simulations that include effects of solar rotation to generate 24-hour synthetic time series of continuum intensity and Doppler velocity for nine viewing angles spanning from $-75^{\circ}$ to $75^{\circ}$. The simulations reveal a systematic decrease in 1D oscillation power toward the limbs and a pronounced East-West asymmetry that increases with frequency, primarily due to rotation-induced flows. Analysis of $\ell-\nu$ diagrams shows a decrease in the amplitude and width of the surface gravity ($f$) and resonant pressure ($p$) modes with increasing angular distance from the disk center. The amplitudes of the corresponding pseudo-modes with frequencies above the acoustic cut-off frequency increase in the intensity power spectra and are suppressed in the velocity spectra. The ring-diagram analysis of the simulation data further demonstrates anisotropic broadening of the modes, and the impact of the foreshortening effect on the energy distribution, and distinct differences in background noise and pseudo-mode structure between the intensity and velocity data. These results indicate that the center-to-limb effects arise from both geometric projection and physical factors such as line-formation height and potential effects of the radial differential rotation. The findings provide a framework for correcting helioseismic observations and demonstrate that realistic simulations are a powerful tool for disentangling geometric and physical biases in solar data.