Stellar Surface Magneto-convection as a Source of Astrophysical Noise. II. Center-to-limb Parameterization of Absorption Line Profiles and Comparison to Observations

Manifestations of stellar activity (such as star-spots, plage/faculae, and convective flows) are well-known to induce spectroscopic signals often referred to as astrophysical noise by exoplanet hunters. For example, setting an ultimate goal of detecting true Earth analogs demands reaching radial velocity (RV) precisions of ∼9 cm s‑1. While this is becoming technically feasible with the latest generation of highly stabilized spectrographs, it is astrophysical noise that sets the true fundamental barrier on attainable RV precisions. In this paper, we parameterize the impact of solar surface magneto-convection on absorption line profiles, and extend the analysis from the solar disk center (Paper I) to the solar limb. Off disk-center, the plasma flows orthogonal to the granule tops begin to lie along the line of sight, and those parallel to the granule tops are no longer completely aligned with the observer. Moreover, the granulation is corrugated and the granules can block other granules, as well as the intergranular lane components. Overall, the visible plasma flows and geometry of the corrugated surface significantly impact the resultant line profiles and induce center-to-limb variations in shape and net position. We detail these herein, and compare to various solar observations. We find our granulation parameterization can recreate realistic line profiles and induced radial velocity shifts, across the stellar disk, indicative of both those found in computationally heavy radiative 3D magnetohydrodynamical simulations and empirical solar observations.