  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. While this is becoming technically feasible with
the latest generation of highly stabilised spectrographs, it is astrophysical
noise that sets the true fundamental barrier on attainable RV precisions. In
this paper we parameterise the impact of solar surface magneto-convection on
absorption line profiles, and extend the analysis from the solar disc centre
(Paper I) to the solar limb. Off disc-centre, 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 centre-to-limb variations in shape and net position. We
detail these herein, and compare to various solar observations. We find our
granulation parameterisation can recreate realistic line profiles and induced
radial velocity shifts, across the stellar disc, indicative of both those found
in computationally heavy radiative 3D magnetohydrodynamical simulations and
empirical solar observations.

Solar and Stellar Astrophysics;Earth and Planetary Astrophysics