  Observations of the Rossiter-McLaughlin (RM) effect provide information on
star-planet alignments, which can inform planetary migration and evolution
theories. Here, we go beyond the classical RM modelling and explore the impact
of a convective blueshift that varies across the stellar disc and non-Gaussian
stellar photospheric profiles. We simulated an aligned hot Jupiter with a 4 d
orbit about a Sun-like star and injected centre-to-limb velocity (and profile
shape) variations based on radiative 3D magnetohydrodynamic simulations of
solar surface convection. The residuals between our modelling and classical RM
modelling were dependent on the intrinsic profile width and v sin i; the
amplitude of the residuals increased with increasing v sin i, and with
decreasing intrinsic profile width. For slowly rotating stars the
centre-to-limb convective variation dominated the residuals (with amplitudes of
10s of cm/s to ~1 m/s); however, for faster rotating stars the dominant
residual signature was due a non-Gaussian intrinsic profile (with amplitudes
from 0.5-9 m/s). When the impact factor was 0, neglecting to account for the
convective centre-to-limb variation led to an uncertainty in the obliquity of
~10-20 degrees, even though the true v sin i was known. Additionally,
neglecting to properly model an asymmetric intrinsic profile had a greater
impact for more rapidly rotating stars (e.g. v sin i = 6 km/s), and caused
systematic errors on the order of ~20 degrees in the measured obliquities.
Hence, neglecting the impact of stellar surface convection may bias star-planet
alignment measurements and consequently also theories on planetary migration
and evolution.
