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The goal of this paper is to investigate the optimal parameters space forusing the reloaded Rossiter-McLaughlin technique to detect differentialrotation (DR) and centre-to-limb convective variations. We simulated astar-planet system with and without convective effects to map the optimalregions of the parameter space for retrieving the injected differentialrotation. Our simulations explored all possible ranges of projected obliquity(spin-orbit angle), stellar inclination, and impact parameter, as well asdifferences in instrumental configuration, stellar magnitude, and exposuretime. We find that DR is more easily retrieved at low-impact parameters,corresponding to system configurations in which the transiting planet crossesthe largest number of stellar latitudes. The main hot-spots for detection (i.e.areas in which DR detectability is high) are$120^{\rm{o}}<|\lambda|<180^{\rm{o}}$ for $i_*<90^{\rm{o}}$ and$|\lambda|<60^{\rm{o}}$ for $i_*>90^{\rm{o}}$ on average, and they tend toshrink as the impact parameter increases. Additionally, in contrast to thecrucial impact of brightness, we identify that exposure time has a negligibleimpact on the difficulty of detecting DR as the increase in signal-to-noiseratio (S/N) at longer exposure times is counteracted by the degraded samplingrate. We determine that an ESPRESSO-like setup of instrumental configurationand sensitivity might retrieve DR up to $V = 12$, compared to $V = 10$ forHARPS. We reach no clear conclusion about limb-dependent convective effects andthe possible confusion with DR; preliminary results suggest, however, thatunder certain circumstances, while it seems that one effect could be mistakenfor the other, the accuracy of the fit (in particular of $\alpha$) does nothold up under additional scrutiny.

Optimal parameter space for detecting stellar differential rotation and centre-to-limb convective variations