What can rotational splittings of low-luminosity subgiants actually tell us about the rotation profile?

Context. Inversions of the rotation profile using rotationally induced splittings of low-luminosity subgiant stars suggest that angular momentum transport mechanisms must be 1-2 orders of magnitude more efficient than theory predicts. The lack of precise high resolution of measurements of the rotation profile limits our understanding of the physical mechanism inducing excess angular momentum transport. Rotational inversions of low-luminosity subgiant stars are limited by current observations. Aims. We study the feasibility of making precise constraints to the rotation profile between the core and surface and the possibility of differentiating between rotation profile shapes using the observed rotational splittings of low-luminosity subgiant KIC 12508433. Methods. We use qualitative assumptions of extreme angular momentum transport mechanisms to prescribe the shape of the five synthetic profiles with the same core and surface rotation rates. We calculate the expected rotational splittings given these five profiles and analyse the differences between them. Markov chain Monte Carlo integration of the synthetic profiles using their associated splittings highlights the limited differentiability between rotation profiles that can currently be made. Results. Despite significant changes to the shape of the rotation profile, the rotational splittings deviate on a scale much smaller than the precision of splittings in current observations. We also find degeneracy between the surface rotation rate and position of strong differential rotation gradient of the inverted profiles. Conclusions. Constraining the physical mechanism contributing to more efficient angular momentum transport during the low-luminosity subgiant phase through the shape of the profile is impossible with current observations of $\ell$ = 1 and 2 rotationally split modes.