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 ℓ = 1 and 2
rotationally split modes.Comment: 11 pages, 9 figures, 1 tabl