Rotation profile inversion in solar-like stars

The observation of a few mixed modes on solar-like oscillating stars would enable their rotation profile to be inverted with success. Here simulated data are used to show that it is possible to find models for solar-like stars that present stochastically excited mixed modes with detectable amplitudes. We take special care to build the mode set by computing the mode amplitudes and selecting those modes with amplitudes compatible with the performance of the forthcoming seismic space experiment, COROT. The frequency set is inverted for various cases where input and trial stellar models differ and where random noise is added to the splittings. We show it is possible to localize a rotation gradient and assess its magnitude. Moreover the use of inverse and forward procedures in parallel gives access to a large part of the profile. We provide several constraints to help the selection of such stars. One looks for a relatively evolved star (still on the main sequence) of $\simeq $$ 1.5 ~ M_\odot$ and the rotation rate on the surface should not be too small