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The dynamics of the solar core cannot be properly constrained through theanalysis of acoustic oscillation modes. Gravity modes are necessary tounderstand the structure and dynamics of the deepest layers of the Sun. Throughrecent progresses on the observation of these modes -- both individually andcollectively -- new information could be available to contribute to inferringthe rotation profile down inside the nuclear burning core. To see thesensitivity of gravity modes to the rotation of the solar core. We analyze theinfluence of adding the splitting of one and several g modes to the data setsused in helioseismic numerical inversions. We look for constraints on theuncertainties required in the observations in order to improve the derived corerotation profile. We compute forward problems obtaining three artificial setsof splittings derived for three rotation profiles: a rigid profile taken as areference, a step-like and a smoother profiles with higher rates in the core.We compute inversions based on Regularized Least-Squares methodology (RLS) forboth artificial data with real error bars and real data. Several sets of dataare used: first we invert only p modes, then we add one and several g modes towhich different values of observational uncertainties (75 and 7.5 nHz) areattributed. For the real data, we include g-mode candidate, l=2, n=-3 withseveral splittings and associated uncertainties. We show that the introductionof one g mode in artificial data improves the rate in the solar core and givean idea on the tendency of the rotation profile. The addition of more g modesgives more accuracy to the inversions and stabilize them. The inversion of realdata with the g-mode candidate gives a rotation profile that remains unchangeddown to 0.2 R, whatever value of splitting we attribute to the g mode.

Sensitivity of helioseismic gravity modes to the dynamics of the solar core