International audienceThe density and structure of liquid Fe-C alloys have been measured up to 58 GPa and 3,200 K by in situ X-ray diffraction using a Paris-Edinburgh press and laser-heated diamond anvil cell. Study of the pressure evolution of the local structure inferred by X-ray diffraction measurements is important to understand the compression mechanism of the liquid. Obtained data show that the degree of compression is greater for the first coordination sphere than the second and third coordination spheres. The extrapolation of the measured density suggests that carbon cannot be the only light element alloyed to iron in the Earth's core, as 8-16 at % C (1.8-3.7 wt % C) would be necessary to explain the density deficit of the outer cor...