Solar-like oscillations are stochastically excited by turbulent convection at the surface layers of the stars. We study the role of the surface metal abundance on the efficiency of the stochastic driving in the case of the CoRoT target HD 49933. We compute two 3D hydrodynamical simulations representative -- in effective temperature and gravity -- of the surface layers of the CoRoT target HD 49933, a star that is rather metal poor and significantly hotter compared to the Sun. One 3D simulation has a solar metal abundance and the other has a surface iron-to-hydrogen, [Fe/H], abundance ten times smaller. For each 3D simulation we match an associated global 1D model and we compute the associated acoustic modes using a theoretical model of stochastic excitation validated in the case of the Sun and Alpha Cen A. The rate at which energy is supplied per unit time into the acoustic modes associated with the 3D simulation with [Fe/H]=-1 are found about three times smaller than those associated with the 3D simulation with [Fe/H]=0. As shown here, these differences are related to the fact that low metallicity implies surface layers with a higher mean density. In turn, a higher mean density favors smaller convective velocities and hence less efficient driving of the acoustic modes. Our result shows the importance of taking the surface metal abundance into account in the modeling of the mode driving by turbulent convection. A comparison with observational data is presented in a companion paper using seismic data obtained for the CoRoT target HD 49933.
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