The Effect of Photospheric Granulation on the Determination of the Lithium Abundance in Solar-type Stars

I investigate non-local thermodynamic equilibrium (non-LTE) formation of the 670.6 nm Li I resonance doublet in the presence of convective surface inhomogeneities in solar-type stars. This doublet is widely used for lithium abundance determination in stars. It has been suggested that the presence of hot and cool elements in a stellar atmosphere due to convective heat transport might lead to an underestimate of lithium abundance by as much as a factor of 10 when the equivalent width of the doublet is analyzed in terms of a one-dimensional plane-parallel model atmosphere.

To explore this possibility, I solved the two-dimensional non-LTE radiative transfer equations for a sufficiently large lithium model atom in a hydrodynamic simulation snapshot of the solar granulation. This was done for different values of the lithium abundance ranging from A_Li = 0.0 to 3.3.

In all cases the effects of the inhomogeneities in the atmosphere on lithium line strength are small, never amounting to more than 0.1 dex in the derived abundance. This occurs mainly for three reasons. First, because of the exponential decrease of density with height in the gravitationally stratified stellar atmosphere, radiation escapes mostly vertically with little horizontal exchange. Some lateral transfer does occur at the boundaries between hot and cold elements, but the effect of this exchange on the spatially averaged line strength cancels out. It leads to a smoothing over the surface rather than to a diminishing overall strength of the doublet. Second, the sharp drop in temperature over hot upwelling material, in contrast to the much shallower gradient over the dark intergranular lanes, causes the 670.6 nm doublet to be deeper and narrower in the former and broader in the latter. Consequently, the contrast of equivalent line width between profiles emerging over hot upflows and cold downflows is small. Finally, because of its small abundance the opacity scale in lithium ionizing continua is mostly set by H^- bound-free processes. Optical depth unity at the photoionization edges, therefore, follows the contours of electron temperature, moderating contrast in the ionizing radiation field.