Mg abundances in metal-poor halo stars as a tracer of early Galactic mixing

. We present results of a detailed chemical analysis performed on 23 main-sequence turno ff stars having − 3 . 4 ≤ [Fe / H] ≤ − 2 . 2, a sample selected to be highly homogeneous in T e ff and log( g ). We investigate the e ffi ciency of mixing in the early Galaxy by means of the [Mg / Fe] ratio, and find that all values lie within a total range of 0.2 dex, with a standard deviation about the mean of 0.06 dex, consistent with measurement errors. This implies there is little or no intrinsic scatter in the early ISM, as suggested also by the most recent results from high-quality VLT observations. These results are in contrast with inhomogeneous Galactic chemical evolution (iGCE) models adopting present supernova (SN) II yields, which predict a peak-to-peak scatter in [Mg / Fe] as high as 1 dex at very low metallicity, with a corresponding standard deviation of about 0.4 dex. We propose that cooling and mixing timescales should be investigated in iGCE models to account for the apparent dis-agreement with present observations. The contrast between the constancy and small dispersion of [Mg / Fe] reported here and the quite di ff erent behaviour of [Ba / Fe] indicates, according to this interpretation, that Mg and Ba are predominantly synthesised in di ff erent progenitor mass ranges.