An investigation of the formation and line properties of MgH in 3D hydrodynamical model stellar atmospheres

Studies of the isotopic composition of magnesium in cool stars have so far relied upon the use of one-dimensional (1D) model atmospheres. Since the isotopic ratios derived are based on asymmetries of optical MgH lines, it is important to test the impact from other effects affecting line asymmetries, like stellar convection. Here, we present a theoretical investigation of the effects of including self-consistent modeling of convection. Using spectral syntheses based on 3D hydrodynamical CO$^5$BOLD models of dwarfs (4000K$\lesssim T_\mathrm{eff}\lesssim5160K$, $4.0\leq$log(g)$\leq4.5$, $-3.0\leq[\mathrm{Fe/H}]\leq-1.0$) and giants ($T_\mathrm{eff}\sim4000$K, log(g)$=1.5$, $-3.0\leq[\mathrm{Fe/H}]\leq-1.0$), we perform a detailed analysis comparing 3D and 1D syntheses. We describe the impact on the formation and behavior of MgH lines from using 3D models, and perform a qualitative assessment of the systematics introduced by the use of 1D syntheses. Using 3D model atmospheres significantly affect the strength of the MgH lines, especially in dwarfs, with 1D syntheses requiring an abundance correction of up to +0.69 dex largest for our 5000K models. The corrections are correlated with $T_\mathrm{eff}$ and are also affected by the metallicity. The shape of the strong $^{24}$MgH component in the 3D syntheses is poorly reproduced in 1D. This results in 1D syntheses underestimating $^{25}$MgH by up to $\sim5$ percentage points and overestimating $^{24}$MgH by a similar amount for dwarfs. This discrepancy increases with decreasing metallicity. $^{26}$MgH is recovered relatively well, with the largest difference being $\sim2$ percentage points. The use of 3D for giants has less impact, due to smaller differences in the atmospheric structure and a better reproduction of the line shape in 1D.