Secondary atmospheres on HD 219134 b and c

We analyze the interiors of HD~219134~b and c, which are among the coolest super Earths detected thus far. Without using spectroscopic measurements, we aim at constraining if the possible atmospheres are hydrogen-rich or hydrogen-poor. In a first step, we employ a full probabilistic Bayesian inference analysis in order to rigorously quantify the degeneracy of interior parameters given the data of mass, radius, refractory element abundances, semi-major axes, and stellar irradiation. We obtain constraints on structure and composition for core, mantle, ice layer, and atmosphere. In a second step, we aim to draw conclusions on the nature of possible atmospheres by considering atmospheric escape. Specifically, we compare the actual possible atmospheres to a threshold thickness above which a primordial (H$_2$-dominated) atmosphere can be retained against evaporation over the planet's lifetime. The best constrained parameters are the individual layer thicknesses. The maximum radius fraction of possible atmospheres are 0.18 and 0.13 $R$ (radius), for planets b and c, respectively. These values are significantly smaller than the threshold thicknesses of primordial atmospheres: 0.28 and 0.19 $R$, respectively. Thus, the possible atmospheres of planets b and c are unlikely to be H$_2$-dominated. However, whether possible volatile layers are made of gas or liquid/solid water cannot be uniquely determined. Our main conclusions are: (1) the possible atmospheres for planets b and c are enriched and thus possibly secondary in nature, and (2) both planets may contain a gas layer, whereas the layer of HD 219134 b must be larger. HD 219134 c can be rocky.