resulting bulk elemental composition. By performing one million such random draws, we can calculate the median elemental composition and the associated 1-σ errors.

[Figure: Figure 1: The top panel shows the bulk carbon-to-oxygen atomic ratio of comet 67P as a function of the refractory-to-ice mass ratio, χ. The dark blue shaded area encompasses 50% of the cases, and the light blue ±1σ. The solar value of 0.594 is taken from Asplund et al. (2021). The bottom panel shows the fraction of cases with a super-solar C/O ratio.]

[Figure: Figure 1 shows the resulting carbon-to-oxygen ratio as a function of χ. The dark blue shaded area encompasses 50% of the cases, and the light blue ±1σ. The error bars are large and become larger as χ increases because of the large uncertainties of the C and O abundances of the refractory component. It would be reasonable to assume that the C/O ratio could be as high as the solar value (Asplund et al., 2021) but should not be super-solar. In the median case, this is true up to χ = 3. The bottom panel of Fig. 1 show the fraction of cases with a super-solar C/O ratio. It shows that even at high χ there are still roughly 40% of cases where 67P would have a sub-solar C/O ratio. This might be acceptable to some, but we would posit that if the condition of having a sub-solar C/O ratio is strongly weighted, that would clearly point in the direction of smaller χ. For example at a χ = 1 almost 80% of cases would be sub-solar. Nevertheless, the C/O ratio, though pointing towards small χ, is not a strong constraint on χ. Therefore, we will have a look next at the oxygen composition as a function of χ. This is particularly interesting because we can split the oxygen into a part that is stored in water (Oex) and the one that is stored in anhydrous material (Oan). This is analogous to what has been done for meteorites (Alexander, 2019), e.g., the primitive CI chondrites. Figure 2 shows the oxygen composition of 67P and its comparison to CI chondrites. The anhydrous oxygen composition compared to silicon is independent of χ because it is simply the composition of the refractory component. But the amount of oxygen in water (with respect to silicon) decreases with increasing χ because the fraction of water decreases with increasing χ. In the median case, if χ = 1.7, the ratio between the abundance of oxygen in water and anhydrous minerals is the same as in CI chondrites (Fig. 2). This case already seems unusual, as we might expect a comet to have more oxygen in water than a carbonaceous chondrite. The comet is non-chondritic if χ < 1.1. Nevertheless, we consider the χ = 1.7 case ("chondritic" case) the upper limit. Remember that for χ < 3, the median C/O ratio is also always sub-solar and therefore, for χ < 1.7, most cases will result in a sub-solar C/O ratio. To summarise this part: When starting with an agnostic stance on what the refractory-to-ice mass ratio, χ, for 67P should be, from the elemental composition alone constrains χ < 1.7. This is lower than what was found very early in the mission (χ = 4 ± 2; Rotundi et al., 2015) but in line with measurements from the coma of 67P (Biver et al., 2019; Marschall et al., 2020b; Läuter et al., 2020; Combi et al., 2020). Initially, there was a significant discrepancy between the estimates for the gas production rates derived from remote sensing (e.g., the MIRO and VIRTIS instrument) and in-situ measurements (ROSINA). Later studies resolved this, and now the different estimates are in line with each other (Biver et al., 2019; Combi et al., 2020). Furthermore, Marschall et al. (2020b) showed that the refractory-to-ice ratio is variable during the mission. It was highest very early on in the mission (∼1.6) when the value of Rotundi et al. (2015) was measured. Between perihelion and summer solstice, when the production rates were the highest and thus the time most representative of the bulk mass loss, the refractory-to-ice ratio dropped to ∼0.5. The similarity between the values we find here and the ones measured in the coma (Biver et al., 2019; Marschall et al., 2020b; Läuter et al., 2020; Combi et al., 2020) suggests that the material falling back to the surface is not significantly different from that of the bulk comet, i.e., it did not lose a significant part of its ice component while in the coma. This is in line with thermophysical models of fallback material, arguing for the retention of a significant amount of ices even for small cm-sized particles (Davidsson et al., 2021). Though we only discussed an upper limit for χ here, we will discuss a lower limit in the next section.]