The results of all simulated scenarios are summarized in Tables 1 and 2 in “Appendix B”. In recent studies on collisional water loss, results are often presented as the escaping fraction of the colliding bodies initial water inventory, either w.r.t. the two largest fragments in case of a hit-and-run (e.g., Maindl et al. 2017), all significantFootnote 2 fragments (Maindl et al. 2014), or considering only the largest one at all, regardless of the actual collision outcome (e.g., Canup and Pierazzo 2006). Especially the latter can result in misleading conclusions, since the smaller body in a hit-and-run encounter can carry large amounts of volatiles with it, which are then counted as lost, even though they are still part of a large body, possibly similar in size to the largest (Fig. 5). In order to connect to these studies and summarize results, we provide a similar plot in Fig. 2, where water loss refers to the fraction of water bound to neither of the two largest fragments after the collisionFootnote 3. However, we do not think that this is a good representation for studying transfer and loss of volatiles in hit-and-run collisions for two reasons, (1) because it does not contain any individual information on the two large post-collision fragments, and (2) because the amount of lost volatiles relative to the pre-collision inventory gives only an approximate figure of the fragments’ actual post-collision water mass fractionsFootnote 4 (wmf), since they can loose (or gain) other material as well in the process. To avoid these issues, we will discriminate the fate of the two largest hit-and-run fragments in the rest of this study and furthermore state results as changes in wmf—relative to overall fragment masses. We believe this measure is more instructive for tracking the compositional evolution of growing planets, than the change relative to the initial (pre-collision) water inventory. Figure 3 shows an illustration of the bulk of our results following these conventions.
While vaporization (mainly due to shocks) of significant amounts of refractory material happens only in the most energetic events, the situation is different for volatiles, owing to their much lower vaporization energy. Once vaporized, and perhaps heated to high temperatures, this material can escape either thermally, or due to interaction with the (stellar) environment, driven mainly by extreme ultraviolet (EUV) radiation of the young star. Odert et al. (2017) studied the loss of steam atmospheres, which is a complicated function of many factors, like the masses of the body and the atmosphere, its thermal state, the distance to the star and its activity, and the frequency of impacts (see also Schlichting et al. 2015). Due to the high uncertainties associated with this large number of influences (and with the determination of the vapor fraction, cf. Sect. 2), we do not directly include loss of vaporized material in the presented post-collision water contents, but rather estimate the amount of vaporized water for some selected scenarios in a separate Sect. (4.5) and discuss the implications thereof. Thus, the resulting water contents presented here include all material that is gravitationally bound to the respective fragments, independent of its actual physical state.
Water transfer and loss
Due to the high dimensionality of the parameter space, most studies on volatile losses in similar-sized collisions hold one or more parameters constant or almost constant, where especially the mass ratio is often fixed to a single value. While we focus on hit-and-run collisions in this study, our scenarios cover a significant range of all basic parameters, and thus, we can comprehensively investigate their influence on post-collision volatile inventories. The general increase in volatile losses with impact velocity (Fig. 2) is not surprising, but the dependencies on impact angle and mass ratio are more interesting. There is a strong trend toward losses decreasing with increasing impact angle. While for head-on impacts water losses are considerable even for low \(v/v_{{\mathrm {esc}}}\), and quickly rise above 50% for higher velocities, this figure changes drastically for more oblique collisions and for \(\alpha \gtrsim 60^\circ \) water losses are small (\(<\,10\%\)) even for high-velocity collisions. For \(\alpha = 45^\circ \), they never rise above 50% for velocities up to \(5\times v_{{\mathrm {esc}}}\). These results for overall water loss are in good agreement with previous ones by Maindl et al. (2014, 2017) who found also a significant decrease in water losses toward oblique impact angles, but studied only fixed mass ratios. There is also broad agreement to earlier results from Canup and Pierazzo (2006), when their definition of water loss as everything that is not bound to the largest fragment is taken into account. However, their treatment ignores that the impactor in a hit-and-run collision also escapes the target’s gravity more or less intact and can still contain a large volatile reservoir which could be delivered to the same or nearby objects later. Reufer et al. (2013) focus on mantle stripping of the second largest fragment and consider variations in the four probably most important parameters (\(v/v_{{\mathrm {esc}}}, \alpha , \gamma , M_{{\mathrm {tot}}}\)) to some degree. Our results for mass ratios between 1:50 and 1:2 show a clear increase in combined water loss for more equally sized bodies, which seems to be more pronounced for lower impact angles (Fig. 2). These large differences can be explained by the fact that the specific energy of a collision \(Q_R\) (see Sect. 4.5) is also a functionFootnote 5 of \(\gamma \) and is roughly doubled when going from \(\gamma \) = 1:9 to 1:2 (cf. Fig. 7). In addition geometry comes into play, because the smaller the projectile, the more it is affected relative to the target, but small projectiles have only small water inventories to loose (for an initially equal wmf), while the target retains much of its volatile inventory.
For collisions in the hit-and-run regime however, not only the combined volatile losses, but rather individual ones, as well as transfer between the colliding bodies are of interest. Figure 3 illustrates outcomes for the \(M_{{\mathrm {tot}}} = 10^{23}\) kg scenarios and shows both bodies before (light gray circles and impact geometry) and after the collision (colored circles). Most interesting in this plot are the big differences between the larger and the smaller one of the colliding pair. The target barely looses neither mass nor large amounts of water, except for low impact angles and high velocities, and even then only if the projectile has almost the same size. Disruption of a larger object by the impact of a smaller one was found to be very difficult once bodies grow large enough (e.g., Asphaug 2010) and indeed in our scenario set target disruption happens only in high-velocity head-on collisions with large impactors. The projectile on the other hand is typically much more affected. Except for slow and oblique scenarios, it looses considerable amounts of mass, and especially of water, often above 50% and in some rather high-velocity impacts up to 90%. In addition, we also did some exploratory simulations with \(\alpha = 75^\circ \) and \(90^\circ \), which can already be considered a tidal collision, but water losses in these cases are negligible. Our results also confirm those of earlier studies (e.g., Marcus et al. 2010), namely that the volatile fraction practically never increases in giant collisions between similarly composed objects, but always decreases for both bodies.
To explore the more subtle consequences of hit-and-run, like to what proportions a post-collision fragment’s water inventory originated from projectile and target, we find it instructive to leave the target–projectile point of view and rather switch to a one-body perspective. In Fig. 5, which illustrates the effects of varying the main collision parameters, projectile and target water are highlighted in different colors. This visualizes compositional mixing (transfer) of projectile and target water (see also Fig. 6), as well as losses from the individual pre-collision inventories. Figure 4 illustrates the consequences for a single body when hit by a range of different impactors, smaller and larger ones. We denote the body of interest always as target and the impacting one as projectile, irrespective of which one is larger, and keep the definition \(\gamma = M_{{\mathrm {proj}}}/M_{{\mathrm {targ}}}\). The six panels in Fig. 4 correspond to the six (\(v/v_{{\mathrm {esc}}}, \alpha \)) parameter pairs enframed in Fig. 3 and exemplify the effects on a single body for common hit-and-run parameters. From the three graphs in each plot, the topmost one shows the post-collision mass and water content if both bodies initially have a wmf of 0.1. Not surprisingly water losses are small for \(\gamma < 1\) and strongly increase up to around 50% for larger projectiles \(\gamma > 1\), except for the calmest scenario (lower left panel). The transition from \(\gamma < 1\) to \(\gamma > 1\) is smooth, and no rapid increase in water losses—as one might expect—is found. The middle graphs in Fig. 4 represent the same collisions but accounting only for water initially on the target; hence, they represent the impact of an entirely dry projectile onto a 0.1 wmf target. The relatively small differences compared to the topmost graphs in most cases indicate only little transfer of water from projectile to target, even for large \(\gamma \gg 1\), where the projectile could in principle provide large amounts of water to the target due to its size. This is further emphasized in the bottom graphs, which correspondingly show the outcome if the target were initially dry. Interestingly, the target’s wmf (originating solely in projectile water) increases with \(\gamma \), peaks at relatively small, positive values of \(\gamma \) and decreases again for even larger projectiles (with even larger volatile contents). Except for rather central \(\alpha = 30^\circ \) impacts the highest transferred water content is only around 1/10 of the (much larger) impactor’s wmf. In the \(\alpha = 30^\circ \) collisions, especially in the low-velocity \(v/v_{{\mathrm {esc}}} = 1.5\) case, there is considerably more transfer of volatiles, and toward \(\gamma \) = 2:1 transfer from the projectile to the target becomes efficient and the combined wmf seems to even increase again. However, obviously this situation occurs only for the lowest velocity hit-and-run encounters, and indeed, this scenario is on the edge to the graze-and-merge regime (Leinhardt and Stewart 2012), indicated by post-collision velocities barely above \(v_{{\mathrm {esc}}}\). For all larger mass ratios and thus lower collision energies, the outcome is not hit-and-run anymore (and therefore not plotted). Hence, it seems that transfer of volatiles between similarly composed bodies in hit-and-run events has a rather minor influence compared to collisional erosion.
Dependence on total mass
While the bulk of this study focuses on collisions of \(\sim \) Moon-sized embryos (\(M_{{\mathrm {tot}}} = 10^{23}\) kg) we also considered different masses between \(10^{22}\) and \(10^{25}\) kg, to study the influence of the total mass on the general collision outcome and especially on vaporization of volatile material (see Sect. 4.5). We already investigated the dependence of similar-sized collision outcomes on total mass in Burger and Schäfer (2017) in detail and will therefore limit ourselves to some important remarks in this paper. The results presented in Fig. 7 indicate that for the larger body the outcome is very similar over the whole investigated range of masses—their volatile inventory remains largely untouched (upper panels). The situation for the smaller body is substantially different (lower panels). For the three simulated mass ratios final wmf are only in the \(\gamma \) = 1:2 case relatively independent of total mass, but show large variations for \(\gamma \) = 1:9, ranging from 0.75 down to only 0.27, and for \(\gamma \) = 1:20 even from 0.79 down to basically zero. The main reasons for these differences are the transition from subsonic to supersonic collision velocities with increasing mass (for other parameters equal), and increasing gravitational compression toward higher masses, resulting in more compact objects with greater hydrostatic pressures to be partly released upon impact. This clearly shows that the total mass is a crucial parameter for stripping of volatiles from the smaller body in a hit-and-run encounter, and at least this aspect of similar-sized collisions can certainly not be assumed to be scale invariant (Asphaug 2010; Burger and Schäfer 2017).
Dependence on water amount and distribution
In order to check the influence of the chosen composition model, we performed additional simulation runs with entirely dry target bodies (with \(v/v_{{\mathrm {esc}}} = 2.5, \gamma \) = 1:9, \(M_{{\mathrm {tot}}} = 10^{23}\) kg and \(\alpha = 45^\circ \) and \(60^\circ \); cf. Table 1) and compared them to runs with otherwise equal parameters and our usual composition model with both bodies covered in water (ice). Naturally the overall post-collision water contents are lower now, but the amount transferred from the projectile to the target and the amount lost from the projectile are expected to be approximately equal and independent of the target’s precise composition. Our results confirm this with differences in wmf (and also in fragment masses and kinetics) around 20% or lower. A dry target consistently accretes more water (from the projectile) than a water-rich one and causes the projectile to loose a larger fraction of its initial volatile content. The projectile also looses more mass in general when colliding with a dry target instead of a water-rich one, where the difference is larger for the \(\alpha = 45^\circ \) case than for \(60^\circ \). We suspect that this behavior is an interplay between the higher density of basalt compared to water, which results in a larger resistance against impacting material, and a slightly different collision geometry, because a dry target is more compact than a volatile-rich one. The latter means not least a higher specific impact energy in the dry-target runs (e.g., in the \(\alpha = 45^\circ \) case about 5%, 1.27 vs. 1.33 MJ/kg), since all other parameters were kept constant. This is consistent with the higher losses in the dry-target run.
A point closely related to the above is the influence of the extent of the water layer. We repeated the \(v/v_{{\mathrm {esc}}} = 2.5, \alpha = 45^\circ , \gamma \) = 1:2, \(M_{{\mathrm {tot}}} = 10^{23}\) kg scenario with wmf of 5 and 20%, in addition to the standard 10% run (see Table 1) and found only relatively small deviations from the expectation that relative water losses and transfers are similar. This means, for instance, that the post-collision water content of the target is roughly twice as large for the 10% water scenario than for the 5% one and again approximately doubled for the 20% run. Considering all three scenarios, deviations are around 25% at most, but if only the 5% and 10% water runs are compared the differences reduce to 10% and less, suggesting a probable convergence toward increasingly thinner volatile layers. The general trend and the expected underlying reasons are the same as in the dry-target case above. Bodies with thinner water ice shell accrete more (from the other body), but also loose more water from their initial inventory, probably again due to slightly different specific impact energies (2.96 vs. 2.86 vs. 2.70 MJ/kg). Maindl et al. (2017) also studied the influence of different initial volatile contents and also found only small variations (\(\sim \) 10%) in relative water losses, in concordance with our results. These authors additionally considered water SPH particles randomly distributed inside the whole projectile body. We did not include such uniform distributions because there is strong evidence that bodies in the mass range considered here are probably largely differentiated. It is also yet unclear how such water inclusions (e.g., in hydrated minerals) can be accurately modeled, and how related and perhaps important effects like degassing due to pressure unloading can be included in a consistent way (but see, e.g., Asphaug et al. 2006). However, at least for collisions in the hit-and-run regime Maindl et al. (2017) found no large differences between randomly distributed water and spherical shell configurations in terms of water losses. The generally low dependence of final (relative) wmf on the extent and distribution of volatile inventories is an important result, which helps to safely reduce the dimensionality of the parameter space in simulations on water delivery. We discuss this further in Sect. 5.
Influence of material strength
The justification for usually modeling sufficiently large bodies as strengthless fluids is motivated by highly dominating gravitational stresses over material strength. Jutzi (2015) studied collisions between similar-sized bodies and found that including a realistic rheology is still necessary for 100 km bodies, and recent results using the same SPH code and material model (Burger and Schäfer 2017) have shown significant differences in fragment characteristics and also in water losses between solid-body simulations and (otherwise identical) purely hydrodynamic runs also for embryo-sized bodies. For a more comprehensive overview, we refer to the latter study and discuss the topic only briefly here, exemplified by two scenarios (see Table 1), which were computed again with the full solid-body model as outlined in Sect. 2. The results are generally in good agreement with their strengthless counterparts and differ by less than 20% for final wmf and losses, which is also consistent with the results of Burger and Schäfer (2017). Larger deviations of up to 50% are found only for the contribution of transferred volatiles (between projectile and target) to the final inventory. However, this is a more subtle process, and only a minor contribution to a fragment’s post-collision water budget compared to the retained amount (cf. Fig. 4); therefore, these relatively large variations are not surprising. These contributions by transferred water are always smaller in the solid scenarios than in the respective strengthless runs, probably because tensile and shear strength act against removal and subsequent transfer. It is yet unclear to what extent and for which aspects of giant collisions material strength becomes important. The large pressures in the interiors of sufficiently massive bodies change the behavior of geologic materials toward high viscosities and ductile, plastic flows (Holsapple 2009), and in general their rheology exhibits a complex dependence on stress, strain, strain rate, temperature and pressure. In addition, even fully damaged rubble pile material is often not strengthless, but can support considerable shear stresses. This makes the here-used von Mises yield criterion not an ideal choice, as already indicated in Sect. 2, since it does not consider pressure-dependent shear strength. A more sophisticated model for the calculation of shear strength of geologic materials has been developed, e.g., by Collins et al. (2004), who use a pressure-dependent yield strength for intact rock and a Coulomb dry-friction law for completely fragmented material. We suggest and plan a dedicated future study to clarify the influence of different rheology models also beyond sizes of the 100 km studied by Jutzi (2015), including also volatile material like water ice. In addition to these complexities, the physical state of volatile inventories prior to the collision is also uncertain, where, for instance, a considerable fraction might be molten, which would put the application of material strength into perspective. The behavior of real objects probably lies somewhere between that of a strengthless fluid and a fully solid body, and thus, these two models may be considered rather limiting cases, where further studies are necessary to clarify the necessity for certain material models.
Water vapor production
Once impact energies rise above the vaporization energy of water (ice), large-scale vapor production can be expected. Here we treat only vaporization caused directly by the impact and the further development of heat-redistribution, like melting or vaporization of ice by an impact-heated mantle, is not included. To exemplarily estimate the post-collision water vapor fraction, we ran scenarios with fixed \(v/v_{esc} = 2.5\) and \(\alpha = 45^\circ \) for several different total masses (and thus impact energies) between \(\sim \,\!M_{{\mathrm {Moon}}}/10\) and \(M_{{\mathrm {Earth}}}\) and for varying mass ratios of 1:2, 1:9 and 1:20 (see Table 1).
The results are summarized in Fig. 7, where the reduced-mass specific impact energy \(Q_R\) of the individual scenarios is also indicated. It is given by (Stewart and Leinhardt 2009)
$$\begin{aligned} Q_R = \frac{\mu \, v_0^2}{2\, M_{{\mathrm {tot}}}}, \end{aligned}$$
(4)
with the reduced mass \(\mu = M_{{\mathrm {proj}}} M_{{\mathrm {targ}}}/M_{{\mathrm {tot}}}\) and collision velocity \(v_0\) (see Fig. 1). Not surprisingly the water vapor fraction strongly increases with \(M_{{\mathrm {tot}}}\), and larger amounts of water vapor are only produced for energies greater than \(e_{{\mathrm {vap}}}\). At this threshold, around 10% of the water inventories are already vaporized on both large fragments, and roughly equal throughout the three investigated mass ratios (note the different y-axis scales). If considered as a function of \(M_{{\mathrm {tot}}}\) the water vapor content is a function of \(\gamma \) as well, because \(Q_R\) is also a function of \(\gamma \) (for all other parameters equal), as elaborated in Sect. 4.1 (see footnote 5), and there is certainly a strong correlation between the available energy and the amount of vaporization. The results in Fig. 7 indicate that water vapor production seems to scale indeed well with \(Q_R\), relatively independent of the mass ratio, well visible when comparing vapor fractions for specific \(Q_R\) values (like indicated by the vertical lines). Also the individual vapor fractions on the two largest fragments are surprisingly similar, also for smaller mass ratios. From the remaining water on the two large fragments after a hit-and-run roughly up to 40% can be vaporized for Moon to Mars-sized embryos, and up to 80% in collisions involving Earth-mass objects. These numbers, however, depend on the mass ratio (for a fixed total mass) and may also deviate significantly for other values of impact velocity and angle. Note that due to the limitations of the Tillotson eos the computed vapor fractions are rather rough estimates, as a first step indicating possible directions for future work.
Dependence on resolution
The resolution in SPH simulations is defined by the particle number. Genda et al. (2015) investigated the influence of resolution on the critical specific impact energy for disruption (where the largest post-collision fragment has half the total mass) for gravity-dominated bodies and found a factor of two difference between 50k and 5 million SPH particles, due to different efficiencies of kinetic energy dissipation. They conclude that approximate convergence is reached only for their highest resolutions. Especially low-density regions, like impact ejecta, are affected by differing particle numbers, where the evolution in such regions is often dominated by resolution instead of physics (Reinhardt and Stadel 2017; Genda et al. 2015). Another closely connected issue is correctly resolving shock waves, where about 10 particles are required in one dimension (e.g., Genda et al. 2015). While our standard resolution (100k) is sufficient for projectile and target diameters being always clearly above this threshold, the thickness of the water envelope alone is usually below it. For example, a single body made of \(n_{{\mathrm {part}}}=10^5\) particles and a wmf of 0.1 has a diameter \(\propto n_{{\mathrm {part}}}^{1/3}\) of \(\sim \) 57 particles, but a water shell thickness of only \(\sim \) 4 particles, while the latter figure is well above 10 for our highest resolution of 2.25 million.
To check the reliability of our results, we ran three selected scenarios (see Table 1) also with increased resolutions of 300k, 1 million and one with 2.25 million particles (in addition to the standard 100k runs). The outcome for several main quantities of interest as a function of particle number is plotted in Fig. 8 for a collision between an \(\sim \) Earth-sized and a \(\sim \) Mars-sized object, indicating approximate resolution convergence for most quantities. The large masses of the involved bodies (\(M_{{\mathrm {tot}}} = 10^{25}\) kg) result in a very energetic collision and thus in large-scale water vapor production (Sect. 4.5), ideal for clarifying the dependence on resolution for the purposes of our topic. In all three scenarios, the global outcomes (fragment masses and their kinetics) of runs with different resolutions show only minor deviations below 10%. Post-collision wmf of the largest fragment are even more accurate within only few %, and for the second largest fragment and the wmf transferred between projectile and target results are still within \(\sim \) 25% (cf. Fig. 8). Note that the outcomes of the 100k runs seem to give an upper limit for the second largest fragment’s wmf, meaning that resolution converged volatile stripping of the smaller of the colliding bodies is even more efficient than indicated by the 100k results. The situation for the water vapor fraction is twofold, with deviations of less than 10% for the largest fragment, and \(\sim \) 20% for the second largest one. A more detailed analysis of the latter showed that these values take particularly long to converge after the actual collision itself, since ongoing accretion of debris continues to dissipate energy, leading to further vaporization even after the two main fragments have clearly separated and the material bridge between them has largely dissolved (cf. Fig. 5). For the 2.25 million particles run, this quantity has still not converged at the end of the simulation time and is therefore not included in Fig. 8. We conclude that simulations with probably even higher resolutions would have to be ran for particularly long (simulated) times to finally clarify this issue.
The deviations for the different quantities described above can also be considered a rough error estimate of the presented results w.r.t. resolution convergence. The results confirm that shock acceleration and energy dissipation are already fairly well resolved in the 100k runs, also for the relatively thin (in terms of particle layers) water shells at this resolution. Albeit true resolution convergence is hard to proof these tests indicate that our results are in general within \(\sim \) 25% of this limit.
Comparison with collision outcome models
The most basic collision outcome model is perfect merging with conservation of linear momentum and the assumption of 100% retention of volatiles. This is certainly not realistic in most situations. Leinhardt and Stewart (2012) and Stewart and Leinhardt (2012) developed a comprehensive analytical model that distinguishes several collision outcome regimes, including partial accretion, erosion and hit-and-run. It has been included in N-body simulations and used in several studies on planet formation (e.g., Dwyer et al. 2015; Bonsor et al. 2015; Leinhardt et al. 2015). It is based on scaling laws to determine the mass of the largest collisional fragment \(M_{{\mathrm {lf}}}\) and also applies corrections for varying mass ratios as well as the reduced interacting mass in oblique collisions. To also track basic changes in bulk composition, they suggest to include a simple model for mantle stripping introduced by Marcus et al. (2010), which considers two idealized cases for the core mass: (1) \(M_{{\mathrm {core}}} = {\mathrm {min}}(M_{{\mathrm {lf}}}, M_{{\mathrm {core,proj}}}+M_{{\mathrm {core,targ}}})\), i.e., mantle is only added to the largest fragment once both cores are used up, and (2) either \(M_{{\mathrm {core}}} = M_{{\mathrm {core,targ}}} + {\mathrm {min}}(M_{{\mathrm {core,proj}}}, M_{{\mathrm {lf}}} - M_{{\mathrm {targ}}})\) on accretion (i.e., if \(M_{{\mathrm {lf}}} > M_{{\mathrm {targ}}}\)), or \(M_{{\mathrm {core}}} = {\mathrm {min}}(M_{{\mathrm {core,targ}}}, M_{{\mathrm {lf}}})\) for target erosion (i.e., if \(M_{{\mathrm {lf}}} < M_{{\mathrm {targ}}}\)). This means model (2) first adds projectile core material to the whole target in case of accretion, but removes material from the target (starting with the mantle) for erosion. To compute the actual change in composition, it is suggested to use the average of (1) and (2). For the second large survivor in hit-and-run events, they suggest to consider the reverse impact, where the projectile is hit by a hypothetical body consisting only of the part of the target that geometrically overlaps with the projectile, and to apply the above model to this (reversed) collision situation to determine compositional changes of the second largest fragment. Even though this model was not directly developed for volatile transfer and loss in hit-and-run collisions, but rather for the less subtle effects of major bulk compositional changes, we compare it to our numerical results. It turned out that it gives only a very crude estimation of the changes in water contents for scenarios like ours. While predictions for the target body are mostly at least in broad agreement with numerical results, those for the projectile are often very far off. Therefore, we have not included these predictions in the one-body perspective results (Fig. 4), but only in the combined view in Fig. 2, as disconnected and smaller but otherwise equal symbols for comparison. The predicted combined water losses are mostly much larger than the numerical results, mainly because the reverse impact is predicted much more destructive than it actually is, leaving the second largest fragment often entirely water-stripped in this model. We suspect that this is at least partly due to the geometry of a hit-and-run event, where the interacting fraction of the impacting body still grazes by the impacted one, which is likely to be less destructive than a more central collision with the same impacting mass. In addition, this model is based on absolute masses of the cores (which is everything except the water layer for our purposes) and the (predicted) largest fragment; thus, uncertainties increase the lower the amount of the material considered for stripping is. Also, taking a closer look at the components (1) and (2) and the analysis and impression of hit-and-run collisions (cf. Fig. 6), it seems that outcomes are typically rather close or even beyond predictions of component (2) instead of an average of (1) and (2), for both accretion of projectile material by the target and also for target erosion. Note also that the model can not be reasonably used for volatile transfer, for instance from a water-rich projectile to a dry target.