**4. Effects of our assumptions on the results**

As noted above we made a number of simplifying assumptions in our calculations that could affect our results. First, we assumed that the snowline remains at 5 A.U. no matter the mass of the nebula. However, since any likely accretion scenario for the Solar Nebula would have a mass considerably larger than the Hayashi Minimum Mass, the snowline for more massive nebulae would occur closer to the proto-sun. This would tend to increase the number of planetesimals containing ice and increase the ice content as a fraction of planetesimal mass for small bodies at 1 A.U. In fact Desch (2008) calculated that the snowline for a nebula 25 times the Hayashi Minimum Mass would occur at 2.5 A.U., well inside the outer asteroid belt. Under these conditions, some outer main belt asteroids would certainly contain significant quantities of ice in their interiors.

Second, we assumed that we could extend the results of Weidenschilling's (W97) numerical calculations from the Outer Planets region to the Terrestrial Planets region and that the efficiency for particulate aggregation would remain unchanged. We find that reasonable changes in the efficiency factor used in these calculations do not change our basic results that smaller planetesimals at 1 A.U. accreted in more massive nebulae contain more rock while larger bodies in lower mass nebulae contain much more ice. Certainly the detailed results are modified with changes to this factor; however, the uncertainty in the actual mass of the Solar Nebula is more important in determining the ice content of the planetesimals than is the exact value of the accretion efficiency factor employed in the calculations. We also use the same factor for the accretion of both icy and anhydrous dust. The relative sizes of the particles and the velocities of the collisions appear to be more important than the exact composition of the accreting material, but the modest experimental results that we have to date indicate that collisions between icy particles are more likely to result in sticking than are collisions between dry rocks and pebbles. Our calculations therefore may overestimate the efficiency of forming ice-free planetesimals.

Why Isn't the Earth Completely Covered in Water? 51

Second, although the models of Kokubo and Ida (2000) span only a very narrow ring within the nebula (a = 0.02 – 0.09 A.U.) the boundary conditions (see their section 3.2) that they apply to these calculations assume a free flow of planetesimals through the model annulus. In other words, as proto-planets grow from the population of planetesimals within an annulus, the model assumes a balance between the inward loss of planetesimals due to gas drag and those that flow into the accretion zone from the outer nebula such that the surface density of the accreting annular disk remains constant. Thus, while the growing protoplanets remain stationary in this scenario, the planetesimal population from which they accrete continuously flows in toward the sun due to gas drag. Again the ice to rock ratio

Finally, there is the possibility that some planetesimals could form on very short timescales due to turbulent-gas-driven gravitational instabilities. In turbulent eddies the local conditions for gravitational instability can be met (Johansen et al., 2006; 2007). The numerical simulations by Johansen et al. show the formation of Ceres-mass planetesimals in a few orbital periods. Also, chondrule-size particles can be concentrated in the low-vorticity regions of the disk (Ormel et al., 2008) and this can allow the formation of 50-100 km planetesimals on a short timescale due to the self-gravity of the chondrule clump. In both cases, the short timescales will prevent any significant radial migration. These mechanisms could easily produce relatively dry proto-planets if all of the components within the

While such processes would aggregate all of the mass of an individual planetesimal or proto-planet within a short timescale and from a very narrow range of heliocentric distances, the composition of such bodies will depend on the composition of the material that one would expect to be present at 1 A.U. while the composition of the proto-Earth would depend on the fraction of planetesimals that form via gravitational instabilities. Gravitational instabilities are unlikely to be the dominant process forming comets in the outer nebula as both the degree of MHD driven turbulence and the surface density of the disk are too low for efficient operation of this accretion mechanism. This argues that collisional aggregation processes that formed ever larger solid bodies that drifted sunward due to gas drag probably dominated in this regime (W97). If such processes dominated in the outer solar system, there is no reason to believe that this mechanism did not also operate at least to some extent in the inner solar nebula. In contrast, there are meteorite samples from asteroids that contained very little water, even at the time of their formation. As almost any sized body ending accretion near 3 A.U. would contain some ice if formed via the collisional-aggregation, gas-drag scenario, this provides evidence for the role of turbulent

accretion or gravitational instabilities in the production of some planetesimals.

We can make the simple approximation that planetesimals formed via gravitational instabilities at 1 A.U. always consist of rocky materials. If half of all planetesimals at 1 A.U. formed via this mechanism, then the ice fraction of materials accreting to form the proto-Earth shown in Table 1 would be reduced by a factor of 2. However, as gas drag mediated migration of meter-to-kilometer scale planetesimals will always occur to some degree, some fraction of the larger planetesimals formed via gravitational instabilities will contain ice that drifted inward within bodies that began to accrete beyond the snowline. While small bodies eventually lose their volatiles in the inner nebula, rapid gravitational accretion could trap considerable fractions of this ice in larger, more robust planetesimals before it was lost. Therefore unless all planetesimals at 1 A.U. formed via gravitational instability and unless

shown in Table 1 would apply to this population.

gravitational instability had equilibrated within the snowline.

Third, we assumed that the snowline represents a sharp compositional boundary in the nebula. Accretion entirely inside the snowline will never incorporate ice into the planetesimal under this assumption. However, in the current solar system there are numerous examples of short period comets making many passes inside the orbit of the Earth, and subsequent apparitions of these comets demonstrate that they continue to retain at least some water vapor over thousands of years. Comets are even known to make several passes through the solar corona without complete loss of the ice in their interiors. The early nebula between 1 and 10 A.U. was certainly more opaque to solar radiation than our modern solar system and was more densely populated by icy planetesimals. Our assumption of a sharp discontinuity in the availability of small icy bodies inside the snowline that might be incorporated into planetesimals, even ones formed by turbulent accretion or gravitational instabilities, certainly favors the formation of ice-free planetesimals.

On each occasion where we made an assumption to simplify our calculations while still using the basic results of Weidenschilling (W97), we tried to consistently err on the side of producing the largest fraction of ice-free planetesimals possible. In spite of our obvious bias in favor of such dry dusty bodies, we nearly always produced a population of ice-rich planetesimals at 1 A.U.

#### **Alternative accretion models**

Weidenschilling's (W97) manuscript describing his model for planetesimal (comet) aggregation acknowledges that as the total mass of the Solar Nebula increases, additional factors, such as gravitational instabilities and other collective effects could increase the efficiency of accretion. In another treatment of the formation of the terrestrial planets Kokubo and Ida (2000) find that the formation of proto-planets occurs as a two stage process. Runaway accretion first produces a mixed distribution of planetesimals and protoplanets (Kokubo and Ida, 1995). The proto-planets initially grow rapidly at the expense of the planetesimal population (Kokubo and Ida, 1996) until a small number of proto-planets have formed in the nebula. These proto-planets then grow much more slowly, entering the "oligarchic growth" stage (Kokubo and Ida, 1998) where the larger proto-planets actually grow more slowly than smaller ones. In this scenario, proto-planets with masses of 1026 g are formed within about 500,000 years at 1 A.U. (Kokubo and Ida, 2000) and thereafter maintain rough separations greater than 5 Hill radii from one another as they continue to accrete planetesimals from their surroundings. These proto-planets form rapidly from young planetesimals that have not had sufficient time to lose any ice that may have been sequestered within, and such proto-planets are sufficiently large that they should retain a reasonable fraction of their accreted volatile complement.

The oligarchic growth stage from proto-planet to planet is a result of the larger bodies accreting materials from their immediate vicinity. While casual readers of these papers might believe that because these proto-planets incorporate materials from only a very narrow range of heliocentric distance, this must imply that the proto-planet that eventually grew to become the Earth could only incorporate rocky material. This impression is incorrect for two reasons. First, the initial distribution of planetesimals from which the population of proto-planets evolved was shaped by gas drag as the planetesimals accreted from the disk. Thus the population of planetesimals from which a proto-planet at 1 A.U. accreted should have been similar to that shown in Table 1.

50 Space Science

Third, we assumed that the snowline represents a sharp compositional boundary in the nebula. Accretion entirely inside the snowline will never incorporate ice into the planetesimal under this assumption. However, in the current solar system there are numerous examples of short period comets making many passes inside the orbit of the Earth, and subsequent apparitions of these comets demonstrate that they continue to retain at least some water vapor over thousands of years. Comets are even known to make several passes through the solar corona without complete loss of the ice in their interiors. The early nebula between 1 and 10 A.U. was certainly more opaque to solar radiation than our modern solar system and was more densely populated by icy planetesimals. Our assumption of a sharp discontinuity in the availability of small icy bodies inside the snowline that might be incorporated into planetesimals, even ones formed by turbulent accretion or gravitational instabilities, certainly

On each occasion where we made an assumption to simplify our calculations while still using the basic results of Weidenschilling (W97), we tried to consistently err on the side of producing the largest fraction of ice-free planetesimals possible. In spite of our obvious bias in favor of such dry dusty bodies, we nearly always produced a population of ice-rich

Weidenschilling's (W97) manuscript describing his model for planetesimal (comet) aggregation acknowledges that as the total mass of the Solar Nebula increases, additional factors, such as gravitational instabilities and other collective effects could increase the efficiency of accretion. In another treatment of the formation of the terrestrial planets Kokubo and Ida (2000) find that the formation of proto-planets occurs as a two stage process. Runaway accretion first produces a mixed distribution of planetesimals and protoplanets (Kokubo and Ida, 1995). The proto-planets initially grow rapidly at the expense of the planetesimal population (Kokubo and Ida, 1996) until a small number of proto-planets have formed in the nebula. These proto-planets then grow much more slowly, entering the "oligarchic growth" stage (Kokubo and Ida, 1998) where the larger proto-planets actually grow more slowly than smaller ones. In this scenario, proto-planets with masses of 1026 g are formed within about 500,000 years at 1 A.U. (Kokubo and Ida, 2000) and thereafter maintain rough separations greater than 5 Hill radii from one another as they continue to accrete planetesimals from their surroundings. These proto-planets form rapidly from young planetesimals that have not had sufficient time to lose any ice that may have been sequestered within, and such proto-planets are sufficiently large that they should retain a

The oligarchic growth stage from proto-planet to planet is a result of the larger bodies accreting materials from their immediate vicinity. While casual readers of these papers might believe that because these proto-planets incorporate materials from only a very narrow range of heliocentric distance, this must imply that the proto-planet that eventually grew to become the Earth could only incorporate rocky material. This impression is incorrect for two reasons. First, the initial distribution of planetesimals from which the population of proto-planets evolved was shaped by gas drag as the planetesimals accreted from the disk. Thus the population of planetesimals from which a proto-planet at 1 A.U.

favors the formation of ice-free planetesimals.

reasonable fraction of their accreted volatile complement.

accreted should have been similar to that shown in Table 1.

planetesimals at 1 A.U.

**Alternative accretion models** 

Second, although the models of Kokubo and Ida (2000) span only a very narrow ring within the nebula (a = 0.02 – 0.09 A.U.) the boundary conditions (see their section 3.2) that they apply to these calculations assume a free flow of planetesimals through the model annulus. In other words, as proto-planets grow from the population of planetesimals within an annulus, the model assumes a balance between the inward loss of planetesimals due to gas drag and those that flow into the accretion zone from the outer nebula such that the surface density of the accreting annular disk remains constant. Thus, while the growing protoplanets remain stationary in this scenario, the planetesimal population from which they accrete continuously flows in toward the sun due to gas drag. Again the ice to rock ratio shown in Table 1 would apply to this population.

Finally, there is the possibility that some planetesimals could form on very short timescales due to turbulent-gas-driven gravitational instabilities. In turbulent eddies the local conditions for gravitational instability can be met (Johansen et al., 2006; 2007). The numerical simulations by Johansen et al. show the formation of Ceres-mass planetesimals in a few orbital periods. Also, chondrule-size particles can be concentrated in the low-vorticity regions of the disk (Ormel et al., 2008) and this can allow the formation of 50-100 km planetesimals on a short timescale due to the self-gravity of the chondrule clump. In both cases, the short timescales will prevent any significant radial migration. These mechanisms could easily produce relatively dry proto-planets if all of the components within the gravitational instability had equilibrated within the snowline.

While such processes would aggregate all of the mass of an individual planetesimal or proto-planet within a short timescale and from a very narrow range of heliocentric distances, the composition of such bodies will depend on the composition of the material that one would expect to be present at 1 A.U. while the composition of the proto-Earth would depend on the fraction of planetesimals that form via gravitational instabilities. Gravitational instabilities are unlikely to be the dominant process forming comets in the outer nebula as both the degree of MHD driven turbulence and the surface density of the disk are too low for efficient operation of this accretion mechanism. This argues that collisional aggregation processes that formed ever larger solid bodies that drifted sunward due to gas drag probably dominated in this regime (W97). If such processes dominated in the outer solar system, there is no reason to believe that this mechanism did not also operate at least to some extent in the inner solar nebula. In contrast, there are meteorite samples from asteroids that contained very little water, even at the time of their formation. As almost any sized body ending accretion near 3 A.U. would contain some ice if formed via the collisional-aggregation, gas-drag scenario, this provides evidence for the role of turbulent accretion or gravitational instabilities in the production of some planetesimals.

We can make the simple approximation that planetesimals formed via gravitational instabilities at 1 A.U. always consist of rocky materials. If half of all planetesimals at 1 A.U. formed via this mechanism, then the ice fraction of materials accreting to form the proto-Earth shown in Table 1 would be reduced by a factor of 2. However, as gas drag mediated migration of meter-to-kilometer scale planetesimals will always occur to some degree, some fraction of the larger planetesimals formed via gravitational instabilities will contain ice that drifted inward within bodies that began to accrete beyond the snowline. While small bodies eventually lose their volatiles in the inner nebula, rapid gravitational accretion could trap considerable fractions of this ice in larger, more robust planetesimals before it was lost. Therefore unless all planetesimals at 1 A.U. formed via gravitational instability and unless

Why Isn't the Earth Completely Covered in Water? 53

nearly twice as massive if much of the incoming ice remained trapped within the growing

The composition of the rocky component of the planetesimals formed via gas-drag mediated accretion should be roughly chondritic. There is no mechanism for metal-silicate fractionation to operate on the dust grains and boulders that would be accreted via this mechanism. Although the overall composition of the planetesimals formed in this scenario bear more resemblance to what we currently call comets than to modern asteroids, for reasonable values of the nebular mass, the majority of the water accreted into these planetesimals originates in the inner solar system within a few A.U. of the snowline. For this reason, the planetesimals would not be expected to have the high D/H ratios or any significant content of volatile

As both the refractory composition of the planetesimals and the isotopic composition of the water would be "normal" when compared to typical models for the formation of the Earth, the only real compositional difference between the scenario described above and current models for the origin of the terrestrial planets is in the total quantity of water that might have been accreted. While current models often require the delivery of water at the end of the accretion process, this scenario requires the loss of water from the proto-Earth to be

We do not have samples of the population of planetesimals that accreted to form the terrestrial planets in our modern meteorite collection [Drake and Righter, 2002]. Such planetesimals would have lost their ice and much of their water of hydration several billion years ago [Nuth, 2008]. The residual dehydrated body that began with more ice than dust and thus contained a smaller radioactive heat source than that which produced the large scale melting and differentiation of Ceres, Vesta and other asteroids would also be much more fragile than such solid rocks, much like loosely compressed sandstone. Collisional processes over the lifetime of the solar system would have gradually reduced the surviving number of these fragile bodies to an insignificant fraction of the asteroid population. It is therefore very likely that we do not have any representative samples of the planetesimal population that contributed to the

We expect that large quantities of water may have been lost from the growing proto-Earth due to impact induced heating, especially considering the lower escape velocity of the less massive, but rapidly growing protoplanet. We must also assume that the rocky terrestrial interior would remain at least fully saturated by water dissolved within the rocks and magma. In fact, given the overburden and likely difficulty of escape to the surface, we would expect that water vapor would become supersaturated within the proto-planet, and that any terrestrial proto-planet in the late stages of accretion would have a thick, watervapor-laden atmosphere that should undergo some loss of water back to space. In the case of the Earth it is likely that this entire atmosphere, as well as any nascent hydrosphere, was lost during the impact of the Mars-scale body that formed the Moon [Cameron and Benz, 1991; Canup and Asphaug, 2001; Canup, 2004]. In addition, such a large impact would dehydrate a significant fraction of the terrestrial mantle as well as virtually all of the material from the impactor that might fall back onto the surface of the Earth. The Late Heavy Bombardment would have further dehydrated the terrestrial crust and uppermost

protoplanet, on its very wet surface, or within its massive, water - rich atmosphere.

organic materials found in modern Kuiper-belt or Oort cloud comets.

formation of the terrestrial planets in our modern meteorite collections.

compatible with the composition of the modern Earth.

**Composition of planetesimals** 

**Loss of volatiles from the Earth** 

there were no small bodies present at 1 A.U. that began accretion beyond the snowline to be incorporated into these planetesimals, then the proto-Earth would have accreted considerably more water than is assumed in models that begin with planetesimals of chondritic composition.
