THE EFFECT OF PLANETS BEYOND THE ICE LINE ON THE ACCRETION OF VOLATILES BY HABITABLE-ZONE ROCKY PLANETS

Oceans cover more than two-thirds of our planets surface, and water as well as other volatile compounds are the dominant constituents of living organisms. However, by cosmic standards, Earth is highly deficient in volatiles. The condensed component of a solar composition mixture that is cool enough for all the H₂O to be in solid form is ≳50% ice by mass. In contrast, the Earth's oceans and other near-surface reservoirs represent only 0.03% of our planet's mass, with several times this amount of water thought to lie in the mantle (Marty & Yokochi 2006). Nonetheless, the Earth was able to accrete enough water and other volatile constituents, such as carbon and nitrogen, to support life as we know it. Understanding where these volatiles originated, and how they made their way to Earth, is important in determining the likelihood that life exists beyond our solar system.

The region of the disk where Earth now resides was too hot for water ice to have condensed during its formation, therefore, the bulk of Earth's water must have originated from other reservoirs. The leading theories on the origin of Earth's water focus on icy comets and water-rich asteroids as the main sources. Comparisons of the isotopic deuterium to hydrogen (D/H) ratio measured in Earth's oceans, atmosphere, and present-day mantle (Lecuyer et al. 1998) and the D/H ratio measured in meteorites and comet spectra have provided valuable clues used to constrain these theories.

The contribution of water from a bombardment of comets is thought to be limited to ≲10% of the Earth's crustal water (Morbidelli et al. 2000, 2012; Marty 2012). These limitations were partially based on the D/H ratios measured from several comet samples that were found to be more than double the D/H ratio of water found on Earth (Balsiger et al. 1995; Bockelée-Morvan et al. 1998; Eberhardt et al. 1995; Meier et al. 1998). The recent discovery of comet Hartley 2 with an Earth-like D/H ratio (Hartogh et al. 2011) sparked new interest in comets as viable sources of Earth's water. However, Alexander et al. (2012) points out that Earth would have accreted entire comets, not just cometary ice, which have compositions that are more deuterium-rich than water due to large amounts of organic material. Despite these developments, the more serious problem that remains is that the collision probability of comets with Earth is very low (Morbidelli et al. 2000), most likely too low to provide the bulk of water collected by Earth.

The best explanation for the origin of Earth's water is that water-rich chondritic planetary embryos formed in the outer asteroid region and were perturbed inward during Earth's formation (Morbidelli et al. 2000). Geochemical data from meteorite samples have uncovered a rough correlation between water content and the heliocentric distance of the disk from which they are thought to have originated. Enstatites and ordinary chondrites from the inner asteroid belt (∼1.8–2.8 AU) tend to be dry (Fornasier et al. 2008; Binzel et al. 1996), whereas carbonaceous chondrites from the middle and outer asteroid belt (approximately 2.5–4 AU) are relatively water-rich (up to ∼20% in mass; Mason 1963). The D/H ratio in Earth's oceans is nearly identical to the mean D/H ratio found in carbonaceous chondrites (Dauphas et al. 2000), supporting the outer asteroid region as the primary source of Earth's water. In addition, the relative abundances of hydrogen, carbon, and noble gases on Earth have been found to be roughly chondritic (Marty 2012). For our dynamical analysis herein, we adopt the model that chondritic material from the outer asteroid region is the principal source of Earth's volatiles.

Giant planets, which likely formed prior to the epoch of terrestrial planet formation that we model herein (Lissauer 1987; Lissauer et al. 2009; Movshovitz et al. 2010), have long been thought to be crucial factors in the induction of the radial mixing among growing protoplanets that is needed for water delivery. Numerous simulations of the accretion of planetesimals from volatile-rich regions of protoplanetary disks by terrestrial planets have been performed (Raymond et al. 2004, 2005a, 2005b, 2006a, 2006b, 2007a, 2007b; Raymond 2006). These studies included various different disk surface density profiles, star masses, and the (in many cases large) influences that varying these parameters have on water content of the planets that are ultimately formed. Giant planets, exterior to the terrestrial region around low mass stars, were found to reduce accretion timescales, leading to typically drier terrestrial planets (Raymond et al. 2005b). High-resolution (large initial number of planetesimals) simulations found that giant planet eccentricities have a large influence on the amount of water delivered to terrestrial planets (O'Brien et al. 2006; Raymond et al. 2009). Simulations that include a solar-type stellar companion show similar results (Haghighipour & Raymond 2007), as expected. However, simulations of accretion in binary star systems are limited due to the much larger parameter space (stellar masses and orbits) available.

In this work, we investigate the effects of different-sized planets in Jupiter's orbit on the accretion of volatiles by terrestrial planets in or near the habitable zone of a Sun-like star during the late stages of planet formation. We first study the case of planet formation around an isolated star with no distant companions perturbing the system. We then perform analogous simulations but include a planet of mass 1 M_⊕, 10 M_⊕, or 1 M_J on an initial orbit comparable to Jupiter's current orbit (semimajor axis a = 5.2 AU and e = 0.05). We examine two additional variations of systems that include a Jupiter-like planet: Jupiter on a circular orbit (e = 0) and Jupiter with e = 0.05 with the addition of a Saturn-like planet (a = 9.5 AU and e = 0.05).

Our N-body simulations begin at the epoch of planet formation in which planetesimals and planetary embryos have already formed in a disk, along with any giant planets, and the gas in the disk has been dispersed. We examine two different models for the water distribution in the disk and follow the accretion evolution of the bodies for 1 Gyr. Our approach employs moderate-resolution simulations that have sufficiently modest computational requirements, allowing us to perform enough simulations to disentangle effects of the companion body from stochastic variations, which are important aspects of terrestrial planet growth. Although these models cannot provide ab initio estimates of the water accreted by terrestrial planets, models of this type are well suited for comparing the relative amounts of water accreted by terrestrial planets with different outer planet companions perturbing the system. Our results are presented in a manner that allows for the incorporation of any model of the distribution of volatiles within the disk, provided these volatiles do not substantially alter the mean densities of the bodies.

Section 2 describes our initial conditions and numerical model. Section 3 presents the results of our accretion simulations and the volatile inventory of the final planetary systems that form, and we summarize our results in Section 4.

Chambers (2001) found that numerical simulations of the final phases of terrestrial planet growth, which began with a bimodal mass distribution consisting of many Mars-sized embryos embedded in a disk of Moon-sized planetesimals, yielded configurations similar to the inner solar system in many respects. Our simulations begin at this epoch and we follow the evolution of embryos and planetesimals (with a 1:10 mass ratio) as they collide and form into terrestrial planets. Outer planets, if included, are assumed to have already formed. Our model begins with a total disk mass of 4.85 M_⊕ and is composed of 26 embryos, each with an initial mass of 0.0933 M_⊕ (2.8 × 10⁻⁷ M_☉) and 260 planetesimals of mass 0.00933 M_⊕ (2.8 × 10⁻⁸ M_☉). All bodies are assumed to have a density of 3 g cm⁻³.

The disk extends from 0.35 AU to 4 AU from the Sun with a surface density of solids that varies as a^−3/2. The embryos and planetesimals each begin on nearly circular (0 ⩽ e ⩽ 0.01) and coplanar (0° ⩽ i ⩽ 05) orbits, and the angular orbital elements (argument of periastron, longitude of ascending node and mean anomaly) were selected at random between 0°–360°. The same random set was used for all simulations apart from the minuscule variations described below.

Simulations have been performed using a similar bimodal disk around the Sun (Chambers 2001; Quintana et al. 2002) and in binary star systems (Quintana et al. 2002, 2007; Quintana & Lissauer 2006, 2010). However, the disks in those studies contained a smaller number of embryos (14) and planetesimals (140) and extended out to only 2 AU from the central star or stars. By extrapolating the disk beyond the snow line (the region in the disk where temperatures are low enough for ice condensation, which is near ∼2.5 AU around a solar-type star such as that used in our simulations), we can examine the dynamics and radial mixing of potentially volatile-rich planetesimals and embryos formed beyond this snow line.

The initial water content in our standard disk was chosen to match that used in simulations performed by Raymond et al. (2004). A step distribution was used in which bodies inside of 2 AU were given a water mass fraction (WMF) of 0.001%, those with 2–2.5 AU were given WMF = 0.1%, and those beyond 2.5 AU were given WMF = 5%. Although the distribution of H₂O and volatiles in a protoplanetary disk depends on numerous factors (including properties of the molecular cloud from which the star and disk system formed, along with masses, orbits, and formation timescales of bodies in the disk and of any stellar or planetary companions), this step disk distribution was chosen as an approximation based on meteorite data as described in Section 1. To quantify the water that the planets accrete, we define a unit of 1 M_ocean = 1.5 × 10²⁴ g = 2.5 × 10⁻⁴ M_⊕ to be an approximation of the mass of water in all of Earth's oceans. The amount of H₂O below the Earth's surface is not well constrained, but typical estimates are several M_ocean (Marty 2012). The total amount of water in our initial disk is ∼340 M_ocean.

We also examine a second disk model that has the same mass distribution and total water content, but the water is distributed among the bodies in the disk using a smooth power-law function. To compute this function, we kept the water content at the inner edge of the disk the same (WMF = 0.001% for the innermost planetesimal) and then solved for the exponent, p, in the following function in order to keep the total amount of water equal to that contained in the step disk model:

$$\begin{eqnarray} &&\rm {\rm {WMF}}({a}) = \rm {\rm {WMF}}({a}_{{\rm in}}) \times \left(\frac{{a}}{{a}_{{\rm in}}}\right)^p, \end{eqnarray} \tag{ 1 }$$

where a_in is the semimajor axis of the innermost body, a is the semimajor axis for a given embryo/planetesimal, and p = 3.741. Note that we neglect any effects of H₂O on the densities in order to facilitate the scaling of results. Alternative disk water distributions can then be examined without having to run additional accretion simulations.

Figure 1 shows the distribution of mass and water for both disk models (which we refer to as "step disk" or "power-law disk"). Here, and in subsequent figures, the symbol size of the embryos and planetesimals are proportional to their physical size. The symbol colors represent their fraction of water by mass on a scale where red bodies are dry (log(WMF) = −5) and blue bodies are water-rich (log(WMF) = −1.3). The top left panels of Figures 2 and 3 (described in the following section) show a view of the initial water distribution in the a–e plane for both disk models.

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We use the Mercury integration package to follow the evolution of all bodies in the disk subject to mutual gravitational interactions and inelastic collisions (perfect accretion) for 1 Gyr. The collisional history is tracked by recording the mass and orbital parameters involved in each impact. The larger body in a collision is taken to be the target, which "grows" by collecting the mass of the impactor, and the mass and orbit of the impactor are no longer recorded after the impact time. We keep track of the semimajor axis (which provides information on the water content) of all impactors that a final planet accretes. If a collision involves two bodies of the same mass (such as two planetesimals), the body with the smaller semimajor axis is taken to be the target.

To account for the stochastic nature of N-body systems with close encounters, five or six simulations were performed for each configuration with very small changes in the initial conditions: a single planetesimal near 1 AU was displaced by 1–5 m along its orbit prior to the integration. In all of our simulations, the mass of the primary star was 1 M_☉, and the mass of the planetary companion at 5.2 AU, if included, ranged from 1 M_⊕ to 1 M_J. We present our results in the next section.

The accretion evolution of a simulation with Jupiter and Saturn, both on initial orbits having e = 0.05, is shown in Figures 2 and 3. The only difference between these figures is the initial H₂O distribution in the disk (step or power-law disk). Each panel shows the semimajor axes and eccentricities of the bodies in the disk for a given integration time. This simulation, which formed three planets within 1.5 AU along with a single outer planetesimal, was chosen from the set of Sun–Jupiter–Saturn runs because it produced the most Earth-like planet in terms of mass (0.9 M_⊕) and orbit (1 AU). Herein, we define a "planet" as a body that grew at least as massive as the planet Mercury (∼0.06 M_⊕), which includes any single embryo or a body consisting of at least seven planetesimals. Note that planets can be smaller or less massive than this (Barclay et al. 2013), but we keep this prescription for simplicity and comparison with our own solar system.

The planet that formed near 1 AU accreted 39 M_ocean of water from the step disk (Figure 2) and 19 M_ocean from the power-law disk (Figure 3). The planets on either side of this, however, were very dry (<0.1 M_ocean) when formed from the step disk and only moderately wet (<4 M_ocean) in the power-law disk case.

A simulation of the step disk around the Sun, with no outer planets perturbing the system, is shown in Figure 4. Note that the semimajor axis scale is nearly twice that shown in Figures 2 and 3. Eight planets formed between 0.5–7 AU from the Sun, and an additional 47 planetesimals remained in this system out to 28 AU. Five of the planets accreted over 10 M_ocean and three formed moderately wet with several M_ocean. Similar water contents were found in the final planets when the step disk was replaced with the power-law water distribution (not shown).

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The inclusion of outer giant planets perturbs more mass out of the system and reduces accretion timescales. As shown in Figures 2–4, the final planets are formed within 100–200 Myr when Jupiter/Saturn are included, whereas bodies are still actively accreting throughout the 1 Gyr Sun-only simulations. These results are consistent with previous simulations of terrestrial planet formation (Chambers 2001; Quintana & Lissauer 2006; Quintana et al. 2002). It is clear that giant planets have a large influence on the dynamics of terrestrial planet formation. Their influence on water delivery to the terrestrial region is discussed further below.

3.1. Final Planetary Systems

Figures 5–8 present the final systems that formed in simulations that included Jupiter and Saturn (Figure 5), a 10 M_⊕ planet (Figure 6), a 1 M_⊕ planet (Figure 7), and around an isolated star (Figure 8). Note the expanded range in semimajor axis shown in Figures 6–8 (a < 10 AU) compared to that of Figure 5 (a < 5 AU). To account for the stochastic nature of these N-body systems, five or six integrations were performed for each configuration, keeping all of the initial conditions the same except for a 1–5 m shift of planetesimal prior to the integration. The only difference between the left and right halves of the figures is the initial distribution of H₂O in the disk: panels in the left columns show results from a step disk WMF distribution and those in the right columns show systems that formed from the smooth power-law WMF disk. The colors and symbols are as described in Figure 2, and the relative size of Earth and Mercury are shown in the legend for comparison (here, Earth is given a conservative H₂O estimate of 10 M_ocean). The final systems formed from the two additional sets of simulations that included Jupiter (either on an e = 0 or e = 0.05 initial orbit) without Saturn are not shown, but the results are presented in Tables 1 and 2 and discussed in this section.

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Table 1. Statistics for Final Planetary Systems

Run	Np	Nm	mp	Sr	Np	Nm	mp	$m_{l_\star }$	$m_{l_\infty }$
	(a < 2 AU)	(a < 2 AU)	(a < 2 AU, %)		(a > 2 AU)	(a > 2 AU)	(a > 2 AU, %)	(%)	(%)
Run0a	3	0	54.6	0.67	2	50	43.4	1.0	1.0
Run0b	3	0	53.7	0.75	5	47	42.1	2.7	1.5
Run0c	3	1	60.2	0.56	3	52	37.5	0.8	1.5
Run0d	3	0	39.8	0.53	4	45	56.5	2.7	1.0
Run0e	3	0	59.2	0.58	4	38	37.3	1.6	1.9
$\bf Run0_{ave}$	3.0	0.2	53.5	0.62	3.6	46.4	43.4	1.8	1.4
Run1a	3	0	57.3	0.67	5	48	36.2	3.3	3.2
Run1b	3	0	64.8	0.58	3	41	21.2	1.5	12.5
Run1c	2	1	47.5	0.58	4	35	42.7	2.3	7.5
Run1d	2	0	50.6	0.71	5	45	44.6	2.5	2.3
Run1e	2	0	42.5	0.56	5	45	43.3	6.2	8.0
$\bf Run1_{ave}$	2.4	0.2	52.5	0.62	4.4	42.8	37.6	3.2	6.7
Run10a	3	0	55.6	0.71	2	15	14.8	1.7	27.9
Run10b	3	0	50.8	0.63	4	7	26.2	1.5	21.5
Run10c	4	0	62.1	0.59	5	2	10.6	1.3	26.0
Run10d	3	0	56.5	0.55	3	2	14.6	1.5	27.4
Run10e	2	0	45.4	0.52	2	2	24.6	3.7	26.3
$\bf Run10_{ave}$	3.0	0.0	54.1	0.60	3.2	5.6	18.2	1.9	25.8
RunJ0a	2	0	54.6	0.69	2	0	6.9	3.3	35.2
RunJ0b	3	0	60.4	0.54	1	0	2.3	1.3	35.9
RunJ0c	3	0	48.5	0.45	1	1	9.8	6.3	35.4
RunJ0d	4	0	56.9	0.65	1	1	2.3	4.4	36.3
RunJ0e	2	0	38.8	0.65	1	0	19.4	2.9	38.8
RunJ0f	2	0	52.7	0.65	1	0	7.1	3.5	36.7
$\bf RunJ0_{ave}$	2.7	0.0	52.0	0.61	1.2	0.3	8.0	3.6	36.4
RunJa	3	0	47.3	0.39	1	0	2.3	10.2	40.2
RunJb	3	0	49.4	0.59	0	0	0.0	8.8	41.7
RunJc	2	0	48.1	0.57	1	0	6.7	10.6	34.6
RunJd	3	0	48.5	0.31	2	0	8.5	6.0	37.1
RunJe	3	0	44.2	0.55	1	0	1.9	7.7	46.1
RunJf	4	0	51.9	0.63	1	0	4.4	8.3	35.4
$\bf RunJ_{ave}$	3.0	0.0	48.2	0.51	1.0	0.0	4.0	8.6	39.2
RunJSa	3	0	46.5	0.55	1	0	1.9	14.5	37.1
RunJSb	2	0	42.3	0.50	1	1	2.3	21.1	34.3
RunJSc	3	0	44.8	0.46	0	1	0.2	24.4	30.6
RunJSd	3	0	45.8	0.35	1	0	1.9	21.9	30.4
RunJSe	4	0	41.2	0.35	1	2	2.3	21.1	35.4
RunJSfx	3	0	44.8	0.34	0	0	0.0	21.3	33.9
$\bf RunJS_{ave}$	3.0	0.0	44.2	0.43	0.7	0.7	1.4	20.7	33.6

Note. Bold indicates the average of each set.

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Table 2. Final Planets with M_f > 0.5 M_⊕ and 0.72 AU <a_f < 1.52 AU

Run	Planet	Mf	a	e	i	$\bf {M}_{\rm {\rm {H_{2}O}}}$	log(WMF)	$\bf {M}_{\rm {\rm {H_{2}O}}}$	$\bf \rm {log(WMF)}$	tEM	tPL
						Step	Step	Power Law	Power Law
		(M⊕)	(AU)		(°)	(Mocean)		(Mocean)		(Myr)	(Myr)
...	Earth	1.000	1.000	0.02	0	∼5	∼−2.9	∼5	∼−2.9	...	...
Run0a	EM06	1.0640	1.1367	0.08	2.55	11.8317	−2.5560	15.8749	−2.4283	89.8	948.1
Run0b	EM04	0.9707	0.9861	0.06	6.03	9.8877	−2.5940	16.5639	−2.3700	587.4	638.8
Run0c	EM03	0.9893	0.8139	0.02	5.83	13.2884	−2.4739	14.3262	−2.4413	42.1	931.6
Run0c	EM06	1.4373	1.5051	0.12	1.42	92.0972	−1.7954	91.2174	−1.7995	845.3	468.5
Run0d	EM02	1.1853	0.7614	0.07	4.32	31.8483	−2.1728	23.5678	−2.3036	94.1	574.8
Run0d	EM08	0.5787	1.2632	0.07	0.08	11.2948	−2.3116	12.5914	−2.2644	7.1	948.7
Run0e	EM03	1.3813	0.7960	0.03	7.15	24.5758	−2.3519	28.5346	−2.2870	90.7	683.5
$\bf Run0_{ave}$	...	...	...	...	...	27.8320	...	27.9198	...	...	...
Run1a	EM08	1.3533	1.1613	0.07	1.95	60.8474	−1.9492	55.9253	−1.9859	446.4	350.4
Run1b	EM13	0.8400	0.9964	0.01	6.49	13.2455	−2.4043	13.7572	−2.3878	9.3	500.0
Run1c	EM08	1.1293	1.2388	0.04	2.97	37.5928	−2.0798	42.3437	−2.0281	146.9	720.2
Run1d	EM11	1.2787	1.3307	0.16	4.67	128.0309	−1.6015	126.4799	−1.6068	847.0	628.6
Run1e	EM10	0.8680	1.2351	0.07	3.24	39.6704	−1.9421	24.0501	−2.1595	22.6	566.5
$\bf Run1_{ave}$	...	...	...	...	...	55.8774	...	50.5728	...	...	...
Run10a	EM03	0.9707	1.0072	0.08	4.14	22.6931	−2.2332	21.1531	−2.2638	139.0	101.7
Run10b	EM02	1.1480	0.7481	0.07	6.07	9.9318	−2.6650	13.9879	−2.5163	41.1	295.3
Run10c	EM07	0.9800	1.3014	0.11	1.80	47.3618	−1.9179	42.5852	−1.9640	52.9	195.9
Run10c	EM08	0.9613	0.7796	0.09	4.22	5.7113	−2.8282	7.1824	−2.7287	18.2	137.2
Run10d	EM03	0.9427	0.8229	0.06	3.86	7.6507	−2.6927	11.9026	−2.5008	25.2	206.6
Run10e	EM05	1.7827	1.0853	0.08	4.02	34.4407	−2.3161	37.6937	−2.2769	501.3	76.9
$\bf Run10_{ave}$	...	...	...	...	...	21.2982	...	23.6404	...	...	...
RunJ0b	EM08	1.7360	1.0839	0.0721	3.2170	32.0182	−2.3362	29.8345	−2.3669	142.6	119.3
RunJ0c	EM04	0.9427	0.9897	0.0285	6.7830	9.8866	−2.5814	14.3867	−2.4185	28.6	214.4
RunJ0d	EM02	0.6720	0.7468	0.0851	9.0870	26.2659	−2.0100	23.6281	−2.0560	21.3	331.4
RunJ0d	EM04	1.0267	1.1357	0.0523	5.6770	10.0748	−2.6103	13.7350	−2.4757	19.4	106.9
RunJ0e	EM02	1.3253	0.8828	0.0832	3.3210	48.7984	−2.0360	27.8365	−2.2798	81.2	59.3
RunJ0f	EM03	0.9333	1.4802	0.1014	4.6340	47.5447	−1.8950	51.8762	−1.8571	55.9	146.5
RunJ0f	EM04	1.6240	0.7384	0.1487	0.8150	10.2095	−2.8036	19.5181	−2.5222	186.0	84.9
$\bf RunJ0_{ave}$	...	...	...	...	...	26.3997	...	28.4658	...	...	...
RunJa	EM16	1.0360	1.5068	0.0690	0.7780	20.1828	−2.3124	26.9599	−2.1867	31.2	39.5
RunJb	EM03	1.0360	1.0336	0.0181	8.7380	22.9914	−2.2559	15.9460	−2.4148	413.8	95.1
RunJc	EM06	1.4840	1.2891	0.1753	5.7690	21.3647	−2.4438	23.4678	−2.4030	170.2	38.3
RunJd	EM03	0.5787	0.9071	0.0336	1.5680	0.0971	−4.3774	2.0838	−3.0456	2.4	51.5
RunJd	EM10	1.0920	1.3786	0.0384	2.3500	21.0534	−2.3170	19.7243	−2.3453	24.2	175.4
RunJe	EM03	0.9053	1.0559	0.0589	3.2300	0.1471	−4.3913	4.1579	−2.9400	51.8	86.0
RunJf	EM03	1.1573	0.7322	0.0572	6.0330	18.8940	−2.3892	10.2374	−2.6553	73.0	226.9
$\bf RunJ_{ave}$	...	...	...	...	...	14.9615	...	14.3710	...	...	...
RunJSa	EM05	1.1107	0.8915	0.06	0.34	2.7238	−3.2125	11.7314	−2.5783	51.9	40.4
RunJSb	EM10	0.8960	1.3564	0.14	2.79	0.4794	−3.8737	8.5170	−2.6241	37.1	96.1
RunJSc	EM04	0.8867	0.9807	0.08	5.08	39.2646	−1.9558	18.7532	−2.2767	172.9	171.3
RunJSc	EM08	0.6627	1.4902	0.11	3.14	0.1004	−4.4215	3.8900	−2.8334	30.7	32.8
RunJSd	EM05	0.8960	1.4412	0.03	4.99	4.5815	−2.8934	10.8548	−2.5187	13.3	64.8
RunJSd	EM11	0.7840	0.9106	0.10	0.87	0.1792	−4.2430	5.5202	−2.7544	27.8	355.2
RunJSe	EM03	0.9427	0.7578	0.02	4.18	0.1116	−4.5287	2.3959	−3.1969	10.6	119.3
RunJSe	EM09	0.5880	1.3696	0.03	3.49	18.7234	−2.0991	25.6518	−1.9623	48.4	105.0
RunJSf	EM08	1.0080	0.8699	0.16	5.88	1.9805	−3.3087	5.0155	−2.9052	22.1	60.6
$\bf RunJS_{ave}$	...	...	...	...	...	7.5716	...	7.3160	...	...	...

Note. Bold indicates the average of each set.

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The first thing to notice is the similarity of the final planetary systems that formed within 2 AU of the Sun in all of the simulations. Between 2–4 planets formed, and at most 1 planetesimal remained, within 2 AU for all of these simulations. Beyond 2 AU, differences in outer planet configurations have a strong influence on the disk. To examine these differences among each type of system more quantitatively, we present the following statistics in Table 1.

• 1.  
  The number of planets, N_p, that are at least as massive as the planet Mercury (0.06 M_⊕) with a < 2 AU (Column 2) and a > 2 AU (Column 6).
• 2.  
  The number of minor planets, N_m, with M_p < 0.06 M_⊕ that remained within a < 2 AU (Column 3) and beyond 2 AU (Column 7).
• 3.  
  The percentage of the initial disk mass that composes the final planets, m_p, that formed within 2 AU (Column 4) and beyond 2 AU (Column 8).
• 4.  
  A radial mixing statistic, S_r, given by

  $$\begin{equation} S_r=\left[\sum _j \frac{m_j|a_{i,j}-a_{f,j}|}{a_{f,j}} \right]/\sum _j m_j, \end{equation} \tag{ 2 }$$

  where a_i and m are the initial semimajor axis and mass of each embryo and planetesimal that become incorporated into a final planet, and a_f is the semimajor axis of that planet. This is essentially a measure of the degree of radial mixing of material in the disk.
• 5.  
  The percentage of the initial disk mass that was lost from the system due to a collision with the Sun, $m_{l_\star }$ (Column 9).
• 6.  
  The percentage of the initial disk mass that was ejected from the system, $m_{l_{\infty }}$ (Column 10). This value also includes the masses of (the small number of) bodies that collided with the giant planet companion.

The simulations in Table 1 are labeled "RunX_Y" (Column 1), where X describes the system (0 = Sun-only, 1 = 1 M_⊕, 10 = 10 M_⊕, J = Jupiter with e = 0.05, J0 = Jupiter with e = 0, and JS = Jupiter + Saturn, both with e = 0.05) and Y is a given realization of that system (a–f).

In the initial disk (at the start of our simulations), 51% of the mass is less than 2 AU from the Sun. The percentage of this initial disk mass, which remains in the planets that orbit within 2 AU, averages ∼53% in most sets of simulations, with the value reduced to 48% with eccentric Jupiter and to 44% in the set that includes both Jupiter and Saturn. Beyond 2 AU, the number of bodies and the amount of mass remaining in the system differs significantly among the various configurations, as does the fate of the mass that is lost. In simulations with the Sun-only, 2–5 planets and 46 planetesimals on average remained beyond 2 AU, and were composed of 43% of the initial disk mass. About 3% of the initial disk mass was lost in these simulations via ejection from the system or collisions with the Sun. When a 1 M_⊕ planet was included in Jupiter's orbit, a larger fraction of mass (10%) was lost from the system and fewer planetesimals remained in the system on average. The mass distribution changes significantly when a 10 M_⊕ planet is introduced. Though, 2–5 planets remain beyond 2 AU, which is consistent with the Sun-only simulation and 1 M_⊕ planet systems. However, a much smaller number of planetesimals remain (6 on average), primarily because a large fraction of the initial disk, 26% on average, is ejected from the systems. Only a few percent of the initial disk mass was perturbed into the star in the simulations described thus far.

In all simulations that included a Jupiter-like planet, only one planet on average, and at most a single planetesimal, remained beyond 2 AU. The systems without Saturn produced fairly consistent results, less than about 10% of the initial disk mass collided with the Sun, and 35%–47% was ejected. A larger percentage of the initial mass was lost when both Jupiter and Saturn were included, 21% on average was perturbed into the Sun and 34% was ejected. This is likely attributed to the strong perturbations induced by the ν₆ secular resonance—predominant near 2.1 AU—due to the presence of Saturn. The radial mixing statistic (S_r) was about 0.6 on average for the sets of simulations with either no distant perturber or one on a circular orbit. S_r was somewhat lower (∼0.5) for the Jupiter-only simulations but on an eccentric orbit, and was even lower (0.4 on average) for the simulations with Jupiter and Saturn, which is not surprising considering the amount of mass that was lost from these systems.

3.2. Characteristics of Planets Near 1 AU

3.3. Loss of Volatiles in Collisions

We have performed 33 simulations of the late stage of planet formation with and without outer planet companions perturbing the disk. Although giant planets can have a profound effect on the types of planetary systems that form, we found that they are not required to provide the radial mixing needed for volatile material from beyond the snow line to accrete onto terrestrial planets in the habitable zone. We present two WMF disk models, but we provide in the electronic edition of this article a full table of all final planets and their composite embryos and planetesimals (and their initial semimajor axes) to allow for the incorporation of any distribution of H₂O in the initial disk. Table 3 provides a sample of the electronic table. Results can also be scaled for different stellar types with the formulae presented in Quintana & Lissauer (2006).

Can we conclude that most terrestrial planets formed around isolated stars are likely habitable? Not quite—a more serious problem for the habitability of terrestrial planets in systems lacking giant planets is that small bodies persist beyond 2 AU for far longer. This allows the tail of the accretionary epoch to extend well beyond that within our solar system. Impacts of objects an order of magnitude less massive than the planetesimals in our simulations (and therefore probably much more numerous in a realistic protoplanetary disk) are still so large that their accretion onto an Earth-like planet would produce environmental damage probably sufficient to wipe out all life as we know it (Zahnle & Sleep 1997). Thus, without giant planets, devastating impacts might well persist for billions of years, rendering Earth-like planets unsuitable for all but perhaps the simplest and most rapidly formed life.

This work was funded in part by the NASA Ames Team of the NASA Astrobiology Institute. E.V.Q. thanks Tom Barclay for useful discussions and assistance with the figures.