Revisiting Planetesimal Accretion onto Proto-Jupiter
Authors: Shibata Sho , Helled Ravit , Kobayashi Hiroshi 
Published: September 2022

&lt;p&gt;&lt;strong&gt;Introduction&lt;/strong&gt;&lt;/p&gt;
&lt;p&gt;The detailed observations by the NASA Juno spacecraft has advanced Jupiter&amp;#8217;s interior structure models which can be used to improve our understanding of Jupiter&amp;#8217;s origin. In this study, we investigate the potential origin of Jupiter's enriched atmosphere. We revisit the planetesimal accretion during Jupiter&amp;#8217;s formation: in previous studies, the planetesimal accretion rate is calculated using N-body simulations that model the swam of planetesimals around proto-Jupiter. It was concluded that the heavy-element enrichment in Jupiter's envelope can be explained by the planetesimal accretion if Jupiter formed in a planetesimal disk that is at least five times more massive than the minimum mass solar nebulae (MMSN). However, this conclusion was inferred under the assumption that the total mass of captured planetesimals linearly increases with the surface density of planetesimals. In reality, in such a massive disk the gravitational interactions between planetesimals and embryos becomes so strong that the initial eccentricity and inclination are excited to &amp;#12316;0.1 at most. In this study, we investigate this scenario in detail accounting for the change of the eccentricity and inclination of the planetesimals and show its affect off Jupiter&amp;#8217;s growth rate and final composition.&lt;/p&gt;
&lt;p&gt;&amp;#160;&lt;/p&gt;
&lt;p&gt;&lt;strong&gt;Model&lt;/strong&gt;&lt;/p&gt;
&lt;p&gt;&lt;img src=&quot;&quot; alt=&quot;&quot; width=&quot;315&quot; height=&quot;210&quot; /&gt;&lt;/p&gt;
&lt;p&gt;&lt;strong&gt;Figure 1:&amp;#160;&lt;/strong&gt;The surface density of planetesimals used in this study. This surface density profile is obtained by Kobayashi &amp; Tanaka (2021).&lt;/p&gt;
&lt;p&gt;&amp;#160;&lt;/p&gt;
&lt;p&gt;We adopt a planetesimal disk obtained by Kobayashi &amp; Tanaka (2021) where the collisional evolution of dust grains in the protoplanetary disk results in a dense-compact planetesimal disk because of pebble drift from the outer disk. Figure 1 shows the surface density profile of planetesimals we use in this study. We start the N-body simulations with a swam of planetesimals around proto-Jupiter which enters the runaway gas accretion phase and increases its mass from 10 M&lt;sub&gt;&amp;#8853;&lt;/sub&gt; to 318 M&lt;sub&gt;&amp;#8853;&lt;/sub&gt;. During its formation, we assume that proto-Jupiter slightly migrates inward due to type II migration. If a planetesimal collides on the surface of proto-Jupiter or loses its escape energy from Jupiter's Hill sphere, we assume that the planetesimal is captured by proto-Jupiter.&lt;/p&gt;
&lt;p&gt;We set the initial eccentricities and inclinations of planetesimals as input parameters. Since the choice of the planetesimal&amp;#8217;s size can significantly affect the accretion rate we consider various planetesimal sizes.&lt;/p&gt;
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&lt;p&gt;&lt;strong&gt;Results&lt;/strong&gt;&lt;/p&gt;
&lt;p&gt;&lt;img src=&quot;&quot; alt=&quot;&quot; width=&quot;275&quot; height=&quot;220&quot; /&gt;&lt;/p&gt;
&lt;p&gt;&lt;strong&gt;Figure 2:&amp;#160;&lt;/strong&gt;The cumulative mass of captured planetesimals as a function of time. Black, red, green and blue lines show correspond to different assumed initial eccentricities of &amp;#8249;e&lt;sub&gt;0&lt;/sub&gt;&amp;#8250;&lt;sup&gt;1/2&lt;/sup&gt;=10&lt;sup&gt;-3&lt;/sup&gt;,10&lt;sup&gt;-2&lt;/sup&gt;,10&lt;sup&gt;-1&lt;/sup&gt;, and 0.4, respectively. The initial inclination is set as &amp;#160;&amp;#160;&amp;#8249;i&lt;sub&gt;0&lt;/sub&gt;&amp;#8250;&lt;sup&gt;1/2&lt;/sup&gt;=0.5&amp;#8249;e&lt;sub&gt;0&lt;/sub&gt;&amp;#8250;&lt;sup&gt;1/2&lt;/sup&gt;.&lt;/p&gt;
&lt;p&gt;&amp;#160;&lt;/p&gt;
&lt;p&gt;In a massive planetesimal disk, proto-Jupiter accretes tens Earth-masses of heavy elements by the end of runaway gas accretion. Figure 2 shows the cumulative mass of captured planetesimals vs. time. We find that the increase of the initial eccentricity and inclination:&lt;/p&gt;
&lt;ul&gt;
&lt;li&gt;weakens resonant trapping and leads to an enhancement of planetesimal accretion,&lt;/li&gt;
&lt;li&gt;reduces the capture probability of planetesimals.&lt;/li&gt;
&lt;/ul&gt;
&lt;p&gt;Due to the combination of these effects, the captured mass of planetesimals decreases with the increase of the initial eccentricity and inclination.&lt;/p&gt;
&lt;p&gt;&amp;#160;&lt;/p&gt;
&lt;p&gt;&lt;strong&gt;Discussion&lt;/strong&gt;&lt;/p&gt;
&lt;p&gt;&lt;img src=&quot;&quot; alt=&quot;&quot; width=&quot;291&quot; height=&quot;233&quot; /&gt;&lt;/p&gt;
&lt;p&gt;&lt;strong&gt;Figure 3:&amp;#160;&lt;/strong&gt;Total mass of captured planetesimals as a function of planetesimal size and the initial eccentricity. The initial inclination is set as &amp;#160;&amp;#160;&amp;#8249;i&lt;sub&gt;0&lt;/sub&gt;&amp;#8250;&lt;sup&gt;1/2&lt;/sup&gt;=0.5&amp;#8249;e&lt;sub&gt;0&lt;/sub&gt;&amp;#8250;&lt;sup&gt;1/2&lt;/sup&gt;. The solid and dashed black line shows the equilibrium eccentricity of planetesimals with and without embryos, respectively.&lt;/p&gt;
&lt;p&gt;&amp;#160;&lt;/p&gt;
&lt;p&gt;The initial eccentricity and inclination of planetesimals are determined by the scattering from other planetesimals/embryos. In a massive planetesimal disk as assumed here, embryos other than proto-Jupiter would form and be in the &amp;#8220;oligarchic regime&amp;#8221;. Considering the eccentricity and inclination excitation from the embryos, we conclude that the total mass of captured planetesimals is about 5-10 M&lt;sub&gt;&amp;#8853;&lt;/sub&gt;, and is larger for larger planetesimals.&lt;/p&gt;
&lt;p&gt;The bulk metallicity of Jupiter is still a matter of debate (e.g., Stevenson 2020). Planetesimal accretion could explain structure models with ~10 M&lt;sub&gt;&amp;#8853;&lt;/sub&gt; of heavy elements in Jupiter&amp;#8217;s outer envelope. However, if Jupiter&amp;#8217;s enrichment is found to be higher, as suggested by some structure models (e.g., Miguel et al. 2022), an additional enrichment mechanism would be required. Such an enrichment could be a result of giant impacts of embryos. Such impacts have been suggested by Liu et al. (2019) for the formation of Jupiter&amp;#8217;s fuzzy core.&lt;/p&gt;
&lt;p&gt;We also compare our results with those presented by Shibata &amp; Helled (2022), where planetesimal accretion was considered for the case of a migrating Jupiter from 20 au to 5 au. We find that the timing of planetesimal accretion must occur earlier for the in-situ formation case, which enriches Jupiter's interior rather than the outer envelope or atmosphere. We suggest that a determination of the heavy-element distribution in Jupiter&amp;#8217;s envelope could constrain Jupiter&amp;#8217;s formation location and formation history.&lt;/p&gt;
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&lt;p&gt;&lt;strong&gt;References&lt;/strong&gt;&lt;/p&gt;
&lt;p&gt;Kobayashi, H., &amp; Tanaka, H. 2021, ApJ, 922, 16, doi: 10.3847/1538-4357/ac289c&lt;/p&gt;
&lt;p&gt;Liu, S.-F., Hori, Y., M &amp;#776;uller, S., et al. 2019, Nature, 572, 355, doi: 10.1038/s41586-019-1470-2&lt;/p&gt;
&lt;p&gt;Miguel, Y., Bazot, M., Guillot, T., et al. 2022, arXiv e-prints, arXiv:2203.01866. https://arxiv.org/abs/2203.01866&lt;/p&gt;
&lt;p&gt;Shibata, S., &amp; Ikoma, M. 2019, MNRAS, 487, 4510, doi: 10.1093/mnras/stz1629&lt;/p&gt;
&lt;p&gt;Shibata, S., &amp; Helled, R. 2022, ApJL, 926, L37, doi: 10.3847/2041-8213/ac54b1&lt;/p&gt;
&lt;p&gt;Stevenson, D. J. 2020, Annu. Rev. Earth Planet. Sci., 48, 465&lt;br /&gt;&lt;br /&gt;&lt;/p&gt;
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