<p>I think this question might trigger more an open-ended discussion, than a definitive answer, but let me try my take on it.</p>
<p>Firstly,</p>
<blockquote>
<p>Is it more likely that one of these collided with Jupiter itself at the head-on angle needed for the core-warping collision?</p>
</blockquote>
<p>In order to collide, a co-orbital configuration is more favourable than a orbit-crossing encounter at high eccentricity (as seen in Liu et al., extended fig. 2), but their 'high angles' don't quantify high eccentricities properly. This is because in their simulations, all planetesimals are initialized at circular orbits, with initial distances of 5-10 mutual Hill-radii (their k parameter).
Why I think they didn't properly compare apples with apples, is because usually an eccentric planet would have more kinetic energy than allowed in their simulations, reducing the collision cross-section.<br />
This would lead to drastically reduced impact rates at high angles, compared to the data they show. Furthermore in the early scattering scenario that you propose, most planetesimals would be of too low mass to trigger the core mixing.</p>
<p>The mass required for the impactors is, I think, the major point why the two scenarios are not compatible. The initial conditions for the impact scenarios are those of 5 densely packed 10 <span class="math-container">$m_{\rm oplus}$</span> planets, of which one undergoes runaway gas accretion and becomes Jupiter. Those conditions are explained to arise due to oligarchic growth. For the 5 planets, this means that 50 <span class="math-container">$m_{\rm \oplus}$</span> are packed in a region of 5 AU size. This is already 1/3 of a median class 0 disc mass, and it necessitates a 100% high efficiency when translating pebbles to planetesimals to planets.<br />
Seeing those numbers lets me strongly doubt the realism of the initial conditions.</p>
<p>Concerning the other part of your question,</p>
<blockquote>
<p>The few million years&quot; timescale is quite vague. Does anyone know any additional detail which might suggest the impact occurred prior to the Grand Tack's timeframe?</p>
</blockquote>
<p>The few-million years are coming from a certain amount of cooling and compactification that is required for the impact to successfully mix Jupiter's envelope. Hence, the impact should not have occurred prior to the Grand Tack.</p>
<p>Taken both those things together, the cooling requirement and the mass/compactness of the initial conditions necessary, I don't think both scenarios are compatible.</p>

CC BY-SA 4.0
2021-04-06T20:05:08.853Z
Can I just make sure I've understood correctly, as there's a lot to unpack here? For the two alternative scenarios, you believe that the scattered planetesimals had too low a mass for the impact to have been with one of them, and you also believe that the collision couldn't have occurred prior to the Grand Tack. So far, I'm pretty sure I'm following you. However, as well as these two, you then give two arguments that the original Grand Tack and Core-Warping Impact theories are not compatible, these being 1/
Astrid_Redfern
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2021-04-06T20:06:55.140Z
(1) that the chance of the original scenario (impact with the 10-Earth-mass planetesimal after the Grand Tack had ended) is lower than anticipated if elliptical orbits are taken into account, and (2) the five densely packed planets stretch credibility too much. If so, do you think there's any leeway from overly-simplified assumptions being used to set up the original models, that could make versions of the two scenarios compatible?
Astrid_Redfern
CC BY-SA 4.0
2021-04-06T22:48:57.580Z
@Astrid_Redfern: I would say (1) of your first comment and (1) of the second go hand-in-hand, and then the entropy and mass arguments are two separate points. Sorry If my writing wasn't clearn enough on that. Overly simplified assumptions, do you mean whether one could take more realistic initial conditions for the impact model to make it happen? I am sure that this would be subject of current research. However, while resonant chains of equal mass, which destabilize after gas disc dispersal, do happen in planet formation models, this amount of solid mass is at the upper limit that you ca build
AtmosphericPrisonEscape
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2021-04-06T22:52:10.697Z
and to selectively only make one of the equal-mass resonant chain planets into a gas giants is also strange. I think, the more realistic you go, the harder it gets to hit Jupiter in a repeatable way, such that the occurrence for this event is something sensible like 50% and not incredibly unlikely. Reality might be stochastic, but a certain school of us would still like solar system formation models to produce high probabilities for the scenarios we envision.
AtmosphericPrisonEscape
CC BY-SA 4.0
2021-04-06T22:56:46.737Z
Another comment is on the necessity of the Grand Tack scenario itself, which was devised initially as a physically self-consistent way to create a planetesimal ring between 0.7 and 1.0-1.5 AU (as earlier work showed that you need this ring to build small Mercury, small Mars and a low-mass planetesimal belt with excited e and i.) Newer work points in the direction that a Grand Tack might not be necessary, and that a one-directional migration with pebble accretion (such as the paper by Pirani et al., that you've cited) can lead to the desired solar system.
AtmosphericPrisonEscape
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2021-04-09T08:33:22.700Z
Thanks. So you're saying that you believe the core-warping impact theory is not likely to be realistic, and that this is the case regardless of whether the Grand Tack theory is true or not. Basically, it's more about the plausibility of the second model than its compatibility with the first?
Astrid_Redfern
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2021-04-09T08:44:11.810Z
Also, is there any alternative explanation for Jupiter's diffuse core that you think is more plausible?
Astrid_Redfern
CC BY-SA 4.0
2021-04-09T13:52:38.587Z
None of the models works without grave problems (some outlined above), that's why none of them is accepted. Furthermore, combining those two scenarios seems to difficult, as the simulation outcome of the GT precludes the initial conditions necessary for the core-impact scenario. Another explanation for Jupiter's diffuse core is core erosion (Militzer et al. 2011), as silicate rock becomes thermodynamically unstable in H/He gas under high pressure and dissolves into the gas. All those scenarios are individual puzzle pieces, no finished puzzle exists yet.
AtmosphericPrisonEscape
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2021-04-17T14:16:05.083Z
What's the name of the Militzer et al paper?
Astrid_Redfern
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2021-04-17T14:48:09.320Z
@Astrid_Redfern: Sorry, i seem to have mixed up the year. https://ui.adsabs.harvard.edu/abs/2012ApJ...745...54W/abstract in 2012 for erosion of high-pressure water ice, https://ui.adsabs.harvard.edu/abs/2012PhRvL.108k1101W/abstract for MgO, https://ui.adsabs.harvard.edu/abs/2014ApJ...787...79G/abstract for SiO2. Applying those to planetary evolution models, would be another batch of papers though.
AtmosphericPrisonEscape
CC BY-SA 4.0
2021-04-18T18:17:22.120Z
Just posting the titles of the papers above. The first one is ["Solubility of Water Ice in Metallic Hydrogen: Consequences for Core Erosion in Gas Giant Planets" (Wilson, H. F.; Militzer, B., January 2012.)](https://ui.adsabs.harvard.edu/abs/2012ApJ...745...54W/abstract) The second is [Rocky Core Solubility in Jupiter and Giant Exoplanets  (Wilson, H. F.; Militzer, B., March 2012.)](https://ui.adsabs.harvard.edu/abs/2012PhRvL.108k1101W/abstract).
Astrid_Redfern
CC BY-SA 4.0
2021-04-18T18:18:45.403Z
The third - which I don't think I've seen cited as much as the other two - is ["Ab Initio Free Energy Calculations of the Solubility of Silica in Metallic Hydrogen and Application to Giant Planet Cores" (González-Cataldo, F.; Wilson, H. F.; Militzer, B., May 2014)](https://ui.adsabs.harvard.edu/abs/2014ApJ...787...79G/abstract)
Astrid_Redfern
CC BY-SA 4.0
2021-04-06T18:59:51.533Z
2021-04-06T18:59:51.533Z
AtmosphericPrisonEscape
<p>In recent years, the <em>Juno</em> mission revealed that Jupiter's core was <a href="https://www.space.com/39348-juno-jupiter-mission-planet-revelations.html" rel="nofollow noreferrer">much more</a> <a href="https://www.space.com/37005-jupiter-fuzzy-core-nasa-juno.html" rel="nofollow noreferrer">diffuse</a> than astronomers had expected.</p>
<p><a href="https://www.nature.com/articles/s41586-019-1470-2" rel="nofollow noreferrer">One</a> <a href="https://astronomynow.com/2019/08/17/a-core-warping-impact-in-jupiters-past/" rel="nofollow noreferrer">theory</a> is that &quot;within a few million years&quot; of its formation, Jupiter experienced a head-on collision with a planetesimal of about <span class="math-container">$10M_{⊕}$</span>, adding a lot more mass to its core from the silicate planetesimal, but also causing the core's contents to be broken up and mixed with the inner envelope.</p>
<p>The models used in this theory placed Jupiter at a distance of 5.2 AU from the Sun, which is approximately the same as its semi-major axis in the present day. The planetesimal in question would be at the higher end of the valid mass range for a Super-Earth.</p>
<p>Now, according to the <a href="https://en.wikipedia.org/wiki/Grand_Tack" rel="nofollow noreferrer">Grand Tack</a> <a href="https://www.nasa.gov/topics/solarsystem/features/young-jupiter.html" rel="nofollow noreferrer">theory</a>, Jupiter originally formed at a distance of <span class="math-container">$\approx 3.5$</span> AU and migrated inwards toward the Sun, before gravitational interactions with Saturn caused the two planets to move outward and brought Jupiter to its present-day orbit.</p>
<p>Saturn itself would have formed at a distance of <span class="math-container">$\approx 4.5$</span> AU, increasing in mass from <span class="math-container">$30M_{⊕}$</span> to <span class="math-container">$60M_{⊕}$</span> during the first <span class="math-container">$10^5$</span> years of Jupiter's inward migration, before starting its own inward migration. This would have been much faster than Jupiter's, enabling Saturn to &quot;catch up&quot; and the gravitational interactions as described to then occur.</p>
<p>The original formations would all have occurred over a timescale of <span class="math-container">$\lessapprox 6Myr$</span>, maybe closer to <span class="math-container">$\approx 3Myr$</span>. (The <a href="https://arxiv.org/abs/1201.5177" rel="nofollow noreferrer">original paper</a> describing the Grand Tack refers only to &quot;a few Myr&quot;; the figures here are based on <a href="https://iopscience.iop.org/article/10.1086/320685/pdf" rel="nofollow noreferrer">&quot;Disc Frequencies and Lifetimes in Young Clusters&quot;</a>, which it cites in support of this.) The inward and outward migrations would then have occurred in an 800,000 year time period (see Figure 1 of the Grand Tack <a href="https://arxiv.org/abs/1201.5177" rel="nofollow noreferrer">paper</a>)</p>
<p>(Incidentally, the cores of Uranus and Neptune are each <span class="math-container">$\approx 5M_{⊕}$</span> at the start of this migration, increasing to values <span class="math-container">$&gt; 10M_{⊕}$</span> at the end of it.)</p>
<p><a href="https://i.sstatic.net/RiHib.png" rel="nofollow noreferrer"><img src="https://i.sstatic.net/RiHib.png" alt="Diagram from arXiv 1201.5177)" /></a></p>
<p>So far, the two models look quite compatible with each other, with the collision occuring after Jupiter settles into its 5.2 AU orbit. But there is one detail I'm not sure about. Here comes the question:</p>
<ul>
<li>Descriptions of the Grand Tack theory describe Jupiter as scattering early planetesimals as its gravity disturbed their orbits. Some collided with each other, some were propelled into the Sun... Is it more likely that one of these collided with Jupiter itself at the head-on angle needed for the core-warping collision? Which would mean the impact occurred before Jupiter reached its final orbit.</li>
</ul>
<p>In addition...</p>
<ul>
<li>The &quot;few million years&quot; timescale is quite vague. Does anyone know any additional detail which might suggest the impact occurred prior to the Grand Tack's timeframe?</li>
</ul>
<p><strong>References (not paywalled):</strong></p>
<p><a href="https://iopscience.iop.org/article/10.1086/320685/pdf" rel="nofollow noreferrer">Haisch Jr, K. E., Lada, E. A., &amp; Lada, C. J. (2001). Disk frequencies and lifetimes in young clusters. The Astrophysical Journal Letters, 553(2), L153.</a></p>
<p><a href="http://www.gps.caltech.edu/classes/ge133/reading/grand_tack_nature.pdf" rel="nofollow noreferrer">Walsh, K. J., Morbidelli, A., Raymond, S. N., O'Brien, D. P., &amp; Mandell, A. M. (2011). A low mass for Mars from Jupiter’s early gas-driven migration. Nature, 475(7355), 206-209.</a></p>
<p><a href="https://arxiv.org/abs/2007.08338" rel="nofollow noreferrer">Liu, S. F., Hori, Y., Müller, S., Zheng, X., Helled, R., Lin, D., &amp; Isella, A. (2019). The formation of Jupiter's diluted core by a giant impact. Nature, 572(7769), 355-357.</a></p>
<p><a href="https://www.nature.com/articles/d41586-019-02401-1" rel="nofollow noreferrer">Guillot, T. (2019). Signs that Jupiter was mixed by a giant impact.</a></p>
<p>with accompanying articles:</p>
<p><a href="https://www.space.com/37005-jupiter-fuzzy-core-nasa-juno.html" rel="nofollow noreferrer">Wall, M. (2017). More Jupiter Weirdness: Giant Planet May Have Huge, 'Fuzzy' Core. (space.com)</a></p>
<p><a href="https://www.space.com/39348-juno-jupiter-mission-planet-revelations.html" rel="nofollow noreferrer">Weitering, H. (2018). 'Totally Wrong' on Jupiter: What Scientists Gleaned from NASA's Juno Mission. (space.com)</a></p>
<p><a href="https://astronomynow.com/2019/08/17/a-core-warping-impact-in-jupiters-past/" rel="nofollow noreferrer">(2019). A core-warping impact in Jupiter's past? (Astronomy Now)</a></p>
<p><strong>A paper cited in earlier versions of this question but which turned out to be incompatible with the Grand Tack theory:</strong></p>
<p><a href="https://www.aanda.org/articles/aa/pdf/2019/03/aa33713-18.pdf" rel="nofollow noreferrer">Pirani, S., Johansen, A., Bitsch, B., Mustill, A. J., &amp; Turrini, D. (2019). Consequences of planetary migration on the minor bodies of the early solar system. Astronomy &amp; Astrophysics, 623, A169.</a></p>
<p>with accompanying article:</p>
<p><a href="https://www.sciencedaily.com/releases/2019/03/190322105706.htm" rel="nofollow noreferrer">Jupiter's unknown journey revealed</a></p>

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2020-12-06T04:25:43.823Z
Unpaywalled: https://arxiv.org/abs/2007.08338
Keith McClary
CC BY-SA 4.0
2020-12-07T11:01:44.893Z
@KeithMcClary Big thanks for that. I'm at work right now but will edit that into the question later. Thanks again!
Astrid_Redfern
CC BY-SA 4.0
2021-02-06T16:35:44.567Z
Something I have concern with though is that your link proposing to take place 2-3 Myr after Jupiter’s formation states that Jupiter formed much further out than present distance and then migrated in. There’s no mention of Jupiter migrating further  inwards and then back out at all. 

I’m not sure if that hypothesis and grand tack are even compatible, unless I am missing some information.
ShroomZed
CC BY-SA 4.0
2021-04-03T11:38:25.750Z
@ShroomZed I've looked at the original paper covered by the article ("Consequences of planetary migration on the minor bodies of the early solar system").

A quote: *"many mechanisms has been proposed in order to explain the low mass of the asteroid belt, such as ... the Grand Tack scenario ... We are not going to explore further this issue since we did not simulate the inner part of the solar system ..."*

I'm investigating further - the papers it cites seem to assume that competing torques cause Type 1 inward migration to cease, and say nothing about outward, but 1/
Astrid_Redfern
CC BY-SA 4.0
2021-04-03T11:39:16.460Z
this may be based on simplifying assumptions, and it may be possible to add in something similar to the Grand Tack in a reasonable modified model. As I say, I'm reading further, and I'm wondering how hot Jupiters/Chthonian planets fit into this. Apologies for not replying sooner, and thanks for bringing it to my attention.
Astrid_Redfern
CC BY-SA 4.0
2021-04-09T08:24:54.213Z
@ShroomZed It looks like "Consequences of planetary migration on the minor bodies of the early solar system" is indeed probably incompatible with the Grand Tack. However, it turns out that a very similar timescale can be obtained from the original Grand Tack paper, and I've edited this in to replace the original. I'll need to edit at least one Wikipedia article at some point too. Thanks again for pointing all this out.
Astrid_Redfern
<solar-system><jupiter><planetary-formation><orbital-migration><core>
The compatibility of the Grand Tack hypothesis with the "core-warping impact" theory of Jupiter's diffuse core
Astrid_Redfern
# The compatibility of the Grand Tack hypothesis with the "core-warping impact" theory of Jupiter's diffuse core

(Asked by: username_0 on 2020-03-23)

In recent years, the *Juno* mission revealed that Jupiter's core was [much more](https://www.space.com/39348-juno-jupiter-mission-planet-revelations.html) [diffuse](https://www.space.com/37005-jupiter-fuzzy-core-nasa-juno.html) than astronomers had expected.

[One](https://www.nature.com/articles/s41586-019-1470-2) [theory](https://astronomynow.com/2019/08/17/a-core-warping-impact-in-jupiters-past/) is that "within a few million years" of its formation, Jupiter experienced a head-on collision with a planetesimal of about $10M\_{⊕}$, adding a lot more mass to its core from the silicate planetesimal, but also causing the core's contents to be broken up and mixed with the inner envelope.

The models used in this theory placed Jupiter at a distance of 5.2 AU from the Sun, which is approximately the same as its semi-major axis in the present day. The planetesimal in question would be at the higher end of the valid mass range for a Super-Earth.

Now, according to the [Grand Tack](https://en.wikipedia.org/wiki/Grand_Tack) [theory](https://www.nasa.gov/topics/solarsystem/features/young-jupiter.html), Jupiter originally formed at a distance of $\approx 3.5$ AU and migrated inwards toward the Sun, before gravitational interactions with Saturn caused the two planets to move outward and brought Jupiter to its present-day orbit.

Saturn itself would have formed at a distance of $\approx 4.5$ AU, increasing in mass from $30M\_{⊕}$ to $60M\_{⊕}$ during the first $10^5$ years of Jupiter's inward migration, before starting its own inward migration. This would have been much faster than Jupiter's, enabling Saturn to "catch up" and the gravitational interactions as described to then occur.

The original formations would all have occurred over a timescale of $\lessapprox 6Myr$, maybe closer to $\approx 3Myr$. (The [original paper](https://arxiv.org/abs/1201.5177) describing the Grand Tack refers only to "a few Myr"; the figures here are based on ["Disc Frequencies and Lifetimes in Young Clusters"](https://iopscience.iop.org/article/10.1086/320685/pdf), which it cites in support of this.) The inward and outward migrations would then have occurred in an 800,000 year time period (see Figure 1 of the Grand Tack [paper](https://arxiv.org/abs/1201.5177))

(Incidentally, the cores of Uranus and Neptune are each $\approx 5M\_{⊕}$ at the start of this migration, increasing to values $> 10M\_{⊕}$ at the end of it.)

[![Diagram from arXiv 1201.5177)](https://i.sstatic.net/RiHib.png)](https://i.sstatic.net/RiHib.png)

So far, the two models look quite compatible with each other, with the collision occuring after Jupiter settles into its 5.2 AU orbit. But there is one detail I'm not sure about. Here comes the question:

* Descriptions of the Grand Tack theory describe Jupiter as scattering early planetesimals as its gravity disturbed their orbits. Some collided with each other, some were propelled into the Sun... Is it more likely that one of these collided with Jupiter itself at the head-on angle needed for the core-warping collision? Which would mean the impact occurred before Jupiter reached its final orbit.

In addition...

* The "few million years" timescale is quite vague. Does anyone know any additional detail which might suggest the impact occurred prior to the Grand Tack's timeframe?

**References (not paywalled):**

[Haisch Jr, K. E., Lada, E. A., & Lada, C. J. (2001). Disk frequencies and lifetimes in young clusters. The Astrophysical Journal Letters, 553(2), L153.](https://iopscience.iop.org/article/10.1086/320685/pdf)

[Walsh, K. J., Morbidelli, A., Raymond, S. N., O'Brien, D. P., & Mandell, A. M. (2011). A low mass for Mars from Jupiter’s early gas-driven migration. Nature, 475(7355), 206-209.](http://www.gps.caltech.edu/classes/ge133/reading/grand_tack_nature.pdf)

[Liu, S. F., Hori, Y., Müller, S., Zheng, X., Helled, R., Lin, D., & Isella, A. (2019). The formation of Jupiter's diluted core by a giant impact. Nature, 572(7769), 355-357.](https://arxiv.org/abs/2007.08338)

[Guillot, T. (2019). Signs that Jupiter was mixed by a giant impact.](https://www.nature.com/articles/d41586-019-02401-1)

with accompanying articles:

[Wall, M. (2017). More Jupiter Weirdness: Giant Planet May Have Huge, 'Fuzzy' Core. (space.com)](https://www.space.com/37005-jupiter-fuzzy-core-nasa-juno.html)

[Weitering, H. (2018). 'Totally Wrong' on Jupiter: What Scientists Gleaned from NASA's Juno Mission. (space.com)](https://www.space.com/39348-juno-jupiter-mission-planet-revelations.html)

[(2019). A core-warping impact in Jupiter's past? (Astronomy Now)](https://astronomynow.com/2019/08/17/a-core-warping-impact-in-jupiters-past/)

**A paper cited in earlier versions of this question but which turned out to be incompatible with the Grand Tack theory:**

[Pirani, S., Johansen, A., Bitsch, B., Mustill, A. J., & Turrini, D. (2019). Consequences of planetary migration on the minor bodies of the early solar system. Astronomy & Astrophysics, 623, A169.](https://www.aanda.org/articles/aa/pdf/2019/03/aa33713-18.pdf)

with accompanying article:

[Jupiter's unknown journey revealed](https://www.sciencedaily.com/releases/2019/03/190322105706.htm)

**Tags:** solar-system, jupiter, planetary-formation, orbital-migration, core
> **Comments:**
> **username_1**: Unpaywalled: https://arxiv.org/abs/2007.08338  
> **username_0**: @KeithMcClary Big thanks for that. I'm at work right now but will edit that into the question later. Thanks again!  
> **username_2**: Something I have concern with though is that your link proposing to take place 2-3 Myr after Jupiter’s formation states that Jupiter formed much further out than present distance and then migrated in. There’s no mention of Jupiter migrating further  inwards and then back out at all.   I’m not sure if that hypothesis and grand tack are even compatible, unless I am missing some information.  
> **username_0**: @ShroomZed I've looked at the original paper covered by the article ("Consequences of planetary migration on the minor bodies of the early solar system").  A quote: *"many mechanisms has been proposed in order to explain the low mass of the asteroid belt, such as ... the Grand Tack scenario ... We are not going to explore further this issue since we did not simulate the inner part of the solar system ..."*  I'm investigating further - the papers it cites seem to assume that competing torques cause Type 1 inward migration to cease, and say nothing about outward, but 1/  
> **username_0**: this may be based on simplifying assumptions, and it may be possible to add in something similar to the Grand Tack in a reasonable modified model. As I say, I'm reading further, and I'm wondering how hot Jupiters/Chthonian planets fit into this. Apologies for not replying sooner, and thanks for bringing it to my attention.  
> **username_0**: @ShroomZed It looks like "Consequences of planetary migration on the minor bodies of the early solar system" is indeed probably incompatible with the Grand Tack. However, it turns out that a very similar timescale can be obtained from the original Grand Tack paper, and I've edited this in to replace the original. I'll need to edit at least one Wikipedia article at some point too. Thanks again for pointing all this out.  

---

## 1 answers

### Answer by username_3 on 2021-04-06. Score: 2

I think this question might trigger more an open-ended discussion, than a definitive answer, but let me try my take on it.

Firstly,

> Is it more likely that one of these collided with Jupiter itself at the head-on angle needed for the core-warping collision?

In order to collide, a co-orbital configuration is more favourable than a orbit-crossing encounter at high eccentricity (as seen in Liu et al., extended fig. 2), but their 'high angles' don't quantify high eccentricities properly. This is because in their simulations, all planetesimals are initialized at circular orbits, with initial distances of 5-10 mutual Hill-radii (their k parameter).
Why I think they didn't properly compare apples with apples, is because usually an eccentric planet would have more kinetic energy than allowed in their simulations, reducing the collision cross-section.  
This would lead to drastically reduced impact rates at high angles, compared to the data they show. Furthermore in the early scattering scenario that you propose, most planetesimals would be of too low mass to trigger the core mixing.

The mass required for the impactors is, I think, the major point why the two scenarios are not compatible. The initial conditions for the impact scenarios are those of 5 densely packed 10 $m\_{\rm oplus}$ planets, of which one undergoes runaway gas accretion and becomes Jupiter. Those conditions are explained to arise due to oligarchic growth. For the 5 planets, this means that 50 $m\_{\rm \oplus}$ are packed in a region of 5 AU size. This is already 1/3 of a median class 0 disc mass, and it necessitates a 100% high efficiency when translating pebbles to planetesimals to planets.  
Seeing those numbers lets me strongly doubt the realism of the initial conditions.

Concerning the other part of your question,

> The few million years" timescale is quite vague. Does anyone know any additional detail which might suggest the impact occurred prior to the Grand Tack's timeframe?

The few-million years are coming from a certain amount of cooling and compactification that is required for the impact to successfully mix Jupiter's envelope. Hence, the impact should not have occurred prior to the Grand Tack.

Taken both those things together, the cooling requirement and the mass/compactness of the initial conditions necessary, I don't think both scenarios are compatible.

> **Comments:**
> **username_0**: Can I just make sure I've understood correctly, as there's a lot to unpack here? For the two alternative scenarios, you believe that the scattered planetesimals had too low a mass for the impact to have been with one of them, and you also believe that the collision couldn't have occurred prior to the Grand Tack. So far, I'm pretty sure I'm following you. However, as well as these two, you then give two arguments that the original Grand Tack and Core-Warping Impact theories are not compatible, these being 1/  
> **username_0**: (1) that the chance of the original scenario (impact with the 10-Earth-mass planetesimal after the Grand Tack had ended) is lower than anticipated if elliptical orbits are taken into account, and (2) the five densely packed planets stretch credibility too much. If so, do you think there's any leeway from overly-simplified assumptions being used to set up the original models, that could make versions of the two scenarios compatible?  
> **username_3**: @Astrid_Redfern: I would say (1) of your first comment and (1) of the second go hand-in-hand, and then the entropy and mass arguments are two separate points. Sorry If my writing wasn't clearn enough on that. Overly simplified assumptions, do you mean whether one could take more realistic initial conditions for the impact model to make it happen? I am sure that this would be subject of current research. However, while resonant chains of equal mass, which destabilize after gas disc dispersal, do happen in planet formation models, this amount of solid mass is at the upper limit that you ca build  
> **username_3**: and to selectively only make one of the equal-mass resonant chain planets into a gas giants is also strange. I think, the more realistic you go, the harder it gets to hit Jupiter in a repeatable way, such that the occurrence for this event is something sensible like 50% and not incredibly unlikely. Reality might be stochastic, but a certain school of us would still like solar system formation models to produce high probabilities for the scenarios we envision.  
> **username_3**: Another comment is on the necessity of the Grand Tack scenario itself, which was devised initially as a physically self-consistent way to create a planetesimal ring between 0.7 and 1.0-1.5 AU (as earlier work showed that you need this ring to build small Mercury, small Mars and a low-mass planetesimal belt with excited e and i.) Newer work points in the direction that a Grand Tack might not be necessary, and that a one-directional migration with pebble accretion (such as the paper by Pirani et al., that you've cited) can lead to the desired solar system.  
> **username_0**: Thanks. So you're saying that you believe the core-warping impact theory is not likely to be realistic, and that this is the case regardless of whether the Grand Tack theory is true or not. Basically, it's more about the plausibility of the second model than its compatibility with the first?  
> **username_0**: Also, is there any alternative explanation for Jupiter's diffuse core that you think is more plausible?  
> **username_3**: None of the models works without grave problems (some outlined above), that's why none of them is accepted. Furthermore, combining those two scenarios seems to difficult, as the simulation outcome of the GT precludes the initial conditions necessary for the core-impact scenario. Another explanation for Jupiter's diffuse core is core erosion (Militzer et al. 2011), as silicate rock becomes thermodynamically unstable in H/He gas under high pressure and dissolves into the gas. All those scenarios are individual puzzle pieces, no finished puzzle exists yet.  
> **username_0**: What's the name of the Militzer et al paper?  
> **username_3**: @Astrid_Redfern: Sorry, i seem to have mixed up the year. https://ui.adsabs.harvard.edu/abs/2012ApJ...745...54W/abstract in 2012 for erosion of high-pressure water ice, https://ui.adsabs.harvard.edu/abs/2012PhRvL.108k1101W/abstract for MgO, https://ui.adsabs.harvard.edu/abs/2014ApJ...787...79G/abstract for SiO2. Applying those to planetary evolution models, would be another batch of papers though.  
> **username_0**: Just posting the titles of the papers above. The first one is ["Solubility of Water Ice in Metallic Hydrogen: Consequences for Core Erosion in Gas Giant Planets" (Wilson, H. F.; Militzer, B., January 2012.)](https://ui.adsabs.harvard.edu/abs/2012ApJ...745...54W/abstract) The second is [Rocky Core Solubility in Jupiter and Giant Exoplanets  (Wilson, H. F.; Militzer, B., March 2012.)](https://ui.adsabs.harvard.edu/abs/2012PhRvL.108k1101W/abstract).  
> **username_0**: The third - which I don't think I've seen cited as much as the other two - is ["Ab Initio Free Energy Calculations of the Solubility of Silica in Metallic Hydrogen and Application to Giant Planet Cores" (González-Cataldo, F.; Wilson, H. F.; Militzer, B., May 2014)](https://ui.adsabs.harvard.edu/abs/2014ApJ...787...79G/abstract)  

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