If there is a Planet Nine out there, I assume we’ll find it soon. That would be a welcome development, in that it would imply the Solar System isn’t quite as odd as it sometimes seems to be. We see super-Earths – and current thinking seems to be that this is what Planet Nine must be – in other stellar systems, in great numbers in fact. So it would stand to reason that early in its evolution our system produced a super-Earth, one that was presumably nudged into a distant, eccentric orbit by gravitational interactions.
The gap in size between Earth and the next planet up in scale is wide. Neptune is 17 times more massive than our planet, and four times its radius. Gas giant migration surely played a role in the outcome, and when considering stellar system architectures, it’s noteworthy as well that all that real estate between Mars and Jupiter seems to demand something more than asteroidal debris. To make sense of such issues, Stephen Kane (University of California, Riverside) has run a suite of dynamical simulations that implies we are better off without a super-Earth anywhere near the inner system.
Image: Artist’s concept of Kepler-62f, a super-Earth-size planet orbiting a star smaller and cooler than the sun, about 1,200 light-years from Earth. What effect would such a planet have in our own Solar System? Image credit: NASA Ames/JPL-Caltech/Tim Pyle.
Supposing a super-Earth did exist between Mars and Jupiter, Kane’s simulations demonstrated the outcomes for a range of different masses, the results presented in a new paper in the Planetary Science Journal. The heavyweight of our system, Jupiter’s 318 Earth masses carry profound gravitational significance for the rest of the planets. Disturb Jupiter, these results suggest, and in some scenarios the inner planets, including our own, are ejected from the Solar System. Even Uranus and Neptune can be affected and perhaps ejected as well depending on the super-Earth’s location.
As the paper notes, the range of possibilities is wide:
…several thousand simulations were conducted, producing a vast variety of dynamical outcomes for the solar system planets. The inner solar system planets are particularly vulnerable to the addition of the super-Earth planet, resulting in numerous regions of substantial system instability. The broad region of 2–4 au contains many locations of MMRs [Mean Motion Resonances] with the inner planets that further amplify the chaotic evolution of the inner solar system. There are also important MMR locations with the outer planets within the 2–4 au region, with potential significant consequences for the ice giants.
Let’s look at one possible outcome. The figure below shows the evolution in the eccentricity of the orbits of the inner planets in our Solar System, assuming a super-Earth with a mass of 7 times Earth’s and a semi-major axis of 2 AU. The simulation covers 107 years.
Image: This is Figure 2 from the paper. Caption: Eccentricity evolution of the solar system terrestrial planets (top four panels) for a 107 yr simulation, where the additional planet (bottom panel) has a mass and semimajor axis of 7.0 M⊕ and 2.00 au, respectively. Credit: Stephen Kane.
The results show the devastating disruption this scenario produces. The orbits of the four inner planets become unstable over time, removing all of them from the system before the simulation concludes. Mars gets knocked out halfway through the simulation period, while Mercury is ejected early due to interactions with Venus and the Earth. The latter two planets see a gradual increase in their eccentricities. The semimajor axis of Venus increases as it decreases for Earth, creating close encounters and removing both worlds from the system 8 to 9 Myr after the simulation starts.
Different things happen, of course, as Kane manipulates the variables. Assuming a super-Earth with a mass eight times the Earth’s at 3.7 AU, the surprising result (surprising to me, at least) is that Mars remains largely unaffected, while it’s the super-Earth whose interactions with the outer planets become intense. The orbits of Venus and Earth begin to become more eccentric, with perturbations to the orbit of Mercury that eventually remove it from the system entirely. It’s fascinating to work through this paper to examine the various scenarios. Take a look at yet another possibility:
Image: This is Figure 8. Caption: Eccentricity evolution of the solar system outer planets (top four panels) for a 107 yr simulation, where the additional planet (bottom panel) has a mass and semimajor axis of 7.0 M⊕ and 3.80 au, respectively. Credit: Stephen Kane.
Here we get Mean Motion Resonances with Jupiter and Saturn after about two million years, increasing the eccentricity of both, with the super-Earth ultimately being ejected from the system. Uranus is lost after about 4 million years and Neptune undergoes significant changes to its eccentricity. As Kane notes, the simulations show changes to system dynamics that are hugely sensitive to initial conditions, and in cases where significant interactions occur in the outer system, the orbits of the inner planets tend to become unstable as well. In the case of Figure 8, Mars is eventually ejected.
And this may have some bearing on our search for Planet Nine:
…the initial orbit for the additional planet was coplanar with Earth. Mutual inclinations between planetary orbits plays a role in overall system stability (Laskar 1989; Chambers et al. 1996), particularly for large inclinations (Veras & Armitage 2004; Correia et al. 2011), and may provide solutions to otherwise unstable architectures (Kane 2016; Masuda et al. 2020). It is therefore possible that there are orbital inclinations for the super-Earth that may reveal further locations of long-term stability, or else enhance unstable scenarios…
The paper implies, as the author adds in his conclusion, the “dynamical fragility” of the Solar System we have, with applications for the study of exoplanetary system architectures. How systems manage to work out sharing arrangements with super-Earths will doubtless become a key question for research as we move further into the era of space-based astrometry and learn more about how systems evolve.
The paper is Kane, “The Dynamical Consequences of a Super-Earth in the Solar System,” Planetary Science Journal Vol. 4, No. 2 (28 February 2023) 38 (full text).
I’m not convinced that a simulation that adds a planet gives a good insight on what happens naturally. After all, if you wrote a simulation of a streambed and started off with a flat water level or some arbitrary slope, you’d see immense floods. If you simulated the sudden departure or arrival of Earth’s Moon, I suppose there would be traumatic seismic events and even some shift of the orbit. My gut feeling is that to understand the effect of a super-Earth in a natural “Solar system”, you’d need a simulation that shows the planet forming in the right place to start with, with whatever accommodations elsewhere that requires.
The approach seems to be an example of perturbation theory modeling. Some of the examples in the paper do appear to become stable and I expect those are the stable architectures that we see in other systems. At least one example suggests that the eccentricities of the planets become cyclical which would have implications for long-term habitability (c.f. Prof Tyrrell’s modeling of long-term habitability that is only quasi-stable and random events can end habitable conditions. Are Planets with Continuous Surface Habitability Rare?)
Back in the 1980s [?] I recall a Scientific American article on modeling solar system planet formation. IIRC, the authors worried that their model couldn’t create the architecture of our system. I vaguely recall that they did show architectures very reminiscent of those we have found around other stars, including possible hot Jupiters and Neptunes. OTOH, I don’t recall that the authors suggested that instabilities could eject planets either, as this OP suggests that Planet 9 is a possible example. Centauri Dreams has had a number of posts over the years on planetary formation models, with interesting results, but which may or may not be realistic depending on the assumptions and physics used. Examples where the formation results in instabilities that eject planets seem more relevant here, both for a possible super-earth that has not been found, but more interesting, I think, in the numbers of rogue/nomadic planets that populate interstellar space and would make interesting targets for precursor interstellar probes. If we could detect them with a more sensitive all-sky IR/microlensing telescope, they would make good targets potentially closer than Proxima b, potential targets for worldships to rendezvous with, and new places for sci-fi stories, somewhat like Hoyle’s “Fifth Planet” but much stranger.
[If planet 9 is out there, how has it managed to evade detection when some rogue planets in interstellar space have been detected? Just bad luck?]
On your last question, I believe (but am not certain) that any rogue planets detected are either very large (several Jupiter masses) and young (i.e. hot), or were detected by microlensing. Microlensing is sensitive to low mass planets, but clearly depends on a lot of luck.
Close to the solar system, they say WISE would’ve detected a Jupiter out to one light-year or a Neptune out to [insert large number] AU.
Inserting 7-8 Earth masses into the system causes instabilities. Huh. Haha. Ok. I love simulations like this, but it’s pretty arbitrary.
It would be nice if Planet nine were a reality and a super Earth(ridiculous term that needs replacing) class object. Would be fascinating to examine.
Super-earths as planetary cuckoos.
Is the prevalence of Super Earths an observer effect caused by our present methods of finding exoplanets
How do researchers define a Super Earth? Must it be rocky or will a “mini-Neptune” do?
A problem with this kind of study is that it analyzes impossible scenarios. I mean that literally. An unstable arrangement of such magnitude cannot come into existence. It would be disrupted long before the planets could reach the posited arrangement. Unstable arrangements would be a rare observation since they are quickly disrupted.
The solar system has long term (not forever!) stability or we would not be here to have a discussion about it. Any large instabilities were resolved eons ago.
I consider a study of this type to be akin to naive questions like: what would happen if the Sun suddenly disappeared? But the Sun cannot suddenly disappear, or you’d need a plausible physical process by which it can occur.
What the study is showing (going by what Paul wrote since I haven’t read it) is that there are unstable arrangements. That’s nothing new. It is perhaps more useful to show broad classifications of arrangements of stable and unstable stellar systems. Our system may have hosted a super-earth long ago, but if it was in an unstable position it would have been ejected, disrupted or it would caused that to happen to the inner planets. But we’re still here.
More likely is that a nascent planet, perhaps a super-earth, formed between Mars and Jupiter and was rapidly disrupted and the pieces gradually ejected or encountered by the inner planets, especially Earth, as the eccentricity was pumped by gravitational resonances. The remaining bits are the asteroids. It is less likely that a super-Earth survived disruption to be ejected whole, and to have done so with enough velocity to boost the orbit hundreds of a.u. and then had a 3rd body interaction (with what?) to keep it there.
Some good points in the comments, that I hadn’t considered. I was interested to see what mass of a Planet could be stable? I’m assuming an Earth mass planet would be stable between 2-3au and I’m sure a few Mars mass planets would be too.
If my understanding is correct, it transitions relatively quickly from a chaotic dust cloud to a planetary disc, then to a set of planets in a somewhat random order, of random sizes and distances from the young star. Suddenly the planets are there, and over a few hundred million years the perturbations work themselves out and you have a stable system. Perhaps the article doesn’t state clearly enough that the starting point for the simulations are at the end of planetary disk formation, when you have a fresh batch of planets in an unstable set up.
This is certainly a case where the details matter and I have not read the paper. Presumably the author(s) speak to the model of formation and a process that happens far faster than the time it takes for instability to cause significant disruption. As the duration of both processes converge, planet formation would tend to disruption and they could not form these unstable configurations.
Once the proto-planet masses are “sufficiently” concentrated, we can apply Newtonian dynamics as if the proto-planets are point sources as seen by other proto-planets, and the clock starts ticking on the instability dynamics.
Question 1, why are the asteroids between Mars and Jupiter still there?
Question 2, how come there are other systems, sometimes with multiple super-Earths, but in much more closely spaced orbits than we see in our own system? Should they not have been disrupted long ago, if this study is correct?
What would a space-based telescope be like if developed specifically for hunting P9?
I suppose continuous observation of a wide swath for stellar occultations, along with “lottery ticket” IR glimpses in more detail in the hope of getting lucky?
Won’t try to do any math, but it doesn’t seem conceptually out of the question. The possibility is exciting, and the lack of movement on the hypothesis lately disappointing.
If the goal of this paper is to show that adding a seven mass super Earth into our solar system makes some of the orbits of our planets unstable, then it certainly convinces me of that. I will add though this might need to be another hypothetical solar system because this idea definitely adds more matter to are primordial accretion disk.
If we use our solar system, the thought experiment has a contingency: We must borrow or subtract seven Earth masses from our solar system’s original gas cloud inside the orbit of Jupiter around the Sun. Consequently, seven Earth masses is more than the inner, rocky planets, so Mercury, Venus, Earth and Mars would be gone and we would only have a Super Earth there. It is interesting to see how easy it is to make the orbits of our planets unstable. Fortunately for us, we never had a super Earth in our solar system otherwise we would not be here today.
What’s strange here is that a planet is added to a simulation, then two million years later, everything goes haywire. There’s this sense we all seem to share that adding arbitrary planets to a system makes it “unstable” even before that is easily visible. What this would seem to imply is that there ought to be some mathematical formula to quantify the instability of a system even before eccentricities change, right at t=0 on these graphs. I don’t know if instability is remotely like a conserved quantity, but if such a formula exists, maybe it could be used to predict positions of unseen exoplanets in well-characterized systems based on an assumption of greatest stability?
Isn’t the 3-body dynamical interaction chaotic? If so, then any n-body interactions are also chaotic, it is just the time for the instabilities to emerge that are at issue. AFAIK, the very nature of the equations does not allow that prediction, as they do not in other situations, such as laminar flow becoming turbulent in fluid flow.
In the approach simulations, it seems that the size of the super-earth and its orbit in relation to other planets may be indicative of the instability perhaps due to the magnitude of the interactions. However, as another commenter mentioned, why are the Trappist-1 planets apparently stable despite being so close to each other? [Maybe it isn’t natural, rather than being very unusual?]
Turbulent flow is one of the things I was thinking of. The distinction between laminar, transitional, or turbulent flow is determined by the Reynolds number. Even though the system is chaotic, a single calculable figure can measure the gradual change in its properties. The first site from a search illustrates this: https://resources.system-analysis.cadence.com
/blog/msa2022-the-differences-between-laminar-vs-turbulent-flow Also, in this case we can’t say the system is totally unpredictable because the very premise is that adding a super-Earth at the asteroid belt reliably causes instability that otherwise won’t be seen. If the observed results don’t vary with the last decimal of the position or mass of the added planet, I don’t think the instability itself is chaotic.
The Trappist-1 system is much smaller than ours: It is a red dwarf star and less gravity,etc which is why the life belt is much loser, the star being much less luminous.
But how does that affect the planets which are gravitationally interacting with each other in what is a smaller HZ? IIRC, in another CD post there was an argument that stability resulted in orbital resonances. IDK if that applies to the planets in the Trappist-1 system.
The same principle general relativity governs the smaller star and system. The red dwarf stars lower gravity means the exoplanets can be stable closer together than our solar system. The moons of Jupiter are a good example.
Like others here, I seriously wonder to what extent such a simulation is universally applicable. Inserting a 7 Me planet in an existing system is hardly comparable to the gradual accretion of the same planet in such a system.
After all, there a numerous stable, compact systems known with super-earths/mini-Neptunes/gas-dwarfs.
And I thought it was widely known and accepted by now that it was the greedy gas giant Jupiter that created the planetary desert between 1.5 and 5.2 AU.
Always interested in these studies since several decades ago, did some of a similar nature ( stability in binary star systems) decades ago. And to state up front, it was with much less fidelity, time scale and precision. But there are a couple of things to note, not that they are likely to change the overall result or outcome.
In the studies then, I noticed a similar cyclic evolution of terrestrial habitable zone planets in terms of eccentricity. Too large a perturbation and the system would blow up, of course. But in addition, and a contributing factor, assuming everything in the same plane, would be the advance in the celestial sphere of the position of perihelion or periastron. The rotation of periastron through 360 degrees of celestial longitude as a result of binary star periastrons incrementally pushed the eccentricity up and down in a 3 body problem. There was descent after 180 of rotation in the eccentricity.
Out of plane was not investigated, but that would complicate the dynamics and obscure underlying reasons for results.
Additionally, so would variations in inclination from an ecliptic plane.
Of course, there are varying ways to gain insights with such tools. For exoplanet systems, we can use them as building blocks. And just as this simulation showed a hazard to our own existence, the report also raised the question why Trappist 1 can be as stable and as long lived as it appears. Perhaps in both cases, maybe backward integration from the current state will uncover some cross roads or points of crisis which resulted in our current configuration. I doubt if an ancient Neptune will show up in a spotlight, but maybe an instability might be shown where the current state cannot be explained any further back in time.
Uranus is 14.5 Earth masses, closer to us than Neptune.