Exactly how astrophysicists model entire stellar systems through computer simulations has always struck me as something akin to magic. Of course, the same thought applies to any computational methods that involve interactions between huge numbers of objects, from molecular dynamics to plasma physics. My amazement is the result of my own inability to work within any programming language whatsoever. The work I’m looking at this morning investigates planet formation within protoplanetary disks. It reminds me again just how complex so-called N-body simulations have to be.
Two scientists from Rice University – Sho Shibata and Andre Izidoro – have been investigating how super-Earths and mini-Neptunes form. That means simulating the formation of planets by studying the gravitational interactions of a vast number of objects. N-body simulations can predict the results of such interactions in systems as complex as protoplanetary disks, and can model formation scenarios from the collisions of planetesimals to planet accretion from pebbles and small rocks. All this, of course, has to be set in motion in processes occurring over millions of years.
Image: Super-Earths and mini-Neptunes abound. New work helps us see a possible mechanism for their formation. Credit: Stock image.
Throw in planetary migration forced by conditions within the disk and you are talking about complex scenarios indeed. The paper runs through the parameters set by the researchers as to disk viscosity and metallicity and uses hydrodynamical simulations to model the movement of gas within the disk. What is significant in this study is that the authors deduce planet formation within two rings at specific locations within the disk, instead of setting the disk model as a continuous and widespread distribution. Drawing on prior work he published in Nature Astronomy in 2021, Izidoro comments:
“Our results suggest that super-Earths and mini-Neptunes do not form from a continuous distribution of solid material but rather from rings that concentrate most of the mass in solids.“
Image: This is Figure 7 from the paper. Caption: Schematic view of where and how super-Earths and mini-Neptunes form. Planetesimal formation occurs at different locations in the disk, associated with sublimation and condensation lines of silicates and water. Planetesimals and pebbles in the inner and outer rings have different compositions, as indicated by the different color coding (a). In the inner ring, planetesimal accretion dominates over pebble accretion, while in the outer ring, pebble accretion is relatively more efficient than planetesimal accretion (b). As planetesimals grow, they migrate inward, forming resonant chains anchored at the disk’s inner edge. After gas disk dispersal, resonant chains are broken, leading to giant impacts that sculpt planetary atmospheres and orbital reconfiguration (c). Credit: Shibata & Izidoro.
Thus super-Earths and mini-Neptunes, known to be common in the galaxy, form at specific locations within the protoplanetary disk. Ranging in size from 1 to 4 times the size of Earth, such worlds emerge in two bands, one of them inside about 1.5 AU from the host star, and the other beyond 5 AU, near the water snowline. We learn that super-Earths form through planetesimal accretion in the inner disk. Mini-Neptunes, on the other hand, result from the accretion of pebbles beyond the 5 AU range.
A good theory needs to make predictions, and the work at Rice University turns out to replicate a number of features of known exoplanetary systems. That includes the ‘radius valley,’ which is the scarcity of planets about 1.8 times the size of Earth. What we observe is that exoplanets generally form at roughly 1.4 or 2.4 Earth size. This ‘valley’ implies, according to the researchers, that planets smaller than 1.8 times Earth radius would be rocky super-Earths. Larger worlds become gaseous mini-Neptunes.
And what of Earth-class planets in orbits within a star’s habitable zone? Let me quote the paper on this:
Our formation model predicts that most planets with orbital periods between 100 days < P < 400 days are icy planets (>10% water content). This is because when icy planets migrate inward from the outer ring, they scatter and accrete rocky planets around 1 au. However, in a small fraction of our simulations, rocky Earthlike planets form around 1 au (A. Izidoro et al. 2014)… While the essential conditions for planetary habitability are not yet fully understood, taking our planet at face value, it may be reasonable to define Earthlike planets as those at around 1 au with rocky-dominated compositions, protracted accretion, and relatively low water content. Our formation model suggests that such planets may also exist in systems of super-Earths and mini-Neptunes, although their overall occurrence rate seems to be reasonably low, about ∼1%.
That 1 percent is a figure to linger on. If the planet formation mechanisms studied by the authors are correct in assuming two rings of distinct growth, then we can account for the high number of super-Earths and mini-Neptunes astronomers continue to find. Such planets are currently thought to orbit about 30 percent of Sun-like stars, meaning that there would be no more than one Earth-like planet around every 300 such stars.
How seriously to take such results? Recognizing that the kind of computation in play here take us into realms we cannot verify through experiment, it’s important to remember that we have to use tools like N-body simulations to delve deeply into emergent phenomena like planets (or stars, or galaxies) in formation. The key is always to judge computational results against actual observation, so that insights can turn into hard data. Being a part of making that happen is what I can only call the joy of astrophysics.
The paper is Shibata & Izidoro, “Formation of Super-Earths and Mini-Neptunes from Rings of Planetesimals,” Astrophysical Journal Letters Vol. 979, No. 2 (21 January 2025), L23 (full text). The earlier paper by Izidoro and team is “Planetesimal rings as the cause of the Solar System’s planetary architecture,” Nature Astronomy Vol. 6 (30 December 2021), 357-366 (abstract).
Does this analysis have anything to say about habitability, especially where rocky super-earths end up in orbits within or outside their star’s HZ? Their greater mass implies that their atmospheres may be thicker and denser, and less likely to be stripped. What about water content? For life, a planet doesn’t need to be Earth-sized, although a super-Earth’s civilization may have more difficulty reaching space without more energetic propulsion systems for rockets, and space elevators may be out of the question. But that doesn’t mean that they couldn’t be space faring. What would life be like on such worlds – would the denser atmosphere more than compensate for the higher gravity allowing more animals to fly or even float (like fish)? Could the biosphere be richer and more diverse than our own. If a hycean world, would we see mostly swimming and flying/floating animals, but few legged animals, except on the ocean bottom? What would the atmosphere composition be – more CO2 and H2? How would that impact energy capture and presumably carbon fixation? Would it affect our expectations of biosignatures?