Can rogue/nomad planets and other starless planetary bodies orbit each other in a stable system?

Question

Nomad planets (also called planemos or rogues planets) which drift in space without a star or substellar object to orbit. The majority of such planets we have discovered are gas planets with thick atmospheres and no landmass, although some of them could be frozen deserts with rocky surfaces like Earth's.

Most nomad planets we have found are alone/solitary, and do not orbit any other companion objects. We have only discovered 1 (as in 1.0) binary planemo called 2MASS J11193254–1137466.

What I'm asking here is that can a large system of 6 or 7 rogue planets and other planetary bodies orbit each other and remain stable; basically like a tiny open cluster or huge multiple star system, just comprised of planets instead of stars?

Answer 1

What I'm asking here is that can a large system of 6 or 7 rogue planets and other planetary bodies orbit each other and remain stable; basically like a tiny open cluster or huge multiple star system, just comprised of planets instead of stars?

Sure! (but...)

If you have a half-dozen bodies in a group, and the total energy (kinetic plus potential) is less than the energy it would take to move any of them to infinity, then they are a gravitationally bound system and they'll stay together forever.†

^†This is probably not true; @RobJeffries' comments (1, 2) bring up pairings, and so even in a situation where moving "any one of them" was energetically possible, it could might for example be possible for a bound pair. I'll update this soon...

An extreme example would be a cluster that are touching and at rest, a second extreme example would be that cluster given a bit of a "kick" to start it jostling.

A good question might be "Given a half-dozen bodies of equal mass $m$ what is the farthest one can be from it's nearest neighbor while the system is still energetically bound?" A follow-up might be the same except remove the "equal mass $m$" part. I don't know the answer to that question, perhaps someone else will post an answer here with it.

Without a "Sun" or particularly large central body, their motion will be chaotic, and any apparent organization (pairings or higher) will sooner or later be disturbed by another body.

Actually there is chaos in (probably) all real-work n-body system, but in cases like our solar system this would take quite a long time to show up.

If you have a particular configuration in mind, you can calculate if the system is bound or not with a little math. Here the total energy $E$ is the sum of potential energy $U$ and kinetic energy $T$:

$$E = U + T = \sum_{i\neq j} -G\frac{m_i m_j}{|\mathbf{r_i}-\mathbf{r_j}|} + \sum_{i} \frac{1}{2}m_i v_i^2 $$

Where $|\mathbf{r_i}-\mathbf{r_j}|$ is the distance between each pair of objects with masses $m_i$ and $m_j$, $v_i^2$ is the square of the speed, and $G$ is the Gravitatinal constant.

but...

Systems are never isolated in the real world, so for example - another body could pass by and disturb the system and eject one or more members. - two bodies could collied and exchange mass, momentum, and energy, allowing one or more fragment to escape. - other things...

Answer 2

One of the main hypotheses for the formation of rogue planets is ejection from a preexisting planetary system. This is an unlikely scenario for the formation of a cluster of rogue planets, because it doesn't seem feasible for a whole bunch of bodies to be ejected together and remain in a stable system. If multiple planets were ejected from a planetary system, I would expect them to exit randomly and separately.

That said, a couple sub-brown dwarfs have been observed to host what may be protoplanetary disks (although that term may not be applicable in these cases). The important objects here are Cha 110913-773444 ($\sim8M_J$) and OTS 44 ($\sim11M_J$). These objects have not been classified yet; they could be considered rogue planets or sub-brown dwarfs (or even brown dwarfs, honestly). Assuming the normal processes active in protoplanetary disks take place - collisions, accretion and the like - then in the future, additional bodies could form.

OTS 44 is thought to have a disk of around 30 Earth masses (Joergens et al. 2013); depending on the efficiency of planet formation, we might see bodies similar in mass to terrestrial planets (note that this also depends on disk composition; much of it is likely to be hydrogen and helium, not silicates). Giant planets seem unlikely, as the disks mass is comparable to those of Uranus and Neptune, within a factor of two, and it is highly unlikely that the entire disk would coalesce into one planet.

If a rogue planet formed in situ, rather than being ejected from a system, we do have a different picture to consider. In this case, it seems more likely for binary rogue planets to form. At this point, of course, the label "sub-brown dwarf" is more appropriate than "rogue planet".