How many planets could be in the Kuiper Belt?

ApJL: 

Motivated by recent measurements of the free-floating-planet mass function at terrestrial masses, we consider the possibility that the solar system may have captured a terrestrial planet early in its history. We show that ∼1.2 captured free-floating planets with mass strictly greater than that of Mars may exist in the outer solar system, with a median predicted distance of ∼1400 au.

To evaluate the expected mass of the most massive captured free-floating planet as a function of the maximum semimajor axis, given the arguments presented in Section 2, we implement a Monte Carlo simulation.

This is an interesting calculation, but the result of ~1 free-floating planet does not have a reported error and seems extremely sensitive to the mass function. Equation 1 gives the mass function of free-forming planets:

The coefficient on the power-law term has substantial errorbars, changing the result of the mass function by up to 75% if alpha ~ 1. Examining alpha as well, the paper reports that alpha ~ 0.96 \pm 0.47, which would have a substantial effect on the value of the mass function. It wasn't immediately clear how this substantial variation affected the number of planets detected. Figure 1 shows the confidence intervals on the mass estimate for a planet of abundance unity, but I wasn't able to immediately grasp how to convert this into an errorbar on the planet abundance estimate. Then Figure 2 shows the cumulative fraction and expected number of captured free-floating planets, but doesn't show the confidence intervals. So overall, it's hard to assess the free-floating planet abundance estimate from their simulations given the huge spread on the parameters. The estimate changes from ~1 to ~3 with a change of binning, which is expected but also highlights how uncertain the estimate and approach are, so it would been interesting to see a more thorough exploration of this.

Phys.org:

A recent study published in the Astrophysical Journal Letters investigates the potential existence of Mars-sized free-floating planets (FFPs)—also known as rogue planets, starless planets, and wandering planets—that could have been captured by our sun's gravity long ago and orbit in the outer solar system approximately 1,400 astronomical units (AU) from the sun.

Scientists currently hypothesize that rogue planets are formed from two scenarios: As part of their own solar system but are then somehow ejected into the cosmos, or they form in isolation. But what is the significance of studying free-floating planets, overall?

After conducting approximately 100,000,000 simulations, the results indicate the potential for the existence of a Mars-sized, or even a Mercury-sized planetary body somewhere in the outer solar system approximately 1,400 AU from the Sun.

Universe Today:

Siraj recommends in his study that future work could include gaining greater understanding of how rogue planets are captured in the first place, along with investigating observational tests to identify where to look in the sky for rogue planets, as well. He also notes how microlensing has become the preferred method in identifying rogue planets based on past studies.

Rogue planet capture is extremely interesting for sure. I'm also super interested in the related phenomenon of JuMBOs (Jupiter-Mass Binary Objects), which are forcing astrophysicists to confront the same tough questions as this study.

Previously on this blog:

• An Earth-sized Planet around an M5 Dwarf Star at 22 pc
• Scientists think they know why interstellar object 'Oumuamua moved so strangely
  

Scientists think they know why interstellar object 'Oumuamua moved so strangely

nature:

In 2017, 1I/‘Oumuamua was identified as the first known interstellar object in the Solar System1. Although typical cometary activity tracers were not detected, ‘Oumuamua showed a notable non-gravitational acceleration. 

Here we report that the acceleration of ‘Oumuamua is due to the release of entrapped molecular hydrogen that formed through energetic processing of an H2O-rich icy body...We show that this mechanism can explain many of ‘Oumuamua’s peculiar properties without fine-tuning.

UChicago:

But when ‘Oumuamua was discovered, it had no tail and was too small and too far from the sun to capture enough energy to eject much water, which led astronomers to speculate wildly about its composition and what was pushing it outward. Was it a hydrogen iceberg? A large, fluffy snowflake pushed by light pressure from the sun? 

Perhaps, they wondered, its strange acceleration actually came from hydrogen...If so, perhaps the force produced by the hydrogen outgassing could explain ‘Oumuamua’s odd movement.

“For a comet several kilometers across, the outgassing would be from a really thin shell relative to the bulk of the object, so both compositionally and in terms of any acceleration, you wouldn’t necessarily expect that to be a detectable effect,” she said. “But because ‘Oumuamua was so small, we think that it actually produced sufficient force to power this acceleration.”

NPR:

Scientists have come up with a simple explanation for the strange movements of our solar system's first known visitor from another star.

Oddly, this interstellar object appeared to be slightly accelerating in a way that normally is associated with the outgassing of some kind of material. But astronomers couldn't detect any comet-like tail of dust or gas...Now, though, in the journal Nature, two researchers say the answer might be the release of hydrogen from trapped reserves inside water-rich ice.

"It's an interesting, creative idea," says Karen Meech, with the Institute for Astronomy at the University of Hawaii, who leads the team that initially found and observed 'Oumuamua. "It doesn't require a super-exotic mechanism." But she still thinks it's possible that 'Oumuamua is just a regular, ordinary comet that released enough water, carbon dioxide, and carbon monoxide to account for the acceleration, and astronomers just didn't detect it.

Meech also finds the elongated shape of the object far more intriguing than the odd acceleration, which could be explained by low quantities of ordinary comet ejecta. The currently accepted explanation for the shape is that 'Oumuamua like objects are kicked out during planetary formation.

Scientific American:

Planet formation is a messy process in which worlds emerge from the embryonic disks of gas and dust that give birth to stars themselves. As debris clumps together and grows, whirling around the central star, its gravity pushes and scatters smaller clumps throughout the disk. 

Multiple theories postulate that such processes are responsible for sending ‘Oumuamua our way. Researchers have proposed that the strange object may have been thrown out of its young system after a brush with a giant planet there.

NASA: 

The object, named ‘Oumuamua by its discoverers, is up to one-quarter mile (400 meters) long and highly-elongated—perhaps 10 times as long as it is wide. That aspect ratio is greater than that of any asteroid or comet observed in our solar system to date. While its elongated shape is quite surprising, and unlike objects seen in our solar system, it may provide new clues into how other solar systems formed.