# Are there any probabilistic models for the likelihood of finding a rogue planet closer to us than Proxima Centauri?

There are some articles that claim there could be more rogue planets than stars in our galaxy such as this one.

Now if this were true one might expect that there is a rogue planet closer to the earth than the star Proxima Centauri. Have any models been built regarding the probability of this? And/or perhaps a curve of mass of rogue object, distance from Earth, and probability?

• Why do we need a model? If there are more rogue planets than stars, moving in the same galactic potential, then the nearest one should be nearer than the nearest star (on average). Commented Aug 17, 2022 at 21:27
• The best place to look would be the study making the claim (linked in the article). It is a poor assumption that just because they out number stars, that they follow the same distribution pattern as stars. So it wouldn't be a given that there'd be one closer than the nearest star. Commented Aug 17, 2022 at 22:04
• @GregMiller I'm sure you're right, but could you outline why they would have a different distribution to say low-mass stars? Presumably their birth velocity distribution? Commented Aug 18, 2022 at 7:51
• @ProfRob: Isn't "same galactic potential" essentially that requested probabilistic model? Imagine for a second that rogue planets could be flung from the arms and end up uniformly distributed, unlike the starts. In this model, the probability of a rogue planet near the Sun is significantly less than 1. Commented Aug 18, 2022 at 8:06
• Why would they be "flung from the arms"? @MSalters Commented Aug 18, 2022 at 8:41

I've found a paper(1) with estimates based on extrapolation of known data for stellar-mass objects toward smaller values, using a power law probability distribution:

Sumi et al.[4] used microlensing data to estimate the ratio of the number density of Jupiter-mass unbound exoplanets, nj , and the number density of main sequence stars n⋆, yielding an estimate nJ / n⋆ = 1.9(+1.3/−0.8) for their power law model. The stellar number density is well known from luminosity data [9], yielding an estimate for nJ ,

nJ = 6.7(+6.4/−3.0) × 10^−3 ly^−3 (1)

and thus an estimate for the expected mean distance to the nearest Jupiter mass nomadic planet, DJ , with

DJ = 3.28(+0.7/−0.6) ly , (2)

the mean minimum distance being ∼77% of the distance to Proxima Centauri.

The error margin is huge, specially when extending the model to poorly constrained low mass objects:

In order to predict the number densities of nomadic exoplanets with masses much smaller than that of Jupiter it is necessary to extrapolate the power law density models into mass regimes not yet well constrained by microlensing [13], leading to the three order of magnitude uncertainty in the number density of Earth-mass nomads in Figure 1 and the factor of almost 6 uncertainty in the distance to the nearest Earth-mass nomad seen in Figure 2.

Then their model points to these expected minimum distances, for the closest object of a given mass, taking the mass of a equivalent solar system object for comparison. If these estimates are correct, we should expect many planetary-mass objects to be found closer to us than Proxima Centauri:

Object          Mass        Expected
Analog                      Rmin

(MJupiter)  (ly)

Earth           0.003       1.85 (+2.99/−1.01)
Uranus          0.046       2.41 (+2.02/−0.99)
Neptune         0.054       2.45 (+1.95/−0.99)
Saturn          0.299       2.91 (+1.24/−0.84)
Jupiter         1           3.28 (+0.71/−0.65)
super-Jupiter   10          4.52 (+1.16/−1.61)


In graph form:

References:

(1) Eubanks, T. M. (2014). Nomadic Planets Near the Solar System.

• Could you just summarise what the paper assumes about the number density and distribution of rogue planets. Does it match the stipulation in the question and by how many times do the planets outnumber stars? Commented Aug 18, 2022 at 8:01
• @ProfRob I'll edit the answer to expand it. Commented Aug 18, 2022 at 11:27
• Yeah, it is just using a number density of Jupiter-mass rogue planets, determined from microlensing, that is twice that of stars, Assuming that they are distributed in the same way as stars, then the nearest one should be a factor of $2^{1/3}$ closer than the nearest star. The rest is extrapolating a power law mass distribution (with significant uncertainties on the index) to lower masses. Nice paper. Commented Aug 18, 2022 at 11:48
• Are they just using "stars" as a single point for a 2 point model with Jupiter sized objects, or taking an existing distribution across various star sizes and using the number of Jupiter sized objects found to extend it below the red dwarf limit? Commented Aug 18, 2022 at 20:41