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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?

Glorfindel
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Sidharth Ghoshal
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    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). – ProfRob Aug 17 '22 at 21:27
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    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. – Greg Miller Aug 17 '22 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? – ProfRob Aug 18 '22 at 07:51
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    @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. – MSalters Aug 18 '22 at 08:06
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    Why would they be "flung from the arms"? @MSalters – ProfRob Aug 18 '22 at 08:41
  • The populations that are behind the claim that they outnumber stars are clearly within the stellar population - in the plane towards the galactic bulge (microlensing surveys) or found as a co-moving population in young star forming regions. – ProfRob Aug 18 '22 at 08:57
  • @ProfRob: Well, the rogue planets are assumed to have left the orbits around the stars where they formed., and did not enter the orbit of another star. Those arms are pretty much defined by the concentration of stars, but if the rogue planets aren't bound by those stars, then why should they still stick to those arms? There's probably evidence, but we cannot blindly assume the distribution of these planets without considering evidence. We need some kind of model which produces verifiable hypotheses. – MSalters Aug 18 '22 at 10:22
  • @MSalters The basis on which it is claimed that planets outnumber stars is on discovered populations that coexst with the stars and, in the case of populations in star forming regions, are co-moving with them. There is no assumption involved. Spiral arms are not major concentrations of mass, they are concentrations of star forming activity. Planets "stick" exactly for the same reason stars do. Gravitational acceleration is independent of inertial mass. You are assuming that rogue planets originate from orbits around stars. It isn't clear where they come from. Continued... – ProfRob Aug 18 '22 at 10:45
  • The majority detected so far may have formed as low mass objects in star forming regions - i.e. they formed like low-mass stars. Only if their "birth" velocity distributions are very different to stars (and by that I mean if they had velocity dispersions that exceeded that of low-mass stars in the galaxy) will their spatial distribution at later times differ from stars. – ProfRob Aug 18 '22 at 10:48

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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:

enter image description here

References:

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

ksousa
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    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? – ProfRob Aug 18 '22 at 08:01
  • @ProfRob I'll edit the answer to expand it. – ksousa Aug 18 '22 at 11:27
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    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. – ProfRob Aug 18 '22 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? – Dan Is Fiddling By Firelight Aug 18 '22 at 20:41