<p>I've found <a href="https://citeseerx.ist.psu.edu/viewdoc/download?doi=10.1.1.674.777&amp;rep=rep1&amp;type=pdf" rel="noreferrer">a paper</a>(1) with estimates based on extrapolation of known data for stellar-mass objects toward smaller values, using a <a href="https://en.wikipedia.org/wiki/Power_law#Power-law_probability_distributions" rel="noreferrer">power law probability distribution</a>:</p>
<blockquote>
<p>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 ,</p>
<p>nJ = 6.7(+6.4/−3.0) × 10^−3 ly^−3 (1)</p>
<p>and thus an estimate for the expected mean distance to the nearest
Jupiter mass nomadic planet, DJ , with</p>
<p>DJ = 3.28(+0.7/−0.6) ly , (2)</p>
<p>the mean minimum distance being ∼77% of the distance to Proxima
Centauri.</p>
</blockquote>
<p>The error margin is huge, specially when extending the model to poorly constrained low mass objects:</p>
<blockquote>
<p>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.</p>
</blockquote>
<p>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:</p>
<pre><code>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)
</code></pre>
<p>In graph form:</p>
<p><a href="https://i.sstatic.net/zh6eX.png" rel="noreferrer"><img src="https://i.sstatic.net/zh6eX.png" alt="enter image description here" /></a></p>
<p>References:</p>
<p>(1) Eubanks, T. M. (2014). Nomadic Planets Near the Solar System.</p>

CC BY-SA 4.0
2022-08-18T08:01:19.500Z
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
CC BY-SA 4.0
2022-08-18T11:27:30.737Z
@ProfRob I'll edit the answer to expand it.
ksousa
CC BY-SA 4.0
2022-08-18T11:48:45.880Z
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
CC BY-SA 4.0
2022-08-18T20:41:12.547Z
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
CC BY-SA 4.0
2022-08-17T22:07:08.450Z
2022-08-18T12:39:18.463Z
2022-08-18T12:39:18.463Z
ksousa
<p>There are some articles that claim there could be more rogue planets than stars in our galaxy such as <a href="https://news.osu.edu/rogue-planets-could-outnumber-the-stars/" rel="nofollow noreferrer">this one</a>.</p>
<p>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?</p>

CC BY-SA 4.0
2022-08-17T21:27:51.563Z
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
CC BY-SA 4.0
2022-08-17T22:04:00.117Z
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
CC BY-SA 4.0
2022-08-18T07:51:22.180Z
@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
CC BY-SA 4.0
2022-08-18T08:06:07.573Z
@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
CC BY-SA 4.0
2022-08-18T08:41:29.427Z
Why would they be "flung from the arms"? @MSalters
ProfRob
CC BY-SA 4.0
2022-08-18T08:57:50.167Z
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
CC BY-SA 4.0
2022-08-18T10:22:26.103Z
@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
CC BY-SA 4.0
2022-08-18T10:45:03.880Z
@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
CC BY-SA 4.0
2022-08-18T10:48:01.193Z
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
<rogue-planet>
Are there any probabilistic models for the likelihood of finding a rogue planet closer to us than Proxima Centauri?
Sidharth Ghoshal
# Are there any probabilistic models for the likelihood of finding a rogue planet closer to us than Proxima Centauri?

(Asked by: username_0 on 2022-08-17)

There are some articles that claim there could be more rogue planets than stars in our galaxy such as [this one](https://news.osu.edu/rogue-planets-could-outnumber-the-stars/).

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?

**Tags:** rogue-planet
> **Comments:**
> **username_1**: 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).  
> **username_2**: 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.  
> **username_1**: @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?  
> **username_3**: @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.  
> **username_1**: Why would they be "flung from the arms"? @MSalters  
> **username_1**: 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.  
> **username_3**: @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.  
> **username_1**: @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...  
> **username_1**: 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.  

---

## 1 answers

### Answer by username_4 on 2022-08-17. Score: 14 | Accepted answer

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.

> **Comments:**
> **username_1**: 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?  
> **username_4**: @ProfRob I'll edit the answer to expand it.  
> **username_1**: 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.  
> **username_5**: 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?  

---

