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I read this question

Why is planet CFBDSIR2149-0403 hot?

and wonder what will happen to this "planemo". Will it attract more mass as it flows around in the gas clouds in space and eventually light up and become a star?

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    $\begingroup$ The word "planemo" (for "planetary-mass object") was new to me. Commenting to save others the hassle of looking it up. $\endgroup$ – rob Jul 13 '19 at 19:00
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It is very unlikely that a planetary mass object will accrete enough mass to take it above the mass limit (about $0.075 M_{\odot}$) to become a bona fide star supported by pp H-burning reactions.

An order of magnitude calculation might suffice.

An average sort of velocity that such objects might be moving at relative to the interstellar medium (ISM) is of order 10 km/s.

The ISM density is the biggest variable here - it could be anywhere between about $10^{-23}$ to $10^{-15}$ kg/m$^{3}$ in the densest molecular clouds. An average value might be around $10^{-21}$ kg/m$^3$.

The sound speed in the ISM is around 1 km/s in molecular clouds, but much higher elsewhere.

The relevant physics here is the Bondi-Hoyle accretion rate - an approximate formula that says a compact object moving through a medium will accrete at $$\dot{M} \simeq \frac{2\pi G^2M^2 \rho}{(v^2 + c_s^2)^{3/2}}, $$
where $M$ is the object's mass, $v$ its velocity with respect to a medium with density $\rho$ and $c_s$ the sound speed.

So, in the optimal case of say a $0.05M_{\odot}$ planetary mass object (well, actually a brown dwarf) moving at 10 km/s through a molecular cloud, then $\dot{M}$ is of order a few $10^{-12} M_{\odot}$/year. Thus it could be that over the course of billions of years an object could accumulate the hundredths of a solar mass required to form a star. However, the case considered above is very optimal. An object travelling at 10 km/s will spend only a small fraction of its life passing through molecular clouds and instead will encounter a medium with a density that is orders of magnitude lower and a sound speed that is order of magnitudes higher.

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  • $\begingroup$ Why does speed of sound matter? Thank you. $\endgroup$ – d-b Jul 15 '19 at 13:47
  • $\begingroup$ @d-b It doesn't if it is less than $v$. However if dynamical effects are unimportant then one has to consider the way that pressure slows down the accretion rate. The sound speed enters as a way of characterising the relationship between pressure and density. See adsabs.harvard.edu/cgi-bin/bib_query?1952MNRAS.112..195B $\endgroup$ – Rob Jeffries Jul 15 '19 at 15:19

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