# We are sure that there are no brown dwarfs closer than ______

I don't quite know how to word this question.

How close could a brown dwarf be to us and have gone undetected until now?

Or maybe, with what probability are we sure that there is no brown dwarf within X light years of the sun? (For different values of X)

(Don't worry about addressing Nemesis or a hypothetical binary partner for the sun. I'm just asking about undetected brown dwarfs..., even outside of the Oort cloud but within Alpha C. I don't know how sensitive the WISE survey was.)

• – Rob Jeffries Jan 20 '16 at 19:24
• The summary answer is a few light years, maybe 5, since ultracool brown dwarfs only a few light years away have been found in all-sky surveys. – Rob Jeffries Jan 20 '16 at 19:26

Some details: As an example let's take a very low mass brown dwarf - say 20 Jupiter masses and 5 billion years old - and place it 4 light years from the Sun. According to the evolutionary models of Saumon & Marley (2008), such an object has an intrinsic luminosity of $10^{-7}$ times (1 ten millionth) that of the Sun and a temperature of 400 Kelvin and would appear to have a spectral type of late T or early Y. This is similar to the coolest brown dwarfs yet found.
From the calibration of absolute magnitudes versus spectral type for cool brown dwarfs in Marsh et al. (2013) we know that at 4 light years, such a brown dwarf would have magnitudes of $H=16$ and $W2=10$. The former is just about bright enough to have been seen in the 2MASS all-sky survey and the latter is easily detected by WISE. The combination of data would also easily have revealed the large parallax of such an object. We can conclude that an object would have to have much lower mass than this to remain undetected and thus would arguaby not be called a brown dwarf, but would really be a "free-floating planet".