A Prediction of Brown Dwarfs in Ultracold Molecular Gas

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Abstract
A recent model for the stellar initial mass function (IMF), in which the stellar masses are randomly sampled down to the thermal Jeans mass from hierarchically structured prestellar clouds, predicts that regions of ultracold CO gas, such as those recently found in nearby galaxies by Allen and collaborators, should make an abundance of brown dwarfs with relatively few normal stars. This result comes from the low value of the thermal Jeans mass, which scales as MJ ∝ T2/P1/2 for temperature T and pressure P, considering that the hierarchical cloud model always gives the Salpeter IMF slope above this lower mass limit. The ultracold CO clouds in the inner disk of M31 have T ~ 3 K and pressures that are probably 10 times higher than in the solar neighborhood. This gives a mass at the peak of the IMF equal to 0.01 M☉, well below the brown dwarf limit of 0.08 M☉. Using a functional approximation to the IMF given by [1 - e-(M/MJ)2]M -1.35d log M for M > MJ, which fits the local IMF for the expected value of MJ ~ 0.3 M☉, an IMF with MJ = 0.01 M☉ in M31 has 50% of the mass and 90% of the objects below the brown dwarf limit. The brightest of the brown dwarfs in M31 should have an apparent extinction-corrected K-band magnitude of ~30 mag in their pre-main-sequence phase. For typical star formation efficiencies of ≤10%, brown dwarfs and any associated stars up to ~2.5 M☉ should not heat the gas noticeably, but if the IMF continues up to arbitrarily high masses, then the star formation efficiency must be ≤10-4 to avoid heating from massive stars.
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