Abstract
In recent years we have learned how tricky is the determination of the IMF at the low luminosity end of the main sequence. I recall here the main reasons why the stellar structure computations produce a functional form of the mass-luminosity relation for M ≤ 0.5M ⊙ which, coupled with the observationally determined luminosity function in the visual band, produces a smoothly increasing IMF down to M=0.1M ⊙.
I discuss then the updates of the theory and the large errors which still weigh on the derivation of luminosity and effective temperature from the observational data.
I further consider whether the recent detection of several infrared (substellar?) companions to intrinsically faint stars may give us further hints on the mass-luminosity relation close to the end of the main sequence, and, second, to the number density expected for single brown dwarfs in the galactic disk.
I finally review the problems emerging from the consideration of the luminosity function based on stellar counts in the infrared bands.
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D’Antona, F. (1990). The Initial Mass Function of Very Low Mass Stars and the Significance of Brown Dwarfs. In: Capuzzo-Dolcetta, R., Chiosi, C., di Fazio, A. (eds) Physical Processes in Fragmentation and Star Formation. Astrophysics and Space Science Library, vol 162. Springer, Dordrecht. https://doi.org/10.1007/978-94-009-0605-1_32
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DOI: https://doi.org/10.1007/978-94-009-0605-1_32
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