Allen, Peter R. and Koerner, David W. and Reid, I. Neill and Trilling, David E. (2005) The substellar mass function: A Bayesian approach. Astrophysical Journal, 625 (1). pp. 385397. ISSN 15384357

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Abstract
We report our efforts to constrain the form of the lowmass star and brown dwarf mass function via Bayesian inference. Recent surveys of M, L, and T dwarfs in the local solar neighborhood are an essential component of our study. Uncertainties in the age distribution of local field stars make reliable inference complicated. We adopt a wide range of plausible assumptions about the rate of Galactic star formation and show that their deviations from a uniform rate produce little effect on the resulting luminosity function for a given mass function. As an ancillary result, we calculate the age distribution for M, L, and T spectral types. We demonstrate that late L dwarfs, in particular, are systematically younger than objects with earlier or later spectral types, with a mean age of 3 Gyr. Finally, we use a Bayesian statistical formalism to evaluate the probability of commonly used mass functions in the light of recent discoveries. We consider three functional forms of the mass function, including a twosegment power law, a single power law with a lowmass cutoff, and a lognormal distribution. Our results show that at a 60% confidence level the powerlaw index α for the lowmass arm of a twosegment power law has a value between 0.6 and 0.6 for objects with masses between 0.04 and 0.10 Mcircle dot;. The bestfit index is alpha = 0.3 plus or minus; 0.6 at the 60% confidence level for a singlesegment mass function. Current data require this function to extend to at least 0.05 Mcircle dot with no restrictions placed on a lower mass cutoff. Inferences of the parameter values for a lognormal mass function are virtually unaffected by recent estimates of the local space density of L and T dwarfs. We find that we have no preference among these three forms using this method. We discuss current and future capabilities that may eventually discriminate between mass function models and refine estimates of their associated parameter values.
Item Type:  Article 

ID number or DOI:  10.1086/429548 
Keywords:  brown dwarfs; dynamical interactions; extrasolar giant planets; formation history; infrared photometry; luminosity functions; solar neighborhood; stars : evolution; stars : lowmass, brown dwarfs; stars : luminosity function, mass function; star spectroscopic survey; tdwarfs; ultracool dwarfs 
Subjects:  Q Science > QB Astronomy 
NAU Depositing Author Academic Status:  Faculty/Staff 
Department/Unit:  College of Engineering, Forestry, and Natural Science > Physics and Astronomy 
Date Deposited:  29 Sep 2015 22:00 
URI:  http://openknowledge.nau.edu/id/eprint/87 
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