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arXiv · 1212.0939

On the function describing the stellar initial mass function

Thomas Maschberger
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Abstract

We propose a functional form for the IMF, the L_3 IMF, which is a natural heavy-tailed approximation to the log-normal distribution. It is composed of a low-mass power law and a high mass power-law which are smoothly joined together. Three parameters are needed to achieve this. The standard IMFs of Kroupa-2001a, Kroupa-2002a and Chabrier-2003b (single stars or systems) are essentially indistinguishable from this form. Compared to other 3-parameter functions of the IMF, the L_3 IMF has the advantage that the cumulative distribution function and many other characteristic quantities have a closed form, the mass generating function, for example, can be written down explicitly.

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Thomas Maschberger. 2012-12-05. On the function describing the stellar initial mass function. https://doi.org/10.1093/mnras/sts479

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