The initial mass function modeled by a left truncated beta distribution

TL;DR

This paper proposes a novel left truncated beta distribution model for the initial mass function of stars, demonstrating its advantages over traditional models through statistical tests on star cluster data.

Contribution

Introduces a left truncated beta distribution for modeling the initial mass function, providing explicit calculations and advantages over existing models.

Findings

The left truncated beta distribution fits star mass data effectively.

Statistical tests show improved fit over traditional models.

Application to star clusters NGC 6611 and NGC 2362 confirms model validity.

Abstract

The initial mass function (IMF) for the stars is usually fitted by three straight lines, which means seven parameters. The presence of brown dwarfs (BD) increases to four the straight lines and to nine the parameters. Another common fitting function is the lognormal distribution, which is characterized by two parameters. This paper is devoted to demonstrating the advantage of introducing a left truncated beta probability density function, which is characterized by four parameters. The constant of normalization, the mean, the mode and the distribution function are calculated for the left truncated beta distribution. The normal-beta (NB) distribution which results from convolving independent normally distributed and beta distributed components is also derived. The chi-square test and the K-S test are performed on a first sample of stars and BDs which belongs to the massive young cluster NGC 6611 and on a second sample which represents the star's masses of the cluster NGC 2362.