The initial mass function modeled by a left truncated beta distribution

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.

21 pages 5 figures

References in corpus (7)

• Galactic Stellar and Substellar Initial Mass Function
• On the variation of the Initial Mass Function
• Problems with Fitting to the Power-Law Distribution
• How many cosmological parameters?
• The Monitor project: Rotation of low-mass stars in NGC 2362 -- testing the disc regulation paradigm at 5 Myr
• Spectroscopy of brown dwarf candidates in IC 348 and the determination of its substellar IMF down to planetary masses
• The low-mass Initial Mass Function in the young cluster NGC 6611

Cited by in corpus (4)

• A left and right truncated lognormal distribution for the stars
• On the number of galaxies at high redshift
• The truncated Lindley distribution with applications in astrophysics
• A nonextensive insight to the stellar initial mass function