A Dual Power Law Distribution for the Stellar Initial Mass Function

TL;DR

This paper introduces a new dual power law distribution for the initial mass function of stars and brown dwarfs, capturing both high and low mass behaviors without relying on traditional seed mass assumptions.

Contribution

The novel dual power law distribution unifies the formation processes of stars and brown dwarfs within a stochastic accretion framework, differing from previous models.

Findings

The DPL distribution fits empirical stellar mass data well.

The critical mass aligns with the substellar mass limit.

Accretion stopping probabilities influence the low mass end.

Abstract

We introduce a new dual power law (DPL) probability distribution function for the mass distribution of stellar and substellar objects at birth, otherwise known as the initial mass function (IMF). The model contains both deterministic and stochastic elements, and provides a unified framework within which to view the formation of brown dwarfs and stars resulting from an accretion process that starts from extremely low mass seeds. It does not depend upon a top down scenario of collapsing (Jeans) masses or an initial lognormal or otherwise IMF-like distribution of seed masses. Like the modified lognormal power law (MLP) distribution, the DPL distribution has a power law at the high mass end, as a result of exponential growth of mass coupled with equally likely stopping of accretion at any time interval. Unlike the MLP, a power law decay also appears at the low mass end of the IMF. This feature is closely connected to the accretion stopping probability rising from an initially low value up to a high value. This might be associated with physical effects of ejections sometimes (i.e., rarely) stopping accretion at early times followed by outflow driven accretion stopping at later times, with the transition happening at a critical time (therefore mass). Comparing the DPL to empirical data, the critical mass is close to the substellar mass limit, suggesting that the onset of nuclear fusion plays an important role in the subsequent accretion history of a young stellar object.