A multiple power-law distribution for initial mass functions

Abstract

We introduce a new multi-power-law distribution for the Initial Mass Function (IMF) to explore its potential properties. It follows on prior work that introduced mechanisms accounting for mass accretion in star formation, developed within the framework of general evolution equations for the mass distribution of accreting and non-accreting (proto)stars. This paper uses the same fundamental framework to demonstrate that the interplay between a mass-dependent and a time-dependent steplike dropout rate from accretion leads to IMFs that exhibit multiple power laws for an exponential mass growth. While the mass-dependent accretion and its dropout is intrinsic to each star, the time-dependent dropout might be tied to a specific history such as the rapid consumption of nebular material by nearby stars or the sweeping away of some material by shock waves. The time-dependent dropout folded into the mass-dependent process of star formation is shown to have a significant influence on the IMFs.

A semi-analytic model for the temporal evolution of the episodic disc-to-star accretion rate during star formation

“…If this is correct, then one can add a period of temporally increasing accretion rate at later times to account for the relatively small fraction of massive stars. A series of works on the stellar initial mass function have assumed an exponentially increasing accretion rate together with equally likely stopping of accretion in each time interval that allows only a small fraction of protostars to reach the high accretion rate phase and become high mass stars (Myers 2000;Basu & Jones 2004;Myers 2011Myers , 2014Basu et al 2015;Hoffmann et al 2018;Essex et al 2020). Future observations are essential to place tighter constraints on the luminosity evolution, and therefore elucidate the mass assembly history of protostars of all masses.…”

Star Formation in Self-gravitating Disks in Active Galactic Nuclei. III. Efficient Production of Iron and Infrared Spectral Energy Distributions

“…We stress that β as a comprehensive parameter covers the effects of the accretion dropout process. Equation ( 14) covers Bondi-like accretion onto low-mass stars, modifying MFs (as discussed by Zinnecker 1982), and Bondi-like modified accretion rates (see discussions in clusters by Adams & Fatuzzo 1996;Basu & Jones 2004;Dib et al 2010), even with accretion dropout (mass lost from protostar disks; Hoffmann et al 2018;Essex et al 2020), which have been applied to explain the power-law tails of MFs in star clusters.…”

The Origin of the Stellar Mass Distribution and Multiplicity

“…On the other hand, some theories considered the accretion being stopped due to the exhaustion of the mass reservoir or the outflow from the protostar, therefore setting the final mass of the star. These models either consider outflow counterbalancing the infall rate (Adams and Fatuzzo, 1996), a functional decay of mass accretion rate (Basu and Jones, 2004;Myers, 2009), or a probability for the core to be ejected from the initial mass reservoir (Bate and Bonnell, 2005;Essex et al, 2020). These models are mostly based on adjustable statistical parameters.…”