Stellar mass spectrum within massive collapsing clumps I. Influence of the initial conditions

TL;DR

This study uses numerical simulations and analytical modeling to explore how initial conditions influence the stellar mass spectrum in collapsing clouds, highlighting the roles of turbulence and thermodynamics in shaping the initial mass function.

Contribution

It introduces an adapted analytical model for collapsing clouds and systematically investigates the impact of initial density and turbulence on the mass spectrum, connecting it to observed stellar distributions.

Findings

Support regimes dominated by thermal energy or turbulence identified.

Mass spectrum peaks around 0.2 solar masses, decreasing at lower masses.

Possible transition to a Salpeter-like slope for higher masses observed.

Abstract

We conduct numerical experiments in which we systematically vary the initial density over four orders of magnitude and the turbulent velocity over a factor ten. In a companion paper, we investigate the dependence of this distribution on the gas thermodynamics. We performed a series of hydrodynamical numerical simulations using adaptive mesh refinement, with special attention to numerical convergence. We also adapted an existing analytical model to the case of collapsing clouds by employing a density probability distribution function (PDF) $\propto \rho^{-1.5}$ instead of a lognormal distribution. Simulations and analytical model both show two support regimes, dominated by either thermal energy or turbulence. For the first regime, we infer that $dN/d \log M \propto M^0$, while for the second, we obtain $dN/d \log M \propto M^{-3/4}$. This is valid up to about ten times the mass of the first Larson core, as explained in the companion paper, leading to a peak of the mass spectrum at $\sim 0.2 M_\odot$. From this point, the mass spectrum decreases with decreasing mass. Although the mass spectra we obtain for the most compact clouds qualitatively resemble the observed initial mass function, the distribution exponent is shallower than the expected Salpeter exponent of -1.35. Nonetheless, we observe a possible transition toward a slightly steeper value that is broadly compatible with the Salpeter exponent for masses above a few solar masses. This change in behavior is associated with the change in density PDF, which switches from a power-law to a lognormal distribution. Our results suggest that while gravitationally induced fragmentation could play an important role for low masses, it is likely the turbulently induced fragmentation that leads to the Salpeter exponent.