Abstract
Context. Stars constitute the building blocks of our Universe, and their formation is an astrophysical problem of great importance.Aim. We aim to understand the fragmentation of massive molecular star-forming clumps and the effect of initial conditions, namely the density and the level of turbulence, on the resulting distribution of stars. For this purpose, 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.Methods. 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) ∝ρ−1.5 instead of a lognormal distribution.Results. Simulations and analytical model both show two support regimes, a thermally dominated regime and a turbulence-dominated regime. For the first regime, we infer that dN∕d logM ∝ M0, while for the second regime, we obtain dN∕d logM ∝ 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 ~0.2 M⊙. From this point, the mass spectrum decreases with decreasing mass except for the most diffuse clouds, where disk fragmentation leads to the formation of objects down to the mass of the first Larson core, that is, to a few 10−2 M⊙.Conclusions. 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.
Highlights
The formation of stars inside a cluster depends on local as well as on global conditions
The analytical model with the power-law density probability distribution function (PDF) stated by Eq (5) and the mass spectra inferred from simulations, solid and dashed blue lines, respectively, generally agree pretty well for M > 0.1 M, where the analytical models are applicable, except for models B1, C1, and D1 at high mass, where the lognormal PDF seems to provide better fits
The changing slope of the mass spectrum around 1 M may be a consequence of the PDF, which shows a transition between a lognormal behavior at low density and a power law at high density
Summary
The formation of stars inside a cluster depends on local as well as on global conditions. Bate (2009a, 2012) simulated 500 M clouds of 0.404 radius with Mach number M = 13.7, with either a polytropic equation of state (eos) or radiation hydrodynamics The mass spectra they presented have Γ slightly higher than –1 in the mass range 0.1–3 M in both cases. Simulated 1000 M clouds at 2.4 × 105 cm−3 and studied the effect of radiation hydrodynamics compared to the isothermal condition Their mass spectra showed Γ > −1 in the mass range 0.1–2 M , either with or without radiation. To isolate the effect of initial density, we intentionally left out magnetic field, cooling, radiative transfer, and all stellar feedback effects, while representing the thermodynamics of the gas with a simple smoothed two-slope polytropic eos These numerical experiments, are not intended to represent fully realistic molecular clouds. The sixth section discusses the results, and the seventh concludes the paper
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