[Paper Review] Simulating star formation in molecular cores II. The effects of different levels of turbulence

S. P. Goodwin, A. P. Whitworth+1 more|arXiv (Cornell University)|May 6, 2004

Astrophysics and Star Formation Studies74 references77 citations

TL;DR

This study uses smoothed particle hydrodynamics (SPH) simulations to investigate how varying levels of initial turbulence in a 5.4 M⊙ molecular core affect star formation, fragmentation, and binary statistics. It finds that a turbulence parameter α_turb ≈ 0.05 best reproduces the observed binary frequency, mass function, and orbital properties of field G-dwarfs, while higher turbulence (α_turb ≥ 0.10) produces a distinct subpopulation of close, comparable-mass binaries consistent with observations in Taurus.

ABSTRACT

(Abridged) We explore, by means of a large ensemble of SPH simulations, how the level of turbulence affects the collapse and fragmentation of a star-forming core. All our simulated cores have the same, except that we vary (a) the initial level of turbulence (as measured by the ratio of turbulent to gravitational energy, $α_{ m turb} \equiv U_{ m turb}/|Ω| = 0, 0.01, 0.025, 0.05, 0.10 { m and} 0.25$) and (b), for fixed $α_{ m turb}$, the details of the initial turbulent velocity field (so as to obtain good statistics). A low level of turbulence ($α_{ m turb} \sim 0.05$) suffices to produce multiple systems. As $α_{ m turb}$ is increased, the number of objects formed and the companion frequency both increase. The mass function is bimodal, with a flat low-mass segment representing single objects ejected from the core before they can accrete much, and a Gaussian high-mass segment representing objects which because they remain in the core grow by accretion and tend to pair up in multiple systems.

Motivation & Objective

• To determine how different levels of initial turbulence influence the fragmentation, mass function, and binary statistics in collapsing molecular cores.
• To assess whether observed binary characteristics in field G-dwarfs and pre-main sequence stars in Taurus can be reproduced by varying turbulence in core collapse simulations.
• To investigate the role of turbulence in shaping the bimodal mass function and the formation of multiple systems during star formation.
• To compare simulation outcomes with observational data from Duquennoy & Mayor (1991) and White & Ghez (2001) to constrain the turbulence level in cores forming solar-type stars.
• To explore the origin of hard, close binaries with high mass ratios in high-turbulence environments and their consistency with pre-main sequence observations.

Proposed method

• Conduct a large ensemble of smoothed particle hydrodynamics (SPH) simulations of a spherically symmetric 5.4 M⊙ core with a Plummer-like density profile matching L1544 observations.
• Vary the initial turbulent energy relative to gravitational energy via the parameter α_turb = U_turb / |Ω|, testing values: 0, 0.01, 0.025, 0.05, 0.10, and 0.25.
• Generate turbulent velocity fields with a power spectrum P(k) ∝ k⁻⁴ to model observed turbulent substructure in molecular clouds.
• For each α_turb, perform multiple realizations (varying random seeds) to ensure statistical robustness and account for stochasticity in turbulent initial conditions.
• Track the formation, mass growth, ejection, and binary pairing of protostars to derive mass functions and binary statistics (separation, eccentricity, mass ratio).
• Compare simulated binary distributions (semi-major axis, eccentricity, mass ratio) with observational data from Duquennoy & Mayor (1991) and White & Ghez (2001).

Experimental results

Research questions

• RQ1 How does the level of initial turbulence (α_turb) affect the number of stars formed and the frequency of multiple systems in collapsing molecular cores?
• RQ2 What value of α_turb best reproduces the observed binary frequency, semi-major axis distribution, eccentricity, and mass ratio distribution of field G-dwarfs?
• RQ3 Why does a subpopulation of close, high-mass-ratio binaries form at higher turbulence levels (α_turb ≥ 0.10), and is this consistent with observations in Taurus?
• RQ4 How does turbulence influence the bimodal structure of the stellar initial mass function, particularly the flat low-mass and Gaussian high-mass segments?
• RQ5 Can the observed properties of pre-main sequence binaries in Taurus be reproduced by a mixture of simulations with different α_turb values?

Key findings

• A minimum turbulence level of α_turb ≈ 0.025 is required to form multiple systems, with a ~20% probability of multiple systems forming at this level.
• The observed binary statistics of field G-dwarfs from Duquennoy & Mayor (1991) are best reproduced by simulations with α_turb ≈ 0.05, matching companion frequency, semi-major axis, eccentricity, and mass ratio distributions.
• At α_turb ≥ 0.10, a distinct subpopulation of close binaries with small semi-major axes and high mass ratios (comparable-mass components) emerges, consistent with observations in the Taurus pre-main sequence population.
• The stellar initial mass function is bimodal: a flat low-mass segment from ejected single objects (<0.5 M⊙), and a Gaussian high-mass segment from accreting, embedded multiple systems.
• Approximately 20% of simulated objects are brown dwarfs (M < 0.08 M⊙), and 50% are low-mass stars (0.08 M⊙ < M < 0.5 M⊙), with the latter predominantly forming in multiple systems.
• The mass function and binary statistics of pre-main sequence stars in Taurus are best reproduced by a mix of simulations with α_turb = 0.05 (20 realizations), 0.10 (20 realizations), and 0.25 (10 realizations), as shown in Goodwin et al. (2004b).