A Turbulent Interstellar Medium Origin of the Binary Period Distribution

In this paper, we present a semi-empirical model of isolated binary star formation. This model includes the effects of turbulence in the initial state of the gas, and has binary orbital parameters consistent with observation. Our fundamental assumption is that the angular momenta of binary star systems is directly related to the net angular momentum induced by turbulence in parent molecular cloud cores. The primary results of this model are as follows. (i) A quantitative prediction of the initial width of the binary period distribution ($\sigma_{\log {P}_d} = 1.6 - 2.1$ for a star formation efficiency in the range $\epsilon_* = 0.1 - 0.9$). (ii) A robust, negative anticorrelation of binary period and mass ratio. (iii) A robust, positive correlation of binary period and eccentricity. (iv) A robust prediction that the binary separation of low-mass systems should be more closely separated than those of solar-mass or larger. These predictions are in good agreement with observations of PMS binary systems with periods $P > 10^3$ d, which account for the majority of all binaries. We conclude with a brief discussion of the implications of our results for observational and theoretical studies of multiple star formation.