Lifetime of the Embedded Phase of Low-Mass Star Formation and the Envelope Depletion Rates

Motivated by a considerable scatter in the observationally inferred lifetimes of the embedded phase of star formation, we study the duration of the Class 0 and Class I phases in upper-mass brown dwarfs and low-mass stars using numerical hydrodynamic simulations of the gravitational collapse of a large sample of cloud cores. We resolve the formation of a star/disk/envelope system and extend our numerical simulations to the late accretion phase when the envelope is nearly totally depleted of matter. We adopt the classification scheme of André et al. and calculate the lifetimes of the Class 0 and Class I phases (τ C0 and τ CI , respectively) based on the mass remaining in the envelope. When cloud cores with various rotation rates, masses, and sizes (but identical otherwise) are considered, our modeling reveals a sub-linear correlation between the Class 0 lifetimes and stellar masses in the Class 0 phase with the least-squares fit exponent m = 0.8 ± 0.05. The corresponding correlation between the Class I lifetimes and stellar masses in Class I is super-linear with m = 1.2 ± 0.05. If a wider sample of cloud cores is considered, which includes possible variations in the initial gas temperature, cloud core truncation radii, density enhancement amplitudes, initial gas density and angular velocity profiles, and magnetic fields, then the corresponding exponents may decrease by as much as 0.3. The duration of the Class I phase is found to be longer than that of the Class 0 phase in most models, with a mean ratio τ CI /τ C0 ≈ 1.5–2. A notable exception are young stellar objects that form from cloud cores with large initial density enhancements, in which case τ C0 may be greater than τ CI . Moreover, the upper-mass (≳1.0 M ☉ ) cloud cores with frozen-in magnetic fields and high cloud core rotation rates may have the τ CI /τ C0 ratios as large as 3.0–4.0. We calculate the rate of mass accretion from the envelope onto the star/disk system and provide an approximation formula that can be used in semi-analytic models of cloud core collapse.