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 hydrodynamics 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 adopted a classification scheme of Andre et al. and calculate the lifetimes of the Class 0 and Class I phases (\tau_C0 and \tau_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 \pm 0.05. The corresponding correlation between the Class I lifetimes and stellar masses in the Class I is super-linear with m=1.2 \pm 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 \tau_CI / \tau_C0 \approx 1.5--2. A notable exception are YSOs that form from cloud cores with large initial density enhancements, in which case \tau_C0 may be greater than \tau_CI. Moreover, the upper-mass (>= 1.0 Msun) cloud cores with frozen-in magnetic fields and high cloud core rotation rates may have the \tau_CI / \tau_C0 ratios as large as 3.0--4.0. (Abdridged).Comment: Accepted for publication by The Astrophysical Journa

A Hybrid Scenario for the Formation of Brown Dwarfs and Very Low Mass Stars

We present a calculation of protostellar disk formation and evolution in which gaseous clumps (essentially, the first Larson cores formed via disk fragmentation) are ejected from the disk during the early stage of evolution. This is a universal process related to the phenomenon of ejection in multiple systems of point masses. However, it occurs in our model entirely due to the interaction of compact, gravitationally-bound gaseous clumps and is free from the smoothing-length uncertainty that is characteristic of models using sink particles. Clumps that survive ejection span a mass range of 0.08--0.35 $M_\odot$, and have ejection velocities $0.8 \pm 0.35$ km s$^{-1}$, which are several times greater than the escape speed. We suggest that, upon contraction, these clumps can form substellar or low-mass stellar objects with notable disks, or even close-separation very-low-mass binaries. In this hybrid scenario, allowing for ejection of clumps rather than finished protostars/proto--brown-dwarfs, disk formation and the low velocity dispersion of low-mass objects are naturally explained, while it is also consistent with the observation of isolated low-mass clumps that are ejection products. We conclude that clump ejection and the formation of isolated low mass stellar and substellar objects is a common occurrence, with important implications for understanding the initial mass function, the brown dwarf desert, and the formation of stars in all environments and epochs.Comment: 20 pages, 6 figures, to appear in The Astrophysical Journa

Mass accretion rates in self-regulated disks of T Tauri stars

We have studied numerically the evolution of protostellar disks around intermediate and upper mass T Tauri stars (0.25 M_sun < M_st < 3.0 M_sun) that have formed self-consistently from the collapse of molecular cloud cores. In the T Tauri phase, disks settle into a self-regulated state, with low-amplitude nonaxisymmetric density perturbations persisting for at least several million years. Our main finding is that the global effect of gravitational torques due to these perturbations is to produce disk accretion rates that are of the correct magnitude to explain observed accretion onto T Tauri stars. Our models yield a correlation between accretion rate M_dot and stellar mass M_st that has a best fit M_dot \propto M_st^{1.7}, in good agreement with recent observations. We also predict a near-linear correlation between the disk accretion rate and the disk mass.Comment: Accepted for publication in ApJ Letter

The burst mode of accretion and disk fragmentation in the early embedded stages of star formation

We revisit our original papers on the burst mode of accretion by incorporating a detailed energy balance equation into a thin-disk model for the formation and evolution of circumstellar disks around low-mass protostars.Our model includes the effect of radiative cooling, viscous and shock heating, and heating due to stellar and background irradiation. Following the collapse from the prestellar phase allows us to model the early embedded phase of disk formation and evolution. During this time, the disk is susceptible to fragmentation, depending upon the properties of the initial prestellar core. Globally, we find that higher initial core angular momentum and mass content favors more fragmentation, but higher levels of background radiation can moderate the tendency to fragment. A higher rate of mass infall onto the disk than that onto the star is a necessary but not sufficient condition for disk fragmentation. More locally, both the Toomre Q-parameter needs to be below a critical value _and_ the local cooling time needs to be shorter than a few times the local dynamical time. Fragments that form during the early embedded phase tend to be driven into the inner disk regions, and likely trigger mass accretion and luminosity bursts that are similar in magnitude to FU-Orionis-type or EX-Lupi-like events. Disk accretion is shown to be an intrinsically variable process, thanks to disk fragmentation, nonaxisymmetric structure, and the effect of gravitational torques. The additional effect of a generic \alpha-type viscosity acts to reduce burst frequency and accretion variability, and is likely to not be viable for values of \alpha significantly greater than 0.01.Comment: Accepted for publication by the Astrophysical Journa

Energy spectrum and phase diagrams of two-sublattice hard-core boson model

The energy spectrum, spectral density and phase diagrams have been obtained for two-sublattice hard-core boson model in frames of random phase approximation approach. Reconstruction of boson spectrum at the change of temperature, chemical potential and energy difference between local positions in sublattices is studied. The phase diagrams illustrating the regions of existence of a normal phase which can be close to Mott-insulator (MI) or charge-density (CDW) phases as well as the phase with the Bose-Einstein condensate (SF phase) are built.Comment: 9 pages, 4 figure

Self-regulated gravitational accretion in protostellar discs

We present a numerical model for the evolution of a protostellar disc that has formed self-consistently from the collapse of a molecular cloud core. The global evolution of the disc is followed for several million years after its formation. The capture of a wide range of spatial and temporal scales is made possible by use of the thin-disc approximation. We focus on the role of gravitational torques in transporting mass inward and angular momentum outward during different evolutionary phases of a protostellar disc with disc-to-star mass ratio of order 0.1. In the early phase, when the infall of matter from the surrounding envelope is substantial, mass is transported inward by the gravitational torques from spiral arms that are a manifestation of the envelope-induced gravitational instability in the disc. In the late phase, when the gas reservoir of the envelope is depleted, the distinct spiral structure is replaced by ongoing irregular nonaxisymmetric density perturbations. The amplitude of these density perturbations decreases with time, though this process is moderated by swing amplification aided by the existence of the disc's sharp outer edge. Our global modelling of the protostellar disc reveals that there is typically a residual nonzero gravitational torque from these density perturbations, i.e. their effects do not exactly cancel out in each region. In particular, the net gravitational torque in the inner disc tends to be negative during first several million years of the evolution, while the outer disc has a net positive gravitational torque. Our global model of a self-consistently formed disc shows that it is also self-regulated in the late phase, so that it is near the Toomre stability limit, with a near-uniform Toomre parameter Q\approx 1.5-2.0. (Abstract abridged).Comment: 9 pages, 9 figures, accepted for publication in MNRA

Embedded protostellar disks around (sub-)solar protostars. I. Disk structure and evolution

We perform a comparative numerical hydrodynamics study of embedded protostellar disks formed as a result of the gravitational collapse of cloud cores of distinct mass (M_cl=0.2--1.7 M_sun) and ratio of rotational to gravitational energy (\beta=0.0028--0.023). An increase in M_cl and/or \beta leads to the formation of protostellar disks that are more susceptible to gravitational instability. Disk fragmentation occurs in most models but its effect is often limited to the very early stage, with the fragments being either dispersed or driven onto the forming star during tens of orbital periods. Only cloud cores with high enough M_cl or \beta may eventually form wide-separation binary/multiple systems with low mass ratios and brown dwarf or sub-solar mass companions. It is feasible that such systems may eventually break up, giving birth to rogue brown dwarfs. Protostellar disks of {\it equal} age formed from cloud cores of greater mass (but equal \beta) are generally denser, hotter, larger, and more massive. On the other hand, protostellar disks formed from cloud cores of higher \beta (but equal M_cl) are generally thinner and colder but larger and more massive. In all models, the difference between the irradiation temperature and midplane temperature \triangle T is small, except for the innermost regions of young disks, dense fragments, and disk's outer edge where \triangle T is negative and may reach a factor of two or even more. Gravitationally unstable, embedded disks show radial pulsations, the amplitude of which increases along the line of increasing M_cl and \beta but tends to diminish as the envelope clears. We find that single stars with a disk-to-star mass ratio of order unity can be formed only from high-\beta cloud cores, but such massive disks are unstable and quickly fragment into binary/multiple systems.Comment: Accepted for publication in the astrophysical Journa