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

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

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

Destruction of massive fragments in protostellar disks and crystalline silicate production

We present a mechanism for the crystalline silicate production associated with the formation and subsequent destruction of massive fragments in young protostellar disks. The fragments form in the embedded phase of star formation via disk fragmentation at radial distances \ga 50-100 AU and anneal small amorphous grains in their interior when the gas temperature exceeds the crystallization threshold of ~ 800 K. We demonstrate that fragments that form in the early embedded phase can be destroyed before they either form solid cores or vaporize dust grains, thus releasing the processed crystalline dust into various radial distances from sub-AU to hundred-AU scales. Two possible mechanisms for the destruction of fragments are the tidal disruption and photoevaporation as fragments migrate radially inward and approach the central star and also dispersal by tidal torques exerted by spiral arms. As a result, most of the crystalline dust concentrates to the disk inner regions and spiral arms, which are the likely sites of fragment destruction.Comment: Accepted by the Astrophysical Journal Letter

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

Vortex stretching in self-gravitating protoplanetary discs

Horseshoe-shaped brightness asymmetries of several transitional discs are thought to be caused by large-scale vortices. Anticyclonic vortices are efficiently collect dust particles, therefore they can play a major role in planet formation. Former studies suggest that the disc self-gravity weakens vortices formed at the edge of the gap opened by a massive planet in discs whose masses are in the range of 0.01<=M_disc/M_*<=0.1. Here we present an investigation on the long-term evolution of the large-scale vortices formed at the viscosity transition of the discs' dead zone outer edge by means of two-dimensional hydrodynamic simulations taking disc self-gravity into account. We perform a numerical study of low mass, 0.001<=M_disc/M_*<=0.01, discs, for which cases disc self-gravity was previously neglected. The large-scale vortices are found to be stretched due to disc self-gravity even for low-mass discs with M_disc/M_*>=0.005 where initially the Toomre Q-parameter was <=50 at the vortex distance. As a result of stretching, the vortex aspect ratio increases and a weaker azimuthal density contrast develops. The strength of the vortex stretching is proportional to the disc mass. The vortex stretching can be explained by a combined action of a non-vanishing gravitational torque caused by the vortex, and the Keplerian shear of the disc. Self-gravitating vortices are subject to significantly faster decay than non-self-gravitating ones. We found that vortices developed at sharp viscosity transitions of self-gravitating discs can be described by a GNG model as long as the disc viscosity is low, i.e. alpha_dz<=10^-5.Comment: 13 pages, 8 figures, appear in MNRA

Observed luminosity spread in young clusters and Fu Ori stars: a unified picture

The idea that non steady accretion during the embedded phase of protostar evolution can produce the observed luminosity spread in the Herzsprung-Russell diagram (HRD) of young clusters has recently been called into question. Observations of Fu Ori, for instance, suggest an expansion of the star during strong accretion events whereas the luminosity spread implies a contraction of the accreting objects, decreasing their radiating surface. In this paper, we present a global scenario based on calculations coupling episodic accretion histories derived from numerical simulations of collapsing cloud prestellar cores of various masses and subsequent protostar evolution. Our calculations show that, assuming an initial protostar mass \mi \sim 1\,\mjup, typical of the second Larson's core, both the luminosity spread in the HRD and the inferred properties of Fu Ori events (mass, radius, accretion rate) can be explained by this scenario, providing two conditions. First, there must be some variation within the fraction of accretion energy absorbed by the protostar during the accretion process. Second the range of this variation should increase with increasing accretion burst intensity, and thus with the initial core mass and final star mass. The numerical hydrodynamics simulations of collapsing cloud prestellar cores indeed show that the intensity of the accretion bursts correlates with the mass and initial angular momentum of the prestellar core. Massive prestellar cores with high initial angular momentum are found to produce intense bursts characteristic of Fu Ori like events. Our results thus suggest a link between the burst intensities and the fraction of accretion energy absorbed by the protostar, with some threshold in the accretion rate, of the order of 10^{-5}\msolyr, delimitating the transition from "cold" to "hot" accretion. [Abridged]Comment: 23 pages, 5 figures, ApJ accepte

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