Collapse Of Molecular Cloud Cores Research Articles

Long-term Protoplanetary Disk Evolution from Molecular Cloud Core Collapse and Implications for Planet Formation. I. Weak and Moderate Disk Self-gravities

We construct a one-dimensional protoplanetary disk model to investigate long-term disk evolution from molecular cloud core collapse. To obtain details of disk evolution, instead of solving the traditional diffusion equation for disk surface density, we suggest a set of equations derived from the basic principles of fluid mechanics. Effects of infalling material, magnetorotational instability, and disk self-gravity are taken into account. According to the role of disk self-gravity, we find that disks can be classified into three types. For a type I disk, disk self-gravity is not important. For a type II disk, disk self-gravity has effects on both disk scale height and gas radial motion. In addition, gravitational instability can cause the transport of angular momentum. For a type III disk, disk self-gravity plays a dominant role in disk evolution. In this paper, we focus on the first two types and the investigation of the third one is presented in a companion paper. For each disk, we find that there are three phases during evolution. Phase 1 is the very early phase during which the radial velocity is on the order of 106 cm s−1 and the transport of angular momentum caused by viscosity is not important. Phase 2 begins when a rotationally supported disk is formed. From this phase, viscosity plays a role in the transport of angular momentum. When the infall ends, phase 3 begins. Since angular velocity is calculated directly, we can reveal the non-Keplerian effect, which has important effects on the radial drift of solids and planetesimal formation.

Long-term Protoplanetary Disk Evolution from Molecular Cloud Core Collapse and Implications for Planet Formation. II. Strong Disk Self-gravity

We continue to investigate long-term protoplanetary disk evolution and focus on the situation of strong disk self-gravity (DSG). We call such a disk a type III disk. A large amount of mass is stored in the disk due to large angular momentum. When the disk becomes massive enough, a dense region (DR) is formed due to gravitational instability. This instability is triggered by the combined effect of radial gravitational attraction and a decrease in disk scale height. Viscosity cannot smooth out the DR due to strong DSG. We further investigate the subsequent disk evolution under the assumption of axisymmetry. Besides the viscous process, angular momentum flux caused by the perturbation of DSG also plays a role in the transport of angular momentum. The combination of the two processes results in the efficient transport of angular momentum in the outer disk and prevents the disk from becoming very massive. Due to the interaction between the DR and the inner disk, a gap between them is formed. This gives a nonplanetary origin of the gap. In ∼106 yr, a surface density plateau and a very low surface density region are formed in the inner disk. In a type III disk, there are several locations where the radial drift of solids can be stopped. Objects formed in the DR may remember some of the properties of the DR, such as large mass and large angular momentum. In particular, a planetary system with wide-orbit giant planets may be formed in the DR. Finally, it is still difficult to identify what type of disk the solar nebula belongs to.

Collapsing index: a new method to identify star-forming cores based on ALMA images

Stars form through the gravitational collapse of molecular cloud cores. Before collapsing, the cores are supported by thermal pressure and turbulent motions. A question of critical importance for the understanding of star formation is how to observationally discern whether a core has already initiated gravitational collapse or is still in hydrostatic balance. The canonical method to identify gravitational collapse is based on the observed radial density profile, which would change from Bonnor-Ebert type toward power laws as the core collapses. In practice, due to the projection effect, the resolution limit and other caveats, it has been difficult to directly reveal the dynamical status of cores, particularly in massive star forming regions. We here propose a novel, straightforward diagnostic, namely, the collapsing index (CI), which can be modeled and calculated based on the radial profile of the line width of dense gas. A meaningful measurement of CI requires spatially and spectrally resolved images of optically thin and chemically stable dense gas tracers. ALMA observations are making such data sets increasingly available for massive star forming regions. Applying our method to one of the deepest dense-gas spectral images ever taken toward such a region, namely, the Orion molecular cloud, we detect the dynamical status of selected cores. We observationally distinguished a collapsing core in a massive star forming region from a hydrostatical one. Our approach would help significantly improve our understanding of the interaction between gravity and turbulence within molecular cloud cores in the process of star formation.

Triggering Collapse of the Presolar Dense Cloud Core and Injecting Short-lived Radioisotopes with a Shock Wave. VI. Protostar and Protoplanetary Disk Formation

Abstract Cosmochemical evaluations of the initial meteoritical abundance of the short-lived radioisotope (SLRI) 26Al have remained fairly constant since 1976, while estimates for the initial abundance of the SLRI 60Fe have varied widely recently. At the high end of this range, 60Fe initial abundances have seemed to require 60Fe nucleosynthesis in a core-collapse supernova, followed by incorporation into primitive meteoritical components within ∼1 Myr. This paper continues the detailed exploration of this classical scenario, using models of the self-gravitational collapse of molecular cloud cores that have been struck by suitable shock fronts, leading to the injection of shock front gas into the collapsing cloud through Rayleigh–Taylor fingers formed at the shock–cloud interface. As before, these models are calculated using the FLASH three-dimensional, adaptive mesh refinement, gravitational hydrodynamical code. While the previous models used FLASH 2.5, the new models employ FLASH 4.3, which allows sink particles to be introduced to represent the newly formed protostellar object. Sink particles permit the models to be pushed forward farther in time to the phase where a ∼1 M ⊙ protostar has formed, orbited by a rotating protoplanetary disk. These models are thus able to define what type of target cloud core is necessary for the supernova triggering scenario to produce a plausible scheme for the injection of SLRIs into the presolar cloud core: a ∼3 M ⊙ cloud core rotating at a rate of ∼3 × 10−14 rad s−1 or higher.

First core properties: from low- to high-mass star formation

Aims. In this study, the main goal is to understand the molecular cloud core collapse through the stages of first and second hydrostatic core formation. We investigate the properties of Larsons first and second cores following the evolution of the molecular cloud core until the formation of Larson’s cores. We expand these collapse studies for the first time to span a wide range of initial cloud masses from 0.5 to 100 M⊙. Methods. Understanding the complexity of the numerous physical processes involved in the very early stages of star formation requires detailed thermodynamical modelling in terms of radiation transport and phase transitions. For this we used a realistic gas equation of state via a density- and temperature-dependent adiabatic index and mean molecular weight to model the phase transitions. We used a grey treatment of radiative transfer coupled with hydrodynamics to simulate Larsons collapse in spherical symmetry. Results. We reveal a dependence of a variety of first core properties on the initial cloud mass. The first core radius and mass increase from the low-mass to intermediate-mass regime and decrease from the intermediate-mass to high-mass regime. The lifetime of first cores strongly decreases towards the intermediate- and high-mass regimes. Conclusions. Our studies show the presence of a transition region in the intermediate-mass regime. Low-mass protostars tend to evolve through two distinct stages of formation that are related to the first and second hydrostatic cores. In contrast, in the high-mass star formation regime, collapsing cloud cores rapidly evolve through the first collapse phase and essentially immediately form Larson’s second cores.

Circumstellar Disks and Outflows in Turbulent Molecular Cloud Cores: Possible Formation Mechanism for Misaligned Systems

Abstract We investigate the formation of circumstellar disks and outflows subsequent to the collapse of molecular cloud cores with the magnetic field and turbulence. Numerical simulations are performed by using an adaptive mesh refinement to follow the evolution up to ∼1000 years after the formation of a protostar. In the simulations, circumstellar disks are formed around the protostars; those in magnetized models are considerably smaller than those in nonmagnetized models, but their size increases with time. The models with stronger magnetic fields tend to produce smaller disks. During evolution in the magnetized models, the mass ratios of a disk to a protostar is approximately constant at ∼1%–10%. The circumstellar disks are aligned according to their angular momentum, and the outflows accelerate along the magnetic field on the 10–100 au scale; this produces a disk that is misaligned with the outflow. The outflows are classified into two types: a magnetocentrifugal wind and a spiral flow. In the latter, because of the geometry, the axis of rotation is misaligned with the magnetic field. The magnetic field has an internal structure in the cloud cores, which also causes misalignment between the outflows and the magnetic field on the scale of the cloud core. The distribution of the angular momentum vectors in a core also has a non-monotonic internal structure. This should create a time-dependent accretion of angular momenta onto the circumstellar disk. Therefore, the circumstellar disks are expected to change their orientation as well as their sizes in the long-term evolutions.

LIFETIMES AND ACCRETION RATES OF PROTOPLANETARY DISKS

ABSTRACT Protoplanetary disks originate in the collapse of molecular cloud cores. The formation and evolution of disks are influenced by the properties of molecular cloud cores. In this paper we investigate the dependence of disk lifetimes and accretion rates on cloud core properties. We find that the lifetime increases as the angular velocities and the mass of cloud cores increase and that the lifetime decreases as the core temperature increases. We have calculated the distribution of disk lifetimes and disk fractions with stellar age. Our calculations show that the lifetime is in the range of 1–15 Myr and that the typical lifetime is 1–3 Myr. There are a few disks with lifetimes greater than 10 Myr and ∼ 30 % ?> of the disks have lifetimes less than 1 Myr. We also fit the disk fraction by an exponential decay curve with characteristic time ∼3.7 Myr. Our results explain the observations of disk lifetimes. We also find that the accretion rate does not change significantly with ω and generally decreases with T cd ?> . At the early evolution of the disks, the M ˙ – M * ?> relation is about M ˙ ∝ M * 1.2 − 2 ?> . Since the effects of the photoevaporation are weak at this stage, this relation is the consequence of the cloud core properties. At the late evolution of the disks, the M ˙ – M * ?> relation is about M ˙ ∝ M * 1.2 − 1.7 ?> . For low accretion rates at this stage, the M ˙ – M * ?> relation results from the effects of X-ray photoevaporation. The calculated M ˙ – M * ?> relations are consistent with the observations.

Masses of discs form from collapse of molecular cloud cores

Masses of discs form from collapse of molecular cloud cores

The Hall effect in star formation

Magnetic fields play an important role in star formation by regulating the removal of angular momentum from collapsing molecular cloud cores. Hall diffusion is known to be important to the magnetic field behaviour at many of the intermediate densities and field strengths encountered during the gravitational collapse of molecular cloud cores into protostars, and yet its role in the star formation process is not well-studied. We present a semianalytic self-similar model of the collapse of rotating isothermal molecular cloud cores with both Hall and ambipolar diffusion, and similarity solutions that demonstrate the profound influence of the Hall effect on the dynamics of collapse. The solutions show that the size and sign of the Hall parameter can change the size of the protostellar disc by up to an order of magnitude and the protostellar accretion rate by fifty per cent when the ratio of the Hall to ambipolar diffusivities is varied between -0.5 <= eta_H / eta_A <= 0.2. These changes depend upon the orientation of the magnetic field with respect to the axis of rotation and create a preferred handedness to the solutions that could be observed in protostellar cores using next-generation instruments such as ALMA. Hall diffusion also determines the strength and position of the shocks that bound the pseudo and rotationally-supported discs, and can introduce subshocks that further slow accretion onto the protostar. In cores that are not initially rotating Hall diffusion can even induce rotation, which could give rise to disc formation and resolve the magnetic braking catastrophe. The Hall effect clearly influences the dynamics of gravitational collapse and its role in controlling the magnetic braking and radial diffusion of the field merits further exploration in numerical simulations of star formation.

Collapse of a molecular cloud core to stellar densities: the formation and evolution of pre-stellar discs

We report results from radiation hydrodynamical simulations of the collapse of molecular cloud cores to form protostars. The calculations follow the formation and evolution of the first hydrostatic core/disc, the collapse to form a stellar core, and effect of stellar core formation on the surrounding disc and envelope. Past barotropic calculations have shown that rapidly-rotating first cores evolve into `pre-stellar discs' with radii up to ~100 AU that may last thousands of years before a stellar core forms. We investigate how the inclusion of a realistic equation of state and radiative transfer alters this behaviour, finding that the qualitative behaviour is similar, but that the pre-stellar discs may last 1.5-3 times longer in the more realistic calculations. The masses, radii, and lifetimes of the discs increase for initial molecular cloud cores with faster rotation rates. In the most extreme case we model, a pre-stellar disc with a mass of 0.22 Msun and a radius of ~100 AU can form in a solar-mass cloud and last several thousand years before a stellar core is formed. Such large, massive objects may be imaged using ALMA. Fragmentation of these massive discs may also provide an effective route to binary and multiple star formation, before radiative feedback from accretion onto the stellar core can inhibit fragmentation. Once collapse to form a stellar core occurs within the pre-stellar disc, the radiation hydrodynamical simulations produce qualitatively different behaviour from the barotropic calculations due to the accretion energy released. This drives a shock wave through the circumstellar disc and launches a bipolar outflow even in the absence of magnetic fields.

Matter infall in collapsing molecular cloud cores with an axial magnetic field

The magnetic fields affect collapse of molecular cloud cores. Here, we consider a collapsing core with an axial magnetic field and investigate its effect on infall of matter and formation of accretion disk. For this purpose, the equations of motion of ions and neutral infalling particles are numerically solved to obtain the streamlines of trajectories. The results show that in non-steady state of ionization and ion-neutral coupling, which is not unexpected in the case of infall, the radius of accretion disk will be larger as a consequence of axial magnetic field.

PROTOSTELLAR COLLAPSE OF MAGNETO-TURBULENT CLOUD CORES: SHAPE DURING COLLAPSE AND OUTFLOW FORMATION

We investigate protostellar collapse of molecular cloud cores by numerical simulations, taking into account turbulence and magnetic fields. By using the adaptive mesh refinement technique, the collapse is followed over a wide dynamic range from the scale of a turbulent cloud core to that of the first core. The cloud core is lumpy in the low density region owing to the turbulence, while it has a smooth density distribution in the dense region produced by the collapse. The shape of the dense region depends mainly on the mass of the cloud core; a massive cloud core tends to be prolate while a less massive cloud core tends to be oblate. In both cases, anisotropy of the dense region increases during the isothermal collapse. The minor axis of the dense region is always oriented parallel to the local magnetic field. All the models eventually yield spherical first cores supported mainly by the thermal pressure. Most of turbulent cloud cores exhibit protostellar outflows around the first cores. These outflows are classified into two types, bipolar and spiral flows, according to the morphology of the associated magnetic field. Bipolar flow often appears in the less massive cloud core. The rotation axis of the first core is oriented parallel to the local magnetic field for bipolar flow, while the orientation of the rotation axis from the global magnetic field depends on the magnetic field strength. In spiral flow, the rotation axis is not aligned with the local magnetic field.

LIMITING ACCRETION ONTO MASSIVE STARS BY FRAGMENTATION-INDUCED STARVATION

Massive stars influence their surroundings through radiation, winds, and supernova explosions far out of proportion to their small numbers. However, the physical processes that initiate and govern the birth of massive stars remain poorly understood. Two widely discussed models are monolithic collapse of molecular cloud cores and competitive accretion. To learn more about massive star formation, we perform simulations of the collapse of rotating, massive, cloud cores including radiative heating by both non-ionizing and ionizing radiation using the FLASH adaptive mesh refinement code. These simulations show fragmentation from gravitational instability in the enormously dense accretion flows required to build up massive stars. Secondary stars form rapidly in these flows and accrete mass that would have otherwise been consumed by the massive star in the center, in a process that we term fragmentation-induced starvation. This explains why massive stars are usually found as members of high-order stellar systems that themselves belong to large clusters containing stars of all masses. The radiative heating does not prevent fragmentation, but does lead to a higher Jeans mass, resulting in fewer and more massive stars than would form without the heating. This mechanism reproduces the observed relation between the total stellar mass in the cluster and the mass of the largest star. It predicts strong clumping and filamentary structure in the center of collapsing cores, as has recently been observed. We speculate that a similar mechanism will act during primordial star formation.

The role of disc self-gravity in the formation of protostars and protostellar discs

We use time-dependent, one-dimensional disc models to investigate the evolution of protostellar discs that form through the collapse of molecular cloud cores and in which the primary transport mechanism is self-gravity. We assume that these discs settle into a state of thermal equilibrium with Q = 2 and that the strength of the angular momentum transport is set by the cooling rate of the disc. The results suggest that these discs will attain a quasi-steady state that persists for a number of free-fall times and in which most of the mass within 100 au is located inside 10-20 au. This pile-up of mass in the inner disc could result in temperatures that are high enough for the growth of MHD turbulence which could rapidly drain the inner disc and lead to FU Orionis-like outbursts. In all our simulations, the inner regions of the discs (r < 40 au) were stable against fragmentation, while fragmentation was possible in the outer regions (r > 40 au) of discs that formed from cores that had enough initial angular momentum to deposit sufficient mass in these outer regions. The large amounts of mass in these outer regions, however, suggests that fragmentation will lead to the formation of sub-stellar and stellar mass companions, rather than planetary mass objects. Although mass accretion rates were largely consistent with observations, the large disc masses suggest that an additional transport mechanism (such as MRI occuring in the upper layers of the disc) must operate in order to drain the remaining disc material within observed disc lifetimes.

VARIABLE ACCRETION IN THE EMBEDDED PHASE OF STAR FORMATION

Motivated by the recent detection of a large number of embedded young stellar objects (YSOs) with mass accretion rates that are inconsistent with the predictions of the standard model of inside-out collapse (Shu 1977), we perform a series on numerical hydrodynamic simulations of the gravitational collapse of molecular cloud cores with various initial masses, rotation rates, and sizes. We focus on the early Class I stage of stellar evolution when circumstellar disks are exposed to high rates of mass deposition from infalling envelopes. Our numerical modeling reproduces the large observed spread in accretion rates inferred for embedded YSOs in Perseus, Serpens, and Ophiuchus star forming regions by Enoch et al. (2009), yielding 37%--75% of objects with "sub-Shu" accretion rates \dot{M} \la 10^{-6} Msun/yr and 1%--2% of objects with "super-Shu" accretion rates \dot{M}>10^{-5} Msun/yr. Mass accretion rates in the Class I stage have a log-normal distribution, with its shape controlled by disk viscosity and disk temperature. The spread in $\dot{M}$ is greater in models with lower viscosity and smaller in models with higher viscosity and higher disk temperature, suggesting that gravitational instability may be a dominant cause of the observed diversity in $\dot{M}$ in embedded YSOs. Our modeling predicts a weak dependence between the mean mass accretion rates and stellar masses in the Class I stage, in sharp contrast to the corresponding steep dependence for evolved T Tauri stars and brown dwarfs.

Submillimeter Observations of the Young Low‐Mass Object IRAS 04158+2805

We present high spatial resolution Submillimeter Array observations and supplementary single-dish photometry of the molecular gas and dust around IRAS 04158+2805, a young source with spectral type M5-M6 in the Taurus star-forming region. A bright, highly elongated dust structure that extends 8'' (~1120 AU) in diameter is revealed in a 883 μm thermal continuum image. This emission geometry is in good agreement with optical observations that show a similar structure in absorption, aligned perpendicular to bipolar scattered light nebulae. However, the interferometric data also clearly demonstrate that the submillimeter continuum emission is not centrally concentrated, but rather appears to have a toroidal geometry with substantially lower intensities inside a radius of ~250-300 AU. Spatially resolved emission from the CO J = 3–2 transition exhibits a velocity gradient along the major axis of the dust structure. If this kinematic pattern is interpreted as the signature of rotation around a central object, then a relatively low mass is inferred (M* ~ 0.3 M☉, with a ~50% uncertainty). We discuss several possible explanations for the observed gas and dust environment around IRAS 04158+2805, including a flattened envelope with an outflow cavity and a large circumbinary ring. This source offers unique views of the gas and dust environment surrounding a young low-mass stellar system. Its properties are generally not commensurate with formation scenarios for such low-mass objects that rely on dynamical ejection, but rather confirms that a single mechanism—molecular cloud core collapse and fragmentation—can produce stars over a wide range of stellar masses (at least an order of magnitude).

Three-fluid plasmas in star formation

Context. Interstellar magnetic fields influence all stages of the process of star formation, from the collapse of molecular cloud cores to the formation and evolution of circumstellar disks and protostellar jets. This requires us to have a full understanding of the physical properties of magnetized plasmas of different degrees of ionization for a wide range of densities and temperatures.

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☉ < M* < 3.0 M☉) 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 and stellar mass M* that has a best fit ∝ M*1.7, in good agreement with recent observations. We also predict a near-linear correlation between the disk accretion rate and the disk mass.

Triggered formation and collapse of molecular cloud cores

AbstractFirst I discuss the dynamics of core formation in two scenarios relevant to triggered star formation, namely the fragmentation of shock-compressed layers created by colliding turbulent flows and the fragmentation of shells swept up by expanding nebulae. Second I discuss the influence of thermodynamics on the core mass spectrum, on determining which cores are ‘pre-stellar’ (i.e. destined to spawn stars) and on the minimum mass for a pre-stellar core. Third, I discuss the properties of pre-existing cores whose collapse has been triggered by an increase in external pressure, and compare the results with observations of collapsing pre-stellar cores and evaporating gaseous globules (EGGs).

The thermodynamics of collapsing molecular cloud cores using smoothed particle hydrodynamics with radiative transfer

We present the results of a series of calculations studying the collapse of molecular cloud cores performed using a three-dimensional smoothed particle hydr odynamics code with radiative transfer in the flux-limited diffusion approximation. The opacities and specific heat capacities are identical for each calculation. However, we find that the temperature evolution during the simulations varies significantly when starting from different initial conditions. Even spherically-symmetric clouds with different initial densities show markedly different development. We conclude that simple barotropic equations of state like those used in some previous calculations provide at best a crude approximation to the thermal behaviour of the gas. Radiative transfer is necessary to obtain accurate temperatures.