Jets and molecular outflows from Herbig-Haro objects

We review status of theoretical development for jets and molecular outflows from young stellar objects. A particular framework for explaining these phenomena is one based on the X-wind theory in an environment of magnetized collapsing molecular cloud cores. The magnetized gravitational collapse follows the standard picture of isolated low-mass star formation, from quasi-static evolution of the parent molecular cloud cores. The outflow phenomena operate throughout the early evolution of young stars as a result of star-disk interaction. We discuss emission mechanisms of jets and formation of molecular outflows in this general framework. The general theoretical framework provides room for self-consistent interpretations for recent observations. Jets and outflows are integral part of earliest evolution of young stellar objects.     

Predicting the properties of binary stellar systems: the evolution of accreting protobinary systems

We investigate the formation of binary stellar systems. We consider a model where a 'seed' protobinary system forms, via fragmentation, within a collapsing molecular cloud core and evolves to its final mass by accreting material from an infalling gaseous envelope. This accretion alters the mass ratio and orbit of the binary, and is largely responsible for forming the circumstellar and/or circumbinary discs.
Given this model for binary formation, we predict the properties of binary systems and how they depend on the initial conditions within the molecular cloud core. We predict that there should be a continuous trend such that closer binaries are more likely to have equal-mass components and are more likely to have circumbinary discs than wider systems. Comparing our results with observations, we find that the observed mass-ratio distributions of binaries and the frequency of circumbinary discs as a function of separation are most easily reproduced if the progenitor molecular cloud cores have radial density profiles between uniform and 1/ r (e.g., Gaussian) with near-uniform rotation. This is in good agreement with the observed properties of pre-stellar cores. Conversely, we find that the observed properties of binaries cannot be reproduced if the cloud cores are in solid-body rotation and have initial density profiles which are strongly centrally condensed. Finally, in agreement with the radial-velocity searches for extrasolar planets, we find that it is very difficult to form a brown dwarf companion to a solar-type star with a separation ≲10 au, but that the frequency of brown dwarf companions should increase with larger separations or lower mass primaries.     

Gravitational collapse of polytropic, magnetized, filamentary clouds

For the case in which the gas of a magnetized filamentary cloud obeys a polytropic equation of state, gravitational collapse of the cloud is studied using a simplified model. We concentrate on the radial distribution and restrict ourselves to a purely toroidal magnetic field. If the axial motions and poloidal magnetic fields are sufficiently weak, we could reasonably expect our solutions to be a good approximation. We show that while the filament experiences gravitational condensation and the density at the centre increases, the toroidal flux-to-mass ratio remains constant. A series of spatial profiles of density, velocity and magnetic field for several values of the toroidal flux-to-mass ratio and the polytropic index, is obtained numerically and discussed.     

A SCUBA survey of L1689 – the dog that didn't bark

We present submillimetre data for the L1689 cloud in the ρ Ophiuchi molecular cloud complex. We detect a number of starless and pre-stellar cores and protostellar envelopes. We also detect a number of filaments for the first time in the submillimetre continuum that are parallel both to each other, and to filaments observed in the neighbouring L1688 cloud. These filaments are also seen in the ¹³CO observations of L1689. The filaments contain all of the star-formation activity in the cloud. L1689 lies next to the well-studied L1688 cloud that contains the ρ Oph-A core. L1688 has a much more active star-formation history than L1689 despite their apparent similarity in ¹³CO data. Hence, we label L1689 as the dog that didn't bark. We endeavour to explain this apparent anomaly by comparing the total mass of each cloud that is currently in the form of dense material such as pre-stellar cores. We note firstly that L1688 is more massive than L1689, but we also find that when normalized to the total mass of each cloud, the L1689 cloud has a much lower percentage of mass in dense cores than L1688. We attribute this to the hypothesis of Loren that the star formation in the ρ Ophiuchi complex is being affected and probably dominated by the external influence of the nearby Upper Scorpius OB association and predominantly by σ Sco. L1689 is further from σ Sco and is therefore less active. The influence of σ Sco appears none the less to have created the filaments that we observe in L1689.     

The effect of magnetic fields on star cluster formation

We examine the effect of magnetic fields on star cluster formation by performing simulations following the self-gravitating collapse of a turbulent molecular cloud to form stars in ideal magnetohydrodynamics. The collapse of the cloud is computed for global mass-to-flux ratios of  ∞, 20, 10, 5  and 3, i.e. using both weak and strong magnetic fields. Whilst even at very low strengths the magnetic field is able to significantly influence the star formation process, for magnetic fields with plasma  β < 1  the results are substantially different to the hydrodynamic case. In these cases we find large-scale magnetically supported voids imprinted in the cloud structure; anisotropic turbulent motions and column density striations aligned with the magnetic field lines, both of which have recently been observed in the Taurus molecular cloud. We also find strongly suppressed accretion in the magnetized runs, leading to up to a 75 per cent reduction in the amount of mass converted into stars over the course of the calculations and a more quiescent mode of star formation. There is also some indication that the relative formation efficiency of brown dwarfs is lower in the strongly magnetized runs due to a reduction in the importance of protostellar ejections.     

Binary formation in stellar clusters

We consider how the tidal potential of a stellar cluster or a dense molecular cloud affects the fragmentation of gravitationally unstable molecular cloud cores. We find that molecular cloud cores which would collapse to form a single star in the absence of tidal shear, can be forced to fragment if they are subjected to tides. This may enhance the frequency of binaries in star-forming regions such as Ophiuchus and the frequency of binaries with separations ≲100 au in the Orion Trapezium Cluster. We also find that clouds which collapse to form binary systems in the absence of a tidal potential will form bound binary systems if exposed to weak tidal shear. However, if the tidal shear is sufficiently strong, even though the cloud still collapses to form two fragments, the fragments are pulled apart while they are forming by the tidal shear and two single stars are formed. This sets an upper limit for the separation of binaries that form near dense molecular clouds or in stellar clusters.     

Simulations of the formation of stellar discs in the Galactic Centre via cloud–cloud collisions

Young massive stars in the central parsec of our Galaxy are best explained by star formation within at least one, and possibly two, massive self-gravitating gaseous discs. With help of numerical simulations, we here consider whether the observed population of young stars could have originated from a large angle collision of two massive gaseous clouds at   R ≃ 1 pc  from Sgr A*. In all the simulations performed, the post-collision gas flow forms an inner, nearly circular gaseous disc and one or two eccentric outer filaments, consistent with the observations. Furthermore, the radial stellar mass distribution is always very steep,  Σ_*∝ R ⁻²  , again consistent with the observations. All of our simulations produce discs that are warped by between 30° and 60°, in accordance with the most recent observations. The three-dimensional velocity structure of the stellar distribution is sensitive to initial conditions (e.g. the impact parameter of the clouds) and gas cooling details. For example, the runs in which the inner disc is fed intermittently with material possessing fluctuating angular momentum result in multiple stellar discs with different orbital orientations, contradicting the observed data. In all the cases the amount of gas accreted by our inner boundary condition is large, enough to allow Sgr A* to radiate near its Eddington limit over ∼10⁵ yr. This suggests that a refined model would have physically larger clouds (or a cloud and a disc such as the circumnuclear disc) colliding at a distance of a few parsecs rather than 1 pc as in our simulations.     

Helical fields and filamentary molecular clouds – I

We study the equilibrium of pressure truncated, filamentary molecular clouds that are threaded by rather general helical magnetic fields. We first apply the virial theorem to filamentary molecular clouds, including the effects of non-thermal motions and the turbulent pressure of the surrounding ISM. When compared with the data, we find that many filamentary clouds have a mass per unit length that is significantly reduced by the effects of external pressure, and that toroidal fields play a significant role in squeezing such clouds.
We also develop exact numerical MHD models of filamentary molecular clouds with more general helical field configurations than have previously been considered. We examine the effects of the equation of state by comparing 'isothermal' filaments, with constant total (thermal plus turbulent) velocity dispersion, with equilibria constructed using a logatropic equation of state.
Our theoretical models involve three parameters: two to describe the mass loading of the toroidal and poloidal fields, and a third that describes the radial concentration of the filament. We thoroughly explore our parameter space to determine which choices of parameters result in models that agree with the available observational constraints. We find that both equations of state result in equilibria that agree with the observational results. Moreover, we find that models with helical fields have more realistic density profiles than either unmagnetized models or those with purely poloidal fields; we find that most isothermal models have density distributions that fall off as r ^−1.8 to r ⁻², while logatropes have density profiles that range from r ⁻¹ to r ^−1.8. We find that purely poloidal fields produce filaments with steep radial density gradients that are not allowed by the observations.     

Why do starless cores appear more flattened than protostellar cores?

We evaluate the intrinsic three-dimensional shapes of molecular cores, by analysing their projected shapes. We use the recent catalogue of molecular line observations of Jijina et al. and model the data by the method originally devised for elliptical galaxies. Our analysis broadly supports the conclusion of Jones et al. that molecular cores are better represented by triaxial intrinsic shapes (ellipsoids) than biaxial intrinsic shapes (spheroids). However, we find that the best fit to all of the data is obtained with more extreme axial ratios (1:0.8:0.4) than those derived by Jones et al.
More surprisingly, we find that starless cores have more extreme axial ratios than protostellar cores – starless cores appear more 'flattened'. This is the opposite of what would be expected from modelling the freefall collapse of triaxial ellipsoids. The collapse of starless cores would be expected to proceed most swiftly along the shortest axis – as has been predicted by every modeller since Zel'dovich – which should produce more flattened cores around protostars, the opposite of what is seen.     

Accretion and dynamical interactions in small-N star-forming clusters: N= 5

We present results from high-resolution hydrodynamical simulations that explore the effects of small-scale clustering in star-forming regions. A large ensemble of small- N clusters with five stellar seeds have been modelled and the resulting properties of stars and brown dwarfs statistically derived and compared with observational data.
Close dynamical interactions between the protostars and competitive accretion driven by the cloud collapse are shown to produce a distribution of final masses that is bimodal, with most of the mass residing in the binary components. When convolved with a suitable core mass function, the final distribution of masses resembles the observed initial mass function, in both the stellar and substellar regimes. Binaries and single stars are found to constitute two kinematically distinct populations, with about half of the singles attaining velocities ≥2 km s⁻¹, which might deprive low-mass star-forming regions of their lightest members in a few crossing times. The eccentricity distribution of binaries and multiples is found to follow a distribution similar to that of observed long-period (uncircularized) binaries.
The results obtained support a mechanism in which a significant fraction of brown dwarfs form under similar circumstances as those of normal stars but are ejected from the common envelope of unstable multiple systems before their masses exceed the hydrogen burning limit. We predict that many close binary stars should have wide brown dwarf companions. Brown dwarfs, and, in general, very low-mass stars, would be rare as pure binary companions. The binary fraction should be a decreasing function of primary mass, with low-mass or substellar primaries being scarce. Where such binaries exist, they are expected either to be close enough (semimajor axis ∼10 au) to survive strong interactions with more massive binaries or to be born in very small molecular cloud cores.     

Collapse and fragmentation of rotating magnetized clouds – II. Binary formation and fragmentation of first cores

Subsequent to Paper I, the evolution and fragmentation of a rotating magnetized cloud are studied with use of three-dimensional magnetohydrodynamic nested grid simulations. After the isothermal runaway collapse, an adiabatic gas forms a protostellar first core at the centre of the cloud. When the isothermal gas is stable for fragmentation in a contracting disc, the adiabatic core often breaks into several fragments. Conditions for fragmentation and binary formation are studied. All the cores which show fragmentation are geometrically thin, as the diameter-to-thickness ratio is larger than 3. Two patterns of fragmentation are found. (1) When a thin disc is supported by centrifugal force, the disc fragments into a ring configuration (ring fragmentation). This is realized in a rapidly rotating adiabatic core as  Ω > 0.2τ⁻¹_ff  , where Ω and  τ_ff  represent the angular rotation speed and the free-fall time of the core, respectively. (2) On the other hand, the disc is deformed to an elongated bar in the isothermal stage for a strongly magnetized or rapidly rotating cloud. The bar breaks into 2–4 fragments (bar fragmentation). Even if a disc is thin, the disc dominated by the magnetic force or thermal pressure is stable and forms a single compact body. In either ring or bar fragmentation mode, the fragments contract and a pair of outflows is ejected from the vicinities of the compact cores. The orbital angular momentum is larger than the spin angular momentum in the ring fragmentation. On the other hand, fragments often quickly merge in the bar fragmentation, since the orbital angular momentum is smaller than the spin angular momentum in this case. Comparison with observations is also shown.     

Fragmentation of a Molecular Cloud Core versus Fragmentation of the Massive Protoplanetary Disk in the Main Accretion Phase

We present three-dimensional numerical simulations on binary formation through fragmentation. The simulations follow gravitational collapse of a molecular cloud core up to growth of the first core by accretion. At the initial stage, the gravity is only slightly dominant over the gas pressure. We made various models by changing initial velocity distribution (rotation speed, rotation law, and bar-mode perturbation). The cloud fragments whenever the cloud rotates sufficiently slowly to allow collapse but faster enough to form a disk before first-core formation. The latter condition is equivalent to Ω₀ t _ff ? 0.05, where Ω₀ and t _ff f denote the initial central angular velocity and the freefall time measured from the central density, and the condition is independent of the initial rotation law and bar-mode perturbation. Fragmentation is classified into six types. When the initial cloud rotates rigidly the cloud collapses to form a adiabatic disk supported by rotation. When the bar-mode perturbation is very minor, the disk deforms to a rotating bar, and the bar fragments. Otherwise, the adiabatic disk evolves into a central core surrounded by a circumstellar disk, and the the circumstellar disk fragments. When the initial cloud rotates differentially, the cloud deforms to a ring or bar in the isothermal collapse phase. The ring fragments into free or more cores, while the bar fragments into only two cores. In the latter case, the core merges due to low orbital angular momentum and new satellite cores form in the later stages.     

Three-dimensional simulations of molecular cloud fragmentation regulated by magnetic fields and ambipolar diffusion

We employ the first fully three-dimensional simulation to study the role of magnetic fields and ion–neutral friction in regulating gravitationally driven fragmentation of molecular clouds. The cores in an initially subcritical cloud develop gradually over an ambipolar diffusion time while the cores in an initially supercritical cloud develop in a dynamical time. The infalling speeds on to cores are subsonic in the case of an initially subcritical cloud, while an extended (≳0.1 pc) region of supersonic infall exists in the case of an initially supercritical cloud. These results are consistent with previous two-dimensional simulations. We also found that a snapshot of the relation between density (ρ) and the strength of the magnetic field ( B ) at different spatial points of the cloud coincides with the evolutionary track of an individual core. When the density becomes large, both the relations tend to   B ∝ρ^0.5  .     

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.     

ASTE observations of the massive-star forming region Sgr B2: a giant impact scenario

We report mapping observations of a 35 pc × 35 pc region covering the Sgr B2 molecular cloud complex in the ¹³CO (3-2) and the CS (7-6) lines using the ASTE 10 m telescope with high angular resolution. The central region was mapped also in the C¹⁸O (3-2) line. The images not only reproduce the characteristic structures noted in the preceding millimeter observations, but also highlight the interface of the molecular clouds with a large velocity jump of a few tens of km s⁻¹. These new results further support the scenario that a cloud–cloud collision has triggered the formation of massive cloud cores, which form massive stars of Sgr B2. Prospects of exciting science enabled by ALMA are discussed in relation to these observations.     

Filamentary structures in planetary nebulae

We have studied small-scale, filamentary features in 14 planetary nebulae and found that some structures are recurrent and shaped like the letters V and Y, with the apex or stem pointing toward the central parts of the nebula. Two such filaments containing dust, one in NGC 3132 and one in NGC 7293, were investigated in more detail. The mass and density of the filaments were obtained from extinction measurements, and their physical properties were derived. We propose that the structures are confined by magnetic fields, and derive magnetic field strengths of about 10⁻⁸ T, in line with earlier estimates. We also estimate the magnitude of the electric currents that we expect are generated in these dynamic systems. We propose a theory where the magnetic fields control the sculpting and evolution of small-scale filaments. This theory demonstrates how the substructures may form magnetized flux ropes that are twisted around each other, in the shape of double helices. Similar structures, and with similar origin, are found in many other astrophysical environments.     

Starlight polarization and CO observations towards the Lupus clouds

We performed an observational study of the dark filaments Lupus 1 and Lupus 4 using both polarimetric observations of 190 stars and a sample of 72 ¹²CO profiles towards these clouds. We have estimated lower limits to the distances of Lupus 1 and Lupus 4 (≳ 140 and ≳ 125 pc, respectively). The observational strategy of the survey allows us to compare the projected magnetic field in an extended area around each cloud with the magnetic field direction observed to prevail along the clouds. Lupus 4 could have collapsed along the magnetic field lines, while in Lupus 1 the magnetic field appears to be less ordered, having the major axis of the filaments parallel to the large-scale projected magnetic field. These differences would imply that both filaments have different pattern evolutions. From the CO observations we have probed the velocity fields of the filaments and the spatial extension of the molecular gas with respect to the dust.     

Fragmentation in molecular clouds and its connection to the IMF

We present an analysis of star-forming gas cores in a smooth particle hydrodynamics simulation of a giant molecular cloud. We identify cores using their deep potential wells. This yields a smoother distribution with clearer boundaries than density. Additionally, this gives an indication of future collapse, as bound potential cores (p-cores) represent the earliest stages of fragmentation in molecular clouds. We find that the mass function of the p-cores resembles the stellar initial mass function and the observed clump mass function, although p-core masses  (∼0.7 M_⊙)  are smaller than typical density clumps. The bound p-cores are generally subsonic, have internal substructure and are only quasi-spherical. We see no evidence of massive bound cores supported by turbulence. We trace the evolution of the p-cores forward in time, and investigate the connection between the original p-core mass and the stellar mass that formed from it. We find that there is a poor correlation, with considerable scatter suggesting accretion on to the core is dependent on more factors than just the initial core mass. During the accretion process the p-cores accrete from beyond the region first bound, highlighting the importance of the core environment to its subsequent evolution.     

Molecular Cloud Collapse

Theoretical models of star formation from the collapse of molecular cloud cores have been evolving in complexity for many years. This work describes the evolution of models from the nonrotating, nonmagnetized singular isothermal sphere to rotating, magnetized singular isothermal toroids. Four members of the same family are studied–the four combinations of nonrotation/rotation and nonmagnetization/magnetization. It is found that although rotation alone can hinder collapse to a pointmass, addition of braking from a magnetic field can transport away much of the angular momentum upward in a low-velocity outflow during the collapse phase. For all magnetized cases, accretion proceeds at a constant rate similar to that of the isothermal sphere.     

Evolution of Class 0 protostars: models versus observations

The rates at which mass accumulates into protostellar cores can now be predicted in numerical simulations. Our purpose here is to develop methods to compare the statistical properties of the predicted protostars with the observable parameters. This requires (1) an evolutionary scheme to convert numerically derived mass accretion rates into evolutionary tracks and (2) a technique to compare the tracks to the observed statistics of protostars. Here, we use a 3D Kolmogorov–Smirnov test to quantitatively compare model evolutionary tracks and observations of Class 0 protostars.
We find that the wide range of accretion functions and time-scales associated with gravoturbulent simulations naturally overcome difficulties associated with schemes that use a fixed accretion pattern. This implies that the location of a protostar on an evolutionary track does not precisely determine the present age or final accrued mass. Rather, we find that predictions of the final mass for protostars from observed   T _bol– L _bol  values are uncertain by a factor of 2 and that the bolometric temperature is not always a reliable measure of the evolutionary stage. Furthermore, we constrain several parameters of the evolutionary scheme and estimate a lifetime of Class 0 sources of  2–6 × 10⁴ yr  , which is related to the local free-fall time and thus to the local density at the onset of the collapse. Models with Mach numbers smaller than six are found to best explain the observational data. Generally, only a probability of 70 per cent was found that our models explain the current observations. This is caused by not well-understood selection effects in the observational sample and the simplified assumptions in the models.