Emission line profiles of tracer molecule H$_2$CO 140 GHz transition from gravitational core collapsing clouds in the dynamic process of forming protostars are calculated, using a simple ray-tracing radiative transfer model. Three self-similar dynamic inside-out core collapse models -- the conventional polytropic model, the empirical hybrid model and the isothermal model -- for star-forming molecular clouds are examined and compared. The isothermal model cannot produce observed asymmetric double-peak molecular line profiles. The conventional polytropic model, which gives flow velocity, mass density and temperature profiles self-consistently, can produce asymmetric double-peak line profiles for a core collapsing cloud. In particular, the blue peak is stronger than the red peak, consistent with a broad class of molecular line profile observations. The relative strengths of the blue and red peaks within a molecular line profile are determined by the cloud temperature gradient. The conventional polytropic model can be utilized to produce molecular line-profile templates, for extracting dynamical information from line spectra of molecular globules undergoing a gravitational core collapse. We show a sample fit using the 140 GHz H$_2$CO emission line from the central region of the molecular globule B335 by our model with $γ=1.2$. The calculation of line profiles and fitting processes also offer a scenario to estimate the protostellar mass, the kernel mass accretion rate, and the evolution time scale of a core collapsing cloud. Our model can be readily adapted to other tracer molecules with more or less constant abundances in star-forming clouds.
The collapse of the magnetic rotating protostellar cloud with mass of $10\,M_{\odot}$ is numerically studied. The initial ratios of the thermal, magnetic, and rotational energies of the cloud to the modulus of its gravitational energy are 0.3, 0.2 and 0.01, respectively. The emphasis is on the evolution and properties of the quasi-magnetostatic primary disk formed at the isothermal stage of the collapse. Simulations show that the primary disk size and mass increase during evolution from $1500$ au to $7400$ au and from $0.3\,M_{\odot}$ to $5.2\,M_{\odot}$, respectively. Magnetic field is quasi-…
Atoms and molecules, and in particular CO, are important coolants during the evolution of interstellar star-forming gas clouds. The presence of dust grains, which allow many chemical reactions to occur on their surfaces, strongly impacts the chemical composition of a cloud. At low temperatures, dust grains can lock-up species from the gas phase which freeze out and form ices. In this sense, dust can deplete important coolants. Our aim is to understand the effects of freeze-out on the thermal balance and the evolution of a gravitationally bound molecular cloud. For this purpose, we perform 3D h…
In nearby star-forming clouds, amplification and dissipation of the magnetic field are known to play crucial roles in the star-formation process. The star-forming environment varies from place to place and era to era in galaxies. In the present study, amplification and dissipation of magnetic fields in star-forming clouds are investigated under different environments using magnetohydrodynamics (MHD) simulations. We consider various star-forming environments in combination with the metallicity and the ionization strength, and prepare prestellar clouds having two different mass-to-flux ratios. W…
We revisit the interpretation of blue-excess molecular lines from dense collapsing cores, considering recent numerical results that suggest prestellar core collapse occurs from the outside-in, and not inside-out. We thus create synthetic molecular-line observations of simulated collapsing, spherically-symmetric, density fluctuations of low initial amplitude, embedded in a uniform, globally gravitationally unstable background, without a turbulent component. The collapsing core develops a flattened, Bonnor-Ebert-like density profile, but with an outside-in radial velocity profile, where the peak…
We employ the three-dimensional magnetohydrodynamic simulation including ambipolar diffusion to study the gravitationally-driven fragmentation of subcritical molecular clouds, in which the gravitational fragmentation is stabilized as long as magnetic flux-freezing applies. The simulations show that the cores in an initially subcritical cloud generally develop gradually over an ambipolar diffusion time, which is about a few $\times 10^7$ years in a typical molecular cloud. On the other hand, the formation of collapsing cores in subcritical clouds is accelerated by supersonic nonlinear flows. Ou…
We discuss the dependence of various properties of the star formation rate (SFR) and efficiency (SFE) in molecular clouds (MCs) on the maximum mass reached by the clouds, based on a previously-published model for MC and SFR evolution in which the clouds were assumed to be undergoing global collapse, and the SFR was controlled by ioniztion feedback. Because the model neglects various other processes, the results presented are upper limits. We find that clouds with $\Mmax \lesssim 10^4 \Msun$ end their lives with a mini-burst, at which the SFR reaches a peak of $\sim 10^4 ~\Msun \Myr^{-1}$, alth…
International Centre for Theoretical Sciences, Tata Institute of Fundamental Research（国际理论科学中心，塔塔基础研究所）；Inter-University Centre for Astronomy and Astrophysics（大学间天体物理与天文中心）；Department of Physics, Ashoka University（阿肖卡大学物理系）；School of Mathematics, Statistics and Physics, Newcastle University（纽卡斯尔大学数学、统计与物理学院）
Stars are often observed to form in clusters. It is therefore important to understand how such a region of concentrated mass is assembled out of the diffuse medium and its properties eventually prescribe the important physical mechanisms and determine the characteristics of the stellar cluster. We study the formation of a gaseous proto-cluster inside a molecular cloud by performing high resolution MHD simulations and associate its internal properties to those of the parent cloud by varying the level of the initial turbulence of the cloud, with a view to better characterize the subsequent stell…
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 density radial profile, which would change from a Bonnor-Ebert type toward power laws as the core collapses. In practice, due to the projection effect, the r…
The aim of this study is to examine dust dynamics on a large scale and investigate the coupling of dust with gas fluid in the star formation process. We propose a method for calculating the dust trajectory in a gravitationally collapsing cloud, where the dust grains are treated as Lagrangian particles and are assumed to be neutral. We perform the dust trajectory calculations in combination with non-ideal magnetohydrodynamics simulation. Our simulation shows that dust particles with a size of $\le 10\,{\rm μm}$ are coupled with gas in a star-forming cloud core. We investigate the time evolution…
Recent observational and theoretical investigations have emphasised the importance of filamentary networks within molecular clouds as sites of star formation. Since such environments are more complex than those of isolated cores, it is essential to understand how the observed line profiles from collapsing cores with non-spherical geometry are affected by filaments. In this study, we investigate line profile asymmetries by performing radiative transfer calculations on hydrodynamic models of three collapsing cores that are embedded in filaments. We compare the results to those that are expected …
We present multi-wavelength data on the globally infalling molecular cloud/protostellar cluster BYF 73. These include new far-IR spectral line and continuum data from SOFIA's Far Infrared Field-Imaging Line Spectrometer (FIFI-LS), mid-infrared (MIR) observations with the Thermal-Region Camera Spectrograph (T-ReCS) on Gemini-South, and 3 mm continuum data from the Australia Telescope Compact Array (ATCA), plus archival data from Spitzer/IRAC, and Herschel/PACS and SPIRE. The FIFI-LS spectroscopy in [OI]$\lambda63 μ$m, [OIII]$\lambda88 μ$m, [OI]$\lambda145 μ$m, and [CII]$\lambda158 μ$m highlight…
We report the results of a numerical study on the initial formation stages of low-mass protostellar binary systems. We determine the separation of protostellar binaries formed as a function of the initial thermal state by varying the initial temperature in a slightly modified version of the Burkert and Bodenheimer collapse test. We find that the outcome is highly sensitive to both the initial temperature of the cloud and the initial amplitude of azimuthal density perturbation A. For A=10 %, variations of only 1 unit Kelvin below 10 K lead to changes of up to 100 AU ( i.e. of order 30 %) in the…
Observations of atomic or molecular lines can provide important information about the physical state of star forming regions. In order to investigate the line profiles from dynamical collapsing massive star forming regions (MSFRs), we model the emission from hydrodynamic simulations of a collapsing cloud in the absence of outflows. By performing radiative transfer calculations, we compute the optically thick HCO+ and optically thin N2H+ line profiles from two collapsing regions at different epochs. Due to large-scale collapse, the MSFRs have large velocity gradients, reaching up to 20 km/s/pc …
Planet-forming disks are fundamental objects thought to be inherited from large scale rotation, through the conservation of angular momentum during the collapse of a prestellar dense core. We investigate the possibility for a protostellar disk to be formed from a motionless dense core which contains non-axisymmetric density fluctuations. The rotation is thus generated locally by the asymmetry of the collapse. We study the evolution of the angular momentum in a non-axisymmetric collapse of a dense core from an analytical point of view. To test the theory, we perform three-dimensional simulation…
We determine the time evolution of the dust particle size distribution during the collapse of a cloud core, accounting for both dust coagulation and dust fragmentation, to investigate the influence of dust growth on non-ideal magnetohydrodynamic effects.The density evolution of the collapsing core is given by a one-zone model. We assume two types of dust model: dust composed only of silicate (silicate dust) and dust with a surface covered by $\mathrm{H_{2}O}$ ice ($\mathrm{H_{2}O}$ ice dust). When only considering collisional coagulation, the non-ideal magnetohydrodynamic effects are not effec…
Observations are revealing the ubiquity of filamentary structures in molecular clouds. As cores are often embedded in filaments, it is important to understand how line profiles from such systems differ from those of isolated cores. We perform radiative transfer calculations on a hydrodynamic simulation of a molecular cloud in order to model line emission from collapsing cores embedded in filaments. We model two optically thick lines, CS(2-1) and HCN(1-0), and one optically thin line, N2H+(1-0), from three embedded cores. In the hydrodynamic simulation, gas self-gravity, turbulence, and bulk fl…
We discuss the mechanism of cluster formation in a numerical simulation of a molecular cloud (MC) undergoing global hierarchical collapse (GHC). The global nature of the collapse implies that the SFR increases over time. The hierarchical nature of the collapse consists of small-scale collapses within larger-scale ones. The large-scale collapses culminate a few Myr later than the small-scale ones and consist of filamentary flows that accrete onto massive central clumps. The small-scale collapses form clumps that are embedded in the filaments and falling onto the large-scale collapse centers. Th…
We investigate the driving mechanism of outflows and jets in star formation process using resistive MHD nested grid simulations. We found two distinct flows in the collapsing cloud core: Low-velocity outflows (sim 5 km/s) with a wide opening angle, driven from the first adiabatic core, and high-velocity jets (sim 50 km/s) with good collimation, driven from the protostar. High-velocity jets are enclosed by low-velocity outflow. The difference in the degree of collimation between the two flows is caused by the strength of the magnetic field and configuration of the magnetic field lines. The magn…
We present the first detailed classification of the structures of Class 0 cores in a high resolution simulation of a giant molecular cloud. The simulated cloud contains 10^4 solar masses and produces over 350 cores which allows for meaningful statistics. Cores are classified into three types according to how much they depart from spherical symmetry. We find that three quarters of the cores are better described as irregular filaments than as spheres. Recent Herschel results have shown that cores are formed within a network of filaments, which we find has had a significant impact on the resultin…
We perform three dimensional smoothed particle hydrodynamics (SPH) simulations of gas accretion onto the seeds of binary stars to investigate their short-term evolution. Our simulation setup is more realistic compared to the previous works by taking into account of dynamically evolving envelope with non-uniform distribution of gas density and angular momentum of accreting flow. Our initial condition includes a seed binary and a surrounding gas envelope, modelling the phase of core collapse of gas cloud when the fragmentation has already occurred. We assume that the seed binary has no eccentric…
The physical conditions in a collapsing cloud can be traced by observations of molecular lines. To correctly interpret these observations the abundance distributions of the observed species need to be derived. The chemistry in a collapsing molecular cloud is not in a steady state as the density and temperature evolve. We therefore need to follow chemical reactions, both in the gas phase and on dust grains, as well as gas-grain interactions, to predict the abundance distributions. Our aim is to model the abundances of molecules, in the gas phase and on grain mantles in the form of ice, from pre…
Spectral molecular line profile observations of star-forming molecular clouds sometimes show distinct red asymmetric double-peaked molecular line profiles with weaker blue peaks and stronger red peaks. For some star-forming molecular clouds, such molecular transitions with red asymmetric line profiles and blue asymmetric line profiles (i.e. blue asymmetric double-peaked molecular line profiles with weaker red peaks and stronger blue peaks) may coexist in spatially resolved spectral observations, while for others, such molecular transitions with red asymmetric line profiles may completely domin…
The formation and evolution of the circumstellar disk in the collapsing molecular cloud is investigated from the prestellar stage resolving both the molecular cloud core and the protostar itself. In the collapsing cloud, the first adiabatic core appears prior to the protostar formation. Reflecting the thermodynamics of the collapsing gas, the first core is much more massive than the protostar. When the molecular cloud has no angular momentum, the first core falls onto the protostar and disappears a few years after the protostar formation. On the other hand, when the molecular cloud has an angu…
We present high-resolution hydrodynamical simulations aimed at following the gravitational collapse of a gas core, in which a turbulent spectrum of velocity is implemented only initially. We determine the maximal value of the ratio of kinetic energy to gravitational energy, denoted here by $\left(\frac{E_{\rm kin} }{E_{\rm grav}}\right)_{\rm max}$, so that the core (i) will collapse around one free-fall time of time evolution or (ii) will expand unboundedly, because it has a value of $\frac{E_{\rm kin}}{E_{\rm grav}}$ larger than $\left( \frac{E_{\rm kin}}{E_{\rm grav}}\right)_{\rm max}$. We c…
The diffusion of astrophysical magnetic fields in conducting fluids in the presence of turbulence depends on whether magnetic fields can change their topology via reconnection in highly conducting media. Recent progress in understanding fast magnetic reconnection in the presence of turbulence is reassuring that the magnetic field behavior in computer simulations and turbulent astrophysical environments is similar, as far as magnetic reconnection is concerned. Our studies of magnetic field diffusion in turbulent medium reveal interesting new phenomena. In the presence of gravity and turbulence,…
The fragmentation of star-forming interstellar clouds, and the resulting stellar initial mass function (IMF), is strongly affected by the temperature structure of the collapsing gas. Since radiation feedback from embedded stars can modify this as collapse proceeds, feedback plays an important role in determining the IMF. However, the effects and importance of radiative heating are likely to depend strongly on the surface density of the collapsing clouds, which determines both their effectiveness at trapping radiation and the accretion luminosities of the stars forming within them. In this pape…
This paper tries to establish whether there are variations of the central wavelengths or the profile shapes of diffuse interstellar bands (DIBs) and whether these variations are caused by different physical parameters of translucent clouds. For this purpose we used spectra of two stars seen through two different single clouds: HD34078 (AE Aur) \& HD73882 acquired using two different instruments: the MIKE spectrograph, fed with the 6.5 m Magellan telescope at Las Campanas Observatory, and the UVES, fed with the 8 m Kueyen telescope at the Paranal observatory. The wavelength displacements of the…
Low-mass stars are generally understood to form by the gravitational collapse of the dense molecular clouds known as starless cores. Continuum observations have not been able to distinguish among the several different hypotheses that describe the collapse because the predicted density distributions are the almost the same, as they are for all spherical self-gravitating clouds. However, the predicted contraction velocities are different enough that the models can be discriminated by comparing the velocities at large and small radii. This can be done by observing at least two different molecular…
We have coupled a chemical model with two dynamical models of collapsing low mass star-forming cores to predict abundances across the core of the commonly used infall tracers, CS and HCO$^+$, at various stages of the collapse. The models investigated are a new ambipolar diffusion model and the `inside-out' collapse model. We have then used these results as an input to a radiative transfer model to predict the line profiles of several transitions of these molecules. For the inside-out collapse model, we predict significant molecular depletion due to freeze-out in the core centre, which prevents…
Motivated by recent numerical simulations of molecular cloud (MC)evolution, in which the clouds engage in global gravitational contraction, and local collapse events culminate significantly earlier than the global collapse, we investigate the growth of density perturbations embedded in a collapsing background, to which we refer as an Inverse Hubble Flow (IHF). We use the standard procedure for the growth of perturbations in a universe that first expands (the usual Hubble Flow) and then recollapses (the IHF). We find that linear density perturbations immersed in an IHF grow faster than perturba…
Outflows and jets are intimately related to the formation of stars, and play an important role in redistributing mass, energy and angular momentum within the dense core and parent cloud. The interplay between magnetic field and rotation is responsible for launching these outflows, whose formation has been generally carried out for idealized systems where the angle $α$ between the rotation axis and large-scale magnetic field is zero. Here we explore, through three-dimensional ideal magneto-hydrodynamic simulations, the effects of a non-zero $α$ on the formation of outflows during the collapse o…
In this paper we study the gravitational collapse of a molecular hydrogen gas cloud composed of a core plus a gas envelope surrounding the core. We numerically simulate the collapse of four cloud models to take a glimpse to the time evolution of several dynamic variables, such as the angular momentum and the $aem$ ratio, as well as the ratios between the thermal and rotational energies with respect to the potential gravitational energy, denoted as $α$ and $β$, respectively, among others. We re-take those models introduced by Arreaga et.al (Astronomy and Astrophysics, {\bf Vol. 509}, (2010), pa…
We examine the effects of self-gravity and magnetic fields on supersonic turbulence in isothermal molecular clouds with high resolution simulations and adaptive mesh refinement. These simulations use large root grids (512^3) to capture turbulence and four levels of refinement to capture high density, for an effective resolution of 8,196^3. Three Mach 9 simulations are performed, two super-Alfvénic and one trans-Alfvénic. We find that gravity splits the clouds into two populations, one low density turbulent state and one high density collapsing state. The low density state exhibits properties s…
Understanding the formation of binary and multiple stellar systems largely comes down to studying the circumstances for the fragmentation of a condensing core during the first stages of the collapse. However, the probability of fragmentation and the number of fragments seem to be determined to a large degree by the initial conditions. In this work we study the fate of the linear perturbations of a homogeneous gas sphere both analytically and numerically. In particular, we investigate the stability of the well-known homologous solution that describes the collapse of a uniform spherical cloud. T…
