Abridged: We use three-dimensional SPH simulations to investigate the collapse of low-mass prestellar cores and the formation and early evolution of protostellar discs. The initial conditions are slightly supercritical Bonnor-Ebert spheres in rigid rotation. The core mass and initial radius are held fixed at M_O=6.1 M_sun and R_O=17,000 AU, and the only parameter that we vary is the initial angular speed Ω_O. Protostellar discs forming from cores with Ω_O<1.35 10d-13 1/s have radii between 100 and 300 AU and are quite centrally concentrated; due to heating by gas infall onto the disc and accretion onto the central object, they are also quite warm, T>100 K, and therefore stable against gravitational fragmentation. In contrast, more rapidly rotating cores form discs which are less concentrated and cooler, and have radii between 400 and 1000 AU; as a consequence they are prone to gravitational fragmentation and the formation of multiple systems. We derive a criterion that predicts whether a rigidly rotating core having given M_O, R_O and Ω_O will produce a protostellar disc which fragments whilst material is still infalling from the core envelope. We then apply this criterion to core samples for which M_O, R_O and Ω_O have been estimated observationally. We conclude that the observed cores are stable against fragmentation at this stage, due to their low angular speeds and the heat delivered at the accretion shock where the infalling material hits the disc.
With respect to earlier investigations, the theory of multi-component, concentric, copolar, axisymmetric, rigidly rotating polytropes is improved and extended, including subsystems with nonzero density on the boundary and subsystems with intersecting boundaries. The formulation is restricted to two subsystems for simplicity but, in principle, can be extended to $N$ subsystems. Equilibrium configurations are independent of the nature of the fluid i.e. collisional or collisionless, provided the polytropic index lies within the range, $1/2\le n\le5$, as in one-component systems. The solution of t…
It is shown that the interior solution of axially symmetric, stationary and rigidly rotating dust configurations is completely determined by the mass density along the axis of rotation. The particularly interesting case of a mass density, which is cylindrical symmetric in the interior of the dust configuration, is presented. Among other things, this proves the non-existence of homogeneous dust configurations.
Axisymmetric, rigidly rotating polytropes are considered in the framework of both the original Chandrasekhar (C33) approximation and a different version (extended C33 approximation). Special effort is devoted to two specific points, namely (i) a contradiction between the binomial series evaluation and the vanishing density on the boundary, which affects the self-consistency of the above mentioned approximations, and (ii) the continuity of selected parameters as a function of the polytropic index. Concerning (i), it is shown the Emdem-Chandrasekhar (EC) associated functions are defined at any i…
The central problem in forming a star is the angular momentum in the circumstellar disk which prevents material from falling into the central stellar core. An attractive solution to the "angular momentum problem" appears to be the ubiquitous (low-velocity and poorly-collimated) molecular outflows and (high-velocity and highly-collimated) protostellar jets accompanying the earliest phase of star formation that remove angular momentum at a range of disk radii. Previous observations suggested that outflowing material carries away the excess angular momentum via magneto-centrifugally driven winds …
The HH 111 protostellar system is a young Class I system with two sources, VLA 1 and VLA 2, at a distance of 400 pc. Previously, a flattened envelope has been seen in C18O to be in transition to a rotationally supported disk near the VLA 1 source. The follow-up study here is to confirm the rotationally supported disk at 2-3 times higher angular resolutions, at ~ 0.3" (or 120 AU) in 1.33 mm continuum, and ~ 0.6" (or 240 AU) in 13CO (J=2-1) and 12CO (J=2-1) emission obtained with the Submillimeter Array. The 1.33 mm continuum emission shows a resolved dusty disk associated with the VLA 1 source …
HH 212 is a nearby (400 pc) Class 0 protostellar system showing several components that can be compared with theoretical models of core collapse. We have mapped it in 350 GHz continuum and HCO+ J=4-3 emission with ALMA at up to ~ 0.4" resolution. A flattened envelope and a compact disk are seen in continuum around the central source, as seen before. The HCO+ kinematics shows that the flattened envelope is infalling with small rotation (i.e., spiraling) into the central source, and thus can be identified as a pseudodisk in the models of magnetized core collapse. Also, the HCO+ kinematics shows …
HH 212 is a nearby (400 pc) Class 0 protostellar system recently found to host a "hamburger"-shaped dusty disk with a radius of ~ 60 AU, deeply embedded in an infalling-rotating flattened envelope. We have spatially resolved this envelope-disk system with the Atacama Large Millimeter/submillimeter Array at up to ~ 16 AU (0.04") resolution. The envelope is detected in HCO+ J=4-3 down to the dusty disk. Complex organic molecules (COMs) and doubly deuterated formaldehyde (D2CO) are detected above and below the dusty disk within ~ 40 AU of the central protostar. The COMs are methanol (CH3OH), deut…
In this paper we suggest the existence in the central regions of spiral galaxies of collisionless, scale-free, rigidly rotating, self-gravitating discs with spiral symmetry. Such discs must be truncated at a finite radius, and they must be stabilized and rendered self-similar by a suitable halo. The halo and the rotating disc share the self-similar class and must form together to arrive at the suggested state. We make comparisons with the well-known rigidly rotating, Kalnajs discs; one of which is axi-symmetric and finite while the other is infinite and decomposed into spiral modes. We find th…
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-…
We present an interferometric kinematic study of morphologically complex protostellar envelopes based on observations of the dense gas tracers N2H+ and NH3. The strong asymmetric nature of most envelopes in our sample leads us to question the common interpretation of velocity gradients as rotation, given the possibility of projection effects in the observed velocities. Several "idealized" sources with well-ordered velocity fields and envelope structures are now analyzed in more detail. We compare the interferometric data to position-velocity diagrams of kinematic models for spherical rotating …
A strong signature of a circumstellar disc around a high-mass protostar has been inferred from high resolution methanol maser observations in NGC7538-IRS1 N. This interpretation has however been challenged with a bipolar outflow proposed as an alternative explanation. We compare the two proposed scenarios for best consistency with the observations. Using a newly developed formalism we model the optical depth of the maser emission at each observed point in the map and LOS velocity for the two scenarios. We find that if the emission is symmetric around a central peak in both space and LOS veloci…
We present results from our SMA observations and data analyses of the SMA archival data of the Class I protostar IRAS 04169+2702. The high-resolution (~0.5") $^{13}$CO (3-2) image cube shows a compact ($r$ ~< 100 au) structure with a northwest (blue) to southeast (red) velocity gradient, centered on the 0.9-mm dust-continuum emission. The direction of the velocity gradient is orthogonal to the axis of the molecular outflow as seen in the SMA $^{12}$CO (2-1) data. A similar gas component is seen in the SO (6$_5$-5$_4$) line. On the other hand, the C$^{18}$O (2-1) emission traces a more extended…
Rotating outflows from protostellar disks might trace extended magneto-hydrodynamic (MHD) disk winds (DWs), providing a solution to the angular momentum problem in disk accretion for star formation. In the jet system HH 212, a rotating outflow was detected in SO around an episodic jet detected in SiO. Here we spatially resolve this SO outflow into three components: a collimated jet aligned with the SiO jet, the wide-angle disk outflow, and an evacuated cavity in between created by a large jet-driven bowshock. Although it was theoretically predicted before, it is the first time that such a jet-…
We investigate collapse of magnetic protostellar clouds of mass $10$ and $1 M_{\odot}$. The collapse is simulated numerically using the two-dimensional magnetohydrodynamic (MHD) code `Enlil'. The simulations show that protostellar clouds acquire a hierarchical structure by the end of the isothermal stage of collapse. Under the action of the electromagnetic force, the protostellar cloud takes the form of an oblate envelope with the half-thickness to radius ratio $Z/R \sim (0.20-0.95)$. A geometrically and optically thin primary disk with radius $0.2-0.7 R_0$ and $Z/R \sim (10^{-2}-10^{-1})$ for…
HH 211-mms is one of the youngest Class 0 protostellar systems in Perseus at ~ 235 pc away. We have mapped its central region at up to ~ 7 AU (0.03") resolution. A dusty disk is seen deeply embedded in a flattened envelope, with an intensity jump in dust continuum at ~ 350 GHz. It is nearly edge-on and is almost exactly perpendicular to the jet axis. It has a size of ~ 30 au along the major axis. It is geometrically thick, indicating that the (sub)millimeter light emitting grains have yet to settle to the midplane. Its inner part is expected to have transformed into a Keplerian rotating disk w…
Understanding the formation mechanisms of protoplanetary disks and multiple systems, and their pristine properties, is a key question for modern astrophysics. The properties of the youngest disks, embedded in rotating infalling protostellar envelopes, have largely remained unconstrained up to now. In the framework of the IRAM-PdBI CALYPSO survey, we have obtained sub-arcsecond observations of the dust continuum emission at 231 GHz and 94 GHz, for a sample of 16 solar-type Class 0 protostars. In an attempt to identify disk-like structures embedded at small scales in the protostellar envelopes, …
We have analyzed rotational spectral line emission of OCS, CH3OH, HCOOCH3, and H2CS observed toward the low-mass Class 0 protostellar source IRAS 16293-2422 Source A at a sub-arcsecond resolution (~0".6 x 0".5) with ALMA. Significant chemical differentiation is found at a 50 AU scale. The OCS line is found to well trace the infalling-rotating envelope in this source. On the other hand, the CH3OH and HCOOCH3 distributions are found to be concentrated around the inner part of the infalling-rotating envelope. With a simple ballistic model of the infalling-rotating envelope, the radius of the cent…
Models of the protostellar source, B335, are developed using axisymmetric three-dimensional models to resolve conflicts found in one-dimensional models. The models are constrained by a large number of observations, including ALMA, Herschel, and Spitzer data. Observations of the protostellar source B335 with ALMA show red-shifted absorption against a central continuum source indicative of infall in the HCO$^+$ and HCN $J = 4\rightarrow 3$ transitions. The data are combined with a new estimate of the distance to provide strong constraints to three-dimensional radiative transfer models including …
It has been argued that the low-mass primordial stars ($m_{\rm Pop III}\,\leq 0.8\,M_\odot$) are likely to enter the main sequence and hence possibly be found in the present-day Galaxy. However, due to limitations in existing numerical capabilities, current three-dimensional (3D) simulations of disk fragmentation are capable of following only a few thousands of years of evolution after the formation of the first protostar. In this work we use a modified version of {\sc Gadget}-2 smoothed particle hydrodynamics(SPH) code to present the results of non-linear collapse of the gas clouds associated…
The HH 211 protostellar system is currently the youngest Class 0 system found with a rotating disk. We have mapped it at ~ 50 au (0.16") resolution, studying its magnetic field morphology with dust polarization in continuum at 232 and 358 GHz and its kinematics in C18O J=2-1 line. A flattened envelope extending out to ~ 400 au from the disk is detected in the continuum and C18O, slightly misaligned with the disk by 8 degree. It is spiraling inwards and expected to transform into a rotating disk at ~ 20 au, consistent with the disk radius estimated before. It appears to have a constant specific…
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…
It is believed that protostellar accretion disks to be formed from nearly ballistic infall of the molecular matters in rotating core collapse. Collisions of these infalling matters lead to formation of strong supersonic shocks, which if they cool rapidly, result in accumulation of that material in a thin structure in the equatorial plane. Here, we investigate the relaxation time of the protostellar accretion post-shock gas using the smoothed particle hydrodynamics (SPH). For this purpose, a one-dimensional head-on collision of two molecular sheets is considered, and the time evolution of the t…
We report molecular line observations of the massive protostellar source G339.88-1.26 with the Atacama Large Millimeter/Submillimeter Array. The observations reveal a highly collimated SiO jet extending from the 1.3 mm continuum source, which connects to a slightly wider but still highly collimated CO outflow. Rotational features perpendicular to the outflow axis are detected in various molecular emissions, including SiO, SO2, H2S, CH3OH, and H2CO emissions. Based on their spatial distributions and kinematics, we find that they trace different parts of the envelope-disk system. The SiO emissio…
In this work we study the properties of rigidly rotating neutral dust solutions in general relativity. This class of solutions gained relevance recently due to applications to the dynamics of spiral galaxies. We show that this class could be interpreted as a rigid body in general relativity and we analyze the different properties respect to the rigidly rotating disk in special relativity: for example, the general relativistic counterpart shows no Doppler effect for a light signal emitted and received from any two points at rest respect to the rigid body. This effect can be important to test th…
We analyse simulations of turbulent, magnetised molecular cloud cores focussing on the formation of Class 0 stage protostellar discs and the physical conditions in their surroundings. We show that for a wide range of initial conditions Keplerian discs are formed in the Class 0 stage already. Furthermore, we show that the accretion of mass and angular momentum in the surroundings of protostellar discs occurs in a highly anisotropic manner, by means of a few narrow accretion channels. The magnetic field structure in the vicinity of the discs is highly disordered, revealing field reversals up to …
HH 111 is a Class I protostellar system at a distance of ~ 400 pc, with the central source VLA 1 associated with a rotating disk deeply embedded in a flattened envelope. Here we present the observations of this system at ~ 0.6" (240 AU) resolution in C18O (J=2-1) and 230 GHz continuum obtained with Atacama Large Millimeter/Submillimeter Array, and in SO obtained with Submillimeter Array. The observations show for the first time how a Keplerian rotating disk can be formed inside a flattened envelope. The flattened envelope is detected in C18O, extending out to >~ 2400 AU from the VLA 1 source. …
The role of accretion disks in the formation of low-mass stars has been well assessed by means of high angular resolution observations at various wavelengths. These findings confirm the prediction that conservation of angular momentum during the collapse leading to the formation of a star is bound to produce flattening and rotation of the collapsing core. What about high-mass stars? At present, several authors have reported on detections of disks around high-mass YSOs. Notwithstanding these important results, the presence of disks rotating about high-mass stars is not sufficient by itself to p…
HH 211 is a young Class 0 protostellar system, with a flattened envelope, a possible rotating disk, and a collimated jet. We have mapped it with the Submillimeter Array in 341.6 GHz continuum and SiO J=8-7 at ~ 0.6 resolution. The continuum traces the thermal dust emission in the flattened envelope and the possible disk. Linear polarization is detected in the continuum in the flattened envelope. The field lines implied from the polarization have different orientations, but they are not incompatible with current gravitational collapse models, which predict different orientation depending on the…
We have observed the three low-mass protostars, IRAS 15398$-$3359, L1527 IRS and TMC-1A, with the ALMA 12-m array, the ACA 7-m array, and the IRAM-30m and APEX telescopes in the C$^{18}$O $J=2$-1 emission. Overall, the C$^{18}$O emission shows clear velocity gradients at radii of $\sim$100-1000 au, which likely originate from rotation of envelopes, while velocity gradients are less clear and velocity structures are more perturbed on scales of $\sim$1000-10,000 au. IRAS 15398$-$3359 and L1527 IRS show a break at radii of $\sim$1200 and $\sim$1700 au in the radial profile of the peak velocity, r…
We numerically model the collapse of magnetic rotating protostellar clouds with mass of 10 $M_{sun}$. The simulations are carried out with the help of 2D MHD code Enlil. The structure of the cloud at the isothermal stage of the collapse is investigated for the cases of weak, moderate, and strong initial magnetic field. Simulations reveal the universal hierarchical structure of collapsing protostellar clouds, consisting of flattened envelope with the qausi-magnetostatc disk inside and the first core in its center. The size of the primary disk increases with the initial magnetic energy of the cl…
