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 simulations of a collapsing prestellar dense core using adaptative mesh refinement. We start from a non-axisymmetrical situation, considering a dense core with random density perturbations that follow a turbulence spectrum. We analyse the emerging disk comparing the angular momentum it contains with the one expected from our analytic development. We study the velocity gradients at different scales in the simulation as it is done with observations. We show that the angular momentum in the frame of a stellar object which is not located at the center of mass of the core is not conserved, due to inertial forces. Our simulations of such non-axisymmetrical collapse quickly produce accretion disks at the small scales in the core. The analysis of the kinematics at different scales in the simulated core reveals projected velocity gradients of amplitudes similar to the ones observed in protostellar cores, and which directions vary, sometimes even reversing when small and large scales are compared. These complex kinematics patterns appear in recent observations, and could be a discriminating feature with models where rotation is inherited from large scales. Our results from simulations without initial rotation are more consistent with these recent observations than when solid-body rotation is initially [abridged]
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-…
The pre-stellar cores in which low mass stars form are generally well magnetized. Our simulations show that early protostellar discs are massive and experience strong magnetic torques in the form of magnetic braking and protostellar outflows. Simulations of protostellar disk formation suggest that these torques are strong enough to suppress a rotationally supported structure from forming for near critical values of mass-to-flux. We demonstrate through the use of a 3D adaptive mesh refinement code -- including cooling, sink particles and magnetic fields -- that one produces transient 1000 AU di…
The role played by protostellar feedback in clustered star formation is still a matter of debate. In particular, protostellar outflows have been proposed as a source of turbulence in cluster-forming clumps, which may provide support against global collapse for several free-fall times. Here, we seek to test the above hypothesis in the case of the well-documented NGC 2264-C protocluster, byquantifying the amount of turbulence and support injected in the surrounding medium by protostellar outflows. Using the HERA heterodyne array on the IRAM 30m telescope, we carried out an extensive mapping of N…
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 …
In order to investigate when and how the birth of a protostellar core occurs, we made survey observations of four well-studied dense cores in the Taurus molecular cloud using CO transitions in submillimeter bands. We report here the detection of unexpectedly warm (~ 30 - 70 K), extended (radius of ~ 2400 AU), dense (a few times 10^{5} cm^{-3}) gas at the heart of one of the dense cores, L1521F (MC27), within the cold dynamically collapsing components. We argue that the detected warm, extended, dense gas may originate from shock regions caused by collisions between the dynamically collapsing co…
The early evolution of protostellar disks with metallicities in the $Z=1.0-0.01~Z_\odot$ range was studied with a particular emphasis on the strength of gravitational instability and the nature of protostellar accretion in low-metallicity systems. Numerical hydrodynamics simulations in the thin-disk limit were employed that feature separate gas and dust temperatures, and disk mass-loading from the infalling parental cloud cores. Models with cloud cores of similar initial mass and rotation pattern, but distinct metallicity were considered to distinguish the effect of metallicity from that of in…
Theoretical studies of collapsing clouds have found that even a relatively weak magnetic field (B) may prevent the formation of disks and their fragmentation. However, most previous studies have been limited to cases where B and the rotation axis of the cloud are aligned. We study the transport of angular momentum, and its effects on disk formation, for non-aligned initial configurations and a range magnetic intensities. We perform 3D AMR MHD simulations of magnetically supercritical collapsing dense cores using the code Ramses. We compute the contributions of the processes transporting angula…
Extinction maps at 8 micron from the Spitzer Space Telescope show that many Class 0 protostars exhibit complex, irregular, and on-axisymmetric structure within the densest regions of their dusty envelopes. Many of the systems have highly irregular and on-axisymmetric morphologies on scales $\sim$1000 AU, with a quarter of the sample exhibiting filamentary or flattened dense structures. Complex envelope structure is observed in regions spatially distinct from outflow cavities, and the densest structures often show no systematic alignment perpendicular to the cavities. We suggest that the observ…
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…
We couple non-magnetic, hydrodynamical simulations of collapsing protostellar cores with radiative transfer evolutionary models to generate synthetic observations. We then use these synthetic observations to investigate the extent to which a simple method for measuring protostellar disc masses used in the literature recovers the intrinsic masses of the discs formed in the simulations. We evaluate the effects of contamination from the surrounding core, partially resolving out the disc, optical depth, fixed assumed dust temperatures, inclination, and the dust opacity law. We show that the combin…
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…
We report Atacama Large Millimeter Array observations of 3 mm dust continuum emission and line emission, in HCO$^{+}$, H$^{13}$CO$^{+}$, N$_{2}$H$^{+}$ and CH$_{3}$CN, towards two massive and dense clumps (MDCs) in early but distinct evolutionary phases (prestellar and protostellar), made with the goal of investigating their fragmentation characteristics at angular scales of $\sim$1 $\arcsec$. Towards the prestellar clump we detected ten compact structures (cores), with radius from 1200 to 4500 AU and masses from 1.6 to 20~M$_\odot$. Half of these cores exhibit inverse P Cygni profiles in HCO$…
Combining the co-evolving chemistry, hydrodynamics and radiative transfer is an important step for star formation studies. It allows both a better link to observations and a self-consistent monitoring of the magnetic dissipation in the collapsing core. Our aim is to follow a chemo-dynamical evolution of collapsing dense cores with a reduced gas-grain chemical network. We present the results of radiative hydrodynamic (RHD) simulations of 1 M$_\odot$ isolated dense core collapse. The physical setup includes RHD and dynamical evolution of a chemical network. To perform those simulations, we merge…
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 de…
We perform two-dimensional axially symmetric radiation-hydrodynamic simulations to assess the impact of outflows and radiative force feedback from massive protostars by varying when the protostellar outflow starts, the ratio of ejection to accretion rates, and the strength of the wide angle disk wind component. The star formation efficiency, i.e. the ratio of final stellar mass to initial core mass, is dominated by radiative forces and the ratio of outflow to accretion rates. Increasing this ratio has three effects: First, the protostar grows slower with a lower luminosity at any given time, l…
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…
A numerical hydrodynamical model for the evolution of spherically symmetric collapsing clouds, designed for the calculation of the thermal structure of these objects in both the prestellar and protostellar stages of their evolution, is presented. Distinctive features of the model include the possibility of independently describing the temperatures of the gas and dust, which is extremely important when calculating the thermal structure of prestellar and protostellar clouds, and the account of the radiation flux from the central protostar. This model is used to compare the theoretical density an…
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…
Low-mass condensations (LMCs) are observed inside the envelope of the collapsing molecular cloud cores. In this research, we investigate the effects of landing LMCs for occurrence of instability through the protostellar accretion disks. We consider some regions of the disk where duration of infalling and landing of the LMCs are shorter than the orbital period. In this way, we can consider the landing LMCs as density bumps and grooves in the azimuthal direction of an initial thin axisymmetric steady state self-gravitating protostellar accretion disk (nearly Keplerian). Using the linear effects …
Recent observations of young stellar systems with the Atacama Large Millimeter/submillimeter Array (ALMA) and the Karl G. Jansky Very Large Array (VLA) are helping to cement the idea that close companion stars form via fragmentation of a gravitationally unstable disk around a protostar early in the star formation process. As the disk grows in mass, it eventually becomes gravitationally unstable and fragments, forming one or more new protostars in orbit with the first at mean separations of 100 astronomical units (AU) or even less. Here we report direct numerical calculations down to scales as …
We present arcsecond resolution mid-infrared and millimeter observations of the center of the young stellar cluster AFGL961 in the Rosette molecular cloud. Within 0.2 pc of each other, we find an early B star embedded in a dense core, a neighboring star of similar luminosity with no millimeter counterpart, a protostar that has cleared out a cavity in the circumcluster envelope, and two massive, dense cores with no infrared counterparts. An outflow emanates from one of these cores, indicating a deeply embedded protostar, but the other is starless, bound, and appears to be collapsing. The divers…
We compared the sizes and fluxes of a sample of protostellar disks in Orion A measured with the ALMA 0.87 mm continuum data from the VANDAM survey with the physical properties of their ambient environments on the core scale of 0.6 pc estimated with the GBT GAS NH3 and JCMT SCUPOL polarimetric data. We did not find any significant dependence of the disk radii and continuum fluxes on a single parameter on the core scale, such as the non-thermal line width, magnetic field orientation and strength, or magnitude and orientation of the velocity gradient. Among these parameters, we only found a posit…
(Abridged) Star and planet formation theories predict an evolution in the density, temperature, and velocity structure as the envelope collapses and forms an accretion disk. The aim of this work is to model the evolution of the molecular excitation, line profiles, and related observables during low-mass star formation. Specifically, the signatures of disks during the deeply embedded stage are investigated. Semi-analytic 2D axisymmetric models have been used to describe the evolution of the density, stellar mass, and luminosity from the pre-stellar to the T-Tauri phase. A full radiative transfe…
We study low-metallicity star formation with a set of high-resolution hydrodynamics simulations for various gas metallicities over a wide range $0$--$10^{-3} \ {\rm Z}_{\bigodot}$. Our simulations follow non-equilibrium chemistry and radiative cooling by adopting realistic elemental abundance and dust size distribution. We examine the condition for the fragmentation of collapsing clouds (cloud fragmentation; CF) and of accretion discs (disc fragmentation; DF). We find that CF is suppressed due to rapid gas heating accompanied with molecular hydrogen formation even with efficient dust cooling f…
The evolution of collapsing clouds embedded in different star-forming environments is investigated using three-dimensional non-ideal magnetohydrodynamics simulations considering different cloud metallicities ($Z/\thinspace Z_\odot$ = 0, 10$^{-5}$, 10$^{-4}$, 10$^{-3}$, 10$^{-2}$, 10$^{-1}$ and 1) and ionisation strengths ($C_ζ$=0, 0.01, 1 and 10, where $C_ζ$ is a coefficient controlling the ionisation intensity and $C_ζ=1$ corresponds to the ionisation strength of nearby star-forming regions). With all combinations of these considered values of $Z/\thinspace Z_\odot$ and $C_ζ$, 28 different st…
The transport of angular momentum is capital during the formation of low-mass stars; too little removal and rotation ensures stellar densities are never reached, too much and the absence of rotation means no protoplanetary disks can form. Magnetic diffusion is seen as a pathway to resolving this long-standing problem. We investigate the impact of including resistive MHD in simulations of the gravitational collapse of a 1 solar mass gas sphere, from molecular cloud densities to the formation of the protostellar seed; the second Larson core. We used the AMR code RAMSES to perform two 3D simulati…
With the advent of ALMA, it is now possible to observationally constrain how disks form around deeply embedded protostars. In particular, the recent ALMA C3H2 line observations of the nearby protostar L1527 have been interpreted as evidence for the so-called "centrifugal barrier," where the protostellar envelope infall is gradually decelerated to a stop by the centrifugal force in a region of super-Keplerian rotation. To test the concept of centrifugal barrier, which was originally based on angular momentum conserving-collapse of a rotating test particle around a fixed point mass, we carry out…
Fragmentation of Dense Rotation-Dominated Structures Fed by Collapsing Gravomagneto-Sheetlets and Origin of Misaligned 100 au-Scale Binaries and Multiple Systems
Extremely large deuteration of several molecules has been observed towards prestellar cores and low-mass protostars for a decade. New observations performed towards low-mass protostars suggest that water presents a lower deuteration in the warm inner gas than in the cold external envelope. We coupled a gas-grain astrochemical model with a one-dimension model of collapsing core to properly follow the formation and the deuteration of interstellar ices as well as their subsequent evaporation in the low-mass protostellar envelopes with the aim of interpreting the spatial and temporal evolutions of…
In the earliest (so-called "Class 0") phase of sunlike (low-mass) star formation, circumstellar disks are expected to form, feeding the protostars. However, such disks are difficult to resolve spatially because of their small sizes. Moreover, there are theoretical difficulties in producing such disks in the earliest phase, due to the retarding effects of magnetic fields on the rotating, collapsing material (so-called "magnetic braking"). With the Atacama Large Millimeter/submillimeter Array (ALMA), it becomes possible to uncover such disks and study them in detail. HH 212 is a very young proto…
We have used the Berkeley-Illinois-Maryland Array (BIMA) to make deep N2H+ 1-0 maps of the pre-stellar core L183, in order to study the spatial and kinematic substructure within the densest part of the core. Three spatially and kinematically distinct clumps are detected, which we label L183-N1, L183-N2 and L183-N3. L183-N2 is approximately coincident with the submillimetre dust peak and lies at the systemic velocity of L183. Thus we conclude that L183-N2 is the central dense core of L183. L183-N1 and 3 are newly-discovered fragments of L183, which are marked by velocity gradients that are para…
Recent observations indicate that mm/cm-sized grains may exist in the embedded protostellar disks. How such large grains grow from the micron size (or less) in the earliest phase of star formation remains relatively unexplored. In this study we take a first step to model the grain growth in the protostellar environment, using two-dimensional (2D axisymmetric) radiation hydrodynamic and grain growth simulations. We show that the grain growth calculations can be greatly simplified by the "terminal velocity approximation", where the dust drift velocity relative to the gas is proportional to its s…
The driving mechanism of protostellar outflows and jets and their effects on the star formation process obtained from recent theoretical and numerical studies are described. Low-velocity outflows are driven by an outer region of the circumstellar disk, while high-velocity jets are driven near an inner edge of the disk. The disk angular momentum is effectively transferred by magnetic effects in the outflow and jet driving regions where the magnetic field is well coupled with neutral gas. On the other hand, in a high density gas region of the disk (or intermediate region), the magnetic field dis…
We present radiation hydrodynamic simulations of collapsing protostellar cores with initial masses of 30, 100, and 200 M$_{\odot}$. We follow their gravitational collapse and the formation of a massive protostar and protostellar accretion disk. We employ a new hybrid radiative feedback method blending raytracing techniques with flux-limited diffusion for a more accurate treatment of the temperature and radiative force. In each case, the disk that forms becomes Toomre-unstable and develops spiral arms. This occurs between 0.35 and 0.55 freefall times and is accompanied by an increase in the acc…
Cosmic rays (CR) play an important role in dense molecular cores, affecting their thermal and dynamical evolution and initiating the chemistry. Several studies have shown that the formation of protostellar discs in collapsing clouds is severely hampered by the braking torque exerted by the entrained magnetic field on the infalling gas, as long as the field remains frozen to the gas. We examine the possibility that the concentration and twisting of the field lines in the inner region of collapse can produce a significant reduction of the ionisation fraction. To check whether the CR ionisation r…
The formation of protostellar discs is severely hampered by magnetic braking, as long as magnetic fields remain frozen in the gas. The latter condition depends on the levels of ionisation that characterise the innermost regions of a collapsing cloud. The chemistry of dense cloud cores and, in particular, the ionisation fraction is largely controlled by cosmic rays. The aim of this paper is to evaluate whether the attenuation of the flux of cosmic rays expected in the regions around a forming protostar is sufficient to decouple the field from the gas, thereby influencing the formation of centri…
Dense, star-forming, cores of molecular clouds are observed to be significantly magnetized. A realistic magnetic field of moderate strength has been shown to suppress, through catastrophic magnetic braking, the formation of a rotationally supported disk during the protostellar accretion phase of low-mass star formation in the ideal MHD limit. We address, through 2D (axisymmetric) simulations, the question of whether realistic levels of nonideal effects, computed with a simplified chemical network including dust grains, can weaken the magnetic braking enough to enable a rotationally supported d…
Most simulations of outflow feedback on star formation are based on the assumption that outflows are driven by a wide angle "X-wind," rather than a narrow jet. However, the arguments initially raised against pure jet-driven flows were based on steady ejection in a uniform medium, a notion that is no longer supported based on recent observations. We aim to determine whether a pulsed narrow jet launched in a density-stratified, self-gravitating core could reproduce typical molecular outflow properties, without the help of a wide-angle wind component. We performed axisymmetric hydrodynamic simula…
We developed a chemical network for modeling the chemistry and non-ideal MHD effects from the collapsing dense molecular clouds to protostellar disks. First, we re-formulated the cosmic-ray desorption rate by considering the variations of desorption rate over the grain size distribution. We find that the differential desorption of volatile species is amplified by the grains larger than 0.1 $μ$m, because larger grains are heated to a lower temperature by cosmic-rays and hence more sensitive to the variations in binding energies. As a result, atomic nitrogen N is $\sim$2 orders of magnitude more…
The formation epoch of protostellar disks is debated because of the competing roles of rotation, turbulence, and magnetic fields in the early stages of low-mass star formation. Magnetohydrodynamics simulations of collapsing cores predict that rotationally supported disks may form in strongly magnetized cores through ambipolar diffusion or misalignment between the rotation axis and the magnetic field orientation. Detailed studies of individual sources are needed to cross check the theoretical predictions. We present 0.06-0.1" resolution images at 350 GHz toward B1b-N and B1b-S, which are young …
We determine the observational signatures of protostellar cores by coupling two-dimensional radiative transfer calculations with numerical hydrodynamical simulations that predict accretion rates that both decline with time and feature short-term variability and episodic bursts caused by disk gravitational instability and fragmentation. We calculate the radiative transfer of the collapsing cores throughout the full duration of the collapse, using as inputs the core, disk, and protostellar masses, radii, and mass accretion rates predicted by the hydrodynamical simulations. From the resulting spe…
Understanding the formation of wide binary systems of very low mass stars (M $\le$ 0.1 Msun) is challenging. The most obvious route is via widely separated low-mass collapsing fragments produced through turbulent fragmentation of a molecular core. However, close binaries/multiples from disk fragmentation can also evolve to wide binaries over a few initial crossing times of the stellar cluster through tidal evolution. Finding an isolated low mass wide binary system in the earliest stage of formation, before tidal evolution could occur, would prove that turbulent fragmentation is a viable mechan…
We investigate the young (proto)stellar population in NGC 2023 and the L 1630 molecular cloud bordering the HII region IC 434, using Spitzer IRAC and MIPS archive data, JCMT SCUBA imaging and spectroscopy as well as targeted BIMA observations of one of the Class 0 protostars, NGC 2023 MM1. We have performed photometry of all IRAC and MIPS images, and used color-color diagrams to identify and classify all young stars seen within a 22'x26' field along the boundary between IC 434 and L 1630. For some stars, which have sufficient optical, IR, and/or sub-millimeter data we have also used the online…
The IRDC SDC335.579-0.292 (SDC335) is a massive star-forming cloud found to be globally collapsing towards one of the most massive star forming cores in the Galaxy. SDC335 hosts three high-mass protostellar objects at early stages of their evolution and archival ALMA Cycle 0 data indicate the presence of at least one molecular outflow in the region. Observations of molecular outflows from massive protostellar objects allow us to estimate the accretion rates of the protostars as well as to assess the disruptive impact that stars have on their natal clouds. The aim of this work is to identify an…
Star formation is regulated through a variety of feedback processes. In this study, we treat feedback by X-rays and discuss its implications. Our aim is to investigate whether star formation is significantly affected when a star forming cloud resides in the vicinity of a strong X-ray source. We perform an Eulerian grid simulation with embedded Lagrangian sink particles of a collapsing molecular cloud near a massive, 10^7 M_o black hole. The chemical and thermal changes caused by radiation are incorporated into the FLASH code. When there is strong X-ray feedback the star forming cloud fragments…
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 …
We report the results of an HCO+ (3-2) and N2D+ (3-2) molecular line survey performed toward 91 dense cores in the Perseus molecular cloud using the James Clerk Maxwell Telescope, to identify the fraction of starless and protostellar cores with systematic radial motions. We quantify the HCO+ asymmetry using a dimensionless asymmetry parameter $δ_v$, and identify 20 cores with significant blue or red line asymmetries in optically-thick emission indicative of collapsing or expanding motions, respectively. We separately fit the HCO+ profiles with an analytic collapse model and determine contracti…
In this paper we present a detailed numerical investigation of the hypothesis that a rotation of astrophysical jets can be caused by magnetohydrodynamic shocks in a helical magnetic field. Shock compression of the helical magnetic field results in a toroidal Lorentz force component which will accelerate the jet material in toroidal direction. This process transforms magnetic angular momentum (magnetic stress) carried along the jet into kinetic angular momentum (rotation). The mechanism proposed here only works in a helical magnetic field configuration. We demonstrate the feasibility of this me…
Fragmentation of rotating gaseous systems via gravitational instability is believed to be a crucial mechanism in several astrophysical processes, such as formation of planets in protostellar discs, of molecular clouds in galactic discs, and of stars in molecular clouds. Gravitational instability is fairly well understood for infinitesimally thin discs. However, the thin-disc approximation is not justified in many cases, and it is of general interest to study the gravitational instability of rotating fluids with different degrees of rotation support and stratification. We derive dispersion rela…
We study the formation and long-term evolution of primordial protostellar disks harbored by first stars using numerical hydrodynamics simulations in the thin-disk limit. The initial conditions are specified by pre-stellar cores with distinct mass, angular momentum, and temperature. This allows us to probe several tens of thousand years of the disk's initial evolution, during which we observe multiple episodes of fragmentation leading to the formation of gravitationally bound gaseous clumps within spiral arms. These fragments are torqued inward due to gravitational interaction with the spiral a…
