Redistribution Of Angular Momentum Research Articles

THE FORMATION AND THE EVOLUTION OF LARGE-SCALE VORTEX STRUCTURES IN STELLAR ACCRETION DISKS

Explaining the causes of angular momentum transfer in accretion stellar disks is an important astrophysical problem, since it is the process that determines the rate of accretion of matter onto the central gravitating body. Previously, within the framework of a two-dimensional approach, it was shown that the introduction of small perturbations into the flow of disk matter leads to the appearance of shear instability. This process is accompanied by the development of large-scale vortex structures. Their movement and evolution lead to a redistribution of angular momentum in the accretion disk. The action of the described mechanism was previously studied numerically only within a two-dimensional approximation, so the goal of the current work is to carry out full-scale three-dimensional modeling. The processes under study are described within the framework of the system of equations of ideal gas dynamics. The article briefly describes the method for their numerical integration, which is based on a conservative finite-difference scheme and the solution of the Riemann problem. The initial data is a stationary toroidal gas state surrounded by a matter with low density and pressure. At the next step, small perturbations of one of the gas-dynamic variables are introduced. The modeling and analysis of the results of numerical calculations show the emergence of vortex structures in the shear flow of a three-dimensional accretion disk. Their movement is accompanied by a redistribution of matter and angular momentum in the volume of the disk, leading to accretion of matter onto the central body.

3D simulations of magnetoconvection in a rapidly rotating supernova progenitor

ABSTRACT We present a first 3D magnetohydrodynamic (MHD) simulation of oxygen, neon, and carbon shell burning in a rapidly rotating $16\hbox{-}\mathrm{M}_\odot$ core-collapse supernova progenitor. We also run a purely hydrodynamic simulation for comparison. After $\mathord \approx 180\mathrm{s}$ ($\mathord \approx$ 15 and 7 convective turnovers, respectively), the magnetic fields in the oxygen and neon shells achieve saturation at 1011 and 5 × 1010 G. The strong Maxwell stresses become comparable to the radial Reynolds stresses and eventually suppress convection. The suppression of mixing by convection and shear instabilities results in the depletion of fuel at the base of the burning regions, so that the burning shell eventually move outward to cooler regions, thus reducing the energy generation rate. The strong magnetic fields efficiently transport angular momentum outwards, quickly spinning down the rapidly rotating convective oxygen and neon shells and forcing them into rigid rotation. The hydrodynamic model shows complicated redistribution of angular momentum and develops regions of retrograde rotation at the base of the convective shells. We discuss implications of our results for stellar evolution and for the subsequent core-collapse supernova. The rapid redistribution of angular momentum in the MHD model casts some doubt on the possibility of retaining significant core angular momentum for explosions driven by millisecond magnetars. However, findings from multidimensional models remain tentative until stellar evolution calculations can provide more consistent rotation profiles and estimates of magnetic field strengths to initialize multidimensional simulations without substantial numerical transients. We also stress the need for longer simulations, resolution studies, and an investigation of non-ideal effects.

General relativistic hydrodynamic simulations of perturbed transonic accretion

Contact. Comparing horizon-scale observations of Sgr A* and M 87* with numerical simulations has provided considerable insight into their interpretation. Most of these simulations are variations of the same physical scenario consisting of a rotation-supported torus seeded with poloidal magnetic fields. However, this approach has several well-known limitations such as secular decreasing trends in mass-accretion rates that render long-term variability studies difficult; a lack of connection with the large-scale accretion flow, which is replaced by an artificial medium emulating vacuum; and significant differences with respect to the predictions of models of accretion onto Sgr A* fed by stellar winds. Aims. We aim to study the flow patterns that arise on horizon scales in more general accretion scenarios that have a clearer connection with the large-scale flow, and are at the same time controlled by a reduced set of parameters. Methods. As a first step in this direction, we performed three-dimensional general relativistic hydrodynamic simulations of rotating transonic flows with velocity perturbations injected from a spherical boundary located far away from the central object (1000 gravitational radii). We studied the general properties of these flows with varying perturbation amplitudes and angular momentum. We analyzed time series of mass and angular-momentum radial fluxes, angle- and time-averaged profiles, and synthetic bremsstrahlung light curves, as well as the three-dimensional structure of the flow, and quantified shock and sonic transitions in the solutions. Results. We observe a rich phenomenology in accretion patterns, which includes smooth Bondi-like flows, turbulent torus-like structures, shocks, filaments, and complex sonic structures. For sufficiently large perturbations and angular momentum, radial profiles deviate from the constant entropy and constant angular-momentum profiles used for initialization and resemble those of advection-dominated accretion flows, showing evidence of entropy generation and angular-momentum redistribution not mediated by magnetic fields. Time series do not show the secular decreasing trend and are suitable for long-term variability studies. We see that the fluctuations are amplified and extend further in frequency than the injected spectrum, producing a red noise spectrum both for the mass-accretion rate and the synthetic light curves. Conclusions. We present a simulation setup that can produce a wide variety of flow patterns at horizon scales and incorporate information from large scale accretion models. The future inclusion of magnetic fields and radiative cooling could make this type of simulation a viable alternative for the numerical modeling of general low-luminosity active galactic nuclei (AGNs).

Manipulation of local angular momentum in the tightly focused optical field via the variation of polarization in radial direction

The redistribution of angular momentum density can be achieved by tightly focusing the special vector optical fields, which can induce the orbital motion of the microscopic particles. Here, we investigate the focusing properties of radial-variant hybridly polarized vector optical fields with the polarization state varying along the different circular trajectories of the Poincaré sphere. It is found that the redistribution of local angular momentum is induced by the assembling of asymmetric spin flow derived from the orthogonal circularly polarized components of the vector optical field. On this basis, we present an effective method for flexibly manipulating the angular momentum density distribution by customizing the variations of polarization corresponding to different circular trajectories on the Poincaré sphere. These works may promote the applications of vector optical field in optical microfabrication and micro-manipulation.

Linear and non-linear properties of the Goldreich–Schubert–Fricke instability in stellar interiors with arbitrary local radial and latitudinal differential rotation

ABSTRACT We investigate the linear and non-linear properties of the Goldreich–Schubert–Fricke (GSF) instability in stellar radiative zones with arbitrary local (radial and latitudinal) differential rotation. This instability may lead to turbulence that contributes to the redistribution of angular momentum and chemical composition in stars. In our local Boussinesq model, we investigate varying the orientation of the shear with respect to the ‘effective gravity’, which we describe using the angle ϕ. We first perform an axisymmetric linear analysis to explore the effects of varying ϕ on the local stability of arbitrary differential rotations. We then explore the non-linear hydrodynamical evolution in three dimensions using a modified shearing box. The model exhibits both diffusive GSF instability and a non-diffusive instability that occurs when the Solberg-Høiland criteria are violated. We observe the non-linear development of strong zonal jets (‘layering’ in the angular momentum) with a preferred orientation in both cases, which can considerably enhance turbulent transport. By varying ϕ, we find instability with mixed radial and latitudinal shears transports angular momentum more efficiently (particularly if adiabatically unstable) than cases with purely radial shear (ϕ = 0). By exploring the dependence on box size, we find the transport properties of the GSF instability to be largely insensitive to this, implying we can meaningfully extrapolate our results to stars. However, there is no preferred length-scale for adiabatic instability, which therefore exhibits strong box-size dependence. These instabilities may contribute to the missing angular momentum transport required in red giant and subgiant stars and drive turbulence in the solar tachocline.

High-resolution Study of Planetesimal Formation by Gravitational Collapse of Pebble Clouds

Planetary embryos are built through the collisional growth of 10–100 km-sized objects called planetesimals, a formerly large population of objects, of which asteroids, comets, and Kuiper Belt objects represent the leftovers from planet formation in our solar system. Here, we follow the paradigm that turbulence created overdense pebble clouds, which then collapse under their own self-gravity. We use the multiphysics code GIZMO to model the pebble cloud density as a continuum, with a polytropic equation of state to account for collisional interactions and capturing the phase transition to a quasi-incompressible “solid” object, i.e., a planetesimal in hydrostatic equilibrium. Thus, we study cloud collapse effectively at the resolution of the forming planetesimals, allowing us to derive an initial mass function for planetesimals in relation to the total pebble mass of the collapsing cloud. The redistribution of angular momentum in the collapsing pebble cloud is the main mechanism leading to multiple fragmentation. The angular momentum of the pebble cloud and thus the centrifugal radius increases with distance to the Sun, but the solid size of the forming planetesimals is constant. Therefore we find that with increasing distance to the Sun, the number of forming planetesimals per pebble cloud increases. For all distances, the formation of binaries occurs within higher hierarchical systems. The size distribution is top-heavy and can be described with a Gaussian distribution of planetesimal mass. For the asteroid belt, we can infer a most likely size of 125 km, all stemming from pebble clouds of equivalent size 152 km.

Origin of eclipsing time variations in post-common-envelope binaries: Role of the centrifugal force

Eclipsing time variations in post-common-envelope binaries were proposed to be due to the time-varying component of the stellar gravitational quadrupole moment. This is suggested to be produced by changes in the stellar structure due to an internal redistribution of angular momentum and the effect of the centrifugal force. We examined this hypothesis and present 3D simulations of compressible magnetohydrodynamics performed with the PENCIL CODE. We modeled the stellar dynamo for a solar-mass star with angular velocities of 20 and 30 times solar. We included and varied the strength of the centrifugal force and compared the results with reference simulations without the centrifugal force and with a simulation in which its effect is enhanced. The centrifugal force causes perturbations in the evolution of the numerical model, so that the outcome in the details becomes different as a result of nonlinear evolution. While the average density profile is unaffected by the centrifugal force, a relative change in the density difference between high latitudes and the equator of ∼10−4 is found. The power spectrum of the convective velocity is found to be more sensitive to the angular velocity than to the strength of the centrifugal force. The quadrupole moment of the stars includes a fluctuating and a time-independent component, which vary with the rotation rate. As very similar behavior is produced in absence of the centrifugal force, we conclude that it is not the main ingredient for producing the time-averaged and fluctuating quadrupole moment of the star. In a real physical system, we thus expect contributions from both components, that is, from the time-dependent gravitational force from the variation in the quadrupole term and from the spin-orbit coupling that is due to the persistent part of the quadrupole.

The effects of non-linearities on tidal flows in the convective envelopes of rotating stars and planets in exoplanetary systems

ABSTRACT In close exoplanetary systems, tidal interactions drive orbital and spin evolution of planets and stars over long time-scales. Tidally forced inertial waves (restored by the Coriolis acceleration) in the convective envelopes of low-mass stars and giant gaseous planets contribute greatly to the tidal dissipation when they are excited and subsequently damped (e.g. through viscous friction), especially early in the life of a system. These waves are known to be subject to non-linear effects, including triggering differential rotation in the form of zonal flows. In this study, we use a realistic tidal body forcing to excite inertial waves through the residual action of the equilibrium tide in the momentum equation for the waves. By performing 3D non-linear hydrodynamical simulations in adiabatic and incompressible convective shells, we investigate how the addition of non-linear terms affects the tidal flow properties, and the energy and angular momentum redistribution. In particular, we identify and justify the removal of terms responsible for unphysical angular momentum evolution observed in a previous numerical study. Within our new set-up, we observe the establishment of strong cylindrically sheared zonal flows, which modify the tidal dissipation rates from prior linear theoretical predictions. We demonstrate that the effects of this differential rotation on the waves neatly explains the discrepancies between linear and non-linear dissipation rates in many of our simulations. We also highlight the major role of both corotation resonances and parametric instabilities of inertial waves, which are observed for sufficiently high tidal forcing amplitudes or low viscosities, in affecting the tidal flow response.

SDSS-IV MaNGA: global properties of kinematically misaligned galaxies

ABSTRACT We select 456 gas–star kinematically misaligned galaxies from the internal Product Launch-10 of MaNGA survey, including 74 star-forming (SF), 136 green-valley (GV), and 206 quiescent (QS) galaxies. We find that the distributions of difference between gas and star position angles for galaxies have three local peaks at ∼0°, 90°, and 180°. The fraction of misaligned galaxies peaks at log (M*/M⊙) ∼ 10.5 and declines to both low- and high-mass end. This fraction decreases monotonically with increasing star formation rate and specific star formation rate. We compare the global parameters including gas kinematic asymmetry Vasym, H i detection rate and mass fraction of molecular gas, effective radius Re, Sérsic index n as well as spin parameter $\lambda _{R_e}$ between misaligned galaxies and their control samples. We find that the misaligned galaxies have lower H i detection rate and molecular gas mass fraction, smaller size, higher Sérsic index, and lower spin parameters than their control samples. The SF and GV misaligned galaxies are more asymmetric in gas velocity fields than their controls. These pieces of observational evidence point to the gas accretion scenario followed by angular momentum redistribution from gas–gas collision, leading to gas inflow and central star formation for the SF and GV misaligned galaxies. We propose three possible origins of the misaligned QS galaxies: (1) external gas accretion, (2) merger, and (3) GV misaligned galaxies evolve into QS galaxies.

Turbulent magnetic field amplification in binary neutron star mergers

Magnetic fields are expected to play a key role in the dynamics and the ejection mechanisms that accompany the merger of two neutron stars. General relativistic magnetohydrodynamic (MHD) simulations offer a unique opportunity to unravel the details of the ongoing physical processes. Nevertheless, current numerical studies are severely limited by the fact that any affordable resolution remains insufficient to fully capture the small-scale dynamo, initially triggered by the Kelvin-Helmholtz instability, and later sourced by several MHD processes involving differential rotation. Here, we alleviate this limitation by using explicit large-eddy simulations, a technique where the unresolved dynamics occurring at the subgrid scales (SGS) is modeled by extra terms, which are functions of the resolved fields and their derivatives. The combination of high-order numerical schemes, high resolutions, and the gradient SGS model allow us to capture the small-scale dynamos produced during the binary neutron star mergers, as shown in previous works. Here, we follow the first 50 milliseconds after the merger and, for the first time, we find numerical convergence on the magnetic field amplification, in terms of integrated energy and spectral distribution over spatial scales. Among other results, we find that the average intensity of the magnetic field in the remnant saturates at $\ensuremath{\sim}{10}^{16}\text{ }\text{ }\mathrm{G}$ around 5 ms after the merger. After 20--30 ms, both toroidal and poloidal magnetic field components grow continuously, fed by the winding mechanism that provides a slow inverse cascade, i.e., gradually transferring kinetic into magnetic energy. We find no clear hints for magnetorotational instabilities and no significant impact of the magnetic field on the redistribution of angular momentum in the remnant in our simulations, probably due to the very turbulent and dynamical topology of the magnetic field at all stages, with small-scale components largely dominating over the large-scale ones. Although the magnetic field grows near the rotation axis of the remnant, longer large-eddy simulations are necessary to further investigate the formation of large-scale, helical structures close to the rotational axis, which could be associated to jet formation.

Evolution of Main-sequence-like Surviving Companions in Type Ia Supernova Remnants

Recent theoretical and numerical studies of Type Ia supernovae (SNe Ia) explosions within the single-degenerate scenario suggest that the nondegenerate companions could survive during the supernova impact and could be detectable in nearby supernova remnants. However, observational efforts show less promising evidence of the existence of surviving companions from the standard single-degenerate channels. The spin-up/spin-down models are possible mechanisms to explain the nondetection of surviving companions. In these models, the spin-up phase could increase the critical mass for explosion, leading to a super-Chandrasekhar-mass explosion, and the spin-down phase could lead to extra mass loss and angular momentum redistribution. Since the spin-down timescale for the delayed explosion of a rotating white dwarf is unclear, in this paper we explore a vast parameter space of main-sequence-like surviving companions via two-dimensional hydrodynamic simulations of supernova impact and the subsequent stellar evolution of surviving companions. Tight universal relations to describe the mass-stripping effect, supernova kick, and depth of supernova heating are provided. Our results suggest that the not-yet-detected surviving companions from observations of nearby SN Ia remnants might favor low-mass companions, short binary separation, or stronger supernova explosion energies than the standard single-degenerate channels.

Asteroseismology of evolved stars to constrain the internal transport of angular momentum

Context. Asteroseismology provides constraints on the core rotation rate for hundreds of low- and intermediate-mass stars in evolved phases. Current physical processes tested in stellar evolution models cannot reproduce the evolution of these core rotation rates. Aims. We investigate the efficiency of the internal angular momentum redistribution in red giants during the hydrogen-shell and core-helium burning phases based on the asteroseismic determinations of their core rotation rates. Methods. We computed stellar evolution models with rotation and model the transport of angular momentum by the action of a sole dominant diffusive process parameterised by an additional viscosity in the equation of angular momentum transport. We constrained the values of this viscosity to match the mean core rotation rates of red giants and their behaviour with mass and evolution using asteroseismic indicators along the red giant branch and in the red clump. Results. For red giants in the hydrogen-shell burning phase, the transport of angular momentum must be more efficient in more massive stars. The additional viscosity is found to vary by approximately two orders of magnitude in the mass range M ∼ 1–2.5 M⊙. As stars evolve along the red giant branch, the efficiency of the internal transport of angular momentum must increase for low-mass stars (M ≲ 2 M⊙) and remain approximately constant for slightly higher masses (2.0 M⊙ ≲ M ≲ 2.5 M⊙). In red clump stars, the additional viscosities must be an order of magnitude higher than in younger red giants of similar mass during the hydrogen-shell burning phase. Conclusions. In combination with previous efforts, we obtain a clear picture of how the physical processes acting in stellar interiors should redistribute angular momentum from the end of the main sequence until the core-helium burning phase for low- and intermediate-mass stars to satisfy the asteroseismic constraints.

Modelling the secular evolution of protoplanetary disc dust sizes – a comparison between the viscous and magnetic wind case

ABSTRACT For many years, protoplanetary discs have been thought to evolve viscously: angular momentum redistribution leads to accretion and outward disc spreading. Recently, the hypothesis that accretion is due, instead, to angular momentum removal by magnetic winds gained new popularity: no disc spreading is expected in this case. In this paper, we run several 1D gas and dust simulations to make predictions on the time evolution of disc sizes in the dust and to assess whether they can be used to understand how discs evolve. We show that viscous and magnetic wind models have very different dust disc radii. In particular, magnetohydrodynamic wind models are compact and their sizes either remain constant or decrease with time. On the contrary, discs become larger with time in the viscous case (when α ≳ 10−3). Although current observations lack enough sensitivity to discriminate between these two scenarios, higher sensitivity surveys could be fruitful to this goal on a $1\!-\!10\, {\rm Myr}$ age range. When compared with the available ALMA (Atacama Large Millimeter/submillimeter Array) Band 7 data, both viscous and magnetic wind models are compatible with the observationally inferred dust radii in Lupus, Chamaeleon I, and Upper Sco. Furthermore, in the drift-dominated regime, the size–luminosity correlation is reproduced in Lupus, both in Band 7 and 3, while in Upper Sco a different slope than in the data is predicted. Sub-structures (potentially undetected) can explain several outliers with large observed sizes. Higher angular-resolution observations will be helpful to test our predictions in the case of more compact discs, expected in both frameworks, particularly at the age of Upper Sco.

Angular momentum transfer in direct numerical simulations of a laboratory model of a tropical cyclone

ABSTRACT Numerical simulations of a laboratory model of a tropical cyclone are carried out for different rotation rates. Particular attention is paid to the non-stationary stage of intensive cyclonic vortex formation. The transfer of angular momentum plays a key role in the formation of cyclonic and anticyclonic flows; therefore, a detailed analysis of the redistribution and variation of angular momentum is given. The time evolution of angular momentum fluxes and total angular momentum strongly depend on the rotation rate. It is shown that intensive cyclonic motion with velocity exceeding initial values substantially (ten or more times) is a result of accumulation in the centre of a small fraction of global angular momentum of a fluid layer (from 0.25% at fast rotation to 2% at slow rotation). The integral angular momentum of the anticyclonic flow is significantly larger than that of the cyclonic flow, mainly because of the relatively large fluid volume of the anticyclonic flow. Another important result is that the rotating fluid layer very quickly adapts to new boundary conditions (heating and cooling). Approximately two rotation periods are required to reach a quasi-stationary state. The application of the obtained results to the evolution of real tropical cyclones is discussed.

Can a Dynamo Mechanism Act at the Magnetopauses of Magnetic Rapidly Rotating Exoplanets?

An astrophysical dynamo converts the kinetic energy of fluids into magnetic energy. Dynamo is a non-local process. Here, we consider whether a dynamo can operate at the magnetopauses of magnetic rapidly rotating planets. We analyze the main necessary condition for the work of this type of dynamo—the rotation transfer from the planet to the magnetopause. We show the role of the current disc around a rapidly rotating magnetic planet in the redistribution of angular momentum depending on the direction of the external magnetic field, using the example of the Jupiter’s magnetodisc.

Формирование и эволюция крупномасштабных вихревых структур в аккреционных звездных дисках

This paper is devoted to the study of the properties of astrophysical objects, namely, the study of the processes of development of large-scale turbulence in accretion stellar disks. Such activity is motivated by the need to explain the nature of the mechanisms that lead to the redistribution of angular momentum in the disk and the subsequent accretion of matter to the central gravitating body. Thus, the complete three-dimensional modeling of the processes of instability development in an initially stationary disk allows us to draw conclusions about the efficiency of the redistribution of angular momentum by large-scale vortex structures.

Monte Carlo simulations of evolving rotational distributions of low-mass stars in young open clusters. Testing the influence of initial conditions

ABSTRACT The rotational evolution of a young stellar population can give informations about the rotation pattern of more evolved clusters. Combined with rotational period values of thousands of young stars and theoretical propositions about the redistribution and loss of stellar angular momentum, it allows us to trace the rotational history of stars according to their mass. We want to investigate how internal and environmental changes on single stars can change the rotational evolution of a young stellar population. We run Monte Carlo simulations of a young cluster composed by solar mass stars of 0.5, 0.8 and 1.0 M⊙ from 1 to 550 Myr taking into account observational and theoretical parameters. In order to compare our results with the observations we run Kolmogorov-Smirnov tests. Our standard model is able to reproduce some clusters younger than h Per and marginally M37, which is 550 Myr old. Varying the disk fraction or the initial period distribution did not improve the results. However, when we run a model with a finer mass grid the Pleiades can be also reproduced. Changing the initial mass distribution to be similar to the empirical ONC mass function also gives good results. Modeling the evolution of a young synthetic cluster from pre-main sequence to early main sequence considering physical mechanisms of extraction and exchange of angular momentum can not be achieved successfully for all clusters for which we have enough rotational data. Clusters of about the same age present different rotational behaviors due perhaps to differences in their initial conditions.

Black hole fuelling in galaxy mergers: a high-resolution analysis

ABSTRACT Using parsec scale resolution hydrodynamical adaptive mesh refinement simulations, we have studied the mass transport process throughout a Galactic merger. The aim of such study is to connect both the peaks of mass accretion rate on to the BHs and star formation bursts with both gravitational and hydrodynamic torques acting on the galactic gaseous component. Our merger initial conditions were chosen to mimic a realistic system. The simulations include gas cooling, star formation, supernovae feedback, and AGN feedback. Gravitational and hydrodynamic torques near pericentre passes trigger gas funneling to the nuclei that is associated with bursts of star formation and black hole growth. Such episodes are intimately related with both kinds of torques acting on the galactic gas. Pericentres trigger both star formation and mass accretion rates of ∼few $(1\!-\!10)\, \mathrm{ M}_\odot$ yr−1. Such episodes last $\sim \, (50\!-\!75)$ Myr. Close passes also can produce black hole accretion that approaches and reaches the Eddington rate, lasting ∼few Myrs. Our simulation shows that both gravitational and hydrodynamic torques are enhanced at pericentre passes with gravitational torques tending to have higher values than the hydrodynamic torques throughout the merger. We also find that in the closest encounters, hydrodynamic and gravitational torques can be comparable in their effect on the gas, the two helping in the redistribution of both angular momentum and mass in the galactic disc. Such phenomena allow inward mass transport on to the BH influence radius, fuelling the compact object and lighting up the galactic nuclei.

A slim disc approach to external photoevaporation of discs

ABSTRACT The photoevaporation of protoplanetary discs by nearby massive stars present in their birth cluster plays a vital role in their evolution. Previous modelling assumes that the disc behaves like a classical Keplerian accretion disc out to a radius where the photoevaporative outflow is launched. There is then an abrupt change in the angular velocity profile, and the outflow is modelled by forcing the fluid parcels to conserve their specific angular momenta. Instead, we model externally photoevaporating discs using the slim disc formalism. The slim disc approach self-consistently includes the advection of radial and angular momentum as well as angular momentum redistribution by internal viscous torques. Our resulting models produce a smooth transition from a rotationally supported Keplerian disc to a photoevaporative driven outflow, where this transition typically occurs over ∼4–5 scale heights. The penetration of ultraviolet photons predominately sets the radius of the transition and the viscosity’s strength plays a minor role. By studying the entrainment of dust particles in the outflow, we find a rapid change in the dust size and surface density distribution in the transition region due to the steep gas density gradients present. This rapid change in the dust properties leaves a potentially observable signature in the continuum spectral index of the disc at mm wavelengths. Using the slim disc formalism in future evolutionary calculations will reveal how both the gas and dust evolve in their outer regions and the observable imprints of the external photoevaporation process.

Formation and evolution of protostellar accretion discs – II. From 3D simulation to a simple semi-analytic model of Class 0/I discs

ABSTRACT We use a 3D radiative non-ideal magnetohydrodynamic simulation to investigate the formation and evolution of a young protostellar disc from a magnetized pre-stellar core. The simulation covers the first ${\sim }10\, {\rm kyr}$ after protostar formation and shows a massive, weakly magnetized disc with radius that initially grows and then saturates at ${\sim }30\, {\rm au}$. The disc is gravitationally unstable with prominent large-amplitude spiral arms. We use our simulation results and a series of physical arguments to construct a predictive and quantitative physical picture of Class 0/I protostellar disc evolution from several aspects, including (i) the angular-momentum redistribution in the disc, self-regulated by gravitational instability to make most of the disc marginally unstable; (ii) the thermal profile of the disc, well-approximated by a balance between radiative cooling and accretion heating; and (iii) the magnetic-field strength and magnetic-braking rate inside the disc, regulated by non-ideal magnetic diffusion. Using these physical insights, we build a simple 1D semi-analytic model of disc evolution. We show that this 1D model, when coupled to a computationally inexpensive simulation for the evolution of the surrounding pseudo-disc, can be used reliably to predict disc evolution in the Class 0/I phase. The predicted long-term evolution of disc size, which saturates at ${\sim }30\, {\rm au}$ and eventually shrinks, is consistent with a recent observational survey of Class 0/I discs. Such hierarchical modelling of disc evolution circumvents the computational difficulty of tracing disc evolution through Class 0/I phase with direct, numerically converged simulations.