A new one-dimensional, dynamical model is proposed for geometrically thin, self-gravitating viscous accretion discs. The vertically integrated equations are simplified using the slow accretion limit and the monopole approximation with a time-dependent central point mass to account for self-gravity and accretion. It is shown that the system of partial differential equations can be reduced to a single non-linear advection diffusion equation which describes the time evolution of angular velocity.
In order to solve the equation three different turbulent viscosity prescriptions are considered. It is shown that for these parametrizations the differential equation allows for similarity transformations depending only on a single non-dimensional parameter. A detailed analysis of the similarity solutions reveals that this parameter is the initial power law exponent of the angular velocity distribution at large radii. The radial dependence of the self-similar solutions is in most cases given by broken power laws. At small radii the rotation law always becomes Keplerian with respect to the current central point mass. In the outer regions the power law exponent of the rotation law deviates from the Keplerian value and approaches asymptotically the value determined by the initial condition. It is shown that accretion discs with flatter rotation laws at large radii yield higher accretion rates.
The methods are applied to self-gravitating accretion discs in active galactic nuclei. Fully self-gravitating discs are found to evolve faster than nearly Keplerian discs. The implications on supermassive black hole formation and Quasar evolution are discussed.
Numerical simulations show the formation of self-gravitating primordial disks during the assembly of the first structures in the Universe, in particular during the formation of Pop.~III and supermassive stars. Their subsequent evolution is expected to be crucial to determine the mass scale of the first cosmological objects, which depends on the temperature of the gas and the dominant cooling mechanism. Here, we derive a one-zone framework to explore the chemical evolution of such disks and show that viscous heating leads to the collisional dissociation of an initially molecular gas. The effect…
The long-term evolution of a circumstellar disk starting from its formation and ending in the T Tauri phase was simulated numerically with the purpose of studying the evolution of dust in the disk with distinct values of viscous α-parameter and dust fragmentation velocity v_frag. We solved numerical hydrodynamics equations in the thin-disk limit, which are modified to include a dust component consisting of two parts: sub-micron-sized dust and grown dust with a maximum radius a_r. The former is strictly coupled to the gas, while the latter interacts with the gas via friction. The conversion of …
Self-gravity becomes competitive as an angular momentum transport process in accretion discs at large radii, where the temperature is low enough that external irradiation likely contributes to the thermal balance. Irradiation is known to weaken the strength of disc self-gravity, and can suppress it entirely if the disc is maintained above the threshold for linear instability. However, its impact on the susceptibility of the disc to fragmentation is less clear. We use two-dimensional numerical simulations to investigate the evolution of self-gravitating discs as a function of the local cooling …
The short--wave asymptotics (WKB) of spiral density waves in self-gravitating stellar discs is well suited for the study of the dynamics of tightly--wound wavepackets. But the textbook WKB theory is not well adapted to the study of the linear eigenmodes in a collisionless self-gravitating disc because of the transcendental nature of the dispersion relation. We present a modified WKB of spiral density waves, for collisionless discs in the epicyclic limit, in which the perturbed gravitational potential is related to the perturbed surface density by the Poisson integral in Kalnaj's logarithmic sp…
There have been several recent detections of candidate Keplerian discs around massive young protostars. Given the relatively large disc-to-star mass ratios in these systems, and their young ages, it is worth investigating their propensity to becoming self-gravitating. To this end, we compute self-consistent, semi-analytic models of putative self-gravitating discs for five candidate disc systems. Our aim is not to fit exactly the observations, but to demonstrate that the expected dust continuum emission from marginally unstable self-gravitating discs can be quite weak, due to high optical depth…
Recent observations of the Class 0 protostar L1527 IRS have revealed a rotationally supported disc with an outer radius of at least 100 au. Measurements of the integrated flux at 870 microns suggest a disc mass that is too low for gravitational instability to govern angular momentum transport. However, if parts of the disc are optically thick at sub-mm wavelengths, the sub-mm fluxes will underestimate the disc mass, and the disc's actual mass may be substantially larger, potentially sufficient to be self-gravitating. We investigate this possibility using simple self-gravitating disc models. To…
Self-gravitating discs are believed to play an important role in astrophysics in particular regarding the star and planet formation process. In this context, discs subject to an idealized cooling process, characterized by a cooling timescale $β$ expressed in unit of orbital timescale, have been extensively studied. We take advantage of the Riemann solver and the 3D Godunov scheme implemented in the code Ramses to perform high resolution simulations, complementing previous studies that have used smoothed particle hydrodynamics (SPH) or 2D grid codes. We observe that the critical value of $β$ fo…
We introduce and discuss an effective model of a self-gravitating system whose equilibrium thermodynamics can be solved in both the microcanonical and the canonical ensemble, up to a maximization with respect to a single variable. Such a model can be derived from a model of self-gravitating particles confined on a ring, referred to as the self-gravitating ring (SGR) model, allowing a quantitative comparison between the thermodynamics of the two models. Despite the rather crude approximations involved in its derivation, the effective model compares quite well with the SGR model. Moreover, we di…
The time irreversibility and fast relaxation of collapsing $N$-body gravitating systems (as opposed to the time reversibility of the equations of motion for individual stars or particles) are traditionally attributed to information loss due to coarse-graining in the observation. We show that this subjective element is not necessary once one takes into consideration the fundamental fact that these systems are discrete, i.e. composed of a finite number $N$ of stars or particles. We show that a connection can be made between entropy estimates for discrete systems and the Nyquist-Shannon sampling …
Our previous works have shown the statistical mechanics of self-gravitating system. In this paper, we will show its thermodynamics and compare our results with observations and simulations. We propose that our statistical mechanics can be based on ergodicity breaking and Boltzmann entropy, and its assumptions do not contradict with the reality. With the principle of statistical mechanics, we will show our definition of temperature and then the capacity of self-gravitating systems. We find that the gravothermal catastrophe may be a special case of our theory. Our results also provide new explan…
Although quasi-Keplerian discs are among the most common astrophysical structures, computation of secular angular momentum transport within them routinely presents a considerable practical challenge. In this work, we investigate the secular small-inclination dynamics of a razor-thin particle disc as the continuum limit of a discrete Lagrange-Laplace secular perturbative theory and explore the analogy between the ensuing secular evolution -- including non-local couplings of self-gravitating discs -- and quantum mechanics. We find the 'quantum' Hamiltonian that describes the time evolution of th…
The secular evolution of an infinitely thin tepid isolated galactic disc made of a finite number of particles is described using the inhomogeneous Balescu-Lenard equation. Assuming that only tightly wound transient spirals are present in the disc, a WKB approximation provides a simple and tractable quadrature for the corresponding drift and diffusion coefficients. It provides insight into the physical processes at work during the secular diffusion of a self-gravitating discrete disc and makes quantitative predictions on the initial variations of the distribution function in action space. When …
In this paper we study the equilibrium configurations of anisotropic self-gravitating fermions, by extending to general relativity the solutions obtained in a previous paper. This treatment also generalizes to anisotropic systems the relativistic self-gravitating Fermi gas model, by considering different degrees of anisotropy. We discuss some important characteristics of the models and the obtained density profiles, and generalize the relation between the anisotropy and the mass of particles in the relativistic regime. These relativistic models may also be applied to the study of superdense ne…
We carry out three dimensional radiation hydrodynamical simulations of gravitationally unstable discs to explore the movement of mass in a disc following its initial fragmentation. We find that the radial velocity of the gas in some parts of the disc increases by up to a factor of approximately 10 after the disc fragments, compared to before. While the movement of mass occurs in both the inward and outward directions, the inwards movement can cause the inner spirals of a self-gravitating disc to become sufficiently dense such that they can potentially fragment. This suggests that the dynamical…
We show, using the N-body code GADGET-2, that stellar scattering by massive clumps can produce exponential discs, and the effectiveness of the process depends on the mass of scattering centres, as well as the stability of the galactic disc. Heavy, dense scattering centres in a less stable disc generate an exponential profile quickly, with a timescale shorter than 1 Gyr. The profile evolution due to scattering can make a near-exponential disc under various initial stellar distributions. This result supports analytic theories that predict the scattering processes always favour the zero entropy g…
The secular thickening of a self-gravitating stellar galactic disc is investigated using the dressed collisionless Fokker-Planck equation and the inhomogeneous multicomponent Balescu-Lenard equation. The thick WKB limits for the diffusion fluxes are found using the epicyclic approximation, while assuming that only radially tightly wound transient spirals are sustained by the disc. This yields simple quadratures for the drift and diffusion coefficients, providing a clear understanding of the positions of maximum vertical orbital diffusion within the disc, induced by fluctuations either external…
The secular thickening of a discrete self-gravitating galactic disc is investigated using the inhomogeneous multi-component Balescu-Lenard equation. The thick WKB limit for the diffusion and drift coefficients is found using the epicyclic approximation, while assuming that only radially tightly wound transient spirals are sustained by the disc. This yields a simple double quadrature for the drift and diffusion coefficients, providing a clear understanding of the positions of maximum vertical orbital diffusion within the disc induced by the effects of a finite number of particles. When applied …
We carry out a resolution study on the fragmentation boundary of self-gravitating discs. We perform three-dimensional Smoothed Particle Hydrodynamics simulations of discs to determine whether the critical value of the cooling timescale in units of the orbital timescale, beta_{crit}, converges with increasing resolution. Using particle numbers ranging from 31,250 to 16 million (the highest resolution simulations to date) we do not find convergence. Instead, fragmentation occurs for longer cooling timescales as the resolution is increased. These results suggest that at the very least, the critic…
We carry out a resolution study on the fragmentation boundary of self-gravitating discs. We perform three-dimensional Smoothed Particle Hydrodynamics (SPH) simulations of discs to determine whether the critical value of the cooling timescale in units of the orbital timescale, beta_{crit}, converges with increasing resolution. Using particle numbers ranging from 31,250 to 16 million (the highest resolution simulations to date) we do not find convergence. Instead, fragmentation occurs for longer cooling timescales as the resolution is increased. These results certainly suggest that beta_{crit} i…
We perform linear analysis of axisymmetric vertical normal modes in stratified compressible self-gravitating polytropic discs in the shearing box approximation. We study specific dynamics for subadiabatic, adiabatic and superadiabatic vertical stratifications. In the absence of self-gravity, four well-known principal modes can be identified in a stratified disc: acoustic p-, surface gravity f-, buoyancy g- and inertial r-modes. After characterizing modes in the non-self-gravitating case, we include self-gravity and investigate how it modifies the properties of these modes. We find that self-gr…
We investigate the role of magnetic fields in the fragmentation of self-gravitating discs using 3D global ideal magnetohydrodynamic simulations performed with the "phantom" smoothed particle hydrodynamics code. For initially toroidal fields, we find two regimes. In the first, where the cooling time is greater than five times the dynamical time, magnetic fields reduce spiral density wave amplitudes, which in turn suppresses fragmentation. This is the case even if the magnetic pressure is only a tenth of the thermal pressure. The second regime occurs when the cooling time is sufficiently short t…
We investigate the fragmentation criterion in massive self-gravitating discs. We present new analysis of the fragmentation conditions which we test by carrying out global three-dimensional numerical simulations. Whilst previous work has placed emphasis on the cooling timescale in units of the orbital timescale, β, we find that at a given radius the surface mass density (i.e. disc mass and profile) and star mass also play a crucial role in determining whether a disc fragments or not as well as where in the disc fragments form. We find that for shallow surface mass density profiles (p<2, where Σ…
An understanding of the long-term evolution of self-gravitating disks ranks among the classic outstanding problems of astrophysics. In this work, we show that the secular inclination dynamics of a geometrically thin quasi-Keplerian disk, with a surface density profile that scales as the inverse square-root of the orbital radius, are described by the time-dependent Schrödinger equation. Within the context of this formalism, nodal bending waves correspond to the eigenmodes of a quasiparticle's wavefunction, confined in an infinite square well with boundaries given by the radial extent of the dis…
Little Red Dots as self-gravitating discs accreting on supermassive stars: Spectral appearance and formation pathway of the progenitors to direct collapse black holes
Niels Bohr International Academy, The Niels Bohr Institute（尼尔斯·玻尔国际学院，尼尔斯·玻尔研究所）；Center of Gravity, Niels Bohr Institute（引力中心，尼尔斯·玻尔研究所）；Department of Astrophysics, University of Zurich（苏黎世大学天体物理学系）
The field which binds a thermal fermionic cloud is defined as a Hartree integral upon its density. In turn, the density results from the field via a Thomas-Fermi occupation of the local phase space. This defines a complete theory of all properties and observables for the cloud. As an application to dark matter halos, comparisons with astronomic data on dwarf spheroidal galaxies are provided and discussed. Estimates of the elementary fermion mass are obtained, serving as a phase-space bound on fermionic dark matter.
Starting from the weak field limit, we discuss astrophysical applications of Extended Theories of Gravity where higher order curvature invariants and scalar fields are considered by generalizing the Hilbert-Einstein action linear in the Ricci curvature scalar $R$. Results are compared to General Relativity in the hypothesis that Dark Matter contributions to the dynamics can be neglected thanks to modified gravity. In particular, we consider stellar hydrostatic equilibrium, galactic rotation curves, and gravitational lensing. Finally, we discuss the weak field limit in the Jordan and Einstein f…
