Self-gravitating Disks Research Articles

Disc distortion revisited

Abstract We revisit the dynamics of razor-thin, stone-cold, self-gravitating discs. By recasting the equations into standard cylindrical coordinates, the linearised vertical dynamics of an exponential disc can be followed for several gigayears on a laptop in a few minutes. An initially warped disc rapidly evolves into a flat inner region and an outward-propagating spiral corrugation wave that rapidly winds up and would quickly thicken a disc with non-zero radial velocity dispersion. The Sgr dwarf galaxy generates a similar warp in the Galactic disc as it passes through pericentre, and the warp generated by the dwarf’s last pericentre ∼35 Myr ago is remarkably similar to the warp traced by the Galaxy’s HI disc. The resemblance to the observed warp is fleeting but its timing is perfect. For the adopted parameters the amplitude of the model warp is a factor 3 too small, but there are several reasons for this being so. The marked flaring of our Galaxy’s low-α disc just outside the solar circle can be explained as a legacy of earlier pericentres.

Direct Collapse Accretion Disks within Dark Matter Halos: Saturation of the Magnetorotational Instability and the Field Expulsion

We have used high-resolution zoom-in simulations of direct collapse to supermassive black hole (SMBH) seeds within dark mater halos in the presence of magnetic fields generated during the collapse, down to 10−5 pc or 2 au. We confirm an efficient amplification of magnetic field during collapse, the formation of a geometrically thick self-gravitating accretion disk inside 0.1 pc, and damping of fragmentation in the disk by the field. This disk differs profoundly from SMBH accretion disks. We find the following: (1) The accretion disk is subject to the magnetorotational instability, which further amplifies the field to near equipartition. No artificial seeding of the disk field has been used. (2) The equipartition toroidal field changes its polarity in the midplane. (3) The nonlinear Parker instability develops, accompanied by the vertical buckling of the field lines, which injects material above the disk, leading to an increase in the disk scale height. (4) With the Coriolis force producing a coherent helicity above the disk, the vertical poloidal field has been generated and amplified. (5) We estimate that the associated outflow will be most probably squashed by accretion. The resulting configuration consists of a magnetized disk with β ≳ 0.1 and its magnetosphere with β ≪ 1, where β = P th/P B is the ratio of thermal to magnetic energy density. (6) The disk is highly variable, due to feeding by variable accretion flow, and strong vortical motions are present. (7) Finally, the negative gradient of the total vertical stress drives an equatorial outflow sandwiched by an inward accretion flow.

General relativistic self-gravitating equilibrium discs around rotating neutron stars

ABSTRACT In modelling a relativistic disc around a compact object, the self-gravity of the disc is often neglected while it needs to be incorporated for more accurate descriptions in several circumstances. Extending the Komatsu–Eriguchi–Hachisu self-consistent field method, we present numerical models of a rapidly rotating neutron star with a self-gravitating disc in stationary equilibrium. In particular, our approach allows us to obtain numerical solutions involving a massive disc with the rest mass $\mathcal {O}(10^{-1})-\mathcal {O}(10^0)\, \mathrm{ M}_\odot$ closely attached to a rotating neutron star, given that the disc is mainly supported by the relativistic electron degeneracy pressure. We also assess the impact of self-gravity on the internal structure of the disc and the neutron star. These axisymmetric, stationary solutions can be employed for simulations involving the neutron star–disc system in the context of high-energy transients and gravitational-wave emissions.

Local gravitational instability of two-component thick discs in three dimensions

Aims. The local gravitational instability of rotating discs is believed to be an important mechanism in different astrophysical processes, including the formation of gas and stellar clumps in galaxies. We aim to study the local gravitational instability of two-component thick discs in three dimensions. Methods. We use as a starting point a recently proposed analytic three-dimensional (3D) instability criterion for discs with non-negligible thickness that takes the form Q3D < 1, where Q3D is a 3D version of the classical 2D Toomre Q parameter for razor-thin discs. Here, we extend the 3D stability analysis to two-component discs, considering first the influence on Q3D of a second unresponsive component, and then the case in which both components are responsive. We present the application to two-component discs with isothermal vertical distributions, which can represent, for instance, galactic discs with both stellar and gaseous components. Finally, we relax the assumption of vertical isothermal distribution, by studying one-component self-gravitating discs with polytropic vertical distributions for a range of values of the polytropic index corresponding to convectively stable configurations. Results. We find that Q3D < 1, where Q3D can be computed from observationally inferred quantities, is a robust indicator of local gravitational instability, depending only weakly on the presence of a second component and on the vertical gradient of temperature or velocity dispersion. We derive a sufficient condition for local gravitational instability in the midplane of two-component discs, which can be employed when both components have Q3D > 1.

The influence of realistic cooling on the structure and spectrum of self-gravitating protoplanetary discs

The influence of realistic cooling on the structure and spectrum of self-gravitating protoplanetary discs

Introducing two improved methods for approximating radiative cooling in hydrodynamical simulations of accretion discs

ABSTRACT The evolution of many astrophysical systems depends strongly on the balance between heating and cooling, in particular star formation in giant molecular clouds and the evolution of young protostellar systems. Protostellar discs are susceptible to the gravitational instability, which can play a key role in their evolution and in planet formation. The strength of the instability depends on the rate at which the system loses thermal energy. To study the evolution of these systems, we require radiative cooling approximations because full radiative transfer is generally too expensive to be coupled to hydrodynamical models. Here, we present two new approximate methods for computing radiative cooling that make use of the polytropic cooling approximation. This approach invokes the assumption that each parcel of gas is located within a spherical pseudo-cloud, which can then be used to approximate the optical depth. The first method combines the methods introduced by Stamatellos et al. and Lombardi et al. to overcome the limitations of each method at low and high optical depths, respectively. The second method, the ‘modified Lombardi’ method, is specifically tailored for self-gravitating discs. This modifies the scale height estimate from the method of Lombardi et al. using the analytical scale height for a self-gravitating disc. We show that the modified Lombardi method provides an excellent approximation for the column density in a fragmenting disc, a regime in which the existing methods fail to recover the clumps and spiral structures. We therefore recommend this improved radiative cooling method for more realistic simulations of self-gravitating discs.

Revisiting the Surface Brightness Profile of the Stellar Disk with the Statistical Mechanics of the Self-Gravitating System with the Central Body.

We have explored the exponential surface brightness profile (SBP) of stellar disks, a topic extensively discussed by many authors yet seldom integrated with the study of correlations between black holes, bulges, and entire disks. Building upon our prior work in the statistical mechanics of disk-shaped systems and aligning with methodologies from other research, we analyze the influence of the central body. This analysis reveals analytical relationships among black holes, bulges, and the entire stellar disk. Additionally, we incorporate a specific angular momentum distribution (SAMD) that aligns more closely with observational data, showing that for the self-gravitating disk, with the same surface density, a reduction in its spin results in only a slight decrease in its radius, whereas with the same SAMD, an increment in its spin significantly limits its extent. A key feature of our model is its prediction that the surface density profile of an isolated disk will invariably exhibit downbending at a sufficient distance, a hypothesis that future observations can test. Our refined equations provide a notably improved fit for SBPs, particularly in the central regions of stellar disks. While our findings underscore the significance of statistical mechanics in comprehending spiral galaxy structures, they also highlight areas in our approach that warrant further discussion and exploration.

Ices on pebbles in protoplanetary discs

ABSTRACT The formation of solid macroscopic grains (pebbles) in protoplanetary discs is the first step towards planet formation. We aim to study the distribution of pebbles and the chemical composition of their ice mantles in a young protoplanetary disc. We use the two-dimensional hydrodynamical code feosad in the thin-disc approximation, which is designed to model the global evolution of a self-gravitating viscous protoplanetary disc taking into account dust coagulation and fragmentation, thermal balance, and phase transitions and transport of the main volatiles (H2O, CO2, CH4, and CO), which can reside in the gas, on small dust ($\lt 1\, \mu\mathrm{ m}$), on grown dust ($\gt 1\, \mu\mathrm{ m}$) and on pebbles. We model the dynamics of the protoplanetary disc from the cloud collapse to the 500 kyr moment. We determine the spatial distribution of pebbles and composition of their ice mantles and estimate the mass of volatiles on pebbles, grown dust, and small dust. We show that pebbles form as early as 50 kyr after the disc formation and exist until the end of simulation (500 kyr), providing prerequisites for planet formation. All pebbles formed in the model are covered by icy mantles. Using a model considering accretion and desorption of volatiles on to dust/pebbles, we find that the ice mantles on pebbles consist mainly of H2O and CO2, and are carbon-depleted compared to gas and ices on small and grown dust, which contain more CO and CH4. This suggests a possible dominance of oxygen in the composition of planets formed from pebbles under these conditions.

Predicting the linear response of self-gravitating stellar spheres and discs with LinearResponse.jl

ABSTRACT We present LinearResponse.jl, an efficient, versatile public library written in julia to compute the linear response of self-gravitating (three-dimensional spherically symmetric) stellar spheres and (two-dimensional axisymmetric razor-thin) discs. LinearResponse.jl can scan the whole complex frequency plane, probing unstable, neutral and (weakly) damped modes. Given a potential model and a distribution function, this numerical toolbox estimates the modal frequencies as well as the shapes of individual modes. The libraries are validated against a combination of previous results for the spherical isochrone model and Mestel discs, and new simulations for the spherical Plummer model. Beyond linear response theory, the realm of applications of LinearResponse.jl also extends to the kinetic theory of self-gravitating systems through a modular interface.

Spiral shocks induced in a galactic gaseous disk: Hydrodynamic understanding of observational properties of spiral galaxies

Context. We investigate the properties of spiral shocks in a steady, adiabatic, non-axisymmetric, self-gravitating, mass-outflowing accretion disk around a compact object. Aims. We obtained the accretion-ejection solutions in a galactic disk and applied them to spiral galaxies in order to investigate the possible physical connections between some observational quantities of galaxies. Methods. We considered the self-gravitating disk potential to examine the properties of the galactic gaseous disk. We obtained spiral shock-induced accretion-ejection solutions following the point-wise self-similar approach. Results. We observed that the self-gravitating disk profoundly affects the dynamics of the spiral structure of the disk and the properties of the spiral shocks. We find that the observational dispersion between the pitch angle and shear rate and between the pitch angle and star formation rate in spiral galaxies contains some important physical information. Conclusions. There are large differences among the star formation rates of galaxies with similar pitch angles. These differences may be explained by the different star formation efficiencies caused by distinct galactic ambient conditions.

Response of gravitationally coupled gaseous and stellar components to asymmetric warp in disc galaxies

ABSTRACT The outer disc region of most spiral galaxies (approximately 50 per cent of all disc galaxies) shows warping above the galactic mid-plane and is primarily asymmetric by nature. In this work, we explore analytically the effect of the gas component on asymmetric warps in a realistic self-gravitating collision-less disc residing in a cold oblate dark matter halo’s potential field. We consider the disc to be composed of gravitationally coupled stars and gas components. The quadratic eigenvalue equation describing the shape and frequency of the bending mode is formulated and solved numerically. Two stable ground-state bending modes m = 0 and m = 1, representing the U-shape and the mostly observed S-shaped warp in the galactic disc are superimposed linearly to generate and examine the asymmetric warps in the disc. The resulting asymmetry in warp is measured by asymmetric index (Aasym) by varying physical parameters such as the mass of the gas components and the halo flattening parameter. It is shown that the gas fraction in the disc has a negligible contribution to the generation of asymmetric warp in the disc. The disc residing in a spherical dark matter halo is found to be more asymmetry than that in the counterpart oblate halo.

Direct Collapse to Precursors of Supermassive Black Hole Seeds: Radiation-feedback-generated Outflows

We use high-resolution zoom-in cosmological simulations to model outflow triggered by radiation and thermal drivers around the central mass accumulation during direct collapse within the dark matter (DM) halo. The maximal resolution is 1.3 × 10−5 pc, and no restrictions are put on the geometry of the inflow/outflow. The central mass is considered prior to the formation of the supermassive black hole seed at a redshift of z ∼ 15.9 and can constitute either a supermassive star (SMS) of ∼105 M ⊙ surrounded by a growing accretion disk or a self-gravitating disk. The radiation transfer is modeled using the ray-tracing algorithm. Due to the high accretion rate of ∼1 M ⊙ yr−1 determined by the DM halo, accretion is mildly supercritical, resulting in mildly supercritical luminosity that has only a limited effect on the accretion rate, with a duty cycle of ∼0.9. We observe a fast development of hot cavities, which quickly extend into polar funnels and expand dense shells. Within the funnels, fast winds, ∼103 km s−1, are mass-loaded by the accreting gas. We follow the expanding shells to ∼1 pc, when the shell velocity remains substantially (∼5 times) above the escape speed. The ionization cones formed by the central UV/X-ray completely ionize the cavities. Extrapolating the outflow properties shows that the halo material outside the shell will have difficulty stopping it. We therefore conclude that the expanding wind-driven shell will break out of the central parsec and will reach the halo virial radius. Finally, the anisotropic accretion flow on subparsec scales will attenuate the UV/soft X-rays on the H2. Hence, the formation of funnels and powerful outflows around, e.g., SMSs can have interesting observational corollaries.

Self-gravity of debris discs can strongly change the outcomes of interactions with inclined planets

ABSTRACT Drastic changes in protoplanets’ orbits could occur in the early stages of planetary systems through interactions with other planets and their surrounding protoplanetary or debris discs. The resulting planetary system could exhibit orbits with moderate to high eccentricities and/or inclinations, causing planets to perturb one another as well as the disc significantly. The present work studies the evolution of systems composed of an initially inclined planet and a debris disc. We perform N-body simulations of a narrow, self-gravitating debris disc, and a single interior Neptune-like planet. We simulate systems with various initial planetary inclinations, from coplanar to polar configurations considering different separations between the planet and the disc. We find that except when the planet is initially on a polar orbit, the planet–disc system tends to reach a quasi-coplanar configuration with low vertical dispersion in the disc. When present, the Zeipel–Kozai–Lidov oscillations induced by the disc pump the planet’s eccentricity and, in turn, affect the disc structure. We also find that the resulting disc morphology in most of the simulations looks very similar in both radial and vertical directions once the simulations are converged. This contrasts strongly with massless disc simulations, where vertical disc dispersion is set by the initial disc-planet inclination and can be high for initially highly inclined planets. The results suggest caution in interpreting an unseen planet’s dynamical history based only on the disc’s appearance.

Formation of Gaps in Self-gravitating Debris Disks by Secular Resonance in a Single-planet System. II. Toward a Self-consistent Model

High-resolution observations of several debris disks reveal structures such as gaps and spirals, suggestive of gravitational perturbations induced by underlying planets. Most existing studies of planet–debris disk interactions ignore the gravity of the disk, treating it as a reservoir of massless planetesimals. In this paper, we continue our investigation into the long-term interaction between a single eccentric planet and an external, massive debris disk. Building upon our previous work, here we consider not only the axisymmetric component of the disk’s gravitational potential, but also the nonaxisymmetric torque that the disk exerts on the planet (ignoring for now only the nonaxisymmetric component of the disk self-gravity). To this goal, we develop and test a semianalytic “N-ring” framework that is based on a generalized (softened) version of the classical Laplace–Lagrange secular theory. Using this tool, we demonstrate that even when the disk is less massive than the planet, not only can a secular resonance be established within the disk that leads to the formation of a wide gap, but that the very same resonance also damps the planetary eccentricity e p via a process known as resonant friction. The resulting gap is initially nonaxisymmetric (akin to those observed in HD 92945 and HD 206893), but evolves to become more axisymmetric (similar to that in HD 107146) as e p (t) → 0 with time. We also develop analytic understanding of these findings, finding good quantitative agreement with the outcomes of the N-ring calculations. Our results may be used to infer both the dynamical masses of (gapped) debris disks and the dynamical history of the planets interior to them, as we exemplify for HD 206893.

Star Formation in Self-gravitating Disks in Active Galactic Nuclei. III. Efficient Production of Iron and Infrared Spectral Energy Distributions

Strong iron lines are a common feature of the optical spectra of active galactic nuclei (AGNs) and quasars from z ∼ 6−7 to the local universe, and [Fe/Mg] ratios do not show cosmic evolution. During active episodes, accretion disks surrounding supermassive black holes (SMBHs) inevitably form stars in the self-gravitating part, and these stars accrete with high accretion rates. In this paper, we investigate the population evolution of accretion-modified stars (AMSs) to produce iron and magnesium in AGNs. The AMSs, as a new type of star, are allowed to have any metallicity but without significant loss from stellar winds, since the winds are choked by the dense medium of the disks and return to the core stars. Mass functions of the AMS population show a pile-up or cutoff pile-up shape in top-heavy or top-dominant forms if the stellar winds are strong, consistent with the narrow range of supernovae (SNe) explosions driven by the known pair-instability. This provides an efficient way to produce metals. Meanwhile, SN explosions support an inflated disk as a dusty torus. Furthermore, the evolving top-heavy initial mass functions lead to bright luminosity in infrared bands in dusty regions. This contributes a new component in infrared bands, which is independent of the emissions from the central part of accretion disks, appearing as a long-term trending of the NIR continuum compared to optical variations. Moreover, the model can be further tested through reverberation mapping of emission lines, including LIGO/LISA detections of gravitational waves and signatures from spatially resolved observations of GRAVITY+/VLTI.

Characterizing fragmentation and sub-Jovian clump properties in magnetized young protoplanetary discs

ABSTRACT We study the initial development, structure, and evolution of protoplanetary clumps formed in three-dimensional resistive magnetohydrodynamic (MHD) simulations of self-gravitating discs. The magnetic field grows by means of the recently identified gravitational instability dynamo. Clumps are identified and their evolution is tracked finely both backward and forward in time. Their properties and evolutionary path is compared with clumps in companion simulations without magnetic fields. We find that magnetic and rotational energy are important in the clumps’ outer regions, while in the cores, despite appreciable magnetic field amplification, thermal pressure is most important in counteracting gravity. Turbulent kinetic energy is of a smaller scale than magnetic energy in the clumps. Compared with non-magnetized clumps, rotation is less prominent, which results in lower angular momentum in much better agreement with observations. In order to understand the very low sub-Jovian masses of clumps forming in MHD simulations, we revisit the perturbation theory of magnetized sheets finding support for a previously proposed magnetic destabilization in low-shear regions. This can help explaining why fragmentation ensues on a scale more than an order of magnitude smaller than that of the Toomre mass. The smaller fragmentation scale and the high magnetic pressure in clumps’ envelopes explain why clumps in magnetized discs are typically in the super-Earth to Neptune mass regime rather than super-Jupiter as in conventional disc instability. Our findings put forward a viable alternative to core accretion to explain widespread formation of intermediate-mass planets.

Effect of magnetic fields on the dynamics and gravitational wave emission of Papaloizou-Pringle instability-saturated self-gravitating accretion disks: Simulations in full GR

Effect of magnetic fields on the dynamics and gravitational wave emission of Papaloizou-Pringle instability-saturated self-gravitating accretion disks: Simulations in full GR

Investigation of the halo effect in the evolution of a nonstationary disk of spiral galaxies

Abstract In this article, we consider the problem of the evolution of the disk subsystem of galaxies, taking into account their halos. The global structure of the disk of galaxies strongly depends on the mass and shape of the halo. To this end, we have studied the evolution of nonradial oscillations of a nonstationary disk surrounded by a passive ellipsoidal halo with a uniform density. A system of equations for the evolution of a self-gravitating disk is obtained, taking into account the halo, in the form of matrix differential equations, and a method for its numerical analysis is developed to study the effect of the halo on disk formation. Numerical calculations were performed for various values of the system parameters, such as the initial perturbation, the circular speed of disk rotation, the ratio of the mass of the halo to the mass of the disk, and the time dependences of the major and minor semiaxes of the disk. The critical values of the system parameters are determined at which the halo stabilizes nonlinear and nonradial oscillations of the disk subsystem of galaxies at an early stage of their evolution.

Filling in the gaps: can gravitationally unstable discs form the seeds of gas giant planets?

ABSTRACT Circumstellar discs likely have a short window when they are self-gravitating and prone to the effects of disc instability, but during this time the seeds of planet formation can be sown. It has long been argued that disc fragmentation can form large gas giant planets at wide orbital separations, but its place in the planet formation paradigm is hindered by a tendency to form especially large gas giants or brown dwarfs. We instead suggest that planet formation can occur early in massive discs, through the gravitational collapse of dust which can form the seeds of giant planets. This is different from the usual picture of self-gravitating discs, in which planet formation is considered through the gravitational collapse of the gas disc into a gas giant precursor. It is familiar in the sense that the core is formed first, and gas is accreted thereafter, as is the case in the core accretion scenario. However, by forming a ∼1 M⊕ seed from the gravitational collapse of dust within a self-gravitating disc there exists the potential to overcome traditional growth barriers and form a planet within a few times 105 yr. The accretion of pebbles is most efficient with centimetre-sized dust, but the accretion of millimetre sizes can also result in formation within a Myr. Thus, if dust can grow to these sizes, planetary seeds formed within very young, massive discs could drastically reduce the time-scale of planet formation and potentially explain the observed ring and gap structures in young discs.

Extreme evaporation of planets in hot thermally unstable protoplanetary discs: the case of FU Ori

ABSTRACT Disc accretion rate onto low mass protostar FU Ori suddenly increased hundreds of times 85 yr ago and remains elevated to this day. We show that the sum of historic and recent observations challenges existing FU Ori models. We build a theory of a new process, Extreme Evaporation (EE) of young gas giant planets in discs with midplane temperatures of ≳ 30 000 K. Such temperatures are reached in the inner 0.1 AU during thermal instability bursts. In our 1D time-dependent code the disc and an embedded planet interact through gravity, heat, and mass exchange. We use disc viscosity constrained by simulations and observations of dwarf novae instabilities, and we constrain planet properties with a stellar evolution code. We show that dusty gas giants born in the outer self-gravitating disc reach the innermost disc in a ∼O(104) yr with radius of ∼10RJ. We show that their EE rates are $\gtrsim 10^{-5} {\rm {\rm M}_{\odot }}$ yr−1; if this exceeds the background disc accretion activity then the system enters a planet-sourced mode. Like a stellar secondary in mass-transferring binaries, the planet becomes the dominant source of matter for the star, albeit for ∼O(100) yr. We find that a ∼6 Jupiter mass planet evaporating in a disc fed at a time-averaged rate of $\sim 10^{-6} {\rm {\rm M}_{\odot }}$ yr−1 appears to explain all that we currently know about FU Ori accretion outburst. More massive planets and/or planets in older less massive discs do not experience EE process. Future FUOR modelling may constrain planet internal structure and evolution of the earliest discs.