Accretion Stresses Research Articles

A Primordial Origin for the Gas-rich Debris Disks around Intermediate-mass Stars

While most debris disks consist of dust with little or no gas, a fraction have significant amounts of gas detected via emission lines of CO, ionized carbon, and/or atomic oxygen. Almost all such gaseous debris disks known are around A-type stars with ages up to 50 Myr. We show, using semianalytic disk evolution modeling, that this can be understood if the gaseous debris disks are remnant protoplanetary disks that have become depleted of small grains compared to the interstellar medium. Photoelectric heating by the A stars’ far-UV (FUV) radiation is then inefficient, while the stars’ extreme-UV (EUV) and X-ray emissions are weak owing to a lack of surface convective zones capable of driving magnetic activity. In this picture, it is relatively difficult for stars outside the range of spectral types from A through early B to have such long-lived gas disks. Less-massive stars have stronger magnetic activity in the chromosphere, transition region, and corona with resulting EUV and X-ray emission, while more-massive stars have photospheres hot enough to produce strong EUV radiation. In both cases, primordial disk gas is likely to photoevaporate well before 50 Myr. These results come from 0D disk evolution models where we incorporate internal accretion stresses, MHD winds, and photoevaporation by EUV and X-ray photons with luminosities that are functions of the stellar mass and age. A key issue this work leaves open is how some disks become depleted in small dust so that FUV photoevaporation slows. Candidates include the grains’ growth, settling, radial drift, radiation force, and incorporation into planetary systems.

Nonlinear mechanics of surface growth for cylindrical and spherical elastic bodies

In this paper we formulate the initial-boundary value problems of accreting cylindrical and spherical nonlinear elastic solids in a geometric framework. It is assumed that the body grows as a result of addition of new (stress-free or pre-stressed) material on part of its boundary. We construct Riemannian material manifolds for a growing body with metrics explicitly depending on the history of applied external loads and deformation during accretion and the growth velocity. We numerically solve the governing equilibrium equations in the case of neo-Hookean solids and compare the accretion and residual stresses with those calculated using the linear mechanics of surface growth.

RADIATION HYDRODYNAMICS MODELS OF THE INNER RIM IN PROTOPLANETARY DISKS

ABSTRACT Many stars host planets orbiting within a few astronomical units (AU). The occurrence rate and distributions of masses and orbits vary greatly with the host star’s mass. These close planets’ origins are a mystery that motivates investigating protoplanetary disks’ central regions. A key factor governing the conditions near the star is the silicate sublimation front, which largely determines where the starlight is absorbed, and which is often called the inner rim. We present the first radiation hydrodynamical modeling of the sublimation front in the disks around the young intermediate-mass stars called Herbig Ae stars. The models are axisymmetric and include starlight heating; silicate grains sublimating and condensing to equilibrium at the local, time-dependent temperature and density; and accretion stresses parameterizing the results of MHD magnetorotational turbulence models. The results compare well with radiation hydrostatic solutions and prove to be dynamically stable. Passing the model disks into Monte Carlo radiative transfer calculations, we show that the models satisfy observational constraints on the inner rim’s location. A small optically thin halo of hot dust naturally arises between the inner rim and the star. The inner rim has a substantial radial extent, corresponding to several disk scale heights. While the front’s overall position varies with the stellar luminosity, its radial extent depends on the mass accretion rate. A pressure maximum develops near the location of thermal ionization at temperatures of about 1000 K. The pressure maximum is capable of halting solid pebbles’ radial drift and concentrating them in a zone where temperatures are sufficiently high for annealing to form crystalline silicates.

TEMPERATURE FLUCTUATIONS DRIVEN BY MAGNETOROTATIONAL INSTABILITY IN PROTOPLANETARY DISKS

The magnetorotational instability (MRI) drives magnetized turbulence in sufficiently ionized regions of protoplanetary disks, leading to mass accretion. The dissipation of the potential energy associated with this accretion determines the thermal structure of accreting regions. Until recently, the heating from the turbulence has only been treated in an azimuthally averaged sense, neglecting local fluctuations. However, magnetized turbulence dissipates its energy intermittently in current sheet structures. We study this intermittent energy dissipation using high resolution numerical models including a treatment of radiative thermal diffusion in an optically thick regime. Our models predict that these turbulent current sheets drive order unity temperature variations even where the MRI is damped strongly by Ohmic resistivity. This implies that the current sheet structures where energy dissipation occurs must be well resolved to correctly capture the flow structure in numerical models. Higher resolutions are required to resolve energy dissipation than to resolve the magnetic field strength or accretion stresses. The temperature variations are large enough to have major consequences for mineral formation in disks, including melting chondrules, remelting calcium-aluminum rich inclusions, and annealing silicates; and may drive hysteresis: current sheets in MRI active regions could be significantly more conductive than the remainder of the disk.

MAGNETIC COUPLING IN THE DISKS AROUND YOUNG GAS GIANT PLANETS

We examine the conditions under which the disks of gas and dust orbiting young gas giant planets are sufficiently conducting to experience turbulence driven by the magneto-rotational instability. By modeling the ionization and conductivity in the disk around proto-Jupiter, we find that turbulence is possible if the X-rays emitted near the Sun reach the planet's vicinity and either (1) the gas surface densities are in the range of the minimum-mass models constructed by augmenting Jupiter's satellites to Solar composition, while dust is depleted from the disk atmosphere, or (2) the surface densities are much less, and in the range of gas-starved models fed with material from the Solar nebula, but not so low that ambipolar diffusion decouples the neutral gas from the plasma. The results lend support to both minimum-mass and gas-starved models of the protojovian disk: (1) The dusty minimum-mass models have internal conductivities low enough to prevent angular momentum transfer by magnetic forces, as required for the material to remain in place while the satellites form. (2) The gas-starved models have magnetically-active surface layers and a decoupled interior "dead zone". Similar active layers in the Solar nebula yield accretion stresses in the range assumed in constructing the circumjovian gas-starved models. Our results also point to aspects of both classes of models that can be further developed. Non-turbulent minimum-mass models will lose dust from their atmospheres by settling, enabling gas to accrete through a thin surface layer. For the gas-starved models it is crucial to learn whether enough stellar X-ray and ultraviolet photons reach the circumjovian disk. Additionally the stress-to-pressure ratio ought to increase with distance from the planet, likely leading to episodic accretion outbursts.

TURBULENCE IN THE OUTER REGIONS OF PROTOPLANETARY DISKS. II. STRONG ACCRETION DRIVEN BY A VERTICAL MAGNETIC FIELD

We carry out a series of local, vertically stratified shearing box simulations of protoplanetary disks that include ambipolar diffusion and a net vertical magnetic field. The ambipolar diffusion profiles we employ correspond to 30AU and 100AU in a minimum mass solar nebula (MMSN) disk model, which consists of a far-UV-ionized surface layer and low-ionization disk interior. These simulations serve as a follow up to Simon et al. (2013), in which we found that without a net vertical field, the turbulent stresses that result from the magnetorotational instability (MRI) are too weak to account for observed accretion rates. The simulations in this work show a very strong dependence of the accretion stresses on the strength of the background vertical field; as the field strength increases, the stress amplitude increases. For gas to magnetic pressure ratios of 1e4 and 1e5, we find accretion rates between 1e-8 and 1e-7 solar masses per year. These accretion rates agree with observational constraints, suggesting a vertical magnetic field strength between 60 and 200 microgauss at 30AU and 10 and 30 microgauss at 100AU in a MMSN disk. Furthermore, the stress has a non-negligible component due to a magnetic wind. For sufficiently strong vertical field strengths, MRI turbulence is quenched, and the flow becomes largely laminar, with accretion proceeding through large scale correlations in the radial and toroidal field components as well as through the magnetic wind. In all simulations, the presence of a low ionization region near the disk mid-plane, which we call the ambipolar damping zone, results in reduced stresses there.

MODELING MAGNETOROTATIONAL TURBULENCE IN PROTOPLANETARY DISKS WITH DEAD ZONES

Turbulence driven by magnetorotational instability (MRI) crucially affects the evolution of solid bodies in protoplanetary disks. On the other hand, small dust particles stabilize MRI by capturing ionized gas particles needed for the coupling of the gas and magnetic fields. To provide an empirical basis for modeling the coevolution of dust and MRI, we perform three-dimensional, ohmic-resistive MHD simulations of a vertically stratified shearing box with an MRI-inactive "dead zone" of various sizes and with a net vertical magnetic flux of various strengths. We find that the vertical structure of turbulence is well characterized by the vertical magnetic flux and three critical heights derived from the linear analysis of MRI in a stratified disk. In particular, the turbulent structure depends on the resistivity profile only through the critical heights and is insensitive to the details of the resistivity profile. We discover scaling relations between the amplitudes of various turbulent quantities (velocity dispersion, density fluctuation, vertical diffusion coefficient, and outflow mass flux) and vertically integrated accretion stresses. We also obtain empirical formulae for the integrated accretion stresses as a function of the vertical magnetic flux and the critical heights. These empirical relations allow to predict the vertical turbulent structure of a protoplanetary disk for a given strength of the magnetic flux and a given resistivity profile.

DIRECT CALCULATION OF THE RADIATIVE EFFICIENCY OF AN ACCRETION DISK AROUND A BLACK HOLE

Numerical simulation of magnetohydrodynamic (MHD) turbulence makes it possible to study accretion dynamics in detail. However, special effort is required to connect inflow dynamics (dependent largely on angular momentum transport) to radiation (dependent largely on thermodynamics and photon diffusion). To this end we extend the flux-conservative, general relativistic MHD code HARM from axisymmetry to full 3D. The use of an energy conserving algorithm allows the energy dissipated in the course of relativistic accretion to be captured as heat. The inclusion of a simple optically thin cooling function permits explicit control of the simulated disk's geometric thickness as well as a direct calculation of both the amplitude and location of the radiative cooling associated with the accretion stresses. Fully relativistic ray-tracing is used to compute the luminosity received by distant observers. For a disk with aspect ratio H/r ~ 0.1 accreting onto a black hole with spin parameter a/M = 0.9, we find that there is significant dissipation beyond that predicted by the classical Novikov-Thorne model. However, much of it occurs deep in the potential, where photon capture and gravitational redshifting can strongly limit the net photon energy escaping to infinity. In addition, with these parameters and this radiation model, significant thermal and magnetic energy remains with the gas and is accreted by the black hole. In our model, the net luminosi ty reaching infinity is 6% greater than the Novikov-Thorne prediction. If the accreted thermal energy were wholly radiated, the total luminosity of the accretion flow would be ~20% greater than the Novikov-Thorne value.

Turbulent Mixing and the Dead Zone in Protostellar Disks

We investigate the conditions for the presence of a magnetically inactive dead zone in protostellar disks, using 3-D shearing-box MHD calculations including vertical stratification, Ohmic resistivity and time-dependent ionization chemistry. Activity driven by the magnetorotational instability fills the whole thickness of the disk at 5 AU, provided cosmic ray ionization is present, small grains are absent and the gas-phase metal abundance is sufficiently high. At 1 AU the larger column density of 1700 g/cm^2 means the midplane is shielded from ionizing particles and remains magnetorotationally stable even under the most favorable conditions considered. Nevertheless the dead zone is effectively eliminated. Turbulence mixes free charges into the interior as they recombine, leading to a slight coupling of the midplane gas to the magnetic fields. Weak, large-scale radial fields diffuse to the midplane where they are sheared out to produce stronger azimuthal fields. The resulting midplane accretion stresses are just a few times less than in the surface layers on average.

On the Vertical Structure of Radiation-Supported Accretion Disks

The vertical structure of a black hole accretion disk in which radiation dominates the total pressure is investigated using a three-dimensional radiation-MHD calculation, in the Stratified shearing-box approximation. Magneto-rotational instability [Balbus, S. A. and Hawley J. F., Astrophys. J. 376 (1991), 214] converts differential rotation to turbulent magnetic and kinetic energy. The gas is cooled by diffusion and advection of radiation through the vertical boundaries. Density is greatest near the midplane, while accretion stresses are greatest in optically-thick surface layers. The thermal time, and the ratio of radiation to gas pressure, are an order of magnitude smaller than in the corresponding Shakura-Sunyaev model [Shakura, N. I. and Sunyaev R. A., Astron. Astrophys. 24 (1973), 337] because dissipation occurs at low column density.

Local Three‐dimensional Simulations of Magnetorotational Instability in Radiation‐dominated Accretion Disks

We examine the small-scale dynamics of black hole accretion disks in which radiation pressure exceeds gas pressure. Local patches of disk are modeled by numerically integrating the equations of radiation MHD in the flux-limited diffusion approximation. The shearing-box approximation is used, and the vertical component of gravity is neglected. Magnetorotational instability (MRI) leads to turbulence in which accretion stresses are due primarily to magnetic torques. When radiation is locked to gas over the length and timescales of fluctuations in the turbulence, the accretion stress, density contrast, and dissipation differ little from those in the corresponding calculations, with radiation replaced by extra gas pressure. However, when radiation diffuses each orbit a distance that is comparable to the rms vertical wavelength of the MRI, radiation pressure is less effective in resisting squeezing. Large density fluctuations occur, and radiation damping of compressive motions converts P dV work into photon energy. The accretion stress in calculations having a net vertical magnetic field is found to be independent of opacity over the range explored and approximately proportional to the square of the net field. In calculations with zero net magnetic flux, the accretion stress depends on the portion of the total pressure that is effective in resisting compression. The stress is lower when radiation diffuses rapidly with respect to the gas. We show that radiation-supported Shakura-Sunyaev disks accreting via internal magnetic stresses are likely to have radiation marginally coupled to turbulent gas motions in their interiors.