skip to main content
OSTI.GOV title logo U.S. Department of Energy
Office of Scientific and Technical Information

Title: Radial Transport and Meridional Circulation in Accretion Disks

Abstract

Radial transport of particles, elements and fluid driven by internal stresses in three-dimensional (3D) astrophysical accretion disks is an important phenomenon, potentially relevant for the outward dust transport in protoplanetary disks, origin of the refractory particles in comets, isotopic equilibration in the Earth–Moon system, etc. To gain better insight into these processes, we explore the dependence of meridional circulation in 3D disks with shear viscosity on their thermal stratification, and demonstrate a strong effect of the latter on the radial flow. Previous locally isothermal studies have normally found a pattern of the radial outflow near the midplane, switching to inflow higher up. Here we show, both analytically and numerically, that a flow that is inward at all altitudes is possible in disks with entropy and temperature steeply increasing with height. Such thermodynamic conditions may be typical in the optically thin, viscously heated accretion disks. Disks in which these conditions do not hold should feature radial outflow near the midplane, as long as their internal stress is provided by the shear viscosity. Our results can also be used for designing hydrodynamical disk simulations with a prescribed pattern of the meridional circulation.

Authors:
 [1];  [2]
  1. Department of Astrophysical Sciences, Princeton University, Ivy Lane, Princeton, NJ 08540 (United States)
  2. Institute for Advanced Study, Einstein Drive, Princeton, NJ 08540 (United States)
Publication Date:
OSTI Identifier:
22661298
Resource Type:
Journal Article
Resource Relation:
Journal Name: Astrophysical Journal; Journal Volume: 837; Journal Issue: 2; Other Information: Country of input: International Atomic Energy Agency (IAEA)
Country of Publication:
United States
Language:
English
Subject:
79 ASTROPHYSICS, COSMOLOGY AND ASTRONOMY; ACCRETION DISKS; ALTITUDE; ASTROPHYSICS; COMETS; DUSTS; ENTROPY; GAIN; HYDRODYNAMICS; PROTOPLANETS; REFRACTORIES; RESIDUAL STRESSES; SIMULATION; STRATIFICATION; THERMODYNAMICS; THREE-DIMENSIONAL CALCULATIONS; VISCOSITY

Citation Formats

Philippov, Alexander A., and Rafikov, Roman R., E-mail: sashaph@princeton.edu. Radial Transport and Meridional Circulation in Accretion Disks. United States: N. p., 2017. Web. doi:10.3847/1538-4357/AA60CA.
Philippov, Alexander A., & Rafikov, Roman R., E-mail: sashaph@princeton.edu. Radial Transport and Meridional Circulation in Accretion Disks. United States. doi:10.3847/1538-4357/AA60CA.
Philippov, Alexander A., and Rafikov, Roman R., E-mail: sashaph@princeton.edu. Fri . "Radial Transport and Meridional Circulation in Accretion Disks". United States. doi:10.3847/1538-4357/AA60CA.
@article{osti_22661298,
title = {Radial Transport and Meridional Circulation in Accretion Disks},
author = {Philippov, Alexander A. and Rafikov, Roman R., E-mail: sashaph@princeton.edu},
abstractNote = {Radial transport of particles, elements and fluid driven by internal stresses in three-dimensional (3D) astrophysical accretion disks is an important phenomenon, potentially relevant for the outward dust transport in protoplanetary disks, origin of the refractory particles in comets, isotopic equilibration in the Earth–Moon system, etc. To gain better insight into these processes, we explore the dependence of meridional circulation in 3D disks with shear viscosity on their thermal stratification, and demonstrate a strong effect of the latter on the radial flow. Previous locally isothermal studies have normally found a pattern of the radial outflow near the midplane, switching to inflow higher up. Here we show, both analytically and numerically, that a flow that is inward at all altitudes is possible in disks with entropy and temperature steeply increasing with height. Such thermodynamic conditions may be typical in the optically thin, viscously heated accretion disks. Disks in which these conditions do not hold should feature radial outflow near the midplane, as long as their internal stress is provided by the shear viscosity. Our results can also be used for designing hydrodynamical disk simulations with a prescribed pattern of the meridional circulation.},
doi = {10.3847/1538-4357/AA60CA},
journal = {Astrophysical Journal},
number = 2,
volume = 837,
place = {United States},
year = {Fri Mar 10 00:00:00 EST 2017},
month = {Fri Mar 10 00:00:00 EST 2017}
}
  • Large-scale magnetic fields are key ingredients of magnetically driven disk accretion. We study how large-scale poloidal fields evolve in accretion disks, with the primary aim of quantifying the viability of magnetic accretion mechanisms in protoplanetary disks. We employ a kinematic mean-field model for poloidal field transport and focus on steady states where inward advection of a field balances with outward diffusion due to effective resistivities. We analytically derive the steady-state radial distribution of poloidal fields in highly conducting accretion disks. The analytic solution reveals an upper limit on the strength of large-scale vertical fields attainable in steady states. Any excessmore » poloidal field will diffuse away within a finite time, and we demonstrate this with time-dependent numerical calculations of the mean-field equations. We apply this upper limit to large-scale vertical fields threading protoplanetary disks. We find that the maximum attainable strength is about 0.1 G at 1 AU, and about 1 mG at 10 AU from the central star. When combined with recent magnetic accretion models, the maximum field strength translates into the maximum steady-state accretion rate of ∼10{sup –7} M {sub ☉} yr{sup –1}, in agreement with observations. We also find that the maximum field strength is ∼1 kG at the surface of the central star provided that the disk extends down to the stellar surface. This implies that any excess stellar poloidal field of strength ≳ kG can be transported to the surrounding disk. This might in part resolve the magnetic flux problem in star formation.« less
  • We study the time evolution of a large-scale magnetic flux threading an accretion disk. The induction equation of the mean poloidal field is solved under the standard viscous disk model. Magnetic flux evolution is controlled by two timescales: one is the timescale of the inward advection of the magnetic flux, τ{sub adv}. This is induced by the dragging of the flux by the accreting gas. The other is the outward diffusion timescale of the magnetic flux τ{sub dif}. We consider diffusion due to the Ohmic resistivity. These timescales can be significantly different from the disk viscous timescale τ{sub disk}. Themore » behaviors of the magnetic flux evolution are quite different depending on the magnitude relationship of the timescales τ{sub adv}, τ{sub dif}, and τ{sub disk}. The most interesting phenomena occur when τ{sub adv} << τ{sub dif}, τ{sub disk}. In such a case, the magnetic flux distribution approaches a quasi-steady profile much faster than the viscous evolution of the gas disk, and the magnetic flux has also been tightly bundled to the inner part of the disk. In the inner part, although the poloidal magnetic field becomes much stronger than the interstellar magnetic field, the field strength is limited to the maximum value that is analytically given by our previous work. We also find a condition for the initial large magnetic flux, which is a fossil of the magnetic field dragging during the early phase of star formation that survives for a duration in which significant gas disk evolution proceeds.« less
  • The meridional energy flux modelled by the Bureau of Meteorology Research Centre general circulation model is examined. It is divided into atmospheric and oceanic components, and the resolved atmospheric and oceanic components, and the resolved atmospheric components in turn into mean and eddy circulations. Comparison with observations shows the modelled total planetary meridional energy transport to below, but shows better agreement for the resolved atmospheric component alone. The overall patterns of the individual circulation and energy components of the model also agree well, although strengths and locations do show some discrepancies. The doubled CO{sub 2} climate change is analyzed inmore » terms of the changes in each of the circulation and energy components. It is found that the changes are the relatively small residual of larger, and generally opposing changes in sensible heat and potential energy fluxes. Despite the general decrease in poleward energy flux, the poleward latent heat flux is found to increase. The reduction in poleward transport is found to be dominated by changes in the mean meridional circulation at low southern latitudes, and changes in both mean circulations and eddy fluxes elsewhere. 37 refs., 11 figs.« less
  • The observed Li abundances in giants are used here to constrain meridional circulation transport on the main sequence. It is shown how meridional circulation, operating over the main-sequence lifetime, can lead to Li depletion in the upper radiative envelope and eventually to extreme Li underabundance in first-ascent giants, following convective dilution on the lower giant branch. In the mass range 1.2-2.0 solar, stars with equatorial rotational velocities greater than 30-35 km/s on the ZAMS should destroy most of their Li. These result are compared to recent Li abundance determination in three moderately old clusters, NGC 7789, NGC 752, and M67.more » Reasonably good agreement is found with data on M67 and NGC 752, but surprising disagreement with data on NGC 7789 is found. Possible explanations are considered. 60 refs.« less