M.Sc Student | Gitelman Larissa |
---|---|

Subject | Meridional Flow and Vertical Structure of Accretion Disks |

Department | Department of Applied Mathematics |

Supervisor | Professor Emeritus Oded Regev |

We present numerical solutions of the meridional flow in axisymmetric thin viscous accretion disk models. The solutions are obtained by simplifying and approximating first the equations, using systematic asymptotic expansions in the small parameter e measuring the relative disk thickness. The equation of state was assumed to be of an ideal gas and the thermal problem was solved using the radiation diffusion approximation.

Hence, the vertical structure is solved with thermal effects explicitly included via an energy equation, containing viscous dissipation and radiative losses (treated in the diffusion approximation). The inclusion of the energy equation will force us to use some quite straightforward numerical ODE integrations.

Carrying out the expansion to second order in e we obtain, for low enough values of the viscosity parameter a solutions containing backflows.

For all values a
< a_{stag } of the
viscosity parameter, we find significant backflow in the midplane of the disk
occuring at all radii larger than a certain value; however, in the inner
regions of the disk the fluid always flows toward the accreting object. The
region of backflow is separated from the region of inflow by a surface
flaring outwards from a circular locus of stagnation points situated in the midplane
of the disk.

The value we find is a_{stag }@ 0.7 and the reason for its being only an approximation is
the fact that in a numerical calculation like ours the truncation error
renders the result unreliable for large r , specifically
for r_{stag} @ 10^{3} r_{+
.}

These results are similar to theapproximate results previously found by Urpin (1984)(which however contained an inconsistency and were valid only for large radii) and the asymptotic analytical solutions of Kluzniak and Kita (1997) (valid only for polytropic disks). Several two-dimensional time dependent numerical simulations of thin viscous disks have also reavealed flow patterns of this type.

The existence of backflows may have important consequences on the properties of accretion disks in astrophysical objects.