Open AccessTime‐dependent quasi‐spherical accretion
Author(s) -
Ogilvie G. I.
Publication year - 1999
Publication title -
monthly notices of the royal astronomical society
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 2.058
H-Index - 383
eISSN - 1365-2966
pISSN - 0035-8711
DOI - 10.1046/j.1365-8711.1999.02637.x
Subject(s) - physics , accretion (finance) , angular momentum , adiabatic process , advection , attractor , classical mechanics , magnetohydrodynamics , dissipation , flow (mathematics) , mechanics , astrophysics , magnetic field , thermodynamics , mathematical analysis , mathematics , quantum mechanics
Differentially rotating, ‘advection‐dominated’ accretion flows are considered in which the heat generated by viscous dissipation is retained in the fluid. The equations of time‐dependent quasi‐spherical accretion are solved in a simplified one‐dimensional model that neglects the latitudinal dependence of the flow. A self‐similar solution is presented that has finite size, mass, angular momentum and energy. This may be expected to be an attractor for the initial‐value problem in which a cool and narrow ring of fluid orbiting around a central mass heats up, spreads radially and is accreted. The solution provides some insight into the dynamics of quasi‐spherical accretion and avoids many of the strictures of the steady self‐similar solution of Narayan & Yi. Special attention is given to the astrophysically important case in which the adiabatic exponent γ =5/3; even in this case, the flow is found to be differentially rotating and bound to the central object, and accretion can occur without the need for powerful outflows.