Exact time-dependent solutions for the thin accretion disc equation: boundary conditions at finite radius

摘要: We discuss Green's function solutions of the equation for a geometrically thin, axisymmetric Keplerian accretion disc with viscosity prescription ν ∝ R n . The mathematical problem was solved by Lynden-Bell & Pringle special cases boundary conditions zero-viscous torque and zero mass flow at centre. While it has been widely established that observational appearance astrophysical discs depends on physical size central object(s), exact time-dependent imposed finite radius have not published general value power-law index n. derive satisfy either zero-torque or zero-flux condition non-zero inner in > 0, an arbitrary initial surface density profile. Whereas viscously dissipated power diverges centre previously known = new 0 expressions luminosity agree, limit t → ∞, standard steady-state luminosities. are applicable to evolution innermost regions thin discs.