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Generalized Similarity for Accretion/Decretion Disks

Decretion (or external) disks are gas disks freely expanding to large radii due to their internal stresses. They are expected to naturally arise in tidal disruption events, around Be stars, in mass-losing post main sequence binaries, as a result of supernova fallback, etc. Their evolution is theoretically understood in two regimes: when the central object does not exert torque on the disk (a standard assumption for conventional accretion disks) or when no mass inflow (or outflow) occurs at the disk center. However, many astrophysical objects - circumbinary disks, Be stars, neutron stars accreting in a propeller regime, etc. - feature non-zero torque simultaneously with the non-zero accretion (or ejection of mass) at the disk center. We provide a general description for the evolution of such disks (both linear and non-linear) in the self-similar regime, to which the disk should asymptotically converge with time. We identify a similarity parameter $λ$, which is uniquely related to the degree, to which the central mass accretion is suppressed by the non-zero central torque. The known decretion disk solutions correspond to the two discrete values of $λ$, while our new solutions cover a continuum of its physically allowed values, corresponding to either accretion or mass ejection by the central object. A direct relationship between $λ$ and central $\dot M$ and torque is also established. We describe the time evolution of the various disk characteristics for different $λ$, and show that the observable properties (spectrum and luminosity evolution) of the decretion disks are in general different from the standard accretion disks with no central torque.