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Black hole accretion disks with outflows II. Time dependent Green's function solutions in Newtonian gravity

We present Green's function solutions of the Newtonian time-dependent thin disk equations in the presence of outflows, showing that simple and exact analytical expressions exist in various natural limits of the problem. These Green's functions are mathematically very similar to the classical Lynden-Bell & Pringle solutions in the absence of outflows, but differ strongly in their precise physical details and observational implications. Solutions are presented for phenomenological radius-dependent outflows which both do and do not torque the local accretion flow, and for outflows which are launched proportional to the local accretion rate. Generically, outflows lead to a more rapid decay of the bolometric luminosity of the disk, flatten the radial dependence of the disk temperature, and suppress variability in the accretion rate at small radii and low frequencies (on long timescales). Observational implications of these four results are discussed in detail.