Maser Flares Driven by Isothermal Shock Waves

We use 3D computer modelling to investigate the timescales and radiative output from maser flares generated by the impact of shock-waves on astronomical unit-scale clouds in interstellar and star-forming regions, and in circumstellar regions in some circumstances. Physical conditions are derived from simple models of isothermal hydrodynamic (single-fluid) and C-type (ionic and neutral fluid) shock-waves, and based on the ortho-H$_2$O 22-GHz transition. Maser saturation is comprehensively included, and we find that the most saturated maser inversions are found predominantly in the shocked material. We study the effect on the intensity, flux density and duration of flares of the following parameters: the pre-shock level of saturation, the observer's viewpoint, and the shock speed. Our models are able to reproduce observed flare rise times of a few times 10 days, specific intensities of up to 10$^5$ times the saturation intensity and flux densities of order $100(R/d)^2$Jy from a source of radius $R$ astronomical units at a distance of $d$ kiloparsec. We found that flares from C-type shocks are approximately 5 times more likely to be seen by a randomly placed observer than flares from hydrodynamically shocked clouds of similar dimensions. We computed intrinsic beaming patterns of the maser emission, finding substantial extension of the pattern parallel to the shock front in the hydrodynamic models. Beaming solid angles for hydrodynamic models can be as small as $1.3\times 10^{-5}$sr, but are an order of magnitude larger for C-type models.