PLANAR H2O MASERS IN STAR-FORMING REGIONS

The planar geometry of shocked material is the key property in enabling the high brightness temperatures of H2O masers in star-forming regions. We solve for the brightness temperature, the beaming angle, and the maser spot size for thin, saturated planar masers under the assumption that the velocity change across the maser due to ordered motions is small compared with the thermal or microturbulent line width. For a given set of physical parameters, the brightness temperature is essentially fully determined by the length of the velocity-coherent region in the shocked plane along the line of sight. The geometry in the transverse direction in the plane is largely irrelevant; a saturated planar maser can generally be modeled as a disk, and a disk maser observed in the plane appears as bright as an equivalent filamentary maser whose length equals the disk diameter. Of the two independent dimensions perpendicular to the filament axis, one is equal to the disk thickness and the other is somewhat smaller than the size of the disk's unsaturated core. In astrophysical shocks, we show that the last two dimensions are approximately equal, so that the equivalent filament is roughly cylindrical. The ratio of the equivalent filament length to its width, or the effective aspect ratio, is determined by the disk diameter ard the pumping scheme. We find effective aspect ratios (approximately 5-50) that are in agreement with values previously inferred from observed brightness temperatures.