Hyperstrong radio-wave scattering in the galactic center. II. A likelihood analysis of free electrons in the galactic center

The scattering diameters of Sgr A* and several nearby OH masers (approximate to 1 " at 1 GHz) indicate that a region of enhanced scattering is along the line of sight to the Galactic center. We combine radio-wave scattering data and free-free emission and absorption measurements in a likelihood analysis that constrains the following parameters of the GC scattering region: The GC-scattering region separation, A,,; the angular extent of the region, psi(l), and psi(b); the outer scale on which density fluctuations occur, l(o); and the gas temperature, T-e. The maximum likelihood estimates of these parameters are Delta(GC) = 133+(+200)(-80) pc, 0.degrees 5 less than or equal to psi(l) less than or similar to 1 degrees, and (l(o)/1 pc)T-2/3(e)-1/2 = 10(-7+/-0.8). The parameter psi(b) was not well constrained, and we adopt psi(b) = 0.degrees 5. The close correspondence between Delta(GC) and psi(l)D(GC) suggests that the scattering region encloses the GC. As host media for the scattering, we consider the photoionized surface layers of molecular clouds and the interfaces between molecular clouds and the 10(7) K ambient gas. We are unable to make an unambiguous determination, but we favor the interface model in which the scattering medium is hot (T-e similar to 10(6) K) and dense (n(e) similar to 10 cm(-3)). The GC scattering region produces a 1 GHz scattering diameter for an extragalactic source of 90 ", if the region is a single screen, or 180 ", if the region wraps around the GC, as appears probable. We modify the Taylor-Cordes model for the Galactic distribution of free electrons in order to include an explicit GC component. We predict that pulsars seen through this region will have a dispersion measure of approximately 2000 pc cm(-3), of which approximately 1500 pc cm(-3) arises from the GC component itself. We stress the uniqueness of the GC scattering region, probably resulting from the high-pressure environment in the GC.