Position-Velocity Diagrams for the Maser Emission coming from a Keplerian Ring

We have studied the maser emission from a thin, planar, gaseous ring in Keplerian rotation around a central mass observed edge-on. The absorption coefficient within the ring is assumed to follow a power law dependence with the distance from the central mass as, k=k0r^{-q}. We have calculated position-velocity diagrams for the most intense maser features, for different values of the exponent q. We have found that, depending on the value of q, these diagrams can be qualitatively different. The most intense maser emission at a given velocity can either come mainly from regions close to the inner or outer edges of the amplifying ring or from the line perpendicular to the line of sight and passing through the central mass (as is commonly assumed). Particularly, when q>1 the position-velocity diagram is qualitatively similar to the one observed for the water maser emission in the nucleus of the galaxy NGC 4258. In the context of this simple model, we conclude that in this object the absorption coefficient depends on the radius of the amplifying ring as a decreasing function, in order to have significant emission coming from the inner edge of the ring.