Statistical Analysis of Water Masers in Star-Forming Regions: Cepheus A and W75 N

We have done a statistical analysis of Very Long Baseline Array (VLBA) data of water masers in the star-forming regions (SFRs) Cepheus A and W75 N, using correlation functions to study the spatial clustering and Doppler-velocity distribution of these masers. Two-point spatial correlation functions show a characteristic scale size for clusters of water maser spots < or ~1 AU, similar to the values found in other SFRs. This suggests that the scale for water maser excitation tends to be < or ~1 AU. Velocity correlation functions show power-law dependences with indices that can be explained by regular velocity fields, such as expansion and/or rotation. These velocity fields are similar to those indicated by the water maser proper-motion measurements; therefore, the velocity correlation functions appear to reveal the organized motion of water maser spots on scales larger than 1 AU.