Water Masers in NGC 4258: Saturation and GR

NGC 4258 is well known for its 22 GHz water maser features that appear to reside in a thin Keplerian disk orbiting at R_0=0.13 pc. The influence of gravitational redshift on the level of saturation and the line shape and strength of water maser emission is studied. It is found, for a Schwarzschild metric, that a time-dependent and asymmetric absorption dip occurs in the systemic emission for an absorbing ring at 2R_0. This absorption is shifted by about +4 km/s with respect to NGC 4258's systemic LSR velocity. Red-shifted systemic maser emission covers a larger range of velocities. Saturation, through the Sobolev length, is enhanced/suppressed for systemic blue-shifted/red-shifted maser features by gravitational redshift of line photons. The asymmetry results from the fact that gravitational redshift is a scalar and gas motion a vector. The effective velocity shift amounts to about twice the thermal velocity width of H2O molecules at 500 K for a masing ring of thickness 0.2R_0. Consequently, approaching systemic features are brighter and wider (~2 km/s) than their receding counterparts (~1 km/s). The brightness of high-velocity emission is impacted by changes in saturation through beam-crossing and is typically weaker than systemic. The need for supersonic turbulence is alleviated by the above effects and nearly subsonic turbulence is favored. The effects are consistent with observations. For black hole masses lower/higher than $4\times 10^7M_\odot$, these effects are negligible/strong