  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 maser saturation and the line strength
and width of systemic water maser emission is studied. The effective
gravitational velocity shift along the gain path through the disk amounts to
about twice the thermal velocity width of H2O molecules at 500 K for a masing
ring of thickness 0.2R_0. This GR induced frequency shift has a sign opposite
to the shift caused by the projected velocity difference vector of Keplerian
motion on the blue side of the systemic maser emission and has the same sign on
the red systemic side. Consequently, the negative optical depth that a line
photon sees as it traverses the masing disk along a path of minimal Keplerian
velocity gradient is larger on the blue side. Note that one is not concerned
here with an overall shift in the maser spectrum caused by the fact that the
masing ring as a whole is located in the black hole's potential well, i.e., it
is the change in the gravitational potential along the gain path that matters.
It is found, for a Schwarzschild metric, that saturation is enhanced
(suppressed) for systemic blue-shifted (red-shifted) maser features by
gravitational redshift of line photons. Approaching peak flux systemic features
are, on average, brighter, due to saturation, and wider (~2 km/s), due to
rebroadening, than their receding counterparts (~1 km/s). The effects are
consistent with observations that span several years, i.e., over periods longer
than needed for disk material to move through the systemic emission region.
Further confirmation of this effect can follow by combining all available
systemic 22 GHz data over the past two decades (abridged).
