Determining velocity gradients from differential Doppler shifts

The problem of spectral line formation in a moving stellar atmosphere is studied. An analytical solution to the transfer equation which is valid when the velocity gradient is large is presented. This solution is then used to show that the difference between the Doppler shifts sometimes observed in lines of different strengths depends on the ionization balance in the atmosphere as well as on the velocity gradient. The results of this paper can be used to explain the anomalously large velocity gradients inferred from the observations of Balmer lines in early-type stars.