How to understand the Einstein Delay?

Question

In pulsar timing, one of the post-Keplerian parameters is the Einstein delay $Delta E$. The total `flight time' of a photon emitted from a pulsar is then given by
$$ Delta t = Delta R + Delta E + Delta S$$
where $Delta R$ and $Delta S$ are the Roemer and Shapiro Delays.
The Einstein delay is apparently due to both Doppler shift and gravitational time delay.
I understand the gravitational time delay part, but cannot see how the motion of the pulsar and consequent Doppler shift would affect the total photon flight time?
Thanks

JMLCarter · Answer

It's just the special relativisitic part of the time dilation.
In special relativity an observer sees a time dilation effect on objects moving relative to them near the speed of light.
In General relativity there is also time dilation due to gravitational effects.

Only Time Dilation due to relative velocity is accounted for by Special Relativity. Gravitational Time Dilation is another effect. Both effects are included in the formulation of General Relativity.

The separation of the effects into aproximately addative terms is possible when $largefrac{GM}{R c^2}≪1$. However in your scenario this may not be the case, which remains a point of confusion.

Doppler shift, as you point out, impacts frequency and not velocity.

How to understand the Einstein Delay?

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