Pulsar timing ($t_n^{\mathrm{arr}}=t_n^{\mathrm{model}}+r_n$)

The mature experiment uses channel-template comparison, pulsar dedispersion, GPS clock-offset transfer, Solar system barycenter corrections and connected pulse counts.^[ref]

For a geometric illustration, let a perfectly uniform source emit pulse $n$ at $t_n=t_0+n{P}_s$, with spin period $P_s$, and let $z_1$ increase away from the observer. At leading order in orbital velocity divided by the speed of light, an extra path length $z_1$ adds ${\Delta }_R=z_1/c$. Consecutive arrivals then obeyA receding source has $v_{\parallel }>0$ and a longer apparent period. This derivation isolates the geometric Doppler effect; a precision relativistic clock model also needs gravitational redshift and time dilation.

The difference between an observed arrival time and its model prediction. Positive pulsar timing residuals mean late arrivals in this convention. A periodic residual can expose an omitted orbit; a smooth long-term residual can also come from a wrong spin model or clock correction. Fitting and checking alternative causes are part of the inference, rather than interpreting every residual as gravitational radiation.

The binary-pulsar Einstein delay is the periodic clock-rate contribution to pulse arrival times from a pulsar moving in an eccentric binary. Near closest approach, the pulsar's orbital speed is larger and the companion's gravitational potential is deeper. Time dilation and gravitational redshift therefore make its clock run at a different rate relative to a distant time coordinate.

At leading order the variable timing term is ${\Delta }_E=\gamma \sin E$, with eccentric anomaly $E$ and time amplitude $\gamma$. Constant clock-rate offsets are absorbed into the fitted pulsar spin. This term is distinct from the geometric binary-pulsar Roemer delay and the propagation Shapiro time delay. Fitting it with other orbital observables constrains the component masses and tests general relativity.^[ref]