High precision pulsar timing and spin frequency second derivatives

Understand

We investigate the impact of intrinsic, kinematic and gravitational effects on high precision pulsar timing.

• We present an analytical derivation and a numerical computation of the impact of these effects on the first and second derivative of the pulsar spin frequency.
• In addition, in the presence of white noise, we derive an expression to determine the expected measurement uncertainty of a second derivative of the spin frequency for a given timing precision, observing cadence and timing baseline and find that it strongly depends on the latter ($\propto t^{-7/2}$).
• We show that for pulsars with significant proper motion, the spin frequency second derivative is dominated by a term dependent on the radial velocity of the pulsar.