Correlated timing noise and high precision pulsar timing: Measuring frequency second derivatives as an example

Research output: Contribution to journalArticle

  • Authors:
  • X J Liu
  • M J Keith
  • C G Bassa
  • B W Stappers


We investigate the impact of noise processes on high-precision pulsar timing. Our analysis focuses on the measurability of the second spin frequency derivative ν¨⁠. This ν¨ can be induced by several factors including the radial velocity of a pulsar. We use Bayesian methods to model the pulsar times-of-arrival in the presence of red timing noise and dispersion measure variations, modelling the noise processes as power laws. Using simulated times-of-arrival that both include red noise, dispersion measure variations and non-zero ν¨ values, we find that we are able to recover the injected ν¨⁠, even when the noise model used to inject and recover the input parameters are different. Using simulations, we show that the measurement uncertainty on ν¨ decreases with the timing baseline T as Tγ, where γ = −7/2 + α/2 for power law noise models with shallow power law indices α (0 < α < 4). For steep power law indices (α > 8), the measurement uncertainty reduces with T−1/2. We applied this method to times-of-arrival from the European Pulsar Timing Array and the Parkes Pulsar Timing Array and determined ν¨ probability density functions for 49 millisecond pulsars. We find a statistically significant ν¨ value for PSR B1937+21 and consider possible options for its origin. Significant (95 per cent C.L.) values for ν¨ are also measured for PSRs J0621+1002 and J1022+1001, thus future studies should consider including it in their ephemerides. For binary pulsars with small orbital eccentricities, like PSR J1909−3744, extended ELL1 models should be used to overcome computational issues. The impacts of our results on the detection of gravitational waves are also discussed.

Bibliographical metadata

Original languageEnglish
JournalMonthly Notices of the Royal Astronomical Society
Early online date2 Jul 2019
Publication statusPublished - 2019