Correlated timing noise and high-precision pulsar timing: measuring frequency second derivatives as an example
Abstract
We investigate the impact of noise processes on high-precision pulsar timing. Our analysis focuses on the measurability of the second spin frequency derivative \ddot{ν }. This \ddot{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 \ddot{ν } values, we find that we are able to recover the injected \ddot{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 \ddot{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 \ddot{ν } probability density functions for 49 millisecond pulsars. We find a statistically significant \ddot{ν } value for PSR B1937+21 and consider possible options for its origin. Significant (95 per cent C.L.) values for \ddot{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, such as 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.
- Publication:
-
Monthly Notices of the Royal Astronomical Society
- Pub Date:
- September 2019
- DOI:
- 10.1093/mnras/stz1801
- arXiv:
- arXiv:1907.03183
- Bibcode:
- 2019MNRAS.488.2190L
- Keywords:
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- methods: data analysis;
- pulsars: general;
- pulsars: individual: PSR B1821-24A;
- PSR J1909-3744;
- PSR B1937+21;
- Astrophysics - High Energy Astrophysical Phenomena
- E-Print:
- 12 pages, 5 figures