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 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 T γ , 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.

A NICER View of PSR J0030+0451: Evidence for a Global-scale Multipolar Magnetic Field

“…The above estimate is for an offset dipole; if quadrupole or higher multipole components dominate the spin-down luminosity, as could be the case for PSR J0030+0451, then the expression for the kick velocity would change. It must be noted that measuring the 3D velocity of a pulsar is difficult because the radial component of the velocity is hard to disentangle from the intrinsic second time derivative of pulsar period P (see the extensive discussion in Liu et al 2018Liu et al , 2019. Even for such a well-timed pulsar as PSR J0030+0451, the radial velocity is at present unknown.…”

Results of 12 Years of Pulsar Timing at Nanshan -- I

“…Also, for a given pulsar, different sections of the data span can have different values of ν, often changing from positive to negative values. Liu et al (2019) investigated the detectability of ν in the presence of red noise for a sample of millisecond pulsars. Using simulations, it was found that a non-zero ν could be recovered when data spans are sufficiently long.…”

A study of dynamical effects in the observed second time-derivative of the spin or orbital frequencies of pulsars

“…We end up with 158 pulsars satisfying these conditions. We take a nominal v rad = 50 km/s, like Liu et al (2019), for the pulsars except for J1024−0719 and JJ1903+0327 whose v rad is known to be 185(4) km/s and 42.1(25) km/s respectively (Liu et al 2018). We get that n varies from −4.2 × 10 7 to 7.7 × 10 7 .…”