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4.3 Timing stability

Ideally, after correctly applying a timing model, we would expect a set of uncorrelated timing residuals with a zero mean and a Gaussian scatter with a standard deviation consistent with the measurement uncertainties. As can be seen in Figure 23View Image, this is not always the case; the residuals of many pulsars exhibit a quasi-periodic wandering with time.
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Figure 23: Examples of timing residuals for a number of normal pulsars. Note the varying scale on the ordinate axis, the pulsars being ranked in increasing order of timing “activity”. Data taken from the Jodrell Bank timing program [281, 124]. Figure provided by Andrew Lyne.
Such “timing noise” is most prominent in the youngest of the normal pulsars [21372] and present at a lower level in the much older millisecond pulsars [155Jump To The Next Citation Point11]. While the physical processes of this phenomenon are not well understood, it seems likely that it may be connected to superfluid processes and temperature changes in the interior of the neutron star [3], or to processes in the magnetosphere [6665].

The relative dearth of timing noise for the older pulsars is a very important finding. It implies that, presently, the measurement precision depends primarily on the particular hardware constraints of the observing system. Consequently, a large effort in hardware development is presently being made to improve the precision of these observations using, in particular, coherent dedispersion outlined in Section 4.1. Much progress in this area has been made by groups at Princeton [258Jump To The Next Citation Point], Berkeley [325Jump To The Next Citation Point], Jodrell Bank [326], UBC [323Jump To The Next Citation Point], Swinburne [305] and ATNF [12]. From high quality observations spanning over a decade [274275155Jump To The Next Citation Point], these groups have demonstrated that the timing stability of millisecond pulsars over such time-scales is comparable to terrestrial atomic clocks.

This phenomenal stability is demonstrated in Figure 24View Image which shows s z [214Jump To The Next Citation Point], a parameter closely resembling the Allan variance used by the clock community to estimate the stability of atomic clocks [308Jump To The Next Citation Point1]. Both PSRs B1937+21 and B1855+09 seem to be limited by a power law component which produces a minimum in sz after 2 yr and 5 yr respectively. This is most likely a result of a small amount of intrinsic timing noise [155Jump To The Next Citation Point]. Although the baseline for the bright millisecond pulsar J0437-4715 is shorter, its s z is already an order of magnitude smaller than the other two pulsars or the atomic clocks. Timing observations of an array of millisecond pulsars in the context of detecting gravitational waves from the Big Bang are discussed further in Section 4.5.3.

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Figure 24: The fractional stability of three millisecond pulsars compared to an atomic clock. Both PSRs B1855+09 and B1937+21 are comparable, or just slightly worse than, the atomic clock behaviour over timescales of a few years [214]. More recent timing of the millisecond pulsar J0437-4715 [126] indicates that it is more stable than the atomic clock.

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