Timing stability

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 23

, this is not always the case; the residuals of many pulsars exhibit a quasi-periodic wandering with time.

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 [328 , 150 ]. Figure provided by Andrew Lyne.

Such “timing noise” is most prominent in the youngest of the normal pulsars [256 , 87 ] and present at a lower level in the much older millisecond pulsars [188 , 12 ]. While the physical processes of this phenomenon are not well understood, it seems likely that they may be connected to superfluid processes and temperature changes in the interior of the neutron star [5 ], or to processes in the magnetosphere [78 , 77 ].

The relative dearth of timing noise for the older pulsars is a very important finding. It implies that the measurement precision presently depends primarily on the particular hardware constraints of the observing system. Consequently, a large effort in hardware development is now 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 [296 ], Berkeley [34 ], Jodrell Bank [164 ], UBC [156 ], Swinburne [66 ] and ATNF [14 ]. From high quality observations spanning over a decade [320 , 321 , 188 ], these groups have demonstrated that the timing stability of millisecond pulsars over such timescales is comparable to terrestrial atomic clocks.

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 [257

]. More recent timing of the millisecond pulsar J0437–4715 [389

] indicates that it is inherently a very stable clock. Data for the latter pulsar provided by Joris Verbiest.

This phenomenal stability is demonstrated in Figure 24 which shows $σz$ [257 , 330 ], a parameter closely resembling the Allan variance used by the clock community to estimate the stability of atomic clocks [355 , 3 ]. Both PSRs B1937+21 and B1855+09 seem to be limited by a power law component which produces a minimum in $σz$ after 2 yr and 5 yr respectively. This is most likely a result of a small amount of intrinsic timing noise [188 ]. The $σz$ based on timing observations [389 ] of the bright millisecond pulsar J0437–4715 is now 1 – 2 orders of magnitude smaller than the other two pulsars or the atomic clock!