4.4 Timing Stability 

Ideally, after correctly applying a timing model, we would expect a set of uncorrelated timing residuals scattered in a Gaussian fashion about a zero mean with an rms consistent with the measurement uncertainties. This is not always the case; the residuals of many pulsars exhibit a quasi-periodic wandering with time.

  

Figure 14: 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'' (Figure provided by Andrew Lyne).

A number of examples are shown in Fig.  14 . These are taken from the Jodrell Bank timing program [141, 114]. Such ``timing noise'' is most prominent in the youngest of the normal pulsars [112, 49] and virtually absent in the much older millisecond pulsars [87]. Whilst the physical processes of this phenomena are not well understood, it seems likely that this phenomenon may be connected to superfluid processes in the interior of the neutron star and its temperature [15] or processes in the magnetosphere [44, 43].

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 de-dispersion outlined in § 4.1 . Much of the pioneering work in this area has been made by Joseph Taylor and collaborators at Princeton University [4]. From high quality observations made using the Arecibo radio telescope spanning almost a decade [134, 135, 87], the group has demonstrated that the timing stability of millisecond pulsars over such time-scales is comparable to terrestrial atomic clocks.

  

Figure 15: Fractional instabilities for PSRs B1855+09 and B1937+21 expressed as the modified Allan variance as a function of time. (After Kaspi, Taylor & Ryba 1994 [87]).

This phenomenal stability is demonstrated in Fig.  15 . This figure shows , a parameter closely resembling the Allan variance used by the clock community to estimate the stability of atomic clocks [148]. Atomic clocks are known to have on time-scales of order 5 years. The timing stability of PSR B1937+21 seems to be limited by a power law component which produces a minimum in its after yr. This is most likely a result of a small amount of intrinsic timing noise [87]. No such noise component is presently seen in the Allan variance of PSR B1855+09. This demonstrates that the timing stability for PSR B1855+09 becomes competitive with the atomic clocks after about 3 yr. The absence of timing noise for B1855+09 is probably related to its characteristic age Gyr which is about a factor of 20 larger than B1937+21.

Recently, a number of millisecond pulsars have been discovered in the all-sky surveys discussed in § 3.1 . These include PSRs J0437-4715 [81] and J1713+0747 [63] -- two bright millisecond pulsars with small duty cycles which allow very high precision measurements (equation 7). Early indications are that their timing stability will be at least as good as B1855+09 [62, 136].

Binary and Millisecond Pulsars D. R. Lorimer (dunc@mpifr-bonn.mpg.de) http://www.livingreviews.org/lrr-1998-10 © Max-Planck-Gesellschaft. ISSN 1433-8351 Problems/Comments to livrev@aei-potsdam.mpg.de