Colloquium: Comparison of astrophysical and terrestrial frequency standards

The stability of pulse arrival times from pulsars and white dwarfs have been reanalyzed using several analysis tools for measuring the noise characteristics of sampled time and frequency data. The best terrestrial artificial clocks are shown to substantially exceed the performance of astronomical sources as timekeepers in terms of accuracy (as defined by cesium primary frequency standards) and stability. This superiority in stability can be directly demonstrated over time periods up to 2 years, where there is high quality data for both. Beyond 2 years there is a deficiency of data for clock-to-clock comparisons, and both terrestrial and astronomical clocks show equal performance being equally limited by the quality of the reference time scales used to make the comparisons. Nonetheless, the detailed accuracy evaluations of modern terrestrial clocks imply that these new clocks are likely to have a stability better than any astronomical source up to comparison times of at least hundreds of years. This article is intended to provide a correct appreciation of the relative merits of natural and artificial clocks. The use of natural clocks as tests of physics under the most extreme conditions is entirely appropriate; however, the contention that these natural clocks, particularly white dwarfs, can compete as timekeepers against devices constructed by mankind is shown to be doubtful.

Figure 1

Derived frequency stability for a range of different frequency sources including astrophysical sources, commercial oscillators, and the best laboratory clocks. See text for a complete description. For clarity, errors have been included only on the most relevant data to the discussion. The solid line arrow indicates the upper limit of the long-term atomic clock stability due to the known accuracy of one of the optical ion clocks at $2.3\times {10}^{-17}$. The dashed line arrow shows the long-term trend for the best millisecond pulsar.

Figure 2

Derived frequency stability for some of the frequency sources of Fig. 1 for comparison over the longest time scales. Included are the pulsar PSR J0437-4715, a commercial cesium oscillator Cs 5071, and some of the best laboratory clocks. The TAI-AT1 time scale comparison data and the pulsar-to-clock comparison data are represented with both the ${\sigma }_y$ and ${\sigma }_z$ statistics.