Application of Millisecond Pulsar Timing to the Long-Term Stability of Clock Ensembles

In 1995, Demetrios N. Matsakis and Roger S. Foster examined whether millisecond pulsars could provide an independent astronomical reference for evaluating the long-term stability of terrestrial atomic-clock ensembles.

Millisecond pulsars are rapidly rotating neutron stars that emit highly regular radio pulses. The pulsar PSR B1937+21, discovered in 1982, completes one rotation approximately every 1.6 milliseconds. Its rotational stability over periods of several years was found to be comparable with that of the best atomic time standards then available.

By measuring the arrival times of its radio pulses and correcting for the motion of the Earth, the position and motion of the pulsar, interstellar propagation and other effects, astronomers can compare the observed pulse sequence with a mathematical timing model.

The paper estimated that the best foreseeable daily averaged pulsar observations could achieve timing precision of approximately 0.1 microsecond, although observations separated by long periods would be required to approach the fractional precision of contemporary atomic timescales.

Comparison with atomic clocks

Atomic time is created by combining measurements from ensembles of terrestrial clocks, principally caesium standards and hydrogen masers. Individual clocks can experience environmental effects, frequency drift, equipment changes and other systematic errors.

A pulsar provides a physically independent reference outside the terrestrial clock system. Because pulsars are observed in a nearly inertial celestial reference frame, their timing can potentially reveal errors or long-term variations that might be difficult to identify when all terrestrial clocks share related technologies and reference systems.

However, the study did not conclude that PSR B1937+21 could replace atomic clocks. Its timing residuals contained long-period correlated noise, often called red timing noise, which appeared to be intrinsic to the pulsar. The paper found that B1937+21 was less accurate than a single high-quality caesium standard under the noise model used.

Why this study matters

The research helped establish the idea of using an ensemble of millisecond pulsars as an independent astronomical timescale.

A sufficiently large collection of stable pulsars distributed across the sky could allow researchers to separate several kinds of timing disturbance:

• a clock error would appear as a common signal in all pulsars;

• an error in the Solar System ephemeris would produce a direction-dependent pattern;

• a gravitational-wave background would produce a different angular correlation among pulsars.

The authors concluded that the immediate quantitative contribution of the two longest-observed millisecond pulsars to terrestrial timescales was likely to be limited. Nevertheless, pulsars could serve as valuable independent standards for detecting long-term systematic errors and might become more useful as additional stable millisecond pulsars were discovered.

Questions for discussion

• Is a pulsar’s spin period itself a cycle, or should the more important cycle be the repeated arrival of its radio pulses?

• What corrections are required before pulse-arrival measurements can be treated as a precise clock?

• How can researchers distinguish irregularities in an atomic timescale from timing noise intrinsic to a pulsar?

• What advantages does an astronomical clock provide over an ensemble of terrestrial atomic clocks?

• How many pulsars are required to create a useful pulsar timescale?

• Could long-term pulsar timing reveal changes that are absorbed into fitted values for pulsar position, motion or spin-down?

• How have modern pulsar timing arrays improved upon the precision available in 1995?

Study details

Authors: Demetrios N. Matsakis and Roger S. Foster
Title: Application of Millisecond Pulsar Timing to the Long-Term Stability of Clock Ensembles
Year: 1995
Source type: Preprint and conference-volume contribution
Principal pulsar: PSR B1937+21
Pulsar spin period: Approximately 1.6 milliseconds
Projected daily averaged timing precision: Approximately 0.1 microsecond
Main conclusion: Millisecond pulsars could provide independent long-term checks on terrestrial clock ensembles, but the pulsars studied were not sufficiently stable to replace atomic time standards.
Source: https://arxiv.org/pdf/astro-ph/9509133