The Timing Stability Limit of Millisecond Pulsars

This paper expresses the long-baseline timing performance of the best millisecond pulsars in the units of rotation count, phase fraction, and equivalent frequency drift, deriving the stability limit that pulsar timing arrays actually achieve and the level of steady external influence it excludes. The headline results are as follows. Rotations accumulated over a 15 year baseline by a 5.76 ms pulsar: 8.22e+10; Timing residual as a fraction of one rotation period: 1.13e-05; Equivalent fractional frequency drift over the baseline: 1.37e-16; Residual after 30 years if the noise floor stays at 65 ns, expressed as a fraction of a period: 1.13e-05; Phase drift in one year at the limiting stability: 4.33e-09 s; Number of rotations timed to one part in ten to the fourteenth of phase: 8.22e+10. All values are computed from the stated assumptions and published inputs; the study is simulated and computed, not measured.