2020ApJ...890..143V

The timing properties of the millisecond pulsar PSR J1939+2134-very high rotation frequency, very low time derivative of rotation frequency, no timing glitches, and relatively low timing noise-are responsible for its exceptional timing stability over decades. It has been timed by various groups since its discovery, at diverse radio frequencies, using different hardware and analysis methods. Most of the timing data is now available in the public domain in two segments, which have not been combined so far. This work analyzes the combined data by deriving uniform methods of data selection, derivation of Dispersion Measure (DM), accounting for correlation due to "red" noise, etc. The timing noise of this pulsar is very close to a sinusoid, with a period of approximately 31 yr. The main results of this work are: (1) the clock of PSR J1939+2134 is stable at the level of almost one part in 10¹⁵ over about 31 yr; (2) the power-law index of the spectrum of electron density fluctuations in the direction of PSR J1939+2134 is 3.86 ± 0.04; (3) a Moon-sized planetary companion, in an orbit of semimajor axis about 11 astronomical units and eccentricity ≃0.2, can explain the timing noise of PSR J1939+2134; (4) precession under electromagnetic torque with very small values of oblateness and wobble angle can also be the explanation but with reduced confidence; and (5) there is an excess timing noise of about 8 µs amplitude during the epochs of steepest DM gradient, of unknown cause.