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The timing properties of the millisecond pulsar PSR J1939+2134 -- very highrotation frequency, very low time derivative of rotation frequency, no timingglitches and relatively low timing noise -- are responsible for its exceptionaltiming stability over decades. It has been timed by various groups since itsdiscovery, at diverse radio frequencies, using different hardware and analysismethods. Most of this timing data is now available in the public domain in twosegments, which have not been combined so far. This work analyzes the combineddata by deriving uniform methods of data selection, derivation of DispersionMeasure (DM), accounting for correlation due to "red" noise, etc. The timingnoise of this pulsar is very close to a sinusoid, with a period ofapproximately $31$ years. The main results of this work are (1) The clock ofPSR J1939+2134 is stable at the level of almost one part in $10^{15}$ overabout $31$ years, (2) the power law index of the spectrum of electron densityfluctuations in the direction of PSR J1939+2134 is $3.86 \pm 0.04$, (3) a Moonsized planetary companion, in an orbit of semi major axis about $11$astronomical units and eccentricity $\approx 0.2$, can explain the timing noiseof PSR J1939+2134, (4) Precession under electromagnetic torque with very smallvalues of oblateness and wobble angle can also be the explanation, but withreduced confidence, and (5) there is excess timing noise of about $8$ $\mu$samplitude during the epochs of steepest DM gradient, of unknown cause.

The 31-year Rotation History of the Millisecond Pulsar J1939+2134 (B1937+21)