21-year timing of the black-widow pulsar J2051-0827
  Timing results for the black-widow pulsar J2051-0827 are presented, using a
21-year dataset from four European Pulsar Timing Array telescopes and the
Parkes radio telescope. This dataset, which is the longest published to date
for a black-widow system, allows for an improved analysis that addresses
previously unknown biases. While secular variations, as identified in previous
analyses, are recovered, short-term variations are detected for the first time.
Concurrently, a significant decrease of approx. 2.5x10-3 cm-3 pc in the
dispersion measure associated with PSR J2051-0827 is measured for the first
time and improvements are also made to estimates of the proper motion. Finally,
PSR J2051-0827 is shown to have entered a relatively stable state suggesting
the possibility of its eventual inclusion in pulsar timing arrays.
