High-precision timing of millisecond pulsars. II - Astrometry, orbital evolution, and eclipses of PSR 1957 + 20

Pulse time-of-arrival measurements have been acquired for PSR 1957 + 20 on 61 days over a 2.7 yr interval, including the times of 44 eclipse disappearance or reappearance events. The timing data provide a reliable measurement of the pulsar's proper motion, 29 +/- 3 mas/yr, at position angle 216 +/- 6 deg; this direction is in excellent agreement with that suggested by the cometlike shape of a surrounding optical emission nebula. The rate of change of the orbital period has been measured: a surprisingly large (-3.9 +/- 0.9) x 10 exp -11, implying that significant orbital evolution must take place on a time scale of 30 Myr. Finally, the present observations extend the eclipse measurements to higher frequencies and provide better statistics for these highly variable phenomena. The eclipse data are used to compute a column-density profile of free electrons in the outer parts of the eclipsing region, and thereby provide an important glimpse into the material being ablated from the companion star.