Timing observations of four millisecond pulsars with the Arecibo and Effelsberg radiotelescopes

We present long-term timing observations of four millisecond radio pulsars with the 305 m Arecibo and the 100 m Effelsberg radiotelescopes. Our analysis of the combined pulse time-of-arrival data from the two telescopes has led to improvements of the precision of timing parameter determination for all the four pulsars. A new, much more significant measurement of a third-order spin frequency derivative of PSR B1257 + 12 adds to the existing evidence that a fourth, distant planet may orbit this pulsar. Proper motions have been measured for PSR J1640 + 2224, PSR B1953 + 29, and PSR J2229 + 2643. The derived low transverse velocities of these objects agree with the kinematic characteristics of the observed millisecond pulsar population. Exceptionally low spindown rates of PSR J1640 + 2224 and PSR J2229 + 2634 have been used to derive useful limits on the initial spin periods of these objects and on the variation of the gravitational constant G.