Long-term timing of two young, energetic pulsars

We report on the long-term phase-coherent timing of two young, energetic pulsars, PSR B1509-58 and PSR B0540-69, using data from the Rossi X-ray Timing Explorer, the Parkes Radio Telescope and the Molonglo Observatory Synthesis Telescope. We present fully phase-coherent timing analyses of both sources, and show that contamination from timing noise can significantly affect measured timing parameters. As a result, we also present, a partially phase-coherent timing analysis which is less sensitive to timing noise.We present an updated measurement of n = 2.839 +/- 0.003 for PSR B1509-58, and we report a measurement of the second braking index, m = 18.3 +/- 2.9, in agreement with the prediction from the simple model of pulsar spin-down. We also examine changes in dispersion measure and present an analysis of the noise, measuring a low-resolution power spectrum corresponding to a spectral index of beta = -4.6 +/- 1.0. This implies that the noise cannot be explained by a pure random walk. We also show that no glitches have occurred in 21.3 yr, implying that this pulsar glitches less often than typical young pulsars.We measure the braking index for PSR B0540-69, n = 2.140 +/- 0.009 and discuss our measurement in the context of other discordant values reported in the literature. In addition, we detect evidence for a glitch which has been previously reported but later disputed. The glitch occurred at MJD 51335 +/- 12 with Deltanu/nu = (1.4 +/- 0.2) x 10-9 and Delta n&d2;/n&d2; = (1.33 +/- 0.02) x 10-4. We present an improved source position from the phase-coherent timing of this pulsar, to our knowledge, the first of its kind from X-ray pulsar timing.We discuss the physical implications of n < 3, the value predicted from the model of pulsar spin down. In addition, we discuss possible causes of timing noise in these two young pulsars. We also discuss the anomalously small glitch activity in very young pulsars which suggests that neutron stars of similar apparent ages, rotation properties and inferred dipolar B fields can have significantly different internal properties