Characterization of the timing noise of the Crab pulsar

Abstract

We present a power spectral analysis of the timing noise of the Crab pulsar, mainly using radio measurements from Jodrell Bank taken over the period 1982-89, an interval bounded by sparse data sampling and a large glitch. The power spectral analysis is complicated by non-uniform data sampling and the presence of a steep red power spectrum that can distort power spectra measurement by causing severe power 'leakage'. We develop a simple windowing method for computing red noise power spectra of uniformly sampled data sets and test it on Monte Carlo generated sample realizations of red power-law noise. We generalize time-domain methods of generating power-law red noise with even integer spectral indices to the case of non-integer spectral indices. The Jodrell Bank pulse phase residuals are dense and smooth enough that an interpolation on to a uniform time-series is possible. A windowed power spectrum is computed, revealing aperiodic or nearly periodic component withaperiod of 568 ± 10d and a 1/f3 power-law noise component in pulse phase with a noise strength Sø = (1.24 ± 0.067) × 10-16cycle2 s-2 over the analysis frequency range f = 0.003-0.1 cycle d-1. This result deviates from past analyses which characterized the pulse phase timing residuals as either 1/f4 power-law noise or a quasiperiodic process. The analysis was checked using the Deeter polynomial method of power spectrum estimation that was developed for the case of non-uniform sampling, but has lower spectral resolution. The timing noise is consistent with a torque noise spectrum rising with analysis frequency as f, implying blue torque noise, a result not predicted by current models of pulsar timing noise. If the periodic or nearly periodic component is due to a binary companion, we find a mass function f(M) = (6.8 ± 2.4) × 10-16 M⊙ and a companion mass, Mc ≥ 3.2 M⊙, assuming a Crab pulsar mass of 1.4 M⊙.