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 a periodic or nearly periodic component with a period of  568 ± 10 d  and a  1/f³  power-law noise component in pulse phase with a noise strength  S_φ= (1.24 ± 0.067) × 10⁻¹⁶ cycle² 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,  M_c≥ 3.2 M_⊕ , assuming a Crab pulsar mass of  1.4 M_⊙ .