On the statistical implication of timing noise for pulsar braking index

Abstract

Abstract. Timing data on 27 radio pulsars spanning more than 13 years were analysed in order to investigate the correlations of radio pulsar timing noise (random fluctuations in the observed pulse phase -RPTN), with the observed electromagnetic torque braking index (n obs ). The results reveal significant correlations (r ≥ 90%) between the statistics used to parameterize RPTN and the absolute magnitude of the observed second time derivative of the pulse (rotation) frequency (ν obs ). These correlations, most plausibly, suggest that the observed braking indices of most pulsars, obtained through the traditional phase-connected method, are strongly dominated by intrinsic variability in their spin rates. The implication of this result for a significant measurement of pulsar systematic frequency second derivative is discussed.

Measurements of radio pulsar braking indices

“…The resultant rms white noise in the observed phase residuals (σ W ) was estimated with pairs of data from the 2nd-order timing models, separated by the time interval Δt ≤ 1 day. The short time scale is required to filter out the more slowly varying red noise component from the white noise estimator (Cordes & Downs 1985;Chukwude 2002). As expected, estimates of σ W represent the upper limit on the error in σ R23 .…”

“…A statistic of interest is the difference between the root-mean-squares phase residuals obtained from 2nd-and 3rd-order polynomial models (σ R23 ). Using a sample of 27 radio pulsars, Chukwude (2003) shows that σ R23 is about 95% correlated with timing noise dominated |ν obs |. This is perhaps the most plausible scenario for the majority of the known radio pulsars.…”

“…These conditions will result in non-stationary braking indices, with either positive or negative values. In particular, the braking indices obtained fromν obs could have anomalous values, some several orders of magnitude greater than or less than the canonical value of 3 (Johnston & Galloway 1999;Chukwude 2003;Hobbs et al 2004). Moreover,ν obs will almost certainly correlate with some timing noise statistics.…”

“…This is perhaps the most plausible scenario for the majority of the known radio pulsars. Following Chukwude (2003), we redefine the timing noise statistic (σ R23 : a measure of timing noise activity absorbed by the observedν) as…”

“…Recently, Chukwude (2003) carried out a detailed qualitative study of the effects of timing noise on radio pulsar braking index measurements. In particular, the author reported an exceptionally strong correlation between the magnitude of the observed second derivative of the pulse rotation frequency (ν obs ), obtained from the conventional phase-coherent timing analysis and the difference between the root-mean-squares (rms) phase residuals from 2nd-and 3rd-order polynomial models (σ R23 ).…”