An insight into chromatic behaviour of jitter in pulsars and its modelling: A case study of PSR J0437-4715

Pulse-to-pulse profile shape variations introduce correlations in pulsar times of arrival (TOAs) across radio frequency measured at the same observational epoch. This leads to a broadband noise in excess of radiometer noise, which is termed pulse jitter noise. The presence of jitter noise limits the achievable timing precision and decreases the sensitivity of pulsar-timing data sets to signals of interest such as nanohertz-frequency gravitational waves. Current white noise models used in pulsar timing analyses attempt to account for this, assuming complete correlation of uncertainties through the arrival times collected in a unique observation and no frequency dependence of jitter (which corresponds to a rank-one covariance matrix). However, previous studies show that the brightest millisecond pulsar at decimetre wavelengths, PSR J0437$-$4715, shows decorrelation and frequency dependence of jitter noise. Here we present a detailed study of the decorrelation of jitter noise in PSR J0437$-$4715 and implement a new technique to model it. We show that the rate of decorrelation due to jitter can be expressed as a power-law in frequency. We analyse the covariance matrix associated with the jitter noise process and find that a higher-rank-approximation is essential to account for the decorrelation and to account for frequency dependence of jitter noise. We show that the use of this novel method significantly improves the estimation of other chromatic noise parameters such as dispersion measure variations. However, we find no significant improvement in errors and estimation of other timing model parameters suggesting that current methods are not biased for other parameters, for this pulsar due to this misspecification. We show that pulse energy variations show a similar decorrelation to the jitter noise, indicating a common origin for both observables.