Characterizing the effects of pulse shape changes on pulsar timing precision

Time-of-arrival (TOA) measurements of pulses from pulsars are conventionally made by a template matching algorithm that compares a profile constructed by averaging a finite number of pulses to a long-term average pulse shape. However, the shapes of pulses can and do vary, leading to errors in TOA estimation. All pulsars show stochastic variations in shape, amplitude, and phase between successive pulses that only partially average out in averages of finitely many pulses. This jitter phenomenon will only become more problematic for timing precision as more sensitive telescopes are built. We describe techniques for characterizing jitter (and other shape variations) and demonstrate them with data from the Vela pulsar, PSR B0833$-$45. These include partial sum analyses; auto-and cross correlations between templates and profiles and between multifrequency arrival times; and principal component analysis. We then quantify how pulse shape changes affect TOA estimates using both analytical and simulation methods on pulse shapes of varying complexity (multiple components). These methods can provide the means for improving arrival time precision for many applications, including gravitational wave astronomy using pulsar timing arrays.