Improving pulsar timing precision through superior Time-of-Arrival creation

The measurement of pulsar pulse times-of-arrival (ToAs) is a crucial step in detecting low-frequency gravitational waves. To determine ToAs, we can use template-matching to compare each observed pulse profile with a standard template. However, using different combinations of templates and template-matching methods (TMMs) without careful consideration may lead to inconsistent results. In pulsar timing array (PTA) experiments, distinct ToAs from the same observations can be obtained, due to the use of diverse templates and TMMs. In other words, employing diverse approaches can yield different timing results and would thus have a significant impact on subsequent gravitational wave searches. In this paper, we examine several commonly used combinations to analyze their effect on pulse ToAs. we evaluate the potential impact of template and TMM selection on thirteen typical millisecond pulsars within the European PTA. We employ pulsar timing methods, specifically the root mean square and reduced chi-square $\chi_r^2$ of the residuals of the best timing solution to assess the outcomes. Additionally, we evaluate the system-limited noise floor (SLNF) for each pulsar at various telescopes operating around 1.4~GHz using frequency-resolved templates. Our findings suggest that utilizing data-derived and smoothed templates in conjunction with the Fourier-domain with Markov-chain Monte Carlo (FDM) TMM is generally the most effective approach, though there may be exceptions that require further attention. Furthermore, we determine that pulse phase jitter noise does not significantly limit the current precision of the European PTA's timing, as jitter levels derived from other studies are much smaller than the SLNF.