| Abstract: Pulse-to-pulse variability in millisecond pulsars (MSPs), driven by intrinsic phase jitter and magnetospheric processes, can fundamentally limit the timing precision required for detecting nanohertz gravitational waves with Pulsar Timing Arrays (PTAs). While single-pulse studies have revealed that jitter noise is a dominant contribution to the timing error budget for many bright MSPs, a systematic, multi-frequency characterization of profile stability and jitter across a wider MSP population remains limited.
We present a comprehensive analysis of pulse-profile stabilization timescales and intrinsic jitter in MSPs using long-term, multi-epoch observations with the upgraded GMRT (uGMRT; 300--750 MHz) and complementary Parkes Ultra-Wideband low-frequency receiver (Parkes UWL; 704--4032 MHz) data for a subset of sources. Using a direct pulse-stacking–based method, we show that stable, ensemble-average profiles typically require integration over $\sim$10$^{5}–10^{6}$ pulses. We find that these stabilization timescales correlate with signal-to-noise ratio, pulse morphology, and surface magnetic field strength, suggesting a link between emission stability and magnetospheric conditions. A complementary single-epoch analysis of bright MSPs reinforces these trends and demonstrates that the slope of the profile-stability curve is strongly correlated with an independently measured jitter parameter, implying that profile-stability analysis can serve as a practical proxy for intrinsic pulse-shape variability in MSPs.
By extending these techniques to MSPs that are key PTA sources, and by probing the frequency dependence of jitter and stability timescales, our study provides a scalable framework for quantifying intrinsic profile variability. For the Square Kilometer Array (SKA) era, where radiometer noise will be dramatically reduced, jitter will become the primary limiting factor for achievable timing precision in bright PTA MSPs. Robust empirical constraints on jitter and stability timescales are therefore crucial for optimizing PTA observing strategies, choosing integration times, refining PTA noise models, and ultimately maximizing the array’s sensitivity to nanohertz gravitational waves.
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