2025MNRAS.540.2486K

Time-correlated variations in the pulse profiles of radio pulsars provide insights into changes in their magnetospheres. For a small number of pulsars (${\sim} 20$), these variations have been shown to correlate with spin-down rate. Many of these profile changes involve small (few per cent) variations in the relative intensity of different profile components, and hence tools such as Gaussian process regression have been employed to separate the time-correlated profile variation from intrinsic noise. In this paper, we present a computationally efficient approximation of a 2D Gaussian process model that enhances sensitivity by simultaneously tracking time- and phase-correlated signals. Applying this model to 26 pulsars observed at the Jodrell Bank Observatory, we detect significant profile shape variations in 21 pulsars. Using principal component analysis, we confirm spin-down correlated shape variations in 11 pulsars where this had been previously observed. Additionally, we find evidence of spin-down correlated shape changes in seven pulsars for the first time (PSRs B0105+65, B0611+22, B0626+24, B1740-03, B1826-17, B1917+00, and B2148+63). We look in greater detail at PSR B0740-28, where the correlation between profile shape and spin-down itself seems to switch between quasi-stable states. Notably the profile shape associated with greater spin-down seems to invert at times, presenting a challenge to our understanding of the physical processes at work.