LOFAR observations of PSR B0943+10: profile evolution and discovery of a systematically changing profile delay in bright mode

We present broadband, low-frequency (25-80 MHz and 110-190 MHz) LOFAR observations of PSR B0943+10, with the goal of better illuminating the nature of its enigmatic mode-switching behaviour. This pulsar shows two relatively stable states: a "bright" (B) and "quiet" (Q) mode, each with different characteristic brightness, profile morphology, and single-pulse properties. We model the average profile evolution both in frequency and time from the onset of each mode, and highlight the differences between the two modes. In both modes, the profile evolution can be explained well by radius-to-frequency mapping at altitudes within a few hundred kilometres of the stellar surface. If both B and Q-mode emissions originate at the same magnetic latitude, then we find that the change of emission height between the modes is less than 6%. We also find that, during B-mode, the average profile is gradually shifting towards later spin phase and then resets its position at the next Q-to-B transition. The observed B-mode profile delay is frequency-independent (at least from 25-80 MHz) and asymptotically changes towards a stable value of about 4 x 10(-3) in spin phase by the end of mode instance, so much too high to be due to a changing spin-down rate. Such a delay can be interpreted as a gradual movement of the emission cone against the pulsar's direction of rotation, with different field lines being illuminated over time. Another interesting explanation is a possible variation in the accelerating potential inside the polar gap. This explanation connects the observed profile delay to the gradually evolving subpulse drift rate, which depends on the gradient of the potential across the field lines.