Correlated spin-down rates and radio emission in PSR B1859+07

We study the spin-down changes of PSR B1859$+$07 over a period of more than 28 years of radio observation. We identify that the time derivative of the rotational frequency ($\nu$) varies quasi-periodically with a period of $\sim$350 days, switching mainly between two spin-down states. The profile shape of the pulsar is correlated with the $\dot \nu$ variation, producing two slightly different profile shapes corresponding to high- and low-$\dot \nu$ states. In addition to these two normal emission states, we confirm the occasional flare-state of the pulsar, in which the emission appears early in spin phase compared to that of the common normal emission. The profile of the flare-state is significantly different from that of the two normal emission states. The correlation analysis further shows that the flare-state is not directly linked with the $\dot \nu$ changes. With a simple emission beam model, we estimate the emission altitude of the normal emission to be 240~km, and explain the origin of the flare-state as an emission height variation from the leading edge of the beam. We also argue that the emission of these states can be explained with a partially active beam model. In this scenario, the trailing portion of the radio beam is usually active and the normal emission is produced. The flare-state occurs when the leading edge of the beam becomes active while the trailing part is being blocked. This model estimates a fixed emission altitude of 360~km. However, the cause of the flare-state (i.e. the emission height variation, or the time-dependent activity across the radio beam) is not easily explained.