Constraining the origin of the long-term periodicity of FRB 20180916B with polarization position angle

Context. The repeating fast radio burst (FRB) FRB 20180916B produces bursts in a 5.1 day active window that repeats with a 16.34 day period. Models have been proposed to explain the periodicity using dynamical phenomena of neutron stars such as rotation, precession, or orbital motion. The polarization position angle (PA) of the bursts can be used to distinguish and constrain the origin of the long-term periodicity of the FRB. Aims. We aim to study the PA variability on short (within an observation) and long timescales (from observation to observation). Given the periodicity of the source, we also study the PA variations within the active window and across multiple windows. Then, we compare the observed PA variability with the predictions of various dynamical progenitor models for the FRB. Methods. We used the calibrated burst dataset detected by uGMRT in Band 4 (650 MHz) published in our earlier work. We transformed the PA measured at 650 MHz to infinite frequency such that PAs measured in different observations are consistent, and finally we measured the changes within and across active windows. Results. We find that the PA of the bursts varies according to the periodicity of the source. We constrained the PA variability to be less than seven degrees on timescales less than four hours for all MJDs. We also tentatively find that the PA varies within an active window with a variability of a few degrees per hour. In addition, we tentatively note the PA measured at the same phase in the active window varies from one cycle to another. Conclusions. Using the findings, we constrained the rotational, precession, and binary progenitor models involving compact objects, where the emission originates from the magnetosphere of the compact object. The rotational model partially agrees with the observed PA variability, but it requires further study to be fully constrained. We robustly rule out all flavors of precessional models where the precession of a neutron star either explains the periodicity of the FRB or the variability from one cycle to another. We can rule out the relativistic spin precession binary model. Lastly, we observed similarities between FRB 20180916B and an X-ray binary system, Her X 1, and explicitly note that the two sources exhibit a similar form of PA variability.