Polarization position angle standard stars: a reassessment of $\theta$ and its variability for seventeen stars based on a decade of observations
Observations of polarization position angle ($\theta$) standards made from 2014 to 2023 with the High Precision Polarimetric Instrument (HIPPI) and other HIPPI-class polarimeters in both hemispheres are used to investigate their variability. Multi-band data were first used to thoroughly recalibrate the instrument performance by bench-marking against carefully selected literature data. A novel Co-ordinate Difference Matrix (CDM) approach - which combines pairs of points - was then used to amalgamate monochromatic ($g^\prime$ band) observations from many observing runs and re-determine $\theta$ for 17 standard stars. The CDM algorithm was then integrated into a fitting routine and used to establish the impact of stellar variability on the measured position angle scatter. The approach yields variability detections for stars on long time scales that appear stable over short runs. The best position angle standards are $\ell$ Car, $o$ Sco, HD 154445, HD 161056 and $\iota^1$ Sco which are stable to $\leq$ 0.123$^\circ$. Position angle variability of 0.27-0.82$^\circ$, significant at the 3-$\sigma$ level, is found for 5 standards, including the Luminous Blue Variable HD 160529 and all but one of the other B/A-type supergiants (HD 80558, HD 111613, HD 183143 and 55 Cyg), most of which also appear likely to be variable in polarization magnitude ($p$) - there is no preferred orientation for the polarization in these objects, which are all classified as $\alpha$ Cygni variables. Despite this we make six key recommendations for observers - relating to data acquisition, processing and reporting - that will allow them to use these standards to achieve $<$ 0.1$^\circ$ precision in the telescope position angle with similar instrumentation, and allow data sets to be combined more accurately.