An improved spin-down rate for the proposed white dwarf pulsar AR scorpii

We analyse rapid-cadence, multiwavelength photometry of AR Scorpii from three observatories, covering five observing seasons. We measure the arrival times of the system's beat pulses and use them to compute an updated ephemeris. The white dwarf spin-down rate is estimated with an uncertainty of only 4 per cent. These results confirm, beyond any doubt, that the white dwarf's spin period is increasing at the rate consistent with by that of Stiller et al. (2018). We study the evolution of the beat pulse's colour index across the orbit. The colour of the primary pulse maxima varies significantly across the orbit, with the peaks being bluer after superior conjunction than in the first half of the orbit. Specifically, at orbital phase 0.5, the colour index of the primary pulse shows a very sharp discontinuity towards bluer indices. This supports the Potter & Buckley (2018b) synchrotron emission model where the two emitting poles differ significantly in colour. However, no corresponding jump in the colour of the secondary pulses is seen. Furthermore, our analysis reveals that the arrival times of the pulses can differ by as much as 6 s in simultaneous u and r photometry, depending on the binary orbital phase. If left uncorrected, this wavelength-dependent timing offset could lead to erroneous measurements of the spin-period derivative, particularly with heterogeneous data sets.