Long-term photometric monitoring and spectroscopy of the white dwarf pulsar AR Scorpii.

AR Scorpii (AR Sco) is the only radio-pulsing white dwarf known to date. It shows a broad-band spectrum extending from radio to X-rays whose luminosity cannot be explained by thermal emission from the system components alone, and is instead explained through synchrotron emission powered by the spin-down of the white dwarf. We analysed NTT/ULTRACAM, TNT/ULTRASPEC, and GTC/HiPERCAM high-speed photometric data for AR Sco spanning almost seven years and obtained a precise estimate of the spin frequency derivative, now confirmed with 50-σ significance. Using archival photometry, we show that the spin-down rate of |$P/\dot{P} = 5.6 \times 10^6$|  yr has remained constant since 2005. As well as employing the method of pulse-arrival time fitting used for previous estimates, we also found a consistent value via traditional Fourier analysis for the first time. In addition, we obtained optical time-resolved spectra with WHT/ISIS and VLT/X-shooter. We performed modulated Doppler tomography for the first time for the system finding evidence of emission modulated on the orbital period. We have also estimated the projected rotational velocity of the M-dwarf as a function of orbital period and found that it must be close to Roche lobe filling. Our findings provide further constraints for modelling this unique system. [ABSTRACT FROM AUTHOR]