A Sibling of AR Scorpii: SDSS J230641.47$+$244055.8 and the Observational Blueprint of White Dwarf Pulsars

Abstract

Radio pulsating white dwarf (WD) systems, known as WD pulsars, are non-accreting binary systems where the rapidly spinning WD interacts with a low-mass companion producing pulsed non-thermal emission that can be observed across the entire electromagnetic spectrum. Only two such systems are known: AR Sco and eRASSU J191213.9$-$441044. Here we present the discovery of a third WD pulsar, SDSS J230641.47$+$244055.8. The optical spectrum is dominated by molecular bands from an M-dwarf companion, with additional narrow emission lines from the Balmer series and He I. The long-term optical light-curve folded on its orbital period ($P_\mathrm{orb} = 3.49$ h) exhibits large scatter (roughly 10 per cent). High-cadence photometry reveals a short period signal, which we interpret to be the spin period of the WD primary ($P_\mathrm{spin} \simeq 92$ s). The WD spin period is slightly shorter than that of AR Sco ($\rm \sim 117$ s), the WD pulsar prototype. Time-resolved spectroscopy reveals emission from the irradiated companion and Na I absorption lines approximately tracing its centre of mass, which yields a binary mass function of $f(M) \simeq 0.2 {\rm M_\odot}$. The H$α$ emission includes a low-amplitude broad component, resembling the energetic emission line flashes seen in AR Sco. Using spectral templates, we classify the companion to be most likely a $\rm M4.0\pm 0.5$ star with $T_\mathrm{\rm eff} \approx 3300$ K. Modelling the stellar contribution constrains the secondary mass ($0.19\,{\rm M_\odot}\lesssim M_2\lesssim 0.28\,{\rm M_\odot}$), system distance ($\simeq1.25\,{\rm kpc}$), and inclination ($i \simeq 45-50^\circ$). We discuss the proposed evolutionary scenarios and summarize the observational properties of all three known WD pulsars, establishing a benchmark for identifying and classifying future members of this emerging class.