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

Radio pulsating white dwarf (WD) systems, known as WD pulsars, are binary systems where the rapidly spinning WD interacts with a low-mass companion, producing pulsed non-thermal emission 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 Balmer and He i lines. The long-term optical light-curve folded on its orbital period (Porb = 3.49 h) shows ∼10 per cent scatter. High-cadence photometry reveals a short period signal, which we interpret to be the spin period of the WD primary (Pspin ≃ 92 s). The WD spin period is slightly shorter than that of AR Sco (~ 117 s), the WD pulsar prototype. Time-resolved spectroscopy reveals emission from the irradiated companion and Na i absorption tracing its centre of mass, yielding a binary mass function of f(M) ≃ 0.2 M⊙. The Hα emission includes a low-amplitude broad component, resembling the energetic flashes seen in AR Sco. Using spectral templates, we classify the companion to be most likely a M4.0± 0.5 with T_ eff ≈ 3300 K. Modelling the stellar contribution constrains the secondary mass (0.19 M⊙ ≲ M2 ≲ 0.28 M⊙), distance (≃ 1.2 kpc), and inclination (i ≃ 45 − 50○). We discuss the proposed evolutionary scenarios and summarise the observational properties of all three known WD pulsars, establishing a benchmark for identifying and classifying future members of this class.