White dwarf + M dwarf Detached Binaries in Long Period Radio Transients: Observed Binary Parameters, Evolution, and Population Constraints
Long period radio transients (LPTs) are the slowest radio-pulsing sources ever found, with the current population spanning periods of seven minutes to over six hours. Two of the thirteen published LPTs, ILT J1101+5521 and GLEAM-X J0704--37, have been associated with an M dwarf closely orbiting a white dwarf (WD) through optical spectroscopy. Here, we present new Keck I/LRIS optical spectroscopy of ILT J1101+5521, which reveals H$α$ emission from the M dwarf and confirms an orbital period nearly matching the radio period (2.092 hr). Radio pulses in both systems arrive just after maximum M dwarf redshift, assuming the radio period matches the orbital period. Based on Gaia proper motions and systemic velocities, we find that these systems are kinematically hotter and less concentrated in the Galactic plane than other LPTs. Both systems harbor unusually massive and cool WDs, with $M_\mathrm{WD} \approx 0.84-1.0 M_\odot$ and $T_\mathrm{eff} \approx 5200-7300$ K, implying that their carbon-oxygen cores are nearly entirely crystallized. Both systems are unusually close to being face-on binaries ($i=13^\circ-28^\circ$), signaling that the production of coherent radio pulses may be a strongly inclination-dependent phenomenon. We present MESA models that show that the M dwarf in each system will fill its Roche lobe within $\sim1$ Gyr, becoming a cataclysmic variable. Finally, we place lower limits on the space density of WD + M dwarf LPTs ($ρ\gtrsim 10^{-8}\;\mathrm{pc}^{-3}$); based on the broader population of WD + M dwarf binaries, we estimate that there are 100 (1000) WD + M dwarf LPTs within 2 kpc if current radio findings are 100% (10%) complete. Current and upcoming radio surveys will be sensitive to many such systems, and M dwarf optical counterparts out to $\sim$2 kpc will be detectable with the Rubin Observatory Legacy Survey of Space and Time (LSST).