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Two recently discovered white dwarfs, WD J041246.84 + 754942.26 and WD J165335.21 − 100116.33, exhibit Hα and Hβ Balmer line emission similar to stars in the emerging DAHe class, yet intriguingly have not been found to have detectable magnetic fields. These white dwarfs are assigned the spectral type DAe. We present detailed follow-up of the two known DAe stars using new time-domain spectroscopic observations and analysis of the latest photometric time-series data from TESS and ZTF. We measure the upper magnetic field strength limit of both stars as B < 0.05 MG. The DAe white dwarfs exhibit photometric and spectroscopic variability, where in the case of WD J041246.84 + 754942.26 the strength of the Hα and Hβ emission cores varies in antiphase with its photometric variability over the spin period, which is the same phase relationship seen in DAHe stars. The DAe white dwarfs closely cluster in one region of the Gaia Hertzsprung–Russell diagram together with the DAHe stars. We discuss current theories on non-magnetic and magnetic mechanisms which could explain the characteristics observed in DAe white dwarfs, but additional data are required to unambiguously determine the origin of these stars.

We identify two ultra-cool (${T_\mathrm{eff}}\lt 4000$ K) metal-polluted (DZ) white dwarfs WD J2147−4035 and WD J1922+0233 as the coolest and second coolest DZ stars known to date with ${T_\mathrm{eff}}\approx 3050$ K and ${T_\mathrm{eff}}\approx 3340$ K, respectively. Strong atmospheric collision-induced absorption (CIA) causes the suppression of red optical and infrared flux in WD J1922+0233, resulting in an unusually blue colour given its low temperature. WD J2147−4035 has moderate infrared CIA yet has the reddest optical colours known for a DZ white dwarf. Microphysics improvements to the non-ideal effects and CIA opacities in our model atmosphere code yields reasonable solutions to observations of these ultra-cool stars. WD J2147−4035 has a cooling age of over 10 Gyr which is the largest known for a DZ white dwarf, whereas WD J1922+0233 is slightly younger with a cooling age of 9 Gyr. Galactic kinematics calculations from precise Gaia EDR3 astrometry reveal these ultra-cool DZ stars as likely members of the Galactic disc thus they could be pivotal objects in future studies constraining an upper age limit for the disc of the Milky Way. We present intermediate-resolution spectroscopy for both objects, which provides the first spectroscopic observations of WD J2147−4035. Detections of sodium and potassium are made in both white dwarfs, in addition to calcium in WD J1922+0233 and lithium in WD J2147−4035. We identify the magnetic nature of WD J2147−4035 from Zeeman splitting in the lithium line and also make a tentative detection of carbon, so we classify this star as DZQH. WD J1922+0233 likely accreted planetary crust debris, while the debris composition that polluted WD J2147−4035 remains unconstrained.