HST/WFC3 Complete Phase-resolved Spectroscopy of White Dwarf-Brown Dwarf Binaries WD 0137 and EPIC 2122

Brown dwarfs in close-in orbits around white dwarfs offer an excellent opportunity to investigate properties of fast-rotating, tidally-locked, and highly-irradiated atmospheres. We present Hubble Space Telescope Wide Field Camera 3 G141 phase-resolved observations of two brown dwarf-white dwarf binaries: WD 0137-349 and EPIC 212235321. Their 1.1 to 1.7 $\mu$m phase curves demonstrate rotational modulations with semi-amplitudes of $5.27\pm0.02$% and $29.1\pm0.1$%; both can be well fit by multi-order Fourier series models. The high-order Fourier components have the same phase as the first order and are likely caused by hot spots located at the substellar points, suggesting inefficient day/night heat transfer. Both brown dwarfs' phase-resolved spectra can be accurately represented by linear combinations of their day- and night-side spectra. Fitting the irradiated brown dwarf model grids to the day-side spectra require a filling factor of ~50%, further supporting a hot spot dominating the emission of the day-sides. The night-side spectrum of WD 0137-349B is reasonably well fit by non-irradiated substellar models and the one of EPIC 212235321B can be approximated by a Planck function. We find strong spectral variations in the brown dwarfs' day/night flux and brightness temperature contrasts, which highlights the limitations of band-integrated measurements in probing heat transfer in irradiated objects. On the color-magnitude diagram, WD 0137-349B evolves along a cloudless model track connecting the early-L and mid-T spectral types, demonstrating that clouds and disequilibrium chemistry have a negligible effect on this object. A full interpretation of these high-quality phase-resolved spectra calls for new models that couple atmospheric circulation and radiative transfer under high-irradiation conditions.