Phase-resolved Hubble Space Telescope WFC3 Spectroscopy of Weakly-Irradiated Brown Dwarf GD 1400 and Energy Redistribution-Irradiation Trends in Six WD$-$BD Binaries

Irradiated brown dwarfs offer a unique opportunity to bridge the gap between stellar and planetary atmospheres. We present high-quality $\mathit{HST}$/WFC3/G141 phase-resolved spectra of the white dwarf + brown dwarf binary GD 1400, covering more than one full rotation of the brown dwarf. Accounting for brightness variations caused by ZZ Ceti pulsations, we revealed weak ($\sim$1\%) phase curve amplitude modulations originating from the brown dwarf. Sub-band light curve exploration in various bands showed no significant wavelength dependence on amplitude or phase shift. Extracted day- and night-side spectra indicated chemically similar hemispheres, with slightly higher day-side temperatures, suggesting efficient heat redistribution or dominance of radiative escape over atmospheric circulation. A simple radiative and energy redistribution model reproduced observed temperatures well. Cloud-inclusive models fit the day and night spectra better than cloudless models, indicating global cloud coverage. We also begin qualitatively exploring atmospheric trends across six irradiated brown dwarfs, from the now complete "Dancing with Dwarfs" WD$-$BD sample. The trend we find in the day-side/night-side temperature and irradiation levels is consistent with efficient heat redistribution for irradiation levels less than $\sim$10$^9$ ergs/s/cm$^2$ and decreasing efficiency above that level.