Time-resolved Hubble Space Telescope Wide Field Camera 3 Spectrophotometry Reveals Inefficient Day-to-Night Heat Redistribution in the Highly Irradiated Brown Dwarf SDSS 1557B

Brown dwarfs in ultra-short period orbits around white dwarfs offer a unique opportunity to study the properties of tidally-locked, fast rotating (1-3 hr), and highly-irradiated atmospheres. Here, we present phase-resolved spectrophotometry of the white dwarf-brown dwarf (WD-BD) binary SDSS 1557, which is the fifth WD-BD binary in our six-object sample. Using the Hubble Space Telescope Wide Field Camera 3 Near-infrared G141 instrument, the 1.1 to 1.7 $\mu$m phase curves show rotational modulations with semi-amplitudes of 10.5$\pm$0.1%. We observe a wavelength dependent amplitude, with longer wavelengths producing larger amplitudes, while no wavelength dependent phase shifts were identified. The phase-resolved extracted BD spectra exhibit steep slopes and are nearly featureless. A simple radiative energy redistribution atmospheric model recreates the hemisphere integrated brightness temperatures at three distinct phases and finds evidence for weak redistribution efficiency. Our model also predicts a higher inclination than previously published. We find that SDSS 1557B, the second most irradiated BD in our sample, is likely dominated by clouds on the night side, whereas the featureless day side spectrum is likely dominated by H$^-$ opacity and a temperature inversion, much like the other highly-irradiated BD EPIC2122B.