Brown dwarfs and giant planets orbiting close to a host star are subjected to significant irradiation that can modify the properties of their atmospheres. In order to test the atmospheric models that are used to describe these systems, it is necessary to obtain accurate observational estimates of their physical properties (masses, radii, temperatures, albedos). Interacting compact binary systems provide a natural laboratory for studying strongly irradiated sub-stellar objects. As the mass-losing secondary in these systems makes a critical, but poorly understood transition from the stellar to the sub-stellar regime, it is also strongly irradiated by the compact accretor. In fact, the internal and external energy fluxes are both expected to be comparable in these objects, providing access to an unexplored irradiation regime. However, the atmospheric properties of such donors have so far remained largely unknown. Here, we report the direct spectroscopic detection and characterisation of an irradiated sub-stellar donor in an accreting white dwarf binary system. Our near-infrared observations allow us to determine a model-independent mass estimate for the donor of $M_2=0.055\pm0.008M_{\odot}$ and an average spectral type of ${\rm L1}\pm{\rm1}$, supporting both theoretical predictions and model-dependent observational constraints. Our time-resolved data also allow us to estimate the average irradiation-induced temperature difference between the day and night sides on the sub-stellar donor, $��{\rm T}\simeq57$~K, and the maximum difference between the hottest and coolest parts of its surface, of $��{\rm T}_{max}\simeq200$~K. The observations are well described by a simple geometric reprocessing model with a bolometric (Bond) albedo of $A_B<0.54$ at 2-$��$ confidence level, consistent with high reprocessing efficiency, but poor lateral heat redistribution in the donor's atmosphere.

19 pages, 4 figures, published in Nature 19 May