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Finding rocky asteroids around white dwarfs by their periodic thermal emission

Since white dwarfs are small, the contrast between the thermal emission of an orbiting object and a white dwarf is dramatically enhanced compared to a main sequence host. Furthermore, rocky objects much smaller than the moon have no atmospheres and are tidally locked to the white dwarf. We show that this leads to temperature contrasts between their day and night side of order unity that should lead to temporal variations in infrared flux over an orbital period of $\sim 0.2$ to $\sim 2$ days. Ground based telescopes could detect objects with a mass as small as $1\%$ of the lunar mass $M_L$ around Sirius B with a few hours of exposure. The James Webb Space Telescope (JWST) may be able to detect objects as small as $10^{-3} M_L$ around most nearby white dwarfs. The tightest constraints will typically be placed on 12,000 K white dwarfs, whose Roche zone coincides with the dust sublimation zone. Constraining the abundance of minor planets around white dwarfs as a function of their surface temperatures (and therefore age) provides a novel probe for the physics of planetary formation.