Looking for Neo-Tokyo in the Kuiper Belt

In Loeb & Turner (2012), a new Solar System SETI method is described. If Kuiper Belt objects (KBOs) are artificially illuminated, we should be able to detect that based on how their brightness changes with distance (both from us and the sun).

If a KBO has artificial illumination on its surface, then its brightness should only decrease with distance (from us on Earth) squared (a geometric effect of the intensity of the light diluting as it gets further from the source, see Wikipedia’s explanation). But, if a KBO is illuminated solely by the Sun (as we expect them to be), the light is coming from the Sun, so the light gets diluted twice and we would expect it to decrease with distance to the fourth power. The distance from the Sun to the KBO and from the Earth to the KBO are essentially the same because the Earth is relatively close to the Sun. KBOs are 30-50 AU away from the Sun while Earth orbits snuggly at 1 AU. So the distances can only be different by at most at most ~3%, a subtlety I feel should have been made explicit in the paper. Presumably this power law identification could be performed (at least in a rudimentary sense) by putting the data into log space and identifying the linear trend of brightness as a function of distance (hopefully with a slope of -2).

With the completion of the Panoramic Survey Telescope and Rapid Response System (Pan-STARRS) and the Large Synoptic Survey Telescope (LSST), there will be an explosion of discoveries of new KBOs (finding ~10-100x more than we know about now). This should open up a window for this new type of proposed search.

Another interesting tidbit was the use of a unit defined as 1% of the solar daylight illumination of Earth, ~ 1.4 · 10^4 erg/(s cm^2). They state that this corresponds roughly to the illumination in a brightly lit office or to that provided by the Sun just as it rises or sets in a clear sky on Earth. I spent an inordinate amount of time wrestling with this fact, as it is repeatedly used as a baseline in the paper and is not immediately obvious to me what this statement even means. It doesn’t feel like outside my office is 100x brighter on a sunny day, but who knows.