Rounding up the wanderers: optimizing coronagraphic searches for extrasolar planets

I derive analytic scalings for coronagraphic imaging searches for extrasolar planets. I compute the efficiency of detecting planets about any given star, and from this compute dimensionless distribution functions for the detected planets as a function of planet-star distance and distance to the host stars. I find the following for blind planet surveys: (1) the optimum wavelength is between 4000 and 5000 angstrom for Earth-like planets and 4200 and 5800 angstrom for Jovian planets; (2) between 21 and 32 per cent of the number of planets per decade of radius can be detected with an optimized survey; (3) target stars should be ranked from greatest to least by their luminosity divided by distance to the sixth or eighth power, depending on the dominant source of noise for the survey; (4) surveys targeting all main-sequence stars will detect similar to 3 times as many planets as surveys only targeting G-type stars and (5) stellar populations with different metallicities should have exposure times that vary with the cube of the metallicity. I apply these results to the current suite of proposed coronagraphic satellite telescopes, of which TPF-C is the most powerful, but a much smaller telescope, TOPS, may have a significant chance of detecting Earth-sized planets due to its small inner working angle and high throughput. The most significant uncertainty in these results is the noise contribution of exo-zodiacal light. These results can be applied to designing coronagraphs, comparing proposed telescope designs, optimizing the observing strategies, determining the properties of detected planet populations and selecting target stars.