Dynamical limits on dark mass in the outer solar system

Dark matter in the outer solar system, such as a hypothetical Planet X or a Kuiper belt of material outside Neptune's orbit, may be detected by its dynamical influence on the orbits of the outer planets and comets. The study of simplified model solar systems with known observational errors offers insights into the best strategies to use in dynamical searches for dark mass, the significance of apparent anomalies, and the minimum detectable amounts of dark mass. We use this approach to establish the following results. (i) The inability of modern ephemerides to predict the longitude of Neptune accurately is a consequence of Neptune's long orbital period, and provides no evidence for the existence of dark mass. (ii) Searching for anomalous residuals when fitting observational data to models of the solar system that do not include dark mass is an inefficient way to detect dark mass; a more powerful test (by about a factor of 3-4) is to examine the improvement in fit when the observations are fitted to models that include dark mass. (iii) It is much harder to locate Planet X than to detect its existence: in order to predict the location of Planet X to within 1° its mass must exceed about 10 times the minimum detectable mass. (iv) If Planet X is massive and close enough to exert a detectable dynamical influence on the outer planets, then it is more likely than not that it would have been detected already in the IRAS survey. (v) Residuals in the orbits of comets such as Halley's are far more powerful probes for the Kuiper belt than are residuals in the orbits of the outer planets.