Searching for planets by differential astrometry with large telescopes

Traditional astrometric methods are limited in accuracy by the atmosphere in a way that does not show much improvement with increased telescope aperture. However, there is the potential for very high accuracy with large telescopes if advantage can be taken of these factors: First, the differential atmospheric distortion of images of closely adjacent stars is less with larger aperture; second, the diffraction limit is sharper, and third, photon statistics are improved. In this paper we analyze and give experimental tests of techniques that could be applied to the detection of planets with the mass of Jupiter or Uranus, if they are present in nearby binary star systems.The atmospheric perturbation of the relative position of the energy centroids measured in short exposure images of binary stars depends on the effective height of the turbulent distortion. For a 4-meter telescope, the error in centroid determination of a 4-arcsec binary can be as small as 20 milliarcsec (mas) in a single 20-millisecond (msec) exposure. The relative position measured by cross-correlation of short exposure speckle images, as suggested by McAlister (1977b), may give even higher accuracy. In this case, Roddier (Roddieret al., 1980) has shown that the atmospheric error depends on the thickness rather than the height of the layers that make the dominant contribution to the turbulence. Through Monte Carlo analysis we show that on occasions when the turbulence arises largely in a thin layer, a single 20-msec exposure of a 4-arcsec binary taken with a 4-m aperture can yield an astrometric accuracy of order 0.5 mas.We report on experiments made at the Steward Observatory 2.3-m telescope which achieved accuracies corresponding to 1.7 mas in a 2.24-arcsec binary and 16.1 mas in a 6.0-arcsec binary with only 15 and 18 specklegram pairs respectively. We plan to use the 6.5-m converted MMT to obtain much higher performance, between 4.0 mas and 0.40 masper independent specklegram pair, depending upon atmospheric conditions, for binaries of 4-arcsec separation. By cycling rapidly through perhaps 100 binaries, thus calibrating systematic errors through the average change in binary separation, Jupiter-mass planets may be detectable with small but regular access to the telescope.Paper presented at the Conference onPlanetary Systems: Formation, Evolution, and Detection held 7–10 December, 1992 at CalTech, Pasadena, California, U.S.A.