SEARCHING FOR PLANETS BY DIFFERENTIAL ASTROMETRY WITH LARGE TELESCOPES

Traditional astrometric methods are limited in accuracy by the atmosph ere in a way that does not show much improvement with increased telesc ope aperture. However, there is the potential for very high accuracy w ith large telescopes if advantage can be taken of these factors: First , the differential atmospheric distortion of images of closely adjacen t 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 applie d to the detection of planets with the mass of Jupiter or Uranus, if t hey are present in nearby binary star systems. The atmospheric perturb ation of the relative position of the energy centroids measured in sho rt exposure images of binary stars depends on the effective height of the turbulent distortion. For a 4-meter telescope, the error in centro id determination of a 4-arcsec binary can be as small as 20 milliarcse c (mas) in a single 20-millisecond (msec) exposure. The relative posit ion measured by cross-correlation of short exposure speckle images, as suggested by McAlister (1977b), may give even higher accuracy. In thi s case, Roddier (Roddier et al., 1980) has shown that the atmospheric error depends on the thickness rather than the height of the layers th at make the dominant contribution to the turbulence. Through Monte Car lo analysis we show that on occasions when the turbulence arises large ly in a thin layer, a single 20-msec exposure of a 4-arcsec binary tak en 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 te lescope which achieved accuracies corresponding to 1.7 mas in a 2.24-a rcsec binary and 16.1 mas in a 6.0-arcsec binary with only 15 and 18 s pecklegram pairs respectively. We plan to use the 6.5-m converted MMT to obtain much higher performance, between 4.0 mas and 0.40 mas per in dependent specklegram pair, depending upon atmospheric conditions, for binaries of 4-arcsec separation. By cycling rapidly through perhaps 1 00 binaries, thus calibrating systematic errors through the average ch ange in binary separation, Jupiter-mass planets may be detectable with small but regular access to the telescope.