Differential atmospheric refraction and limitations on the relative astrometric accuracy of large telescopes

Recent advances have made ground-based relative astrometry accurate to 100 microarcseconds (mu as) or better a possibility. An important systematic effect on such measurements is the refraction induced by the atmosphere, which tends to alter the apparent separation of two stars. For stars separated by 30 " and observed in the K band at a zenith angle of 45 degrees, this change in observed separation can amount to as much as 12,000 mu as, or some 120 times the desired accuracy. Given a model of the atmosphere, the magnitude of this effect on observations made with large telescopes can be calculated and corrected. Mie have demonstrated that the differential refraction call effectively be divided into two independent components: one chat is determined by the separation of the stars on the sky, and another that depends on the difference in their colors, the former component dominating in most cases. According to the atmospheric model we have adopted, there are seven quantities that must be measured in order to perform a calculation of the differential refraction Delta R. These are the zenith angle of the first star, the observed separation of the stars along the zenith direction, the ground-level atmospheric parameters of temperature, pressure, and relative humidity, as well as the effective surface temperatures of the two stars. We discuss how accurately these must be measured to limit the error in the Delta R correction to 10 mu as or less per input parameter. The most stringent of these requirements is that the stellar surface temperature should be known accurately (approximate to 100 K) if the star is cool.