Micro-arcsecond relative astrometry by ground-based and single-aperture observations

We present an observation method to obtain a relative astrometric precision of about 100 . . . 150 μas with ground-based and single-aperture observations. By measuring the separation of double or triple stars we want to determine the astrometric signal of an unseen substellar companion as a periodic change in the separation between the stellar components. Using an adaptive optics system we correct for atmospheric turbulences and furthermore by using a narrow band filter in the near infrared we can suppress differential chromatic refraction effects. To reach a high precision we use a statistical approach. Using the new observation mode ”cube-mode” (where the frames were directly saved in cubes with nearly no loss of time during the readout), we obtain several thousand frames within half an hour. After the verification of the Gaussian distributed behaviour of our measurements (done with a Kolmogorov-Smirnov-Test) the measurement precision can be calculated as the standard deviation of our measurements divided by the square root of the number of frames. To monitor the stability of the pixel scale between our observations, we use the old globular cluster 47 Tuc as a calibration system.