A deep search for the optical counterpart to the anomalous X-ray pulsar 1E 2259+58.6

We present Keck R and I band images of the field of the anomalous X-ray pulsar 1E 2259+58.6. We derive an improved X-ray position from archival ROSAT HRI observations by correcting for systematic (boresight) errors. Within the corresponding error circle, no object is found on the Keck images, down to limiting magnitudes R = 25.7 and I = 24.3. We discuss the constraints imposed by these limits, and conclude that it is unlikely that 1E 2259+58.6 is powered by accretion from a disk, irrespective of whether it is in a binary or not, unless the binary is extremely compact.