Observing conditions at Mount Graham: Vatican Advanced Technology Telescope UBVR sky surface brightness and seeing measurements from 1999 through 2003

We present measurements of sky surface brightness and seeing on Mount Graham, obtained at the Vatican Advanced Technology Telescope (VATT) during 16 observing runs between 1999 April and 2003 December. We show that the sky surface brightness is significantly darker during photometric conditions and can be highly variable over the course of a single observing run, as well as from one run to the next, regardless of photometricity. In our photometric observations, we find an average low air mass (sec z < 1.2) sky surface brightness of 22.00, 22.53, 21.49, and 20.88 mag arcsec^-2 in U, B, V, and R, respectively. The darkest run (2000 February in U and 2001 February in BVR) had an average sky surface brightness of 22.38, 22.86, 21.72, and 21.19 mag arcsec^-2 in U, B, V, and R, respectively. With these results, we show that under the best conditions, Mount Graham can compete with the darkest sites in Hawaii and Chile, thanks in part to the strict dark-sky ordinances in place in Tucson and Safford. We expect the sky over Mount Graham to be even darker than our 1999-2003 results during solar minimum (2006-2007). We find a significant improvement of about 0″.45 in our measured stellar FWHM after improvements to the telescope were made in summer and fall 2001. Stellar FWHM values are highly variable, with median R-band focus FWHM values in each observing run ranging from 0″.97 to 2″.15. Significant subarcsecond seeing was occasionally achieved, with values as low as 0″.65 FWHM in R. There may still be a significant telescope contribution to the seeing at the VATT, but nearby trees as high as the dome are currently the dominant factor.