The distance to M13 via a subdwarf fit in the optical–infrared colour–magnitude plane

We present results of K(22 μm) band photometry of stars in the globular cluster M13 (NGC 6205), reaching to some 2 mag below the main-sequence turn-off, which we combine with previously published optical photometry to produce optical–infrared colour–magnitude diagrams. A comparison of these with a sequence of five subdwarfs of known parallax has enabled us to determine a distance modulus for M13 of 14.27±0.05 mag without Lutz–Kelker corrections, or 14.44±0.06 mag if full Lutz–Kelker corrections are included. We have measured the colour of the main-sequence turn-off to be (V–K) = 1.20 mag, and by assuming a realistic gravity for the turn-off, we have used model atmosphere calculations to convert this to a temperature of (6260±100) K. From simulations made with theoretical isochrone calculations, we have determined the sensitivity of the distances derived from different colour–magnitude planes to various sources of error. We find that, at worst, combining optical with infrared magnitudes of equivalent photometric accuracy enables temperatures to be determined with much greater accuracy, and gives a photometrically independent contribution to the isochrone and subdwarf fits. At best, it gives the above and also offers isochrone and subdwarf fits which are more stable against errors in the photometry, the isochrones or in the adopted reddening parameters.