Appendix A: Data reduction and photometry

The 12 observed fields were imaged in 3 dithered positions each band, namely A, B and C. From these, 3 sky subtracted frames were obtained performing B-A, B-C and C-A, and were divided by a normalized flat field differentially generated (so as to remove any bias) by illuminating a dome screen at two different levels of light intensity. The images were subsequently cleaned for the presence of bad pixels by interpolating across them, and finally registered and co-added, using thresholding and median filtering in order to remove any signal below the sky level introduced by the subtraction, providing a single frame suitable for photometric analysis.

We used the DAOFIND task (Stetson 1987) to identify point sources down to a 4$\sigma$ level; subsequently, each frame was visually inspected at different contrast levels in order to remove false detection or add faint sources undetected by DAOFIND. Then, aperture photometry was performed using PHOT routines with an aperture radius of 2 pixels (about the FWHM of PSF's); this low value was needed in order to accurately measure source brightness in the most crowded areas of the imaged fields, but we checked that it was appropriate for relatively isolated stars as well. Due to the extremely variable background, the sky was sampled in 10-pixel wide annuli centred on each star, with inner radii of 10 pixels. An aperture correction was estimated using the brightest and most isolated stars in each image. The standard deviation of magnitude corrections both within a frame and within a band is generally mag. The small annulus we have been forced to use because of crowdedness and sky variations, obviously introduces a systematic error in the given JHK magnitudes (which, however, we estimate mag), but we expect that this is severely reduced, at least at the first order, when colours are derived. The modal value of pixels within each annulus was chosen for background subtraction; since the sky is extremely variable where also crowdedness is important, the modal value may not adequately sample it; however, we expect that this error may become dominant only for the faintest objects.