We use a combination of deep optical (gri) and near-infrared (H) photometry to study the radially-resolved colours of a broad sample of 300 Virgo cluster galaxies. For most galaxy types, we find that the median g-H colour gradient is either flat (gas-poor giants and gas-rich dwarfs) or negative (i.e., colours become bluer with increasing radius; gas-poor dwarfs, spirals, and gas-poor peculiars). Later-type galaxies typically exhibit more negative gradients than early-types. Given the lack of a correlation between the central colours and axis ratios of Virgo spiral galaxies, we argue that dust likely plays a small role, if at all, in setting those colour gradients. We search for possible correlations between galaxy colour and photometric structure or environment and find that the Virgo galaxy colours become redder with increasing concentration, luminosity and surface brightness, while no dependence with cluster-centric radius or local galaxy density is detected (over a range of ~2 Mpc and ~3-16 Mpc^-2, respectively). However, the colours of gas-rich Virgo galaxies do correlate with neutral gas deficiency, such that these galaxies become redder with higher deficiencies. Comparisons with stellar population models suggest that these colour gradients arise principally from variations in stellar metallicity within these galaxies, while age variations only make a significant contribution to the colour gradients of Virgo irregulars. A detailed stellar population analysis based on this material is presented in Roediger et al (2011b; arXiv:1011.3511).
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