Broad-band photometric colors and effective temperature calibrations for late-type giants. I. Z=0.02

We present new synthetic broad-band photometric colors for late-type giants based on synthetic spectra calculated with the PHOENIX model atmosphere code. The grid covers effective temperatures T_eff=3000...5000K, gravities log g=-0.5...+3.5, and metallicities [M/H]=+0.5...-4.0. We show that individual broad-band photometric colors are strongly affected by model parameters such as molecular opacities, gravity, microturbulent velocity, and stellar mass. Our exploratory 3D modeling of a prototypical late-type giant shows that convection has a noticeable effect on the photometric colors too, as it alters significantly both the vertical and horizontal thermal structures in the outer atmosphere. The differences between colors calculated with full 3D hydrodynamical and 1D model atmospheres are significant (e.g., \Delta(V-K)~0.2 mag), translating into offsets in effective temperature of up to ~70K. For a sample of 74 late-type giants in the Solar neighborhood, with interferometric effective temperatures and broad-band photometry available in the literature, we compare observed colors with a new PHOENIX grid of synthetic photometric colors, as well as with photometric colors calculated with the MARCS and ATLAS model atmosphere codes. (abridged)