We have conducted a systematic and comprehensive monitoring programme of the Type Ia supernova 2000cx at late phases using the VLT and HST. The VLT observations cover phases 360 to 480 days past maximum brightness and include photometry in the BVRIJH bands, together with a single epoch in each of U and Ks. While the optical bands decay by about 1.4 mag per 100 days, we find that the near-IR magnitudes stay virtually constant during the observed period. This means that the importance of the near-IR to the bolometric light curve increases with time. The finding is also in agreement with our detailed modeling of a Type Ia supernova in the nebular phase. In these models, the increased importance of the near-IR is a temperature effect. We note that this complicates late-time studies where often only the V band is well monitored. In particular, it is not correct to assume that any optical band follows the bolometric light curve at these phases, and any conclusions based on such assumptions, e.g., regarding positron-escape, must be regarded as premature. A very simple model where all positrons are trapped can reasonably well account for the observations. The nickel mass deduced from the positron tail of this light curve is lower than found from the peak brightness, providing an estimate of the fraction of late-time emission that is outside of the observed wavelength range. Our detailed models show the signature of an infrared catastrophe at these epochs, which is not supported by the observations.
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