Optical and infrared observations of the Crab Pulsar and its nearby knot

Aims. We study the spectral energy distribution (SED) of the Crab Pulsar and its nearby knot in the optical and in the infrared (IR) regime. We want to investigate how the contribution from the knot affects the pulsar SED in that regime, and examine the evidence for synchrotron self-absorption in the IR. We also draw the attention to the predicted secular decrease in luminosity of the Crab Pulsar, and attempt to investigate this with CCD observations. Methods. We present high-quality UBVRIz, as well as adaptive optics $JHK_{\rm s}L'$ photometry, achieved under excellent conditions with the FORS1 and NAOS/CONICA instruments at the VLT. We combine these data with re-analyzed archival Spitzer Space Telescope data to construct a SED for the pulsar, and quantify the contamination from the knot. We have also gathered optical imaging data from 1988 to 2008 from several telescopes in order to examine the predicted secular decrease in luminosity. Results. For the Crab Pulsar SED we find a spectral slope of $\alpha_\nu = 0.27 \pm 0.03$ in the optical/near-IR regime, when we exclude the contribution from the knot. For the knot itself, we find a much redder slope of $\alpha_\nu = -1.3 \pm 0.1$. Our best estimate of the average decrease in luminosity for the pulsar is $2.9 \pm 1.6$ mmag per year. Conclusions. We have demonstrated the importance of the nearby knot in precision measurements of the Crab Pulsar SED, in particular in the near-IR. We have scrutinized the evidence for the traditional view of a synchrotron self-absorption roll-over in the infrared, and find that these claims are unfounded. We also find evidence for a secular decrease in the optical light for the Crab Pulsar, in agreement with current pulsar spin-down models. However, although our measurements of the decrease significantly improve on previous investigations, the detection is still tentative. We finally point to future observations that can improve the situation significantly