4. Concluding remarks
The size limits given in this work illustrate the precision which can nowadays be reached in TeV gamma-ray astrophysics; a number of potential galactic and extragalatic sources are predicted to be extended sources on this scale.
A few remarks concerning the interpretation of the limits: the values quoted above refer to the rms source size, with the implicit assumption that source strength is distributed over an area which is similar to, or small compared to the angular resolution of the instrument, such that the convolution of the source distribution and the Gaussian response function can again be approximated by a Gaussian distribution. This is obviously the case for a roughly Gaussian source, and was explicitly checked for two alternative distributions, namely (a) the case that the source strength is uniformly distributed over the surface of a sphere of radius r, resulting in an rms source width of , and (b) the case that the source is uniformly distributed inside a sphere of radius r, with an rms size of . The limit on 1.5´ rms size can be reliably translated into a limit on the radius of a surface source of 2.6´, or on the radius of a volume source of 3.4´. We note, however, that one can construct source models with a large rms source width which would not be detected by our method. One example is a combination of a localized source at the center with a weak halo with an extension of a few degrees or more. Such a faint, diffuse halo could not be detected, yet formally results in a large rms width of the source. However, given that it is hard to imagine to have TeV emission even beyond the radio emission region, such scenarios are hardly relevant for the Crab Nebula.
The limit on the size of the TeV emission region of the Crab Nebula is, by a factor around 4, larger than the size predicted by the standard inverse Compton models for gamma-ray production in the nebula. The limits, however, approach the sizes expected for hadronic production models, where high-energy gamma-rays are produced by nucleon interactions, more or less uniformly throughout the nebula.
© European Southern Observatory (ESO) 2000
Online publication: October 10, 2000