Leptonic origin of TeV gamma-rays from Supernova Remnants

The lineless power-law emission observed by ASCA from the northeastern rim of the supernova remnant SN1006 has recently been interpreted as synchrotron radiation of electrons with energies around 100 TeV. In this letter we calculate the flux of inverse Compton emission at TeV photon energies that is a natural consequence of the existence of such high energy electrons and the cosmic microwave background. We find that the predicted flux is near the present sensitivity limit of the southern \v Cerenkov telescope CANGAROO, and should be detectable with the next performance improvements. The spectrum of SN1006 at a few TeV will be very soft. The existence of such highest energy electrons in SN1006 may not be a unique to this remnant. We can therefore conclude that the detection of TeV $\gamma$-ray emission in any supernova remnant does not necessarily provide evidence for a large number of cosmic ray nucleons in these objects, and thus is no simple test of cosmic ray origin as far as nucleons are concerned.