Upper limits to the SN1006 multi-TeV gamma-ray flux from HESS observations

Observations of the shell-type supernova remnant SN1006 have been carried out with the HESS system of Cherenkov telescopes during 2003 (18.2 h with two operating telescopes) and 2004 (6.3 h with all four telescopes). No evidence for TeV $\gamma$-ray emission from any compact or extended region associated with the remnant is seen and resulting upper limits at the 99.9% confidence level are up to a factor 10 lower than previously-published fluxes from CANGAROO. For SN1006 at its current epoch of evolution we define limits for a number of important global parameters. Upper limits on the $\gamma$-ray luminosity (for E = 0.26 to 10 TeV, distance d = 2 kpc) of $L_\gamma < 1.7$ $\times$ 1033 erg s-1, and the total energy in corresponding accelerated protons, $W_{\rm p}<1.6$ $\times$ 1050 erg are estimated (for proton energies $E_{\rm p} \sim 1.5$ to 60 TeV and assuming the lowest value n=0.05 cm-3 of the ambient target density discussed in literature). Extending this estimate to cover the range of proton energies observed in the cosmic ray spectrum up to the knee (we take here $E_{\rm p} \sim$ 1 GeV to 3 PeV, assuming a differential particle index -2) gives $W_{\rm p}<6.3$ $\times$ 1050 erg. A lower limit on the post-shock magnetic field of $B>25~\mu$G results when considering the synchrotron/inverse-Compton framework for the observed X-ray flux and $\gamma$-ray upper limits.