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We discuss astrophysical implications of $\kappa$-Minkowski space-time, inwhich there appears space-time noncommutativity. We first derive a velocityformula for particles based on the motion of a wave packet. The result is thata massless particle moves at a constant speed as in the usual Minkowskispace-time, which implies that an arrival time analysis by $\gamma$-rays fromMarkarian (Mk) 421 does not exclude space-time noncommutativity. Based on thisobservation, we analyze reaction processes in $\kappa$-Minkowski space-timewhich are related to the puzzling detections of extremely high-energy cosmicrays above the Greisen-Zatsepin-Kuzmin cutoff and of high-energy ($\sim$20 TeV)$\gamma$-rays from Mk 501.Comment: 10 pages, 6 figures, submitted to PRD, corrected some mistake

Have we already detected astrophysical symptoms of space-time noncommutativity?