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tokens: We are thankful to Dan Harris for providing us with the M87 NRAO radio data, flux measurements and many insightful comments on the manuscript. AP acknowledges M. Krause, E. Churazov, and R. Sunyaev for discussions. SM is grateful to the University of Texas in Austin for its support, through a Tinsley Centennial Visiting Professorship. AP acknowledges financial support from the Spanish 2011 Severo Ochoa Program SEV-2011-0187, and the hospitality of the CAST group of the Ludwig Maximilians University of München (LMU) and the Max-Planck Institute für extraterrestrische Physik where most of this work was done. Based on VLT 4.B-0404(A), 76.B-0493(A), ALMA 2011.0.00754.5, NRAO AH 822, 862, 885, Chandra 3088.