Detailed high-resolution observations of the innermost regions of nearby galaxies have revealed the presence of supermassive black holes^{1, 2, 3, 4}. These black holes may interact with their host galaxies by means of 'feedback' in the form of energy and material jets; this feedback affects the evolution of the host and gives rise to observed relations between the black hole and the host⁵. Here we report observations of the ultraviolet emissions of massive early-type galaxies. We derive an empirical relation for a critical black-hole mass (as a function of velocity dispersion) above which the outflows from these black holes suppress star formation in their hosts by heating and expelling all available cold gas. Supermassive black holes are negligible in mass compared to their hosts but nevertheless seem to play a critical role in the star formation history of galaxies.

1. Department of Physics, University of Oxford, Oxford OX1 3RH, UK
2. Center for Space Astrophysics, Yonsei University, Seoul 120-749, Korea
3. Laboratoire d'Astrophysique de Marseille, 13376 Marseille Cedex 12, France
4. California Institute of Technology, MC 405-47, Pasadena, California 91125, USA
5. Laboratory for Astronomy and Solar Physics, NASA Goddard Space Flight Center, Greenbelt, Maryland 20771, USA
6. Department of Astronomy, Columbia University, MC 5246, New York, New York 10027, USA
7. Department of Physics and Astronomy, Johns Hopkins University, Baltimore, Maryland 21218, USA
8. Observatories of the Carnegie Institution of Washington, 813 Santa Barbara St, Pasadena, California 91101, USA
9. Department of Physics and Astronomy, UCLA, Los Angeles, California 90095-1562, USA

Correspondence to: Sukyoung K. Yi² Correspondence and requests for materials should be addressed to S.K.Y. (Email: yi@yonsei.ac.kr).

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