Black holes and galaxies may grow up together.

Here's a weighty rule. If you want to find a really heavy black hole, you've got to look in a really heavy galaxy.

Astronomers analyzing 33 black holes at the centers of galaxies have found new evidence that the biggest galaxies house the biggest black holes. The study includes eight newly discovered black holes. For the first time, researchers have come up with a quantitative prescription: A black hole typically weighs 0.2 percent of the mass of its galaxy's bulge--the high-density, central portion believed to be one of the first parts of a galaxy to form.

The relationship suggests that black holes are intimately connected with bulge formation. Every galaxy with a bulge contains a black hole, and galaxies without bulges are likely not to have one, proposes John Kormendy of the University of Texas at Austin. His team reported the findings last week at a meeting of the American Astronomical Society in Rochester, N.Y.

The mass of the black holes in the new census ranges from 1 million to 2.4 billion suns. A key question is whether the link between black holes and bulges "will extend to lower masses or whether there is some threshold below which the formation process is less efficient," says Martin J. Rees of the University of Cambridge in England.

To weigh the black holes, the astronomers measured the velocity of stars at the cores of the galaxies using an imaging spectrograph on the Hubble Space Telescope. The more massive the black hole, the faster the stars move around it.

Two theories may explain the findings, says Kormendy. In one scenario, black holes come in a standard initial size, 0.2 percent of the mass of the first galaxy fragments. After that, black holes and bulges grow only when galaxies merge. The mergers preserve the relationship between black hole and bulge masses.

Alternatively, a black hole may start out small and grow during galaxy formation, feeding on the same gas that the bulge of a newborn galaxy draws in to make stars. If the hole consistently swallows 0.2 percent of the gas that makes stars, it will always weigh that fraction of the mass of the bulge.

Abraham Loeb of Harvard University says that he subscribes to the second hypothesis because it may explain the rarity of bright quasars. Scientists believe that these brilliant beacons, lying at the cores of some galaxies, are powered by the growth of black holes. If a black hole does most of its feeding early in the life of a galaxy, then its ability to power a quasar will diminish over time. Active quasars would become much less common than black holes.

Kormendy agrees: "Galaxy formation directly results in the black hole feeding that makes quasars shine."