Black Holes Sizes Follow A Formula

Gabriel Pérez Díaz: Artist's impression of the supermassive black hole at the center of a galaxy

The mass of a supermassive black hole can be determined from that of the galactic bulge in which it lies, astronomers at Australia's Swinburne University of Technology claim. However, rather than a simple formula to relate the two, they have found that the relationship changes with size.

Very large black holes appear to have a linear relationship with the bulge in which they sit – double the mass of the bulge and the black hole usually doubles too. However, the relationship breaks down for smaller galaxies. Moreover, astronomers have been puzzled by exceptions even at larger values, such as a black hole reported in 2012 to contain 59% of the mass of the bulge in which it lies, rather than a fraction of a percent.

In 2013, Professor Alister Graham proposed that smaller galaxies still show a relationship, but it's not linear. “The formula is quadratic, in that the black hole mass quadruples every time the bulge mass doubles,” Graham says. “If the bulge mass increases 10 times, the black hole mass increases 100 times.”

Now, in a paper published in The Astrophysical Journal, Graham offers further evidence for this theory, more than doubling his data points. He also provides some theories for those black holes that don't seem to fit the pattern. If he's right, his work could open up major opportunities for understanding how black holes form and grow.

Graham says the cross-over point between quadratic and linear growth occurs at around 100 million solar masses, compared to around 4 million for the black hole at the center of our own galaxy. He thinks the change occurs because smaller black holes grow largely by drawing in gas. “When galaxies run out of gas, black holes can't grow this way, and mainly grow through mergers. If two similar galaxies merge, you get double the mass of both the bulge and the hole.”

This paper provides plenty of evidence for Graham's contention that the quadratic relationship applies down to a black hole size of 100,000 solar masses, but he is interested in what happens below that. Astronomers have been bothered by the lack of intermediate mass black holes that lie between the 100 solar masses left from supernova explosions and the smaller holes in Graham's study.

While a few candidates for holes in this range have been found, Graham says “they are not in anything like the numbers expected.” He suggests we should be checking galaxies whose bulges are the right size to hold galaxies a little under the 100,000 suns mark. Unfortunately, as he notes, “The sphere of influence of a smaller black hole is smaller, and so harder to resolve.” The Large Magellanic Cloud is around the right mass for such a search, but lacks a distinctive central bulge, and more suitable galaxies are too distant for easy searching.

As for the holes that don't fit well on Graham's line, he thinks some are simply cases of mismeasurement. However, in other cases, “the universe may just have kept feeding the galaxy gas somehow,” allowing the hole to grow unusually large.



Credit: Swinburne University of Technology. 


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