ultramassive black holes

The Milky Way has a roughly 3 million solar mass black hole at its center.
The nearby M87 galaxy in the Virgo cluster has a roughly 3 billion solar mass black hole at its center.
How much more massive do black holes get?

Prof Priya Natarajan at Yale thinks she knows the answer: and that is that black hole mass maxes out at at measly 10 billion times the mass of the Sun, or so.

It is hard to measure the mass of a black hole. Since we can't see it, mass measurements are generally indirect and represent bounds, sometimes only upper bounds, on the mass.
The Milky Way's black hole is the nearest supermassive (roughly speaking over 100,000 solar masses) black hole, that we know of, and one of the black holes with the best measured masses, since it is quite close.



Black Hole at the Center of the Milky Way (from Andrea Ghez at astro.ucla.edu)

The Milky Way is a mediocre sized spiral galaxy, with a moderate, peanutty central bulge.

In contrast, M87 is the central galaxy of the Virgo cluster, about 50 million light years away, it is a massive elliptical galaxy. It almost certainly has a very respectable black hole in its center, about a thousand times more massive than that in the center of the Milky Way.



M87 seen through Hubble

M87 is a pretty impressive elliptical galaxy, as these things go, but there are galaxies several times bigger, the central Dominant galaxies of big clusters. Although, to be fair, the cD galaxies sometimes get a but fuzzy, hard to tell where, or if, the break between the galaxy proper and the cluster ambient medium is.



Now, there is a famous "mass-bulge relationship", a close relation of the visually less stimulating "mass-sigma relationship", that tells us that the mass of the central supermassive black hole scales nicely with the mass in the spheroid of the host galaxy.



Black hole mass-bulge mass relationship

In fact, the relationship is "too good" - just random effects, and selection bias, should drive a bigger scattered than observed in the relation.

But, can we extrapolate it beyond the observed range and figure out something about the most massive black holes in, presumably, the most massive galaxies.
I have long been interested in this, because you can do some interstingly funky things with 100 billion solar mass black holes.

Alas, it is not to be.
Priya, and her co-authors, show fairly convincingly that black holes are hard to feed to bloating and that the black hole mass maxes out at a nice 10 billion or so solar masses, and that there are ultramassive black holes out there that mass more than the one in M87 but no more than about 10 billion solar mass black holes.

Better still, this is a testable prediction - so go prove a theorist wrong, and find a 30100 billion solar mass black hole out there!
We need one for some engineering experiments...

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Does M87 count as a cD galaxy, and what kind of "interestingly funky things" can be done with 100-billion-solar-mass black holes?

I read the abstract at the link you provided but could you provide a brief explanation of why there would be an upper limit on the mass of a UMBH, in the vernacular if possible?

Coby: If I'm reading the abstract right, the derived upper limit is based on observational constraints. IOW, if there were UMBHs with masses much larger than 10^10 solar masses, it would not be possible to explain the observed distribution of UMBHs as a function of mass.

Which is definitely *not* what I see in the press release. There, they propose a physical mechanism for why there would be an upper limit. Namely, the radiation given off in the vicinity of such a black hole would be so great as to disrupt further mass influx. I suspect that at the moment that's speculation on their part; if they could prove it it would be in the abstract. I also don't see how it would prevent such a black hole from ingesting other UMBHs.

By Eric Lund (not verified) on 15 Sep 2008 #permalink

Having read the paper (a few days ago, and then again today)... I don't see any real predictions of an upper limit to black hole masses -- or at least no model generating one.

What the paper really appears to do (parts of it are rather vague) is compare a prediction of what present-day black hole masses might be -- assuming that black holes grow by accretion, and that this accretion can be estimated from the hard-X-ray luminosity function -- with (an extrapolation of) the observed local distribution of black hole masses. This prediction appears to fail, since it predicts too many present-day black holes with masses greater than a billion suns, compared with what's observed. [*]

Then they come up with an ad-hoc tweak to the X-ray luminosity function (LF) which makes the prediction match the observations better. I think what they do is assume that the X-ray LF falls off more steeply, but only for black holes with masses greather than a billion suns. (They claim this doesn't conflict with the data for the X-ray LF, but don't provide any demonstration.) Then they speculate a little about possible causes of such a change -- i.e., why the most massive black holes might accrete proportionally less mass than lower-mass black holes do -- but this is basically just a short review of the literature, as far as I can tell.

Eh, I'm not really impressed. To be honest, most of this seems like a re-capitulation of things done in earlier papers, such as Marconi et al. 2004 (which Natarajan & Treister do reference), except that the earlier papers were more detailed and explicit about their calculations, and this paper doesn't discuss why they get a different answer.

[*] The "observed" distribution is constructed by taking a particular version of the black hole mass-sigma relation and applying it to a known distribution of sigma values for the local universe -- although they don't seem to say where they got the latter, which is rather annoying. (People have been doing this sort of thing since the mass-sigma relation was discovered in 2000, so it's not original to this paper.)

Mechanical upper limit for a black hole accreting at Eddington for the entire lifetime of the universe (ignoring that it will actually start about 20Myr or so after the Big Bang) is exp(30 * t_d/eps) times what you start with, t_d being the duty cycle and eps being the accretion to luminosity efficiency. Assuming you start off with a couple hundred solar mass black hole from a PopIII star, and a 10% duty cycle and efficiency, you finish with a 10^15 solar mass black hole.

As pointed out in the earlier post, in theory, starting out from a pop III remnant with
steady accretion at a modest rate, black hole masses today could be significantly higher
than we have claimed in our recent paper. And that is precisely why this work is interesting. In order to explain consistently the optical luminosity function of quasars, the X-ray luminosity of AGN and the local black hole mass function self-consistently, the X-ray luminosity function needs to be steepened at the bright end. This is not ad-hoc, there
have been many attempts to get the massive end of the local black hole mass function
by several authors over the past couple of years without success (including models with
all manner of bells and whistles). No other attempted solution, changing the accretion efficiency, Eddington ratio etc. works. The measured velocity dispersion function of nearby galaxies (as determined by the Sloan Digital Sky Survey) is used to obtain the local black hole mass function. The reason we think this is cute, is that independently in 1998, a physical explanation was suggested for the observed Mbh-circular velocity relation (alas we did not write it in terms of sigma) that provided such a limit. This calculated limit coincides with the limit obtained from the required steepening of the X-ray luminosity function. There are many theoretical models out there that attempt to the explain the correlation between black hole mass and host galaxy properties, ours in 1998 happened to be the first one. But hey here is a testable prediction, so if you are an observer, go find one that exceeds this mass limit!