Some supermassive black holes are much more super than others

Supermassive black holes (SMBHs) can get to be pretty large. Astrophysicists don’t really know what the upper limit is, if any. But before some recent research, the mass of the largest SMBH yet determined was 6.3×10⁹ M_⊙ (solar masses). That value is known fairly precisely, since the SMBH is in the nearby giant elliptical galaxy M87, which is a mere 53 million light-years away.

The latest research has identified two substantially larger SMBHs, but the masses are known less precisely, since the objects are a lot farther away. One SMBH is in NGC 3842 and has estimated mass of 9.7×10⁹ M_⊙, at a distance of 320 million light-years. The other is in NGC 4889. Its mass is known considerably less precisely but may be more than twice that of the SMBH in NGC 3842. (2.1×10¹⁰ M_⊙ is the midpoint of the possible range.) It’s 336 million light years away. Both of these galaxies are also giant ellipticals. The uncertainty in the SMBH mass is much larger for NGC 4889 than for NGC 3842 because the mass estimates are based on the velocities of stars very close to the SMBH, and the uncertainties of velocity measurements in the former case were more than in the latter.

The establishment of new records for directly measured SMBH masses is actually not the most interesting aspect of the new research. (Although the amount of media attention to the results might lead one to think it was.) One thing that’s more interesting is that a fairly straightforward method of estimating SMBH mass can be used out to a distance of several hundred million light-years with present technology.

There are several basic methods for estimating SMBH mass. In the case of an active galaxy, there is a large amount of gas close to the SMBH, and as it is sucked in closer it forms an accretion disk that is heated to high temperatures by internal friction. The high temperature causes the gas to glow and produce an spectrum in which there are various prominent emission lines. These lines are somewhat broadened due to Doppler shift, because half of the disk is approaching us while the other half is receding. The width of the lines reflects the rotational velocity of the disk, and this in turn indicates the mass of the SMBH. This technique works well for very active galaxies in the distant universe – i. e. quasars – because such objects were much more common at early times.

Unfortunately for the convenience of measurement, quasars and less luminous active galaxies are now much rarer than in the past, so estimating SMBH mass using spectroscopic information from accretion disks is not possible with relatively inactive galaxies, which are now by far the most common type. One alternative is to measure the velocities of individual stars close to the SMBH, at distances out to about a thousand light-years from the SMBH. This is currently impossible for very distant galaxies, and difficult at distances of ~300 million light-years.

The orbital velocities of stars relatively close to a SMBH can be used to estimate SMBH mass because there is a simple relationship between orbital velocity and mass: v ≅ √(GM/r). Here G is Newton’s gravitational constant, M is the mass of the SMBH, and r is the distance of the star from the SMBH. This relation is only approximate, because the mass of the star also matters. However, the mass of the SMBH is so much greater than the mass of any star that the mass of the latter is almost irrelevant. It’s also approximate because there are many other stars near the SMBH, and each of these has some effect on the others, though that’s usually negligible.

Of course, at distances of hundreds of millions of light-years, individual stars can’t be resolved, so individual Doppler shifts can’t be measured. What can be measured is the width of individual spectral lines from stars close to the SMBH. This gives an indication of the overall distribution of stellar velocities of many stars. If the reading can be taken only from a small region near the SMBH, the average velocities of stars in the region can be inferred. The mass of the SMBH can then be estimated from the degree to which these velocities exceed the velocities of other stars in the galaxy.

In the galaxy as a whole, the average velocities of stars depend on the mass of the whole galaxy, including all associated dark matter. It’s only relatively close to the SMBH that its mass has an influence on orbiting stars. With existing telescopes and spectroscopic equipment, data can be obtained from regions as small as a few tenths of an arc second. At a distance of 300 million light-years one arc second corresponds to 1454 light-years, which is near the limit of the SMBH radius of influence. The velocities of stars that close to a SMBH should reflect the mass of the SMBH, but velocities of stars farther from the SMBH would not.

A few interesting conclusions can be drawn from the two SMBH masses estimated in this research. One concerns the relationship between SMBH mass and other properties of the galaxy as a whole. It’s well known that there’s a rough correlation between SMBH mass and the mass of the whole galaxy (including dark matter). Although it’s difficult to determine the actual mass of a galaxy, the stellar velocity dispersion of stars in the central bulge of the galaxy is often taken as a proxy for the galaxy mass (for the same reason that velocity dispersion of stars close to a SMBH indicates its mass). This relationship has been found to hold fairly well for nearby galaxies in which it’s been possible to get reasonable direct estimates of SMBH mass. But there are outliers, and the SMBHs of the two galaxies in this research may be almost 10 times as massive as expected from the mass of their galaxy.

Another correlation has been recognized between SMBH mass and the luminosity of a galaxy’s central bulge. There seems to be somewhat more scatter in this relationship. However, again, the SMBHs of the galaxies in this research have almost an order of magnitude more mass than the best linear fit of the SMBH-mass to bulge luminosity relation would imply. The divergences from expected SMBH masses in both cases may be a result of some non-linearity in the relationships, since both galaxies are at the upper end of the mass and luminosity scales. They are also the brightest galaxies of the clusters in which they reside, and this may imply that their evolutionary history is not typical of most galaxies.

Simulations of mergers between large galaxies that are relatively deficient in star-forming gas suggest that stellar velocity dispersions don’t increase substantially after the merger. But SMBH masses do increase in mergers of large galaxies, as the previously separate SMBHs merge. This may be the reason that the correlation of galaxy properties to SMBH mass weakens at the high end.

There’s one additional interesting conclusion from this research. The high luminosity of some very distant quasars (redshifts 2≤z≤4.5, i. e. as early as 1.4 billion years after the big bang) implies that even in the early universe they contained SMBHs with masses at least 10¹⁰ M_⊙. The two SMBHs of the present research are the first ever found that are this massive. Using the standard relationship between SMBH mass and either stellar velocity dispersion or central bulge luminosity, then data on the distribution of galaxies with known values of these quantities is not consistent with known frequencies of bright quasars in the early universe. There would simply be far too few sufficiently massive SMBHs in the nearby universe. But if the new results on the SMBHs of NGC 3842 and NGC 4889 are any indication, there really should be enough very large SMBHs actually around today.

McConnell, N., Ma, C., Gebhardt, K., Wright, S., Murphy, J., Lauer, T., Graham, J., & Richstone, D. (2011). Two ten-billion-solar-mass black holes at the centres of giant elliptical galaxies Nature, 480 (7376), 215-218 DOI: 10.1038/nature10636

Further reading:

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