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Cosmic triangles and black-hole masses

Nature volume 515, pages 498499 (27 November 2014) | Download Citation

A geometric measurement of the distance to a nearby galaxy implies a larger mass for its central black hole than previously calculated, and a consequent increase for most other masses of such black holes. See Letter p.528

Most distance measurements in astronomy rely on bright sources of light with known power output. How bright an object looks in the sky depends on both its actual light output and its distance from an observer on Earth, so knowing the object's real and apparent brightness allows the distance to be determined. The type 1a supernovae used to discover that the Universe's expansion is accelerating are the best-known examples of such sources. However, a better method for estimating astronomical distances is to use simple geometry, and in this issue Hönig et al.1 (page 528) demonstrate a new geometric-distance method.

If we know the length of the base of an isosceles triangle, with the two long (very long!) sides being the distance to an object, then we can solve for that distance given just one angle. Unfortunately, such a situation is rare in astronomy. The only well-used example is a star's parallax, in which the diameter of Earth's orbit is the base of the triangle and the angle is how much the star moves against the background stars as Earth moves from one side of its orbit around the Sun to the other every six months (Fig. 1). A star that moves 1 arcsecond would be one 'parsec' away. Although the European Space Agency's Gaia satellite is taking parallax to a new level of micro-arcsecond precision, even it cannot use this geometric-distance method on anything distant enough to track the expansion of the Universe.

Figure 1: Geometric distances.
Figure 1

a, The distance to a star (Dstar) from Earth can be measured by solving an isosceles triangle. The base of the triangle corresponds to twice the distance between Earth and the Sun, and the angle between its sides (θ) is the angular displacement of the star against a background of distant stars (not shown) as Earth moves from one side of its orbit to the other every six months. b, The distance to a quasar or an active galactic nucleus (AGN), Dquasar, can be solved if we know the angular size (θ) of some region in the quasar using an interferometer and its linear size (dregion) from the time that light takes to move from the quasar's central source out to that region3. Hönig et al.1 used the region of hot dust that surrounds the central source of a nearby AGN, and that radiates in the infrared, to measure the distance to this AGN with a roughly 13.5% uncertainty.

Quasars, and their less-luminous cousins the active galactic nuclei (AGNs), are objects powered by supermassive black holes that pull (accrete) matter towards them at high speeds. This accretion process releases enough kinetic energy as radiation for some of them to be bright enough to be seen across the Universe. But quasars and AGNs would seem to be unpromising prospects for applying geometric-distance measurements because almost all of the emission from these sources comes from a compact region that cannot be spatially resolved.

However, Hönig et al. show that there is a way to obtain the geometric distance to these objects. They invert the triangle used for parallax and put the base of the triangle at the AGN. The sizes of regions in the interior of AGNs are known from a technique called reverberation mapping. The central luminous source in an AGN is tiny, only a few tens of times larger than the supermassive black hole's event horizon — the boundary beyond which no radiation can escape. This source is unstable and varies quite rapidly. Imagine a single flash of light from this small source. This flash travels out at the speed of light. When, after some delay, it encounters gas or dust in its neighbourhood, that material lights up in response; in other words, it 'reverberates'. We can measure how far from the source the lit-up material is just by multiplying the time delay by the speed of light. This distance gives the length of the base of a triangle (Fig. 1; the actual details of this calculation get complicated2). To get the required angle, that is, the angular size of the region that lights up, Margarita Karovska and I suggested3 using optical interferometers to detect light reverberation from fast-moving clouds located at distances from the central source that are several hundred times the size of the event horizon. But this method has proved to be a step too far for existing interferometers because the angular sizes involved are too small for them to measure.

Hönig and colleagues realized that the hot dust found in AGNs, which radiates in the infrared, was distributed on a sufficiently larger spatial scale than the fast-moving clouds for the Keck interferometer on Mauna Kea, Hawaii, to be able to measure the angular sizes of hot-dust regions in the nearest AGNs at half a milliarcsecond resolution, which is about 100 times better than can be obtained by imaging with the Hubble Space Telescope. The authors relied on the successful Japanese MAGNUM dust-reverberation project4 for the lengths of the bases of the triangles. Armed with the angular sizes determined using Keck and the lengths from MAGNUM, they have successfully solved the triangle to get the distance to a nearby AGN called NGC 4151, which turns out to be 19.0 (+2.4, −2.6) megaparsecs.

The authors' method is direct, avoiding the usual uncertainty-enhancing steps found in distance measurements that rely on sources with known luminosity. That is the great virtue of using geometry. Although the details of the method are complex, their measurement has an uncertainty of about 13.5% and seems reliable, because the researchers have made several tests of its robustness (see Extended Data for the paper1).

This result is noteworthy in two ways. First, NGC 4151 is the AGN with the best-measured black-hole mass from reverberation mapping that also has a black-hole-mass estimate from the kinematics of the surrounding gas and stars5. Estimates of black-hole masses from reverberation mapping involve a scale factor that is pinned down by the kinematic mass calculation. Hence, NGC 4151 anchors this reverberation-based, black-hole mass scale, which has been applied to tens of thousands of AGNs and quasars. The kinematic black-hole mass depends on the distance to the AGN, so an accurate distance yields a more reliable scale factor. Hönig and colleagues' distance estimate for NGC 4151 suggests a larger value for this factor and a consequent increase for most black-hole masses of quasars and AGNs obtained using reverberation. Extending this work to more AGNs, as they become better measured in terms of gas and stellar kinematics, will show how much this factor varies from one object to another — a basic requirement if supermassive black-hole masses are to be measured confidently.

Second, and perhaps more importantly, this result is a dramatic demonstration of the power of high-angular resolution in astronomy. Optical and infrared astronomers have mostly plumped for bigger light-collecting areas in the next generation of giant, ground-based telescopes, which will have apertures of 25 to 39 metres in diameter. These telescopes will be equipped with adaptive-optics instruments that correct for the blurring effect of the wobbling of the atmosphere, and will deliver images of higher angular resolution than can Hubble. However, the resolution will still be about three times lower than that of the now-shuttered Keck interferometer.

But Hönig et al. have demonstrated that quasar structure and distances can be measured by interferometry. This opens up the prospect of extending AGN size and distance measurements out to the earliest cosmic times, and thus of measuring cosmological properties at distances far beyond where supernovae can take us. New interferometer designs promise great sensitivity increases6, and the CHARA array has already attained a higher angular resolution than could Keck7. Thanks to Hönig et al., we may now have to consider whether some of our resources should soon be put into building a next generation of optical interferometers.


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  1. Martin Elvis is at the Harvard-Smithsonian Center for Astrophysics, Cambridge, Massachusetts 02138, USA.

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Correspondence to Martin Elvis.

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