Measuring the distance to black holes

It’s not often that you come across a new method of distance determination in astronomy, but today’s Nature contains a paper (“A dust-parallax distance of 19 megaparsecs to the supermassive black hole in NGC 4151” by Sebastian Hönig, Darach Watson, Makoto Kishimoto and Jens Hjorth) that describes a method for directly determining the distances to quasars and galaxies with active nuclei.

As I’m sure you’re aware, over the course of many decades astronomers have developed a “cosmological distance ladder”. If astronomers understand an object – how bright it really is, how big it really is – they can determine its distance by measuring how bright or how big it appears. However, each time astronomers step up one rung on the distance ladder they introduce a source of error. It’s inevitable. A much better way of measuring distance is to use a direct method: to use geometry, in other words.

The most familiar example in astronomy of distance determination through geometry is that of annual parallax. As Earth moves around the Sun, the position of a nearby star is seen to shift relative to the background of the more distant, “fixed” stars. Draw lines between Earth, Sun and star and we generate a huge triangle. But we can measure the angular shift, and we know the diameter of Earth’s orbit, so we have all the information we need to solve the triangle. (Assuming we’ve done basic geometry in school.)

Annual parallax

Earth, Sun and star form a triangle. We know the base of the triangle and we can measure the parallactic shift caused by Earth’s motion. We can solve the triangle and determine the star’s distance.

If a star moves by 1 second of arc then by definition it would be at a distance of one parsec. All stars (except the Sun, of course) are further away than 1pc and so all angular shifts exhibited by stars are less than 1 second of arc. Indeed, although this method formed one of the earliest and most important rungs in the cosmological distance ladder, it is difficult to apply it to very distant objects because the angles involved are simply too small to measure.

How, then, can Hönig and his colleagues apply a geometrical technique to a galaxy that lies 19 million parsecs away? Aren’t the angles way too small to measure?

Well, these astronomers have “inverted” the familiar parallax triangle. The base of the triangle isn’t the diameter of Earth’s orbit, it’s size of a region surrounding an active galactic nucleus (in this particular case, it’s the size of a dust region surrounding the supermassive black hole in the nucleus of the galaxy NGC 4151).


The Seyfert galaxy NGC 4151 lies 62 million light years from Earth. In this image, blue is from X-ray observations; yellow dots are from optical observations; and red is from radio observations. (Credit: NASA, ESA)

In order to solve the triangle formed by Earth, the supermassive black hole in NGC 4151, and the dust region surrounding the black hole, astronomers need to measure two things: (i) the base of the triangle – in other words, the true distance between the black hole and the dust, and (ii) the smallest angle in the triangle – in other words, angular size of the dust cloud.

The distance between the black hole and the dust cloud is easy to measure in principle – though difficult and messy in practice. As matter falls towards the black hole it heats up, so infalling matter produces radiation from a region just outside the event horizon. (Note that, although the black hole has a huge mass the radius of the event horizon is small. This is not a big object.) The radiation spits, and flickers, and flares: it’s highly variable. So suppose there’s a flash of light from just outside the event horizon. Some of the light will take a path directly towards our telescopes; some of the light will head of at right angles and continue until it interacts with dust clouds. This interaction will cause the dust to light up (or “reverberate”), which our telescopes will detect some time after the detection of the initial flash. By measuring the time delay astronomers can thus calculate the length of the base of the triangle (it’s just the delay multiplied by the speed of light). The technique is called “reverberation mapping”.

The angular size of the hot dust clouds that surround active galactic nuclei can be determined with a sufficiently precise interferometer. The Keck interferometer has sufficient resolution to measure the angular size the dust clouds in NGC 4151, and this is what Hönig and his colleagues did. By using the angular size determined by the Keck interferometer with lengths determined by a previous reverberation mapping project they were able to solve the NGC 4151 triangle: it’s 19 Mpc away (give or take 2.5 Mpc).

This distance comes from geometry. There’s no chain of inference involved as there is with the cosmological distance ladder: geometry gets you there directly.

The method has great potential because active galactic nuclei are bright enough to shine all the way across the universe. If we were to develop interferometers with increased resolving power (rather than just developing telescopes with ever-greater light-collecting ability) then we would have the ability to use geometry to measure distances over cosmological scales.