Tag Archives: parallax

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.

Gaia flys

Close your left eye and align your upright index finger against some distant object. Then open your left eye and close your right eye. Your finger has moved, relative to the background object. This is the phenomenon known as parallax, and it arises whenever you look at an object from two spatially separated vantage points.

The importance of parallax is that it enables you to calculate distances. Since you know the distance between your eyes, and you can measure the angle through which the object has appeared to move, the application of some simple trigonometry gives the distance to your finger. Of course, figuring out the distance from your eyes to your finger isn’t a big deal – but precisely the same logic allows you to figure out the distance to nearby stars.

The Earth moves around the Sun, so when we look at a nearby star in January and in July we look at it from different vantage points: the nearby star appears to move relative to the background of the distant “fixed” stars. In other words, the nearby stars exhibit a so-called annual parallax. Since we know the distance between Earth and Sun (this is one of the earliest rungs on the cosmological distance ladder) and we can measure the angle through which the star appears to move over the course of a year, the application of some simple trigonometry gives us the distance to the star.

Annual parallax

As Earth makes its yearly orbit of the Sun, a nearby star is seen to make a tiny ellipse (relative to the distant “fixed” stars).

In Measuring the Universe I devoted a lot of space to a discussion of parallax, since it was the first technique that enabled astronomers to obtain accurate distances to nearby stars – the first successful measurement of an annual stellar parallax was made by Bessel in 1838 for the star 61 Cygni. However, there’s a difficulty in trying to use parallax as method of distance measurement in astronomy: the angles involved are so tiny. Even the nearest star has an annual parallax of less than 1 second of arc. (The parsec is defined as the the distance at which an object will possess an annual parallax of 1 second of arc; it corresponds to 3.26 light years. The Centauri system, of course, is 4.37 light years distant.) As time goes by, however, the accuracy with which astronomers can make measurements increases. Indeed, the other reason I spent so long discussing parallax was that, during the writing of the book, the results of the Hipparcos mission were being disseminated – Hipparcos (“High precision parallax collecting satellite”) represented a step-change in the field of astrometry.

Hipparcos  was an ESA mission, which was launched in 1989 and ran until 1993. It was the first space experiment devoted to astrometry – the accurate measurement of the position of stars. The final Hipparcos Catalogue contained information on the parallaxes of about 120,000 stars – with a median accuracy of better than 0.001 seconds of arc.

In Measuring the Universe I wrote that ESA were hoping to develop a successor mission to Hipparcos. The planned mission, called Gaia, would map not 100,000 stars but a billion stars. And the positional accuracy would not be measured in milliarcseconds but in microarcseconds (20 microarcseconds at a stellar magnitude of 15, and 200 microarcseconds at a magnitude of 20). Gaia would measure the distances of 20 million stars to a precision of 1%, and of 200 million stars to better than 10%. Such a mission would inevitably impact on many other fields (such as extrasolar planet determination, the testing of general relativity, quasar discovery…)

When I wrote the book, the Gaia mission was so far in the future that I found it difficult to imagine that it would ever fly; I thought it would be lost in the maze of technological, computational and political obstacles that were in its way. But Gaia is on its way! It launched successfully today, 19 December 2013, at 09:12GMT and in a month or so it will be at its new home at the Earth-Sun L2 point.

The plan is for Gaia to observe the sky for five years; astronomers will be analysing the Gaia data for much longer than that. This new astrometric mission is going to have a huge impact on all aspects of astronomy.