Title: “A Test of A New Type of Stellar Interferometer on Sirius” (the original 1956 Nature paper)

 “Interferometry of the intensity fluctuations in light IV. A test of an intensity interferometer on Sirius A” (a 1958 follow-up paper with more details)

Authors: R. Hanbury Brown, R. Q. Twiss

First Author’s Institution: Jodrell Bank Experimental Station, University of Manchester

Status: published in Nature (1956 paper) and Proceedings of the Royal Society A (1958 paper)

Knowing the sizes of stars is important to build models of how they work – but it’s a hard measurement to make. In today’s classic paper, two astronomers found an innovative way to directly measure the diameter of a main-sequence star for the first time. Not only did they succeed in their astrophysical goal, their technique became important to several other branches of physics!

How big is that star?

If you know the distance between you and an object, you can use its angular diameter – the angle you (or your telescope) have to turn to look between one edge and the other – and some trigonometry to calculate how big it is:

Fig 1: How to calculate the size of the star, where x is the distance to the star, θ is the angular diameter, and D is the diameter of the star.

You can measure the distance to a star by parallax, but what about angular diameter? You might have looked through a telescope and seen a planet change from an apparent point of light to a disk with a noticeable angular size, but the stars behind it still look like points.

Thanks to the physical effect called diffraction, there is a limit on the smallest angular detail you can see given by the Rayleigh criterion:  sinθ=1.22*λ/d, where θ is the angle, λ is the wavelength of light and d is the size of the opening, or aperture, through which you are collecting light. A telescope mirror is bigger than the pupil of your eye, allowing you to see finer details, and the bigger the telescope, the smaller the details you can see. 

Even though stars are big, they’re really far away, so they have tiny angular diameters. But you can view the star from two different locations and combine the information to create an effective aperture: the distance between the two observing locations counts as d in the Rayleigh criterion.

One way to do this is collect beams of starlight at two different locations and interfere them with each other, using the resulting fringe pattern to learn about the source. (We won’t go into detail here, but it’s kind of like Young’s double-slit experiment.) This is sometimes called amplitude interferometry, and Albert Michelson and his student Francis Pease used it on Betelgeuse to measure a star for the first time in 1919. They set up a 20-foot interferometer at Mt. Wilson, but that was only big enough to measure seven nearby red (super)giants, which aren’t called giants for nothing. Making a bigger interferometer to measure smaller stars was just too hard at the time: to get a good fringe pattern, you have to stabilize the optical paths of the two beams to within a single wavelength – for optical light this can be as small as a thousandth the width of a hair. Differences in atmospheric twinkling between the two collection locations count against your optical path too. More measurements would have to wait, and star sizes were estimated from temperature in the mean time.

The intensity interferometer

In the early 1950s, radio engineer Robert Hanbury Brown had an idea for a new interferometer design, and he recruited mathematician Richard Twiss to help him work out the details. The idea goes something like this: as wavefronts travel to you from various points on a star, they constructively and destructively interfere with each other, creating fluctuating dark and bright patches. The smaller the angles between rays, the bigger the patches will tend to be; the bigger the angles, the smaller the patches (see Fig. 2).

Fig. 2 A very rough illustration of the intensity interferometer idea. Bigger angle between wave origins: smaller light/dark interference patches; smaller angle: larger light/dark interference patches.

If you place two telescopes much closer to each other than the typical size of an interference patch, they’ll almost always be inside the same patch and either both see a bright fluctuation or both see a dark fluctuation at any given time. As you gradually move them apart, they’ll be less likely to be inside the same patch, and the degree of correlation between the intensity fluctuations at the two locations will decrease. The distance it takes to observe the drop-off in correlation depends on the angular diameter of the source and the wavelength.

Hanbury Brown’s first intensity interferometer was built for radio astronomy, where the wavelengths of meters limit the angular resolution, but why not also try it in the optical? It should be way easier than optical amplitude interferometry because you don’t have to actually get light from one side of the interferometer to the other; you can convert the light intensity to an electrical signal via a photodetector at each location and then combine the electrical signals, which are way easier to handle than beams of light. (You can even just record them and compare them later, provided you timestamp them well.) You can also filter the typical frequencies of atmospheric twinkling out of your electrical signal.

Today’s classic paper: trying it out on Sirius

After trying a lab demonstration with a lamp, Hanbury Brown and Twiss set out to measure the angular diameter of Sirius, the brightest star in the sky after the Sun. They chose Sirius because it was bright and because the sizes of hot, blue-white stars were the least well-constrained by theory at the time (but no main sequence star’s angular diameter had been directly measured before!)

Hanbury Brown and Twiss borrowed a pair of searchlights from the army and replaced the light bulb at the focus of each searchlight’s 1.5-meter reflector with a photomultiplier, so that instead of enlarging the light bulb’s beam, the reflectors concentrated starlight down onto the detector. They mixed the voltages from the two detectors and recorded the results with the searchlights placed 2.56, 5.35, 6.98, and 8.93 meters apart. Between November 1956 and March 1957, they took data “on all possible occasions”…which turned out to be a grand total of 18 hours over 5 months. Because they did this at Jodrell Bank, England. In the winter. Where it rains on roughly half of all days and Sirius never gets more than 20 degrees above the horizon. Their paper notes that they didn’t correct for variations in atmospheric water vapor variation “since all the observations were carried out with the air temperature close to freezing point.” It’s the sort of observing campaign that makes you want to move to Australia.

Nonetheless, it was enough data for success. The level of correlation followed the predicted curve shape as they moved the detectors farther apart, and when they fit their data, they found an angular diameter for Sirius of 6.8 milliarcseconds, within about 10% of the theoretical prediction of 6.3 milliarcseconds.

Can we take this measurement Siriusly?

But wait! many physicists objected. It’s all very well to treat radio emission, with wavelengths as big as your equipment, as semi-classical waves. But quantum mechanics tells us that light should act like both a wave and a particle, and in this experiment the particle nature should be impossible to ignore. In fact, the detectors used by Hanbury Brown and Twiss work by the photoelectric effect, which is often used as the archetypical example of how light arrives in discrete packets called photons instead of behaving purely like a wave. Surely the correlation effect couldn’t be real?

Theorists got to work. It turned out that the correct answer, viewed from the particle picture, is that photons bunch – when emitted by a chaotic source, instead of coming along at random times, they clump. That’s weird – and it lead physicists to think about what other weird effects might be observable if you took the photon seriously as a really, truly quantum particle. The HBT experiments launched the whole new field of quantum optics.

Moreover, the HBT effect isn’t limited to photons. Any particle with integer quantum mechanical spin will bunch, while any particle with half-integer spin will antibunch (spread out). While stars look small because they’re far away, subatomic processes look small because they’re actually really small, and observing bunching and antibunching of particles turned out to be an invaluable tool for particle and nuclear physics.

Interferometry today

So where did the story go next for astronomy? Hanbury Brown and Twiss got funding for a bigger, purpose-built instrument in Australia. The Narrabri Stellar Intensity Interferometer operated from 1962 to 1974 and, among other projects, measured the diameters of 32 bright blue-white stars, which allowed astronomers to calibrate the theory and make accurate estimates for dimmer such stars.

As time went on, optics technology improved and started making bigger Michelson-Pease amplitude interferometers look feasible again. Since intensity interferometers carry a brightness penalty relative to amplitude interferometers (you get less signal for a source with the same brightness), attention turned back to the amplitude design. Today, with technologies like fiber optics to carry beams of light and adaptive optics to correct for the twinkling of the atmosphere, amplitude-interferometry instruments like GRAVITY at Mt. Paranal and CHARA on Mt. Wilson can do incredible things like map sunspots on other stars and directly detect exoplanets.

But modern gamma-ray observatories called Imaging Atmospheric Cherenkov Telescope (IACT) arrays just might bring intensity interferometry back. IACT arrays use sensitive spread-out telescopes to observe the Cherenkov radiation from particle showers created by gamma rays slamming into the atmosphere. Different telescopes see the shower from different angles, and the data is timestamped carefully so you can reconstruct the event in 3D. When the moon is too bright to see the Cherenkov light, you can use all these same ingredients to perform intensity interferometry measurements! Just since 2019, at least three IACT arrays – VERITAS, MAGIC, and HESS – have all made star-diameter measurements and have ambitions for more intensity-interferometry observations to come.

Astrobite edited by Ryan White

Featured image credit: NASA 

See also: Michelson and Pease’s Betelgeuse paper; The Narrabri Stellar Intensity Interferometer: A 50th birthday tribute (closed access); HBT effect with interacting particles; how to estimate stellar diameter from temperature (to be more accurate, you have to use an “effective temperature” calibrated by angular diameter measurements); the HESS intensity interferometry paper