Scientists defy Einstein’s prediction and use relativity to measure a star’s mass

Astronomer Terry Oswalt uses props to show how a star’s gravity deflects light. Scientists can then use this deflection of light to calculate the weight of star. (Embry-Riddle Aeronautical University / Robert H. Score)

Astronomers scanning the skies with NASA’s Hubble Space Telescope have pulled off a feat that even Albert Einstein had declared all but impossible: they’ve witnessed the subtle bending of one star’s light by another star’s gravity and used that distortion to measure a star’s mass.

The findings, unveiled Wednesday at a meeting of the American Astronomical Society and published in the journal Science, confirm a key tenet of Einstein’s landmark general theory of relativity and introduce a new tool with which to explore a fundamental property of stars.

The general theory of relativity, presented in 1915, describes how gravity can distort the path of light, altering its trajectory. In 1919, the theory was proved correct when, during a solar eclipse, an expedition led by Sir Arthur Eddington discovered that stars near the edge of the blocked sun’s disc were not where they were supposed to be. Their apparent position had moved because the sun’s gravity had distorted the path of their starlight, just as Einstein had predicted.

Since then, astronomers have used this insight as a powerful tool with which to observe distant phenomena. That’s because, when lined up just right, a massive object in the foreground can bend the light of a background light source and magnify it the way a lens does. This phenomenon, known as gravitational lensing, has allowed astronomers to observe distant galaxies that otherwise would be too faint to study.

But lensing events enabled by galaxies and other large structures have been fuzzy at best, said Terry D. Oswalt, an astronomer at Embry-Riddle Aeronautical University’s Daytona Beach campus, who was not involved in the study.


“They are lousy lenses because they’re not point sources,” Oswalt said. “They’re big and splotchy. They’ve got spiral arms and nuclei and sometimes companion galaxies, and sometimes there’s clusters of galaxies.”

But stars are point sources, not large and lumpy like galaxies. If you could catch a lensing event between two stars, it could offer a much more focused effect. You might even be able to capture an Einstein ring — a phenomenon in which a lensing object eclipses a background light source so perfectly that the background object is rendered as a luminous circle. (This has been documented for galaxies, but not for individual stars.)

For this paper, lead author Kailash Sahu of the Space Telescope Science Institute in Baltimore and his colleagues set out to find a lensing event between two stars. This was a much more difficult feat, partly because the effect for single stars is so tiny compared with the size of galaxies. To make matters worse, astronomers are far less likely to catch two stars overlapping than to find two galaxies doing so.

Sahu’s team looked for stars that were set to cross in front of background stars in the hopes of catching a stellar Einstein ring. Using the Hubble Space Telescope, they zeroed in on a white dwarf star called Stein 2051 B, which they knew would pass in front of a more distant star.

Even though they knew where to look, this was no easy task: The background star was 400 times dimmer than Stein 2051 B.

“It’s like measuring the motion of a firefly next to a light bulb from 1,500 miles away,” Sahu said.

Einstein described such rings in a paper in 1936, but said that because of their rarity and the physical limitations of scientific instruments, they weren’t likely to ever be seen.

“Of course, there is no hope of observing this phenomenon directly,” he wrote in that paper, which also appeared in Science.

But as Sahu and his colleagues observed Stein 2051 B, the background star seemed to jump, appearing to do a tiny somersault over the white dwarf passing in front of it.

Here’s what was happening: As Stein 2051 B began to line up with the background star, its gravity distorted the background star’s light, creating an Einstein ring. However, because the two stars’ alignment was not perfect relative to Earth, that Einstein ring took the form of an ellipse, with one side brighter than the other.

As Stein 2051 B moved in front of and across the dimmer star, the elliptical Einstein ring shifted positions, with the brighter side appearing as a point that traced a tiny arc across the sky.

While Hubble is not strong enough to resolve that ellipse, the telescope did see the background star appear to shift positions.

“It’s not actually moving — it’s [an] apparent motion caused by the bending of the light,” said Oswalt, who wrote a commentary that accompanied the study.

What’s more, the fact that this series of Einstein rings was elliptical rather than a perfect circle actually allowed scientists to calculate the mass of Stein 2051 B — a measurement that has dogged the astronomical community for years.

Stein 2051 B is part of a binary pair of stars that circle one another, and researchers have used the motion of the pair to calculate the white dwarf’s mass. According to this method, the star apparently was so heavy that it would have to have an iron core, which doesn’t make sense for a white dwarf. It also would mean this star was ancient, about as old as the universe itself, which scientists were pretty sure could not be right.

But thanks to this gravitational lensing event, scientists were able to directly determine Stein 2051 B’s mass. They found that the white dwarf is about two-thirds the mass of our sun — much more in line with our understanding of white dwarf evolution.

“This is like putting the star on a scale and just seeing how the scale changes,” Sahu said of the lensing method. “The deflection [of light] is the movement of the scale, and that tells you the mass. So it’s a very direct way to determine its mass.”

White dwarfs are the remnants of dead stars; some 97% of the stars in our galaxy are destined to become one. Surprisingly little is known about their masses — only a handful have been measured, typically indirectly by using binary star pairs. This lensing method could change that.

“This is the debut of a new tool,” Oswalt said.

Understanding the masses of stars is key to understanding their origins and development, Sahu added: mass determines how big a star is, how bright it is, how long it lives — and what happens to it when it dies.

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7:05 p.m.: The story was updated with additional information throughout.

The story was originally published at 10:20 a.m.