Weighing A Star With Gravity: Einstein’s ‘Impossible’ Experiment

10:03 minutes

This illustration reveals how the gravity of a white dwarf star warps space and bends the light of a distant star behind it. Credit: NASA/ESA/A. Feild (STSCI)

In 1915, Albert Einstein proposed one practical application for his theory of general relativity: Calculate the mass of a star based on how its gravity distorts the light passing by it. Four years later, a research team was able to prove him right, using our sun’s distortion of a background star during an eclipse. But Einstein wrote in a 1936 paper that it would be impossible to observe the same for a star not in our solar system, because the distance would be too great, and our instruments would be unable to resolve to a sufficient level of detail. “There is no hope of observing this phenomenon directly,” he wrote.

[One hundreds years of general relativity.]

Now, reporting in Science, a research team describes having done just that: They’ve successfully calculated the mass of Stein 2051B, a white dwarf, based on how it distorts the light of a background star. What changed? The Hubble Telescope received an instrumentation upgrade in 2009 that gave it just the power needed to detect the distortion, which measured just a few thousandths of an arcsecond.

[Checking in on our planetary neighbors.]

Lead author Kailash Sahu, an astronomer at the Space Telescope Science Institute in Baltimore, Maryland, and astrophysicist Mario Livio, describe the painstaking observation involved in the task, and what other applications could await.

Segment Guests

Kailash Sahu

Kailash Sahu is an astronomer at the Space Telescope Science Institute in Baltimore, Maryland.

Mario Livio

Mario Livio is an astrophysicist and author of several books, including Galileo: And the Science Deniers (Simon & Schuster, 2020). He’s based in Baltimore, Maryland.

Segment Transcript

IRA FLATOW: This is Science Friday. I’m Ira Flatow. Scientists have now completed a test of general relativity that Einstein said would be impossible. And the success allows astronomers to do something new, and that’s weigh a star. Let me go back and retrace a bit.

Back in 1915, Einstein’s theory of general relativity predicted that stars, being massive, would warp space. And that theory was tested successfully during the solar eclipse of 1919, using the sun as the test star. But Einstein said it would be impossible to make this observation on a star outside of our solar system.

Well, 100 years later, a team of astronomers has done just that, measuring the bending of light around a distant white dwarf star. And in doing so, they verified a method with which you can calculate its gravitational force and, therefore, its mass. Voila, you can weigh the star. How hard was this?

Well, here to tell us all about it is my guest, Kailash Sahu. He’s an astronomer with the Space Telescope Science Institute in Baltimore, Maryland. He’s the lead author on the research. Also Mario Livio, an astrophysicist and author also based in Baltimore.

Welcome back to Science Friday, Mario. Good to meet you, Dr. Sahu

MARIO LIVIO: My pleasure.

KAILASH SAHU: Good to be with you.

IRA FLATOW: Thank you, Mario. Dr. Sahu, explain this process a bit more thoroughly than I did. How can how can bending light give us a mass of a star? And exactly what did you accomplish on this?

KAILASH SAHU: You explained. You gave a very nice introduction. So you said that Einstein said it was not possible. So I would like to give a little analogy of how difficult it is. So this particular project, the measuring the deflection caused by a white dwarf, the deflection itself is about 1,000 times smaller than what Eddington measured. Eddington measured more than 1.75 arcseconds. And this is 2 milliarcseconds.

And that– so to give you an example, 2 milliarcseconds, what we are measuring is– imagine a US quarter in New York, let’s say, on the Imperial State Building. And so a firefly is crawling across that US quarter from one end to the next, one end to the other. And right next to that, there is a bright light bulb. And your job is to measure that firefly’s most from one end to the other from Kansas City, about 1,500 miles away. So yes, Einstein thought it was impossible. But we were able to do that.

So this gives, actually, a very new method to measure the mass of a star. So the principle is very simple. So there’s a massive body and light gets bent. And so that causes a slight deflection, the displacement of the background star. So if a foreground star comes very close to a background star, then the background star’s light gets slightly displaced by the amount that I just described. And that displacement tells you directly what the mass of this foreground star is.

It’s like putting you on a scale and just the movement of the scale just tells your weight similar. This is exactly like that. You just measure the deflection. And that tells the mass. It also depends, of course, on the distance. Because the angle depends on the distance. But once you know the distance, that deflection just tells you the mass. It’s a very direct method of measuring the mass.

IRA FLATOW: Very elegant. Mario, was this experiment more a test of Einstein or of our theories about star mass?

MARIO LIVIO: Well, at some level, of course, it tests Einstein’s general relativity, if that’s still needed testing. Because we have had many tests of general relativity. To me, as a theorist, I think the importance of this particular observation is twofold.

One is, as Kailash pointed out, it’s an entirely new method for determining masses of stars, for weighing stars, basically. And this is very important. Because until now, the methods we had always depended either on models or you had to have stars in binary systems, two stars. This allows you to determine the mass of single stars, in principle of black holes, of neutron stars. And in particular, there is a mission by the European Space Agency called Gaia, which is supposed to determine the positions and motions of maybe a billion stars. So this will allow for hundreds or maybe thousands of instances in which you will be able to use this method and determine masses of stars directly.

So that’s one point. The second point is that, in this particular experiment, Kailash and his collaborators determined that this white dwarf star– they determined its mass and its radios. And thereby, they could test the theoretical relation between the radius and the mass of a white dwarf. And that is extremely important. Because for example, I’m sure you know that astronomers discovered that the expansion of our universe is speeding up. It’s accelerating.

That discovery was made by using some types of stellar explosions called supernova explosions. And those are explosions of white dwarfs of the type that was measured here. Now, if they discovered a different mass radius relation, this would not have disproved the accelerating expansion of the universe. But it would have shown that the objects that do the explosions, the white dwarves, that we don’t understand them, which, to me, as a theorist, would have been extremely disturbing. So by confirming this relation between mass and radius, they have shown that both our theories of stellar evolution and our theory of white dwarves are both correct.

IRA FLATOW: Very interesting.

KAILASH SAHU: So if I can add to that a little bit, is that OK?

IRA FLATOW: Yes, sure, certainly.

KAILASH SAHU: So this particular white dwarf was interesting. So what we did was to actually show that, as a method, we took all the stars, all the high proper motion nearby stars. Nearby because once it is nearby, the star is close by. Then, it’s easier to measure the deflection. And high proper motion– there are few high proper motion. High proper motion allows the probability that it will come close to another star is higher.

So we proactively looked for all future events. And this particular one we chose– there are several other events. In fact, Proxima Centauri would be our next. But this particular one we chose because this is very interesting. This is effectively an isolated white dwarf. So measure the mass of an isolated– It’s also in a binary. But effectively, isolated, in the sense its binary companion is more than 55 astronomical units, five billion miles apart. So there is no mass transfer. So it’s effectively an isolated one.

So to measure that and to put it in theory, that was very important. And the other aspect is this particular one had a lot of controversy. In the sense, people had used this binary. Even though it’s a wide binary of 3,000 years of orbital period, they had used this to get the mass. And that mass was very small, which did not fit in the mass radius relation. And that would imply the age to be almost the age of the universe. So that was a bit uncomfortable.

So we measured using this technique. And it fell right exactly on the radius relationship that was expected. That was a nice confirmation of the theory.

IRA FLATOW: It’s always good to have your theory confirmed by the evidence, isn’t it?


MARIO LIVIO: Right. And by the way, Ira, there was one amusing fact that I would like to add, which is, of course, this is a confirmation of Einstein’s theory. Einstein, in German, means a stone. And this particular system is called Stein 2051B, just a coincidence that the word stone appears in both.

IRA FLATOW: I like that. I like that.

KAILASH SAHU: Stein happens to be– he was a Dutch priest, who was working till the age of 78. At 78, he was still observing stars, until he was no more able to move the eyepiece. He was a pretty amazing man. He discovered this.

IRA FLATOW: That’s an amazing discovery yourselves. You guys, Kailash and your whole team, deserve great credit for coming up with this. And we thank you for taking time to be with us today and sharing that journey with us.

KAILASH SAHU: Thank you.

IRA FLATOW: Kailash Sahu, astronomer for the Space Telescope Science Institute and lead author of this paper discovering this new weighing of the star. Mario Livio, astrophysicist and author in Baltimore. Always good to have you two on, Mario. Thank you for taking time to be with us today.

MARIO LIVIO: Thank you for having us.

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