02/22/2019

When Black Holes Burp, Stars Sense It

28:52 minutes

Priya Natarajan. Credit: G.A. Miller

When Einstein published his general theory of relativity in 1915, he didn’t have any evidence his idea was true. The math worked out, yes, and he had a few examples he could point to that seemed to agree with his theory, like the hard-to-explain orbit of Mercury, for example.

But it wasn’t until the total solar eclipse of May 29, 1919 that Sir Arthur Eddington and his two teams of scientists were able to confirm that, during the eclipse, a few stars seemed off-kilter, displaced from their usual spot in the sky. It was the first evidence that the mass of the sun had caused a bulge in spacetime, sending the starlight on a very slight detour. Einstein was on the front page of newspapers worldwide the next morning.

And that’s how it works in science, right? You got an idea? Prove it. Or at least wait until someone else can. As a grad student in astrophysics at Cambridge University, Priya Natarajan devised a theory that might explain a mysterious relationship between black holes and nearby stars, proposing that as black holes gobble up nearby material, they “burp,” and the resulting winds affect the formation of nearby stars. Now, 20 years later, the experimental evidence has finally come in: Her theory seems correct.

This hour, Ira talks with Priya about her theory. And Nergis Mavalvala of MIT joins to talk about why “squeezing light” may be the key to detecting more distant black hole collisions with the gravitational wave detector LIGO.


Further Reading

  • Read more about how black holes produce wind that effect nearby objects in Science News.
  • Learn how the oldest black hole’s became so large in Scientific American.
  • Explore how LIGO is going to double its detecting power in Nature.

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Segment Guests

Priyamvada Natarajan

Priyamvada Natarajan is a theoretical astrophysicist and author of Mapping the Heavens: The Radical Scientific Ideas The Reveal The Cosmos (Yale University Press, 2016). She’s a professor in the departments of physics and astronomy at Yale University in New Haven, Connecticut.

Segment Transcript

IRA FLATOW: This is Science Friday. I’m Ira Flatow coming to you today from KQED in San Francisco. Later in the hour, California’s other big one could be a flood of biblical proportions. 

But first, when Einstein published his general theory of relativity in 1915, he still didn’t have any evidence it was actually true. Yes, the math worked out. And he had a few examples he could point to that seemed to confirm and conform to his way of thinking, for example, the hard to explain orbit of Mercury. 

But it wasn’t until the total solar eclipse of May 1919 that Sir Arthur Eddington and his two teams of scientists were able to confirm that, during the eclipse, a few stars whose light shot past the sun seemed a little displaced from their usual position– a sign that the mass of the sun had caused a warp in spacetime, sending the starlight on a very slight detour. Einstein was on the front page of newspapers worldwide the next morning. 

And that’s how science works, right? You got an idea, like Richard Feynman says, you get an idea. You prove it. You find the evidence or at least wait until someone else can find the evidence. 

My next guest devised a theory that might explain a mysterious relationship between black holes and nearby stars back in grad school. And it wasn’t until 20 years later that the experimental evidence came in. The theory seems correct. Priya Natarajan is a professor in the Department of Astronomy and Physics at Yale in New Haven. Congratulations, Priya, and welcome back. 

PRIYA NATARAJAN: Thank you very much. Happy to be back on Science Friday. 

IRA FLATOW: So take us back. What have you and other astronomers noticed about black holes that spurred you to develop this theory in the first place? 

PRIYA NATARAJAN: You mean going back 20 years ago? 

IRA FLATOW: Way back when we were all babies. [CHUCKLES] 

PRIYA NATARAJAN: That’s right. So in 1999, we didn’t know a whole lot about black holes. We knew that black holes sat in the center of pretty much every galaxy. And we knew that there were some black holes that were feeding copiously, and we see them as quasars. 

But in 1998, there was a curious correlation that was published for the first time, so a relationship between the mass of a black hole that is harbored in the heart of a galaxy and the mass of stars right around it. So this was very peculiar because black holes have intense gravity. But the range of influence for them is really tiny, right? 

So for example, if you take the black hole in the center of the Milky Way, which is 4 million times the mass of the sun, it’s like having a penny at the center of the entire Earth, comparative. So that’s the scaling in terms of our galaxy and the size of the hole. 

And so this was peculiar. How does the black hole that have such outsized influence on the stars which are like the inner core of the Earth’s core? How would the black hole actually influence that distance? It was a mystery. And so in my thesis, I was trying to actually work on the larger question of the connection between black holes and galaxies, whether they grow together, and not much was known. 

So then I had this bizarre idea, a speculative idea– it was a bit of an imaginative leap– that perhaps, just as black holes gobble matter, maybe they could push some matter out. They could drive a wind or an outflow. So maybe there’s gas that they could actually push out, right? 

And that’s because a lot of energy is released when a black hole is fed. And some of this energy could– the luminosity could give pressure, radiation pressure, and drive a wind that would sweep up material that’s outside. So I calculated that because that allows you, then, to connect to the large scale to the small scale. And then I did this calculation, and we wrote up a paper. 

And I did this with a postdoc at the time at the Institute of Astronomy in Cambridge, where I was doing my PhD, Stein Sigurdsson, and realized that there was a very peculiar signature that such a gassy, windy outflow around a black hole would have. And that would be that it would cast a very ghostly shadow on the cosmic microwave background radiation. So this is the relic radiation from the Big Bang that pervades us everywhere in the universe. 

And those photons, that light, would actually be quite cold in the nearby universe. So when we receive it now, it’s about 3 degree Kelvin. And this hot outflows from quasars would actually cast a shadow. And this is called the Sunyaev-Zel’dovich effect. And this is known. This was already predicted in the 1970s. 

But it was believed that you need a huge amount of hot electrons that are at a much higher temperature than this relic radiation to produce a shadow. And the only objects in the universe at the time we thought could do it were clusters of galaxies because they have a hot ball of gas in their centers. And nobody had thought that quasars could actually produce these big gassy bubbles that could cost a similar shadow. 

And it turns out that there’s not enough gas in quasars. But the Sunyaev-Zel’dovich effect has another piece. So there’s a piece that comes from the gas being hot. And then there’s a piece that comes from the gas moving fast. So if you add those two bits for these quasar outflows, then you get a pretty outsized [? oomphy ?] effect that was potentially detectable. 

But in 1999, there was no apparatus. There was no radio telescope. So this would be in radio frequencies, like 130 gigahertz. And there was no instrument operating at that time. So you know I sort of did– we did this calculation. And it was cool and interesting. But we knew that radio telescopes were going to come online in the next decade or so, 10, 15 years. 

And I just moved on. And I worked. I wrote another paper on the implications of this gas, the fate of this gas, what this [? burped ?] gas is going to do. It might make globular clusters. It might make little dwarf galaxies with peculiar properties, and so on. 

And then I moved on to working on other aspects of black hole physics. And then, lo and behold, 20 years later, late last year in December, I noticed that there was a first detection of this effect. And so it was pretty, pretty cool. 

IRA FLATOW: Was the detection– could it be isolated to a spot in the universe where it was all coming from? 

PRIYA NATARAJAN: Yeah. They saw a quasar. And they saw this decrement, this Sunyaev-Zel’dovich decrement, offset from the quasar at roughly the kind of scale. So it’s a large scale outflow. This is how it’s different from– when stars form in galaxies, you also drive little winds, and so on. But those winds don’t reach out to such large extent. 

So Mark Lacey and his collaborators at the National Radio Astronomy Observatory did this measurement. And they did a very careful and thorough job, right? So first you have to look to see that, indeed, there’s a quasar that’s implicated, and that there isn’t another hidden cluster of galaxies somewhere, hot ball of gas, that’s actually doing this. 

So they looked at [? multi-wavelength ?] data. And they looked very carefully. And they were able to isolate and implicate this one quasar that’s driving this wind. And what is really, super exciting from the physics point of view is that we had predicted that these bubbles should be fairly long-lived. 

And that quasars, they blink, right? They have feeding episodes when they’re bright, and then they turn off. And so these bubbles, these ghostly bubbles, should linger. And that seems to have been proven right too. So these estimates of the age suggest that these are long-lived bubbles. 

IRA FLATOW: So how do you feel about all of– are you feeling– are you walking around like, hey, see? I was right. 

PRIYA NATARAJAN: Well, walking a little bit on air. 

IRA FLATOW: Come on. You’re allowed to gloat. 

[LAUGHTER] 

PRIYA NATARAJAN: Walking at little bit on air, I have to say. I mean, I think this is the first detection, right? I think what is super exciting about it is that our prediction is that there should be a lot more of these ghostly bubbles. And that this might be a new way to find quasars that have turned off, right? They have an on/off switch. 

And so we might actually start to find very distant quasars with this bubble signature. So I’ve always been intrigued by the first black holes in the universe. So I think it feels really good. 

And I think that when I was younger, I used to take other kinds of risks– skydiving, climbing buildings. And then when I went to grad school, I cleaned up. And I started taking intellectual risks. So this is really nice to see that this has come full circle. 

IRA FLATOW: Had you– I mean 20 years is a long time. I mean, not in the history of physics, it isn’t. But do you just forget about it for 20 years? Or are you always in the back of your mind that maybe this year someone– 

PRIYA NATARAJAN: No, I wasn’t actually watching for it year by year. But I did notice that when ALMA went on, and I knew that in about three years after ALMA was operational, it should become doable. So I was kind of watching to see. But I’m not an observer. So this kind of work would take a big dedicated team. 

And so I was looking out, but I wouldn’t say that I was desperately waiting, or whatever. I knew that it would happen. But I like this element of surprise and thrills. 

IRA FLATOW: We talk about physicists here. And most people think physicists are physicists. But there are the theoretical physicists like you. And then there are the experimentalists who have to make the device to measure it, right? 

PRIYA NATARAJAN: Absolutely. 

IRA FLATOW: I mean, so you really– you had to depend on those folks to come up with something that could find the evidence you were looking for. 

PRIYA NATARAJAN: Right. And so but I think what’s really gratifying is to think that we live at a time– well, I feel lucky to be alive at a time where you can propose an idea, and people will actually take it seriously, and go look for it, and want to validate it or not validate it. And for me, that, itself, felt like a complete treat. 

IRA FLATOW: Did you pop any champagne, or anything like that? 

PRIYA NATARAJAN: Yes, actually, with my family. So I went to India right after I heard about this. I was in India with my family in December. And so we had a nice little celebration. And my parents were really thrilled that I had moved to intellectual risks from the other risks. 

IRA FLATOW: That’s great. We’re going to take a break, and if you have questions for Priya, our number is 844-724-8255. We’re going to talk more about black holes. 

We’re going to get an update on LIGO, the gravitational wave detector that could allow us to hear the cosmic collisions of black holes. I want to get to Priya’s take on that. We’re also going to bring in another scientist who works with LIGO to talk about it. And our number 844-SCITALK, 844-724-8255. Priya, stay around and talk a little bit more with us? 

PRIYA NATARAJAN: Sure. Happy to hang around. 

IRA FLATOW: I’m sure because this LIGO stuff, new kinds of LIGO information may be getting everybody’s attention. We’ll be right back after this break. Stay with us. This is Science Friday. I’m Ira Flatow. 

We’re talking this hour about the black holes with my guest Priya Natarajan, professor in the Department of Astronomy and Physics at Yale University in New Haven. And I’d like to bring on another guest now whose work sounds like something superheroes would do– squeezing light. 

It’s a technique that will make the gravitational wave detector LIGO even more sensitive to the rumblings of distant black hole collisions. Nergis Mavalvala is a professor of physics at MIT in Cambridge. Welcome to Science Friday. 

NERGIS MAVALVALA: Thank you, Ira. Good to be here. And hi, Priya. 

PRIYA NATARAJAN: Yes. 

IRA FLATOW: I know that you must know each other. 

[LAUGHTER] 

NERGIS MAVALVALA: Yes. 

PRIYA NATARAJAN: Oh, we do. 

NERGIS MAVALVALA: Yes. 

IRA FLATOW: How long have you known each other? 

PRIYA NATARAJAN: Probably for decades, right, Nergis? We’ve known of each other. I was an undergraduate when Nergis was in grad school at MIT. So I was an MIT undergrad, yeah. 

IRA FLATOW: Oh, all right. Well, Nergis, tell us about that. Let’s talk about– it’s old home week. Let’s talk about how LIGO works for people who don’t know. How does it detect black holes merging? 

NERGIS MAVALVALA: Yeah, so LIGO has an L in it that stands for Laser, and an I in it that stands for Interferometer. And those are two words that we can deconstruct. So the way that the LIGO works in the simplest way to think about it is to ask, what does a gravitational wave from a black hole do here on the Earth? And what it does is it actually changes distances between objects. 

And so if a gravitational wave passed between, say, me and Priya, the distance between us would change. And the way we measure that is by shining laser light into that space. So if I shown a laser light from myself to Priya, and if she was a good mirror and reflected it back to me, I could measure the light travel time. It comes back to me. If I have a good clock, I just measure how long it took. 

Now, when the gravitational wave comes through, that distance between us would change. It would get longer and shorter. And the light travel time would change. And my excellent clock would tell me that the distance between us changed and, therefore, a gravitation wave was going by. 

Well, it turns out that we don’t have clocks that are good enough to do this kind of measurement because these gravitational waves are extremely, extremely faint. And so what we really do in the end is, instead of having one laser beam reflecting off a mirror and coming back to the laser, we split the laser beam into two parts that go at right angles to each other. 

They reflect off mirrors that are 4 kilometers or 2 and 1/2 miles away. And then they come back, and they interfere. And it’s that process, by which one laser beam acts as a reference to tell us how long the other laser beam took to come back, that allows us to make this measurement. 

IRA FLATOW: And the thing that’s most amazing about this instrument is how accurate it is, right? I mean the tiny– 

NERGIS MAVALVALA: It’s crazy accurate. 

PRIYA NATARAJAN: Correct. 

NERGIS MAVALVALA: So the precision with which you have to make this measurement is that the mirrors of LIGO that are separated by kilometers, by 4 kilometers, typically move by one thousandth the size of a single proton as the gravitational wave goes by. So for people who like to think in terms of really small numbers, that’s 10 to the minus 18 meters. 

IRA FLATOW: Wow, poof, my head’s going. 

PRIYA NATARAJAN: I think this is the most precise measurement human beings have ever made, right, Nergis? 

NERGIS MAVALVALA: I like to think so. 

IRA FLATOW: Well, let’s move on to the next generation because, Nergis, you’re working on something called squeezed light, which could allow LIGO to see even more of the cosmos? 

NERGIS MAVALVALA: Yeah, so me and many of my colleagues and students together, of course, we’re working on this technology called squeezed light. And what it is, is essentially it’s a somewhat exotic quantum state of light that we engineer in our labs to improve the sensitivity of LIGO. 

And so to wrap our heads around what in the world is squeezed light, the easiest way to think about it is that light is a quantum mechanical object. We know light is made up of photons. And therefore, it must be uncertain. Quantum mechanics tells us that measurements are uncertain. 

And so, really, what we do is– so here’s a nice way to think about what happens in the LIGO measurement. Imagine– so we use the laser light. And the laser light acts like the tick marks on a ruler for us. It’s essentially the wavelength of the light, the number of times per second that the wave has a peak or a trough, tells us– acts like a tick mark on a ruler. 

Now, imagine, I gave you a piece of paper. And I told you– and I gave you a ruler. And I said, could you measure the length of this piece of paper? You would say, oh, that’s easy. You’d put your ruler down. You’d make a measurement. And there you go. 

Now, imagine for a moment that the ruler, the tick marks on that ruler jittered about a little. They actually move ever so slightly, slosh back and forth. Now you try to make a measurement of the length of the piece of paper. And every time you make the measurement, your tick marks have moved a little bit. And you make a slightly different measurement. 

Which is the correct measurement of the length of the piece of paper? You don’t know because your measuring apparatus is jittering. Now, it turns out, laser light does that. And it does that because of quantum mechanics, not because we’ve made a bad laser. It’s because quantum mechanics says it must do that. 

So squeeze light is a way of getting around that quantum uncertainty. You can never fully make it go away. But what you can do, what quantum mechanics allows you to do, is to take some uncertainty in the measurement that you’re making and tuck it away into a measurement you’re not making. 

So I’ll give you a nice example. Imagine that your laser light was of a wave. And you drew that wave with a very sharp pencil. And now, if you look very carefully, as you zoom down into that, it will start to look fuzzier and fuzzier. It won’t look so sharp anymore because of quantum mechanics. 

And what we do when we make a– as you can imagine, in fact, as you get closer and closer to the piece of paper, that very sharp pencil line starts to look like you drew it with crayon or something thicker. And what our– what squeeze light allows us to do is it allows us to make some parts of that wave that we drew pencil sharp, as long as we make other parts of the wave very fuzzy. 

So if we make the peaks and troughs pencil sharp, then we would make the center of the wave very fuzzy. And we do that in our labs precisely so that when we make the gravitational wave measurement, we measure the phase of the light. And we make that sharper than quantum mechanics would allow, as long as the amplitude of the light becomes fuzzy. 

IRA FLATOW: So you’re doing like what video people do if they enhance a photo. You’re enhancing the wavelength, the wave picture. 

NERGIS MAVALVALA: Yeah, except that in– we have to obey the rules of quantum mechanics. What happens in– the way that the video folks enhance a photo would be the same as if I took my– the pencil that I used to draw my light wave, and I just made it sharper and sharper. 

Well, quantum mechanics doesn’t allow that. Quantum mechanics says, if I make some part of the wave sharper, I must make some other part of the wave fuzzier. And that’s the difference. 

PRIYA NATARAJAN: Right. There’s a trade-off, right? That quantum mechanics imposes a trade-off. 

IRA FLATOW: Always. So Priya, what is this greater sensitivity of LIGO going to allow us to see more of, better of, different? 

PRIYA NATARAJAN: I think it appears that the universe is just littered with black holes. And these are tinier cousins of the ones that I like, right? So my windy, gassy, powering black holes are supermassive. And what LIGO and the enhancement of LIGO will be sensitive to is their lower mass cousins, so black holes that are anywhere from 10 times the mass of the sun to 100 plus times the mass of the sun. 

I think these enhancements, this improved precision, would allow you to detect, A, these black hole mergers that are happening farther out into the universe, so increases the reach of what we can detect. But also, am I right, Nergis, now, that the event rate we expect when you’re done with your squeezing is about almost one a day? I mean, we should start to see almost one event on average, a gravitation– that’s the expectation, right? 

NERGIS MAVALVALA: For black holes, yeah. For black holes, it could be that much. Yeah. 

IRA FLATOW: Would any of these improvements allow you to actually zoom in on a black hole, so you can get closer to the actual event horizon, where all the good stuff is happening, and see what’s going on? 

NERGIS MAVALVALA: Yeah, so you can– if it were nearby enough that we could measure it in our instruments with high enough signal to noise ratio, then what you would expect is that these very subtle effects of what’s happening closer to the horizons of the black holes would be encoded in the actual signal that we measure. At the moment, our signal to noise ratios are not high enough for us to look with that kind of fine resolution. But in time, I think that will be very much possible. 

PRIYA NATARAJAN: Right. But I think, I read they’re kind of mapping. So this would be indirect mapping that you would get out of LIGO. But the direct mapping you want is, of course, going to come soon, right? 

We’ve talked about this before. The Event Horizon Telescope that’s going to map the light shadows around the event horizon of the black hole in the center of the Milky Way. So that experiment, remember, is ongoing. And I think results are expected anytime now, right? 

So that’s going to be the closest that we ever get to a black hole. Because all the LIGO black holes, and even the supermassive black holes that are going to merge that we are hoping to detect with this apparatus L-shape that Nergis talked about, it needs to be in space for detecting the gravitational waves from supermassive black holes because they happen at a much lower frequency. And so we need this apparatus in space. 

And so the Europeans are planning a mission and NASA is part of it. And it’s called LISA– expected to fly in the late 2020s, early 2030s. And I think that we will be able to actually say something about the populations of black holes and get at some of the fundamental questions like, what masses of the first black holes, and how do black holes actually grow? 

And the exciting thing is that when black holes actually merge, not only do they set up these tremors in spacetime that we detect as gravitational waves. Oftentimes, with supermassive black holes because there is a lot of gas– they’re in gassy environments– we will see other accompanying electromagnetic signatures, right? 

So the gas will be turned around. It will glow. And we expect to see one very heavy-duty feeding episode just when they merge, so a lot of gas going in that should glow in the X-rays and the infrared. So I think we have a lot of black holes in our future. 

IRA FLATOW: That’s good. 

NERGIS MAVALVALA: Hear, hear. 

PRIYA NATARAJAN: Of that good kind, of the good kind, yes. 

IRA FLATOW: (LAUGHING) Of the good kind. Here, a listener– here’s a listener question for you. What is Priya’s advice– and I’ll also ask Nergis to chime in on this. What is your advice for women who feel like they’re being discouraged from doing astronomy? 

PRIYA NATARAJAN: Well, I think you can count me and Nergis as test cases, right? Just do what you love, and I think it works out. 

IRA FLATOW: Is there is a glass ceiling for women astronomers and physicists? 

PRIYA NATARAJAN: I don’t think it’s quite a glass ceiling. But there are obstacles, to be honest. But I just think that at this point in time, the awareness of all the biases and stuff is really high. And I think the astronomy community is very open-minded. So I’m very, very optimistic. And I encourage every young child, girl, boy, whoever wants to do science and astronomy that just follow your passion. 

NERGIS MAVALVALA: I’ll add one other thing. I think I agree with everything Priya said. I think it’s also very important– we’re the lucky ones in the sense that we’ve had a good path into science. I know many young people don’t. 

And so the one thing I would say is to find your mentors and your champions, whether they’re within your family, or within your school networks, or friendship networks, find someone or a few people who will hold you up and support you as you make your way, sometimes upstream, and therefore need these champions to help you through. 

PRIYA NATARAJAN: Right. And I think this is absolutely important and has to be stressed that at every stage in the career, you need these people. And I think that’s what can be challenging. But for a lot of young people, there are many enthusiastic teachers, mentors, and professors in college who are very supportive. So yes, find yourself people who will cheer you on, and help you build confidence, and and help you to really understand that this is a passion and encourage you to follow it. 

IRA FLATOW: I’m Ira Flatow. This is Science Friday from WNYC Studios. One last question– we’re running out of time, so many questions people are phoning in. I’ll try to summarize one major question people are asking, which is your understanding of black holes going to solve the problem of we don’t know what 96% of the universe is made out of, dark energy, dark matter? I mean, it’s crazy, isn’t it? We don’t know what 96% of the universe is made of. 

PRIYA NATARAJAN: I know. I know. This is the paradox of cosmology– that we know so much, and yet we know so little. We don’t even know what the dark matter particle is, which is almost all of matter. So I think that black holes per se are a tiny constituent in terms of the budget. But they’re really important in how they shape the universe. 

So for example, because of the impact on spacetime, we really hope that gravitational wave events can be used like standard candles, like standard light bulbs, and can help us map the geometry and the fate of the universe. So I think indirectly learning a lot about black holes has the potential to impact a lot of the other open problems in cosmology. But in and of themselves, I think they’re super cool and exciting. 

IRA FLATOW: Nergis, super cool, exciting? 

NERGIS MAVALVALA: Completely, completely, and I think one of the things that people sometimes wonder is would LIGO be able to see dark matter, for example. And the answer is dark matter is very diffuse. It’s spread out all through galaxies. 

It doesn’t clump into compact objects like black holes or neutron stars, which is the only things we are sensitive enough to see with these detectors like LIGO and Virgo. So that’s one of the things we can’t do is see dark matter, even though we’d love to be able to. 

IRA FLATOW: But dark matter must be some kind of particle, right? A particle that we may need new physics to understand? 

PRIYA NATARAJAN: Maybe. I mean, we have some pet candidates. They are not being born out as possibilities. We are looking hard indeed for them. I personally believe that a lot of the constraints on dark matter might come indirectly from astrophysics, from the light bending that you mentioned. 

So although dark matter is lightly smeared everywhere in the universe, it clumps on galaxy scales and much larger scales. And that bends light. And we see that. That’s gravitational lensing. And I think going forward, with all the big surveys and telescopes– you have WFIRST as a satellite that’s going to measure the shapes and distances to thousands and thousands of galaxies. 

We should be able to say something deeper, more meaningful about dark matter. I’m hopeful that maybe we’ll experimentally detect it, right? I don’t know. There are many direct detection experiments. 

IRA FLATOW: Well, we’ll be watching for it and having both of you back to talk about it. Is that a deal? 

PRIYA NATARAJAN: Absolutely. 

NERGIS MAVALVALA: Good. 

IRA FLATOW: Mavalvala is professor of physics at the Massachusetts Institute of Technology in Cambridge. Nergis, thank you for taking time to be with us today. 

NERGIS MAVALVALA: It was a pleasure. Thank you. 

IRA FLATOW: And Priya Natarajan is a professor in Departments of Astronomy and Physics at Yale University in New Haven. Priya, thank you for taking time to be with us today. 

PRIYA NATARAJAN: Thank you so much, Ira.

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