Extracting Even More Gravitational Waves from The Pulsar Timing Array

We are now deeply in the era of gravitational wave astronomy, with the LIGO, KAGRA, VIRGO instruments detecting on the order of a new gravitational wave event from black hole mergers every couple of days. But these are stellar mass black holes, not the much larger supermassive black holes at the hearts of galaxies. But we also know this is happening thanks to the Pulsar Timing Array. And these are groups of rapidly rotating neutron stars where they are sending out signals, radio signals that rival the accuracy of an atomic clock. And thanks to these networks, astronomers have detected this hum, this background gravitational hum of supermassive black holes that are emerging across the universe. Millions of these mergers near and far. But can we pin down individual specific events? This is the hope of the upcoming LISA Observatory, which is going to be the space based interferometer of spacecraft that should be able to detect actual direct supermassive black hole mergers. But this information should also be detectable thanks to the Pulsar Timing Array. So my guest today is Dr. Chiara Mingherelli. She is assistant professor of physics at Yale University and recently wrote a paper about how Pulsar Timing Arrays, these existing observatories of natural objects, can help us find merging supermassive black holes. And this would be above and beyond the general hum we know of these merging supermassive black holes. So if this is a fascinating topic, enjoy this interview. Chiara, can you give us a good description of what the Pulsar Timing Array is? Yes, I'd love to. So pulsars are these really stable clocks that exist in our own galaxy. So they are about the size of Manhattan and more than one and a half times the mass of the sun normally. And they're so compactified and spin so fast that it's like you took the sun, you know, compactified it and then put it in a blender. Right. So like that's how fast these pulsars turn around. And then these pulses that we get from the pulsars are so regular that they're like clocks. And so with the millisecond pulsar, which is the ones that we use for these experiments, we get hundreds of pulses a second. And so what that means is that a gravitational wave that's transiting through the galaxy will change the proper distance between us and the pulsar. So pulsar pulses have a bit further to travel and then less distance to travel. So the gravitational waves are stretching and squashing space time. And so as it stretches, the ticks arrive late from our little lighthouses that are sending us all these radio waves because they have longer to travel. And then they arrive early and then they arrive late and they arrive early. So it's like turning the whole galaxy into a gravitational wave detector. When I think about like the incredible science that went into just building, say, LIGO here on on Earth for a while, they weren't even sure this was going to be possible because of the tolerances that were required. And even like the first observing run, they didn't make their detections, had to keep boosting the technology. And like now we're getting them once a week, sometimes every couple of days now at this point. But but this is like a natural thing that you just go to these neutron stars, these dead stars that are everywhere, and you just use them as detectors. How accurate are they? I mean, it's I agree with you. It's a beautiful idea. I wish it had been my idea. I wish one day I have an idea that's that good. But these but they didn't start as experiments with pulsars. They actually started as experiments with spacecraft. So in 1975, when they were developing the Pioneer mission, someone thought, well, like, why don't we look for the arrival time delays in the radio signals that these spacecraft will send us as they're leaving the solar system and a gravitational wave should give us an advance or a delay in these spacecraft. And then they got discouraged because they were like, well, this is too noisy. We're you know, that maybe pulsars could be used for this. And then in 1982, millisecond pulsars were discovered, which are these super stable clocks. And so this whole field starts even with like this one really core idea of using spacecraft for gravitational wave detection. But but back to your question, sorry, it's just so exciting. So these clocks are so stable that they can keep time to about 100 nanoseconds over a decade. How does that compare to like our best atomic clocks? It's very similar. In fact, pulsars used to be better than our best atomic clocks. But in 2012, the atomic clocks caught up. And so now it's about, you know, one part in 10 to the 15 and atomic clocks now can get us to 10 to the minus 18. However, so you can think about these timing stabilities in that way. But another interesting way to think about it is the way that LIGO describes it as a change in distance over distance instead of a change in time over time. And so LIGO likes to say that it's, you know, the fraction of the size of a proton divided by one of their arm lengths, which can be several kilometers. For us, it's the size of a virus divided by the diameter of the Earth. Right. Yeah. And yet, statistically, these things have delivered us proof of this background gravitational wave ocean of merging supermassive black holes. That's right. And it took 15 years of, you know, timing these pulsars every two weeks or or better to find this result. So you can imagine all of the graduate students, all of, you know, the radio astronomers getting these measurements every two weeks of now we have 67 pulsars. I mean, imagine like all of the blood, sweat and tears to making that 15 year data set. And now we have a 20 year data set that we're working on. But it's really a monumental feat. And one of the great things with us is that we don't have these down periods where we're upgrading everything. We can just keep timing pulsars and things just keep getting better and better. Of course, we do like to have instrument upgrades. You know, we went we want to update the receivers on the telescopes and have these ultra wide band receivers that can help us improve the way that we time the pulsars. But that in reality, we can just, you know, take our pulse, our telescopes and point them at a pulsar and go. Is it more important to get more pulsars into the network or longer timelines? Yeah, that's a great question. So normally things when you think about the signal, it squares is the square root of all of the quantities. But when we're looking for gravitational waves with one of the original papers, but the big insight was is that you can cross correlate all the pulsars. And so instead of looking for gravitational wave signal in just one pulsar, you look for the same signal and pairs of pulsars. And so this cross correlation method lets you reduce the noise and boost the signal. So if you cross correlate one pair, then you get, you know, what's common to that one pair. And then you take another pair and then another pair and then another pair. And then you cross correlate everything in your pulsar timing array. And that gives you this n squared term. And so you always want more pulsars. So right now signal and when you say pair, though, are you talking about like actual binary pulsars or just you're Oh, wow. The answer is yes. And so I say that because it's typically, you know, the millisecond pulsars that we use are typically in binary systems, but normally they're not both pulsars. So there's like a neutron star and a pulsar, or there is a white dwarf and a pulsar, sometimes a main sequence star and a pulsar. And so when my colleagues are trying to do the timing, they have to take into account all these orbital dynamics, but they're very smart and they know how to figure that out. And so what we do is that we take these signals, these arrival times that we sit on the earth with our clocks and we measure when the signals actually do arrive from the pulsar. And then we correlate them with the signals from another pulsar. So even though all of these pulsars are 80% of them are in binary systems, there's only one of them that's actually doing the pulsing. And so when I say pairs of pulsars, I mean, you know, individual pulsars that are themselves in binaries. And to make things worse, we're looking for super massive black hole binaries. So it's binaries all the way down. Right. Yes. So, so, and this is sort of the paper that you recently published that kind of led me to you, which is, you know, up into this point, we've got this confirmation for this background gravitational wave ocean, but it doesn't give us any specific events. But you think that we can actually start to zero in on specific events? Yes. So we have evidence for this gravitational wave background. It's between three and four sigma. So it's still at an evidence level of, of detection. We can't say detection until we have stronger statistics, but it's really exciting. The primary source of the background, we think is this cosmic hum of supermassive black holes that are merging. And right now it's still a bit ambiguous as to what the signal could be. So the signal will need to get cleaner and stronger. We'll have to do more work on, on tidying up the signal before we can really understand what's But if there's any justice in the universe, um, and there may not be, uh, the signal should come from, uh, supermassive black holes that are, uh, slowly merging with each other. Would you find a specific one, or would this be like a new background hump of just now we know that we can detect the rate of binary black hole mergers? So when we measured the amplitude of the related to the number of individual binaries in each, uh, you know, frequency bin. So wherever you measure your signal, the amplitude of the signal will tell you, uh, how many individual sources more or less you have. And so at the very low frequencies, it's likely millions of simultaneously in spiraling supermassive black hole binaries, which is wild. It's fun to think that the likeliest explanation of the signal is millions of simultaneously merging supermassive black holes, but that seems to be the case. Um, and then at higher frequencies, the number of binaries goes down pretty quickly. And then we get into this transition where there's not enough, uh, individual binaries to make this, you know, random stochastic signal where you can no longer tease apart the individual signals and you can start to measure the individual ones. And so measuring the individual ones, um, in my view is now the name of the game that will eventually beat down the noise for the background. Uh, but now people want to know, well, if there's millions of these in spiraling supermassive black holes, where are they right? We should be able to find them. Right. And so do you think that you would actually get a location or do you think, or would it just be more like, we know there's one that is close because it's sort of the most prominent thing in the data from these, from these pulsars? That is very much the, the state of play right now. So, um, you mentioned a paper that I just put on the archive and, and we, I would love to talk to you about that one, but before that, I think what's relevant to this particular question is the targeted searches. Uh, so with nanograv, there's two, there's now two, uh, very mature search techniques. One is the first that you're referencing when you kind of search the whole sky and you look for some sort of blob of power somewhere. And then you're like, aha, there is a thing over here. We're not really sure where it is, but it's over there. Um, if this technique that, uh, I am developing and, and just wrote this huge paper on, uh, it's about targeted searches. So instead of saying, we don't know, we can't possibly know where these black holes are. Um, you know, I led this international team where we came up with a galaxies that, um, people believe host supermassive black hole binaries. And so instead of searching the whole sky, we search at a particular gravitational wave frequency and sky location. So kind of looking under the lamppost and then, um, and then try to say, do the data prefer a gravitational wave signal or no gravitational wave signal? Okay. So, so let me see if I understand this correctly. Like, I know that, that gravitational waves from colliding black holes are this sort of perfect, uh, siren because you can sort of pull at the Hubble constant directly out of the, the signal that you're receiving. And so what you're saying is, is that if you think that there is a supermassive black hole in that galaxy over there, then you're estimating that you're going to get a frequency of gravitational waves at this number. And then you're tuning the network of pulsars to try and detect that wavelength. So, so yes, there's a, there's a lot of things that you said there. So number one, if we want all the wrong things, first clear out all the wrong things I just said, and then we'll move on to measure the Hubble constant. Then we can't fix the distance to the galaxy because the distance to the galaxy is set by, um, the Hubble constant. And so that makes a kind of circular loop. So we can't do that. Um, but we can find the galaxy and then search over the distance to the galaxy. And then that way you can get an estimate of the Hubble constant because you can get an independent redshift of the galaxy from a catalog or some other independent source. So you can definitely do that. And, and we're starting to do that. And that is like papers on the archive in the last few months describing what you're talking about. Um, yeah, I mean, that's what I've been seeing. So you are, you are there, you know exactly what's happening. Um, but the targeted searches, uh, we don't measure the Hubble constant right now. We may in the future, but for the targeted searches, we know the sky location of the galaxy. We know the luminosity distance to the galaxy. And we estimate the gravitational wave frequency from these optical periodic light curves that come out of these galaxies. So there's lots of different, uh, potential electromagnetic tracers. So optical light or x-rays or infrared light, um, that could trace these binaries in different ways. And, and now the name of the game is to try to figure out like which ones are real. Uh, you know, if I see some sort of optical period, um, periodic behavior coming from a galaxy, is that really, um, the black holes in the center that are interacting with their accretion disc, or is it just noise or does something look periodic for five years? Because I'm looking at it for five years, but then it just stops being periodic. I just kind of looked at it during that particular time when it appeared that way, and then now it's gone. Uh, and so we have a lot of questions about separating, um, these red herrings from what's really happening. And that was part of why this paper was so hard to write. It took us almost three years to write this paper. We had to like settle on our, on our source list, uh, and then look for these individual signals and then figure out a way, even when we got two candidates that looked really interesting, to like fold in more detection statistics and, um, you know, try to figure out, should we have two false positives in this sample anyway, because the signal is so weak, um, a kind of look elsewhere effect. So, so in fact we did, we looked at 114 candidates looking for these gravitational wave signals. And then almost all of them, there was no, uh, gravitational wave signal that was preferred over noise. The two candidates had, you know, weak, uh, they're called Bayes factors, but it's just, you know, what should I bet on this is true or not? So two of them were around four, um, which is very low. You typically want something that's, you know, maybe hundreds or thousands, something, you know, something big, like for the gravitational wave background, the Bayes factor for having the cross correlations was something like 900 to one. And so these little guys, these, these supermassive black hole candidates that we found, um, the Bayes factors were four, which is very low. And so we were incredibly skeptical, but you know, we had to be, um, but they got these cute nicknames. One was called Rohan after the student who found it the first time. And so we called it Rohan's binary. And then when we found the second one, we felt honor bound as call it Gondor, uh, from Lord of the Rings, especially because the beacons were lit, right? Like there was light coming out of it. So, I mean, you can understand how we were, there was no choice really, and how these candidates were named. Yeah. But, and, and I think, you know, to make it clear that that was the name of the student in the beginning. So no, this wasn't another Tolkien nerdy reference right from the get-go. This was inspired by someone's actual name. All right. Yes. And I will make sure that I retell the story appropriately and in, you know, future to future generations. Um, so then, so, uh, what it's going to take to, to get those, those Bayes numbers higher, get into the thousands. Yeah. So we're, we're going to need more pulsars and the way that we do that because we can't magic them out of thin air, but with Nanograv, we have 67 pulsars that we've been timing, but our, together with our international partners, it's actually 131 unique millisecond pulsars that are being timed. And so we have, you know, maybe half, but Europe has another sample that's largely overlaps with ours. And so does China, India, um, Australia. And so there's a lot of key players here that are timing similar pulsars. And so we need to make this big combined data set. And that will, you know, if we double the number of pulsars and we can double the signal to noise, um, which is awesome. But then also you get these other added benefits. Like if someone else's timing them, if you imagine every time you go to your telescope and time your pulsar, you get like one, one dot, one arrival time that you can put in your gravitational wave. So imagine like, this is your gravitational wave. And you go to the telescope and you're like, okay, now I measured this dot. Now I measured that dot. Now I measure this one. Now I measure that one. And then you're, you know, reconstructing the gravitational wave as it transits. But everyone's got different measurements of this, right? That are taken at different times. So you can make it denser, uh, and then better sample the potential waveform. And so it's not only the longer baselines and the bigger number of pulsars, but also the cadence at which you're sampling, um, the number of data points that you have increasing also helps. So these combined data sets, I think are going to be really important for making these big detections. Also. So our, our, our partners in Australia, right? They see the Southern hemisphere. We don't see the Southern hemisphere. And there's a few exceptions, but, um, it's really hard to see that from North America. And so it also gives us access to the whole Southern part of the sky, which is really important. Yeah. And that sort of led into what my question was going to be, which is that the square kilometer ray is, is under development now. And when it does finally arrive, then the most powerful radio telescope on earth is going to be in the Southern hemisphere, which is this place that is less studied so far. And so hopefully that'll change things. It's already starting to change things. The, um, the square kilometer array now has this pathfinder telescope called meerkat. And they have, uh, I think 83 millisecond pulsars and already four and a half years of data. And so they turned on and after four and a half years, they already had evidence for the background. Whereas it took us in North America, 15 years, of course we have a, right. They're just like, Oh, you found it. Yeah. And we're like, that's amazing, but it's an amazing, it's an amazing instrument. Of course we have a, a more constrained measurement of the amplitude of the background. We have, you know, smaller error bars, but it's still a very impressive machine. And it's not to say that we won't have something similar, uh, in the U S so they're proposing a telescope called DSA 2000. And that'll give us something similar to the square kilometer array, but here in the U S. Right. Right. That's the, the sort of next generation, uh, array in, in the U S in North America is other ones going to stretch into Mexico and Canada as well. Or is that the, I'm thinking of the very large array. Um, I'm not sure. Yeah, it's okay. No problem. Don't worry about it. Don't worry about it. Um, so, uh, so, so did that kind of, so the, I guess the sort of the final or the future version of, of this research down this pathway is that you'll get to this place where, where you will see a galaxy, you'll see some behavior that tells you might be a supermassive black hole here. You'll turn to this vast network of pulsars, um, and, and confirm its existence and get more information about it. Yes. And that's when they'll merge. Exactly. That's, that's not real. That's not the hard part right now. We can, you know, we can do that pretty easily, but, but so, so right now the really tough part is so, so we're right there. So now let's say you have a galaxy, you have an L you have a, some sort of counterpart that you can see with a regular telescope. You have your gravitational wave signal. How do you actually know that that's the galaxy? And it's not like something that's like over here along the line of set. Like, how do you understand that what you're measuring is really real and that it's not just some noise that right now looks like a gravitational wave. Um, and so the way that we figured that out is this new paper. Um, you mentioned at the very beginning of this chat. And so when we were looking for the gravitational wave background, we were looking for these cross correlations between the pulsar pairs and we were looking for that similar signal in all the pulsars. Um, it's kind of funny that the answer to understanding like, is there a gravitational wave signal or not was under our noses the whole time because we had it for the gravitational wave background. It's called the Hellings and Downs curve. It's like a swoopy, um, thing that looks kind of like a cosine. It kind of looks like the Big Dipper. Um, and when you cross correlate all these pulsar pairs, you get a very specific geometric pattern that comes out. And that tells you that what you're looking at is a gravitational wave and not noise. But until now we didn't have anything similar for the individual supermassive black hole binaries. Uh, and so it could always be noise. Someone could always argue that it's noise, but now, um, my students and I calculated what these geometric patterns were for any, uh, individual binary at any position on the sky. And so now we can do a similar kind of analysis. We can say, you know, is this a real gravitational wave? Yes, no, because now I have this very specific pattern, um, that the cross correlated pulsars make that I can look for. And some of the really fun unexpected, unexpected consequences of this are that we can now separate this one strong individual binary from the background because the background has one correlation signature and the individual binary has a different one. And so now you can tease them apart. Whereas before you were just like, everything is, you know, everything is the same. I can't like pick this one binary out of the bin and say, this is just one and then everything else is the background. But now we can, because now we know that they have different correlation structures. And so we can tease them apart and say this much of the signal is from the background and this much of the signal is from this individual binary. So will you get to the place where you can tell the observational astronomers, check this galaxy. I'll bet you there's a binary black hole in there. A hundred percent. I think we will definitely get there. Uh, one of the other things that we found was that when we, even when we didn't know where we were looking and we just did an all sky scan using these cross correlation functions, our sky localization improved by a factor of 11. And so I think that we'll get there. No problem. You know, it's just going to take more pulsars and more time and denser datasets, but there's no reason that we can't get there. But often in, in this kind of work, when we think about, say the discovery of the first exoplanets or even the, just the first planets around a pulsar, but the, the first exoplanets, you know, they're these hot Jupiters that the first thing that you tend to find is the weird anomalies, the things that are outrageously large and not the standard, but they just pop out just because they're so unusually large. And so it could be that there is, I don't know, a binary black hole at the heart of say Andromeda that's, that's going off and suddenly it will be screaming in the data. Or do you think you're already past that point and now it's, it's more subtle? Well, so I think that we're, we're beyond Andromeda because that one is right next door. Even though it's, you know, we think that the black hole in there is about 100 million solar masses, 10 to the 8th. If there were an equal mass secondary one, we would have seen it for sure. It would have been screaming loud. But I do think that you're right in the sense that when we do start finding these individual binaries, I bet you they'll be really big. They'll be the ones that are inevitable to have detected, right? So I think we'll get fun things like what you're saying. Like I think we might get a strongly lensed gravitational wave system because if the binaries are really big, galaxies can lens these gravitational wave signals and that'll make them even louder sometimes. And so stuff like that, we'll probably start seeing like anything that makes a signal whopping loud, even if it's rare, as you're describing, I think we'll, we'll probably see, and that'll be really fun. Dr. Mingarelli, a question I always ask my guests, what are you obsessed with right now? I'm obsessed with supermassive black holes. Right. Which, which, you know, so not, not, not gardening, not, you know, not your sports team, but no, the, the supermassive black holes. That's interesting because that kind of you might want to research, go into research about that. Yeah. I don't know. I don't know if, if you could do that as a job, wouldn't everyone be doing it? Yeah. I guess what aspect about them? Cause they're just bigger black holes. Come on. What's interesting about them? To me, they're like magic. I can't believe that these things are real, right? They're like fundamental particles. They have mass and spin and sometimes charge, but maybe, maybe, maybe not. I So they're like these kind of mega protons that are floating in space that may or may not have like a thing in the middle. That's a singularity that no one can describe. And so it's this fascinating combination of something that's incredibly simple, but you know, that makes you dream. And then also like the kind of defining point where quantum mechanics and general relativity just clash and everything that we know breaks down. So it's this, this tension between them being really simple and being really complicated and just, you know, the ability to make your, you know, your mind like segfault every now and again, like just make your brain melt because it's this, this tension of the, you know, sublimely simple and like that, you know, and desperately difficult kind of physics. So I think that that's really fun and there's always something more you can do with black holes. They're just like this really fun sandbox and you can, you know, go as deep as you want. You know, like, because it's impossible to probe them because you, you, information can't get back out from them. But if there was like, just like one question that you could just write an envelope and then have, you know, open it up and see the answer inside of it, what would it be? I would want to see a movie of what it looks like inside of a black hole from every wavelength. I want my eyes to be the entire electromagnetic spectrum. I want to have a layer for a gravitational wave spectrum and I want there to be a camera that can record all of this so I can effectively, you know, just sit back and like watch everything evolve in front of me. And then, you know, someone telling me what it means. Right. Yeah. You do know that you're like probably the person best qualified on Earth to try and provide some explanation to other people about that. So, yeah, I think that's that's good. Even you would appreciate something even more, more directed that you can try and follow. Yes. Something like just talk to me like I'm five. Tell me what this means. Yes. What does it mean? What does it mean, man? On that note. Yeah. Well, thank you so much for taking the time to chat and good luck with your research. Thank you. I've been following this story in general and it was great to get a lot of the specifics kind of hammered out in my brain. So good luck with your research and I look forward to that future movie. Wonderful. Thank you. I hope you enjoyed this interview with Dr. Now, we had a longer conversation where we shifted gears and talked about a very different method of detecting supermassive black holes. We talked about Lisa and not just Lisa, but what comes after Lisa. Astronomers are already thinking about what it might take to be able to expand this space based interferometer concept to be able to see even more sensitive nearby, smaller, larger, and maybe get us to this place where we can detect the primordial gravitational waves, this background hum from the Big Bang itself, how if we get really good at detecting gravitational waves of supermassive black holes, then we can peel away that layer and find the background of the universe itself and maybe understand more about what the earliest stage of the universe was all about. So, as always, we have that longer interview over on Patreon, which is available ad free. You don't have to sign up. You can just go watch it right now. That is our preferred way of showing you our videos. And so that's why we put this link down in the show notes. You can go check it out right now. I'm going to give you some final thoughts. But first, I'd like to thank our patrons. Thanks to Abe Kingston, Andrea Pedretti, BarelyGrooving, Brian Bode, Caridwyn, Chuck Hawkins, Commander Balak, Darkfinger, David Mass, Evan.bro, James Clark, Janice Smith, Jeremy Mattern, Jim Burke, Jordan Young, Josh Schultz, Marcel Smits, Michael Purcell, NordSpace, OneStepForAnimals.org. Please follow my nephew at vbrick6994, Ray Kaidu, Richard Williams, Sean Sargent, Steven from The Money, Team49, TelescopesCanada, Vlad Shiplin, Wolfgang Klotz, and Zeldaborg Galactic Defender who support us at the Master of the Universe level. And all our patrons, all your support means the universe to us. So I mentioned to Dr. Minarelli, maybe in the extra part, but anyway, we talked a bit about how I've interviewed a lot of people about gravitational wave observatories, both LIGO here on Earth, as well as the the LISA mission. And I did an interview like very recently about gravitational waves and everything that we've discovered with LIGO so far and what comes next. And so we're going to put a link to that interview down in the comments. And then, of course, this incredible interview with the architect of LISA. What can we expect from that mission when it finally launches in about 10 years from now, so less than a decade, we should see LISA finally launch. So if you want to learn a lot more about gravitational waves, I've got a lot of great content here on the channel for you to check out. All right, we'll see you next time.