Interview with Lee Lindblom

0:00 And we're off and running, and it's the 23rd of March at about 12.30, and I'm talking with Lee Lindblom. Well, Ben was telling me something about what you're working on right now, and I'm interested in that, from what I hear, so maybe you could tell me a bit about how that came to the end. So are you interested in the science of what we're doing, or the... In science, yeah, and I suppose, you know, I'm interested, it's, from what Ben tells me, it sounds like a new source, an exciting new source for gravitational waves, so obviously it's interesting. Probably, yeah, it's looking that way. Yeah. Julia's on the phone. Oh, okay. Okay, we can postpone this. Okay, I'll come back. Sure, why don't you turn that off? Yeah, good if I was given it a chance. Okay, so that's all. Anyway, I guess you were going to tell me about this work on instabilities in pulsars. Right. So, I mean, this is something we've been interested in for a long time, since Chandra in 1970 found that gravitational radiation could drive instability in rotating stars, and Friedman and Schutz showed in the mid-70s that it was generic, in the sense that there's some mode in every rotating star that can go unstable. The problem with the original analysis, it's centered on a set of modes called the F modes, or the fundamental modes of stars, which are sort of the modes that everybody thinks about. They're the big sort of waves on the surface, sort of pressure, some combination of pressure and gravity, the restoring forces for those modes. And it just turns out that for those modes, the coupling to gravitational radiation isn't quite strong enough in the sense that if you put in other things in the fluid, viscosity, thermoconductivity, that sort of stuff, those processes tend to suppress those modes. You put them in, they just cause the modes to fade away. And for the F-modes, it's much stronger than the gravitation-radiation coupling. So the instability really doesn't ever have a chance to get going. About a year ago, Nils Andersen was doing some numerical work studying these things called R-modes.

2:30 and he noticed that they had some of the physical characteristics of the modes that tend to go unstable to gravitational radiation and the characteristic that he noticed is the modes that are unstable to gravitational radiation have the following property. If you look at them in the inertial frame of reference, pattern of nodes on the mode or whatever tend to be co-rotating with the star. So if you just watch the little bumps, the rotation of the star drives them around. But if you watch them from the point of view of somebody who's riding along with the star, they tend to be counter-rotating. And the reason that that signals an instability is because they are counter-rotating with respect to the fluid that means that they lower the angular momentum of the star a bit. Okay, so formally the mode has negative angular momentum. Whereas since, as seen from infinity, they appear to propagate in the same direction as the star. They carry away positive angular momentum gravitation or radiation because the bumps are all going in the same way the star is going. And so that means that there's going to be instability because positive angular momentum is going away, all it can do is grow to conserve angular momentum. So he noticed that the modes in this numerical study that he was looking at had that property. And then also about a year ago, Friedman and Schoen Morsink, when they heard about this, sort of went and did a sort of careful formal proof that in fact this always happened in all our modes and all rotating stars and sort of really nailed down that this was an important physical possibility. At least at that time, nobody had calculated properly what all the other effects were. And since that spoiled the problem in the F-mode case, people didn't really know whether these were going to be interesting or not. And in fact, most people, in particular myself, felt that it was hopeless, that these modes would never be interesting or important. and the sort of the physical reasoning

5:00 on which that was incorrectly based, as it turns out, if you look, so these R modes, they're like ocean currents. Okay, so they have the fluid rotates around basically on equal potential surfaces and it just sort of oscillates back and forth. And the restoring force is basically the Coriolis force, right? The lowest order expressions for these things are completely independent of the equation of state of the star. They're very funny moments. So you just have these big currents which just oscillate back and forth, and they get dragged along by the rotation of the star in a way which has this peculiar property that Nils noted. That is, from infinity, they look like they're co-rotating, and with respect to the fluid on the star, they're counter-rotating. So, first of all, they have almost no density perturbation at all. Density perturbations are almost zero. It's a very high order in a certain expansion parameter that people use. So, all you've got is these big currents. So, I mean, all of my intuition about gravitational radiation says that it's density perturbations or mass multipoles that really drive things. And then you also have the higher order effect, current multipoles, which, you know, can change things a bit, but they're certainly not, they're much weaker than the mass multipoles kind of coupling. And that's all you've got in this case. So since the viscosity was strong enough to suppress things in the case where you've got real big density perturbations, I figured it was just hopeless in this case that the gravitational radiation would have been out. And so it wasn't until, I don't know, sometime last fall, everybody realized, everybody being the group of people who were interested in these issues, you know, me, Schutz, Nils Anderson, Jim Ipser, John Friedman, you know, sort of the community of people who talk about such things, that the current multipoles really were probably going to be more important than the mass multipoles in this case. And then I, so finally Ben and I were the first ones who actually did it and the results were astonishing. And from my perspective it was absolutely not what I expected.

7:30 So that's sort of the history of how the idea evolved. You know, in retrospect, I can now see a couple of physical things that, you know, we should have realized at the time that is clear why these modes couple more strongly than we should have guessed. I mean, one was I had just never looked carefully at how current multipoles couple the things because it's something you usually neglect, and so I never actually looked at those terms. And in fact, you know, for a given L, they couple just as strongly as the mass multipoles. It's just that for typical kinds of sources, they're typically smaller than the corresponding mass multipole by some sort of V over C kind of term, so you know, they're just not important. zero, so it's all we've got. But there's another thing that I now realize that should have been a clue that these things were likely to be more important than we had guessed. In the F modes, frequency of the modes at zeroing at a velocity starts out at some big value, sort of millisecond or less type periods for non-rotating stars. But then as you spin up the the frequency actually decreases and goes to zero at some point and that's basically what you've got this mode and it's it's counter rotating but then as you spin up the star the frequency gets smaller and smaller until you get to the place where it's just sort of at rest with respect to infinity and then as you spin a little faster it actually goes unstable as it starts getting dragged in the same direction as the star but as a result the frequencies are fairly low at the point where the instability actually sets in because it's it's gone through zero so it has to be down it's a small fraction of what was it that sort of low angular velocity and since the coupling of these things it depends on sort of the time derivative of the multiple moment it all goes like some power of the frequency of the mode and so it's actually fairly small for these F modes, the time derivative part of things, because it goes like frequency and the frequency is small when it happens. For the W modes, they start out at zero frequency

10:00 for non-rotating stars, and the frequency is basically just proportional to the angular velocity. So by the time you get up to a rapidly rotating star, the frequency is huge, and so the time derivatives of these current multipoles is enormous compared to the time derivatives So that's another reason that the coupling is much stronger than sort of what it normally does. Patrick. Can I borrow your CV? I'm going to attempt to boot up my machine. Thank you. I doubt that I will, but I'll try. Yeah, well, as you say, one's experience in other areas doesn't leave one to look at the current Right. So, as Ben described it to me, the instability's effect would be to break the neutron star very hard over the course of about a year. That's right. Which would have quite strong gravitational waves. So we're in the process of doing some fairly decent cooling. So the neutron star is cooling like crazy for the first year. It starts out at maybe 10 to the 11th degrees as a typical sort of birth temperature. And within about a year, it's down to about 10 to the 9th degrees. and it turns out that viscosity at very high temperatures is very strong. There's effectively a bulk viscosity that happens in neutron star matter at high temperatures, which roughly speaking, if you take something and compress it, then it doesn't quite stay in beta equilibrium as you do the compression. And so it's in a state that would really like to emit some neutrinos, change some of the neutrons into protons and sort of get the right beta-equilibrium balance back. And so when you compress it, it does a little bit of that, it loses a few neutrinos. But then when you let it pulse back, you've now lost some energy because neutrinos are just gone. And so as you sit there and oscillate this stuff, it just loses energy on this compressional cycle. And the cross-sections for emitting the neutrinos

12:30 go like some high power of the temperature, T to the 6, it turns out. at very high temperatures, it's possible and easy for it to meet neutrinos. As the temperature cools, it quickly loses its ability to do that. And so until you get down to about 10 to the 9th degrees, it really likes to have bulk viscosity suppress things if it can. Below that, bulk viscosity is essentially irrelevant. There's also a sort of standard kind of viscosity that happens in these stars, comes from either neutron-neutron scattering or electron-electron scattering, that sort of thing. And those have just the opposite temperature dependence. At high temperature, it's very easy for these, well, at low temperature, it's hard for neutrons to scatter off of each other. And the reason is they're all sitting in this big Fermi sea, and the ones whose energies are well below the Fermi level can't scatter off of anybody for them to scatter into, because all the states around them are filled. So the only guys that can actually do any scattering at all are the ones within about KT of the Fermi surface, and you have to have two of them, so things go like T squared. So at low temperature, the viscosity is very high, basically because they can't scatter, which means that they can go a long way before they hit somebody else. You can transport the momentum long distances very efficiently, which is what good viscosity does for you. so at low temperatures there's the sheer viscosity and above about 10 to the 9th it's irrelevant so there's this window between about 10 to the 5th at the bottom and about 10 to the 10th at the top in which viscosity is small enough that you can do something and 10 to the 9th is sort of the minimum value that the two are least interested in affecting things and sort of coincidentally it turns out a year to 10.9 degrees. So over this first year, the star can emit gravitational radiation through this instability and lose probably 90% of its rotational kinetic energy into gravitational radiation. And so then it just ends up spinning much, much slower than it might have. Not having this not happened. So it's the cooling down?

15:00 If the cooling were very, very slow, for example, then this could just never happen, because the bulk viscosity would just suppress it. Or, conversely, if the cooling were very quick, say it cooled to 10 to 5 degrees in one second, then you would just go over and you'd hit this sheer viscosity wall, and that would be the end of it, too. But it's not terribly sensitive to the cooling, but the cooling is fast enough that it just gets out of its way and just allows it to free fall gravitationally basically and just radiate all of its, most of its rotational kinetic energy away. So it seems to me that there are a couple of interesting observational consequences of this. One is that there has been known for some time that there's a sort of mystery as to why most young pulsars are fairly slow by dynamical standards. The best estimates based on the equation of state should be able to spin the periods of about a millisecond or so. I mean, certainly there are one-and-a-half-millisecond objects, and most equations of state that are sort of reasonable and sociologically acceptable these days have something like one millisecond rotational periods. But if you take the crab, for example, which is the youngest pulsar around, period is 33 milliseconds, and even if you take the sort of the current measured spin down and the next derivative and just extrapolate back, I think 19 milliseconds is the best estimate of the initial period of the crab. So it's possible it was just born slow, but if people have systematically taken sort of all pulsars in supernova remnants, and I think that the average birth rate that they get is something like 12 milliseconds, okay, but that's, you know, that's an order of magnitude longer than one millisecond, so why are there no fast pulsars, fast young pulsars? certainly the white dwarf precursors are all rapidly rotating if you just take the sun and ask how much angular momentum does it have it's plenty to make it spin at one millisecond if you compressed it down a neutron star size so there's a real mystery about where all this angular momentum went

17:30 certainly the hydro is so complicated that one could easily a rapidly rotating collapse that, you know, mass is ejected with high angle momentum or something. Yeah. But this mechanism that comes out of this gravitational radiation reaction does it for you automatically. So if you start with something spinning it at one millisecond, then the number we get is about 12 or 13 times that. So 12 or 13 milliseconds would be the predicted period. so there are lots of other things that could go wrong when superfluids happen in neutron star cores and that is expected to happen somewhere around 10 to the 9th degrees the calculations that have been done on that sort of paradoxically has much higher viscosity than regular matter in neutron stars the reason is there's this funny dissipation mechanism people call mutual friction. And what it does is you scatter electrons which turn out are not superfluid at sort of typical probably if you cooled them to 5 degrees Kelvin they would be in the usual BCS kind of picture. But at 10 to the 7th, 10 to the 9th degrees they're certainly not superfluid. So those guys can scatter Fermi particles. And in particular, they can scatter off of the magnetic fields that are trapped in the cores of the neutron vortices. And that turns out to be a very efficient viscous mechanism for coupling the various kinds of fluid in the star together, sort of using the vortices around, and the superfluid material has to follow. So the expectation is as soon as it goes superfluid, this game is going to be over. So in particular, it means that old, cold neutron stars could be spun back up. So 1.5 millisecond object is perfectly reasonable from this perspective. So once it cools below about 10 to the 9th, then it becomes effectively very viscous. Therefore, even if it were rapidly rotating,

20:00 this hormone instability would not set in. And so if you spin it back up in a way that doesn't heat it back up above about 10 to the 9th, then you're all right. The typical Eddington temperature for a neutron star is like 10 to the 7th degrees, so you're not going to get it simply from sort of the kinetic energy of things falling on the surface. You can heat things additionally. When you creep stuff on in the neutron star, it's basically hydrogen because that's what everything is. a thick layer of hydrogen, stuff at the bottom can start fusing and making carbon or iron or whatever. And actually you can get fairly high temperatures from that. But this guy Lars Bildsten at Berkeley has been doing calculations on that kind of effect. And he gets temperatures in the cores of these things of sort of 10 to the 8th to a few times 10 to the 8th. And again, that's below where people expect the superfluid transition to be. My guess is that once it gets cold enough to go superfluid, there's no way to heat it back up, and therefore this gravitational radiation instability will be suppressed, and therefore you can spin it back up to probably almost Kepler velocity by accretion, and still have it stable. I mean, we know they're fast pulsars, So whatever this mechanism is, it's got to be able to account for them as well as the non-existence of the fast hot ones. So your picture would provide an explanation of why young pulsars are... Slow, and why old ones can be fast if they can find a way to spin themselves up. So I think that's one interesting aspect of this thing. It provides an interesting way of spinning things down. It's very natural. There are some interesting, I mean, as soon as you do something, there are always new data that confuse the issue. So just in the last week, there has appeared in the literature an object which is a pulsar in the Large Magellanic Cloud in a supernova remnant. The current period of this thing is like 16 milliseconds, but the age of the remnant they estimate is about 5,000 years. is older than the crab, and yet it's spinning twice as fast as the crab, okay?

22:30 So, I think that all of the measurements haven't been made to properly do the extrapolation back to zero age, but I haven't looked carefully at this paper yet, but my understanding is is that you can get initial ages that are plausible that range between 5 milliseconds and about 10 or 12 milliseconds. So our mechanism suggests that you can't get anything faster than about 12 milliseconds this way, assuming that the minimum, well, so what we really calculate is that you can't get anything spinning faster than about 12 times the minimum period whatever that is so one millisecond is sort of standard folklore if it were a half a millisecond then we're okay with this measurement and we can we don't have to make any accommodation for it if the standard folklore is right that is it's one millisecond this thing appears that it's probably spinning faster than that okay so there are several the model the calculation we did only uses sort of the standard Navier-Stokes-type viscosities to suppress this, and there are other things. So superfluids, for example. Say the superfluid transition temperature were not 10 to the 9th, but were in fact a few times 10 to the 9th. Then before this thing actually has time to spin all the way down, superfluid would come in and perhaps suppress it and stop the spin down. or are estimates if you have a really thick solid crust that would also kill this so we've done estimates about how thick people expect crust to be and sort of when do they occur and with the sort of standard models crust do not appear to be an issue that is they can't stop the instability within the first year, but maybe the standard models of crusts aren't right. Maybe the crusts are much bigger. Maybe they set in at higher temperatures. Maybe something like a crust could come in and suppress it. Or something else. Maybe there are magnetic field issues that we, again, we did some sort of rough calculations of those. We haven't done them properly. Maybe there's some magnetic field. But what it does tell you is that if it is faster than some other interesting non-standard physics,

25:00 has to be coming in at a stage where people didn't really expect it. So that's also interesting. Sort of messier astrophysics. I'd rather it be cleaner and simpler, but maybe it isn't. Is this the first phase of gravitational radiation and instability being shown to be likely to have a big role in pulsar evolution? Impulsory evolution, I think that's right. I mean, of course, you know, the standard binary end spiral is really just a gravitation or radiation instability. Yeah, sure. But associated with sort of a single rotating neutron strike, this is the first one that really looks like it has interesting astrophysical consequences. As I said, people knew about, it's the same mechanism, it's just a different set of modes 20 years ago, But it just turned out that when you did the sort of viscous part of the calculation, they just turned out not to be as interesting as people had hoped at the time. So the other side of the picture, when obviously that's interesting, is the question of whether you can detect the orientation of these things. Yeah, so that's what we're working on now. So that's the other interesting thing, is if these things can radiate this stuff, is gravitation radiation can measure it. So we're just in the process of estimating what the waveforms look like and figuring out whether that's going to be detectable. And so all I can tell you is what things look like today, but they're still in a pretty high state of flux. I think the current numbers that we've got are if you do a sort of perfect match template that the signal to noise for LIGO 2 is something like, I think it was 19 was the number we were getting last week. So that's pretty good. For LIGO 1 it's like 3 or something like that. However, the caveat, Kirk Cutler, who's also working on this phase of the project with us, is getting exactly half those numbers, and so clearly somebody has a factor of two wrong, and we don't, at the moment, we don't know who's, so it may well be half that.

27:30 I think that the problem, the likelihood of really being able to do a match filter on this is actually pretty low, unfortunately, and the problem is there are just too many uncertainties, it's going to depend crucially on exactly how it cools and things like that. So to really predict where all the 10 to the 9th cycles of gravitation of waves that come off in the first year are, accurately enough to build a template that can go over a whole year, I think is really hopeless. So I think the situation is worse than that. But there are some hopeful features. When the instability first starts, what happens is you've got, presumably what happens is the neutron star collapses, or the pre-supernova, whatever it was, collapses, forms this neutron star. And initially, you would expect that to be very noisy. I mean, there's going to be convection. It's going to be a little asymmetrical. You know, it's just going to be a messy, hot, boiling, seething system. And some component of that chaotic, turbulent mass ought to have a projection along this mode of ours that grows. So we've been assuming that, you know, initially there's some small, you know, sort of 10 to the minus 6, 10 to the minus 8, 10 to the minus 4 amplitude, dimensional amplitude in this mode. Once you get the mode started, the gravitational radiation time scale initially is something like three seconds for this thing to exponentiate. So I think the calculations we've done is that something like in 1,000 seconds, the amplitude of the mode grows by a factor of a million. So it doesn't really matter what the initial amplitude is. Wait 1,000 seconds, 10 minutes, and you've got one factor of a million. If you want another factor, you know, you just wait a while. So this thing is exponentially growing very quickly. During that initial phase, the mode itself doesn't have much energy in it and it can't really radiate that much gravitational radiation because it's just a small perturbation on the star so far. So during that period of time, the radiation that does give off is incredibly monochromatic.

30:00 It's basically just the frequency of the mode turns out to be four-thirds times the angular velocity of the star. So until the mode becomes sort of big enough that it can start telling the star where to go, that is until the amplitude mode becomes an order of unity, it's very monochromatic radiation. So if you calculate these sort of characteristic gravitational wave amplitudes, divided by DFDT, those turn out to be huge. Should we stop here? No, it's okay. Those turn out to be huge initially just because DFDT is very, very small. And so it's possible that just by doing a Fourier transform on sort of 1,000 seconds worth of data can pick up this signal in a way that it's sort of acting like a piece of the match filter, but it ought to be a good piece. And so it's conceivable that it can be picked up using sort of standard pulsar-type search techniques without the need of having a full template. And these people who know more about gravitational wave extraction then seems to be hopeful that there are other strategies without having a full DTL template that would give you some substantial fraction of the signal noise without knowing everything. So initially you have a kind of a monochromatic burst, and then over the course of a year or so? And then it sort of, so our, we don't know how to do the nonlinear hydrodynamics, so we have to fake it in some way. And we're sort of faking it by analogy with one case that we do understand how to do the calculation. If you look at, so you probably know about these Maclaurin spheroids and Riemann-S ellipsoids and all of that kind of stuff. So that's one arena in which one knows how to solve all the equations properly. So what you can do is you can take one of these ellipsoidal figures, which is very close to Maclaurin, that is it's basically just Maclaurin plus a little piece of a mode, and you can ask if you put in gravitational radiation in the action.

32:30 And it turns out what happens is initially, the mode just grows exponentially. Okay, but that doesn't happen forever. I mean, it doesn't rip itself apart. What happens is the nonlinear hydrodynamics sort of saturates, and when the mode becomes sort of an order of unity, then it just sort of radiates away all of the excess and the momentum that it has, and it evolves towards one of these time-independent So the basic picture is you exponentially grow until the amplitude of the mode is in order of unity, and then it just evolves in that saturated phase until you lose all the angular momentum. So you can write down equations that describe that kind of exponential growth, saturation, and spin down. So that's what we've done for this set of modes. We do the real R mode until the amplitude is in order of unity, and then we just let it spin down the angular momentum of the star with a motive or a unity and strength until it just loses everything. So my guess is that that's reasonably accurate in sort of crude sort of conservation law level, right? I don't think in detail we'll describe how the actual evolution will develop but it's the best we can do at the moment. So that's the kind of models we're using, and you know, there are parameters you can play with, sort of, you can set where does the saturation occur, is it a mode of amplitude 1 or a 10 or a 100 or a 2, so you can fiddle with that parameter, turns out it doesn't change things very much, which is nice, because it's something we really don't have. The signal noise you mentioned again, how far away would the source be? 20 megaparsecs, so that's here, though. So you would expect, what is it, about a supernova a week and if some fraction of those produce neutron stars rather than black holes, you know, maybe there could be one a month of fast-touching slides. That's a long story. you must be getting a lot of reaction to your initially since it has two communities that it obviously feels to

35:00 I don't know how rapidly things have circulated we just posted on the web about a week ago so we've gotten reactions from the relativity community and we're just starting to get some reactions from the astrophyses yeah Ben said you posted on GRQC but not astrophyses Yeah, so we need to do that. Although we're starting to... So I just got an email from John Middleditch this morning who does optical observations of pulsars or possible pulsars. Right. So there's some interest in moving? Yeah. But you've already had some interest about this? Yeah, sure. I mean, we've been in close contact with people who are sort of vitally interested in these things. And I'm starting to get emails from people who are perforately interested as well. In fact, I have one. I'm not going to jail. Oh, that's good. Glad to hear it. Congratulations. What was the original reason? Oh, travel audit. It turns out they're just very confused. So, that's all we're getting sorted out. So, I got a little more crap to clean out of the way, but I should be getting on this angle averaging stuff within the hour. Oh, you'll be interested in this. So, this is the energy flux of neutrino luminosity due to the cooling. Right. And this is the rate at which energy is being dumped into the thermal bath by sheer viscosity. So it starts out hot here, exponentially grows, and then gets in the saturation phase, and you can see that the two aren't comparable until you get down to just exactly what we compute analytically. And yeah, as we have. About one and a half times 10 of the night, so it's really not relevant. We're worrying about, since gravitational radiation is carrying off energy from these modes, but also viscosity is sitting in there, it's also dissipating energy. and part of viscosity energy is dumping energy from the rotational kinetic energy effectively into the thermal bath well if you dump that too quickly the star won't be able to cool and that could foul up everything

37:30 so if it cools too slowly then basically the radiation gravitational radiation can't get out in some sense so what Ben and I compared here rate at which neutrino cooling is taking energy out of the thermal bath. And this is the rate at which shear viscosity is dumping rotational kinetic energy back into the thermal bath. And until these become comparable, it's clear that this extra heat source is just irrelevant. So basically, it doesn't matter until everything is over. it's kind of convenient all of the deadly stuff that we don't understand all happen at the same point and we give up let the astrophysicists take over and do it right Nir can do the calculation yeah sure as if I know how to make 3D MHD you don't do better than we do so is there is there sort of a definable boundary market which is sort of a changeover from what people like yourself can do and what people who do yeah a couple times 10 to the 9 kelvins somewhere in there I mean presumably given enough time we could learn how to do those things But somebody else will do it first, so my interests lie elsewhere. So, I mean, the background of a lot of people that you mentioned, well, obviously working on the interested in gravitational radiation instabilities in person, basically in relativity. Right. Has any of the astrophysicists ever shown much interest in this? Well, the ones that we've talked to have, but I don't think it's widely circulated in that community yet. So, I think my guess is that they will be interested. So, I mean, the people, you know, we've talked to Sterl Finney, we've talked to Roger Blandberg, people here, and they're interested. And, let's see, I guess last week we talked to Jim, Jim Immora, at University of Oregon. We were up at this Pacific Coast Gravity meeting, and he does this sort of thing, and he's an old friend, so we were talking to him about it. And he works with John Middleditch,

40:00 so that's how Middleditch found out about this and fired off this letter to us this morning. so I mean things things are starting to get around yeah give it about another week saturate it when we put when we put it on astrophage then things would be really interesting probably probably should my guess is that because I don't know I don't know and then it'd be we'd be kind of dorks for withholding too long so this could be a crucial a great boo to a sort of gravitational wave of astronomy in the sense that here is a good candidate for an interesting problem in astrophysics that LIGO could actually verify assuming it did see this phenomenon and you could say you're really good I mean in the same the nice thing is you don't have to postulate a huge asymmetry to start with it generates its own it's sort of like the binary in spiral problem from that right It's sort of self-generating, and things like that are much more reliable than having to calculate the height of mountains on pulsars and then calculate sort of how they spin down. I think that stuff is always much trickier and harder to believe the answers when you get there. Yeah, sure. And I mean, I don't know what, you know, on the Facebook it doesn't seem likely that astronomers like Minnabich could very easily find out for a reason that it's something like this. what are the chances that you're going to be able to see something like this? Well, Middleditch claims he has. Well, so we haven't read the paper, or at least I haven't, but the email that he sent said that they have evidence looking at 1987A of a 2.18 millisecond optical periodicity. Okay, well, that's the same group that found the half millisecond periodicity, in one year and later turned out to be VCR 1987A instead of PSR 1987A. So I'm sure that there will be a great deal of skepticism among the experts on looking for those things when this comes out. I'm not qualified to judge one or the other. If it's true, then from our perspective, it seems strange to us.

42:30 can this thing be rotating that rapidly, it would indicate that there is some enormous suppression mechanism that we haven't thought of. So that in itself is interesting. The part of the calculation that I'm pretty confident that we've done right is the gravitational radiation part. I think we're not particularly qualified to write down the complete list and sort of correctly do all of those calculations. But I think we've done an above-average first crack at that, and unless superfluids set in at much higher temperature than people, well, not much higher, but somewhat higher temperatures than people, gas- not gas- calculated, then things should be much slower at birth. so we'll just have to wait and see what this new observation means well it sounds very exciting yeah well it's we don't get a chance to do real astrophysics inadvertently very often so it's fun Okay, so it's actually started and it's going, and it's the 25th of March at 1.30pm, and I'm talking with Frank Estebrough. Well, as I mentioned, since you referred to the early days of Kip's group here in Cobb Town, I was interested in Bill Burke, because the work that I did for my thesis concerns a radiation reaction problem a lot, and I know that you were a big influence on that. Not specifically on that problem, but of course he and I were lifelong friends and colleagues. He goes back to, what, 1962, I think, when the relativity course at Caltech needed to be taught. H.P. Robertson, who was, well, the Caltech Apostolic Succession started with R.C. Tolman.

45:00 And I was lucky enough to be able to take Relativity from him the last time he taught it, which was just after the war. And then he was succeeded by Bob Robertson, H.P. Robertson, who taught Relativity several Ken was absent from the campus quite a bit because he was, as I remember, Chief Scientist to General Eisenhower after the war. There was a series of, I don't know what to say, shape, something called shape, Supreme Headquarters, Allied Powers in Europe, and Robertson was a big gun in that. But he taught relativity until, my guess would be 1961, when he was killed in an automobile accident here in Pasadena. So I was lucky, in that sense it was lucky for me, because 1962 was time for the relativity course at Caltech to be taught. Again, it was taught every other year. Yes. And Carl Anderson knew me and I was working in JPL by that time and he asked if I could teach it, which is a great opportunity for me. I've been studying relativity on my own after having it from Tolman, but I've really never been exposed to the kind of rigor that you get when you have to teach a bunch of Caltech kids. Yes. And Bill Burke wanted to take the course. He was a junior. And it was a graduate course. As I remember, there were a couple of good graduate students named Jim Gunn and Bill Kinnersley and some other ones. with Bill Burke, one to take it, and it was fine with me, and he must have, whether he had to get any authorization from the undergraduate dean, and I don't remember, but he anyway took the course, and he got an A in the course. He was a great student, and he loved it. And I taught that course a second time, which was two years later, and by that time Bill was in graduate school, and he was my TA for the course.

47:30 I remember that I had a TA the first time. And so Bill and I became lifelong friends, starting right then. Now, as far as his PhD research goes, he did that under Kip. Kip came about a year later, maybe 63, 64, I'm not quite sure which, and became the young professor of relativity at Caltech, and then Burke was one of his very early, very first graduate students, research students. So, then he, Bill, did research that he and Kip pushed and became rather well known for in the gravitational radiation reaction in the quadrupole formula. I'm sort of curious as to if you knew what attracted to that problem. Because the impression that Kip gave me was that Kip himself hadn't really thought that it was that urgent problem at the time Probably Bill self-motivated. I think he motivated his research. I don't remember giving him the problem either. Bill was quite Catholic in his interests. He interacted a lot with a good friend of ours in the philosophy department, a man named Professor Burish, B-U-R-E-S, taught philosophy of science and logical positivism and such things and very influential probably unknown to most people in the physics department but anyway Bill discovered him Bill became very friendly with a friend of mine named Eugene Cowan who is an emeritus professor there now and I think worked with him on maybe some electromagnetic problems There's some references to Bill in Cowan's book on electromagnetism. If I had that right, you could ask Cowan. He'd be good on the interview. He's there almost every day in West Bridge. Bill became quite influenced by Paco Lagerstrom.

50:00 Bill took a course in the Applied Mathematics Department. And I think it was all Paco Lagerstrom. It could have been a man named Julian Cole also. Lagerstrom is dead now. Cole is a professor at Cornell or Rensselaer somewhere there. He's a very well-known Applied Mathematician there. The interests in the applied math department at Caltech were one role, they were just what I say, they were applied mathematics, usually of relevance to aerodynamics. Physically, they're located near Gausset. And as I understand it, they at Caltech had developed this method of matched asymptotic expansions. Coal and Lagerstrom and maybe others and had used it a lot in non-linear fluid flow problems. And Bill picked up on that and realized it could be applied to the non-linear equations of general activity. And whether that came first, after his interest in the quadruple formula, or the quadruple formula, somewhere along there it fell together and Kip must have given him the go ahead and work on it. But Mill also was a very independent guy, following his own views. That's interesting. So it was certainly the Caltech environment that he flourished in, and it stimulated him to do that work. So you were at JPL? All that time. Yeah, all that time. What were you working on at that time? Well, I came to JPL in 1960, and in those days there was a lot of money at JPL. program was just underway. NASA was only two years old. JPL was a key part of NASA. We put up the first explorer, the first U.S. Earth satellite. And so money was really no problem if you had interesting work to do or someone here had some interesting work to do.

52:30 And the man I first came to work under had the rather mistaken idea that nuclear reactor power might somehow be used in propulsion in space. A rather crazy idea. But I had been faced with a job transfer. My previous job in passing had been moved essentially to North Carolina. And I didn't want to go to North Carolina. Yes. And so I knew Dr. Pickering at JPL and I came up here looking for a job. And they just formed a physics section at that time at JPL. And the guy who was forming it up was interested in nuclear rocket propulsion possibilities. I had a background. After college I worked for North American Aviation for a while and I knew nuclear reactor theory, transport theory. So essentially he and I hatched a deal that I could work part-time in relativity if I also worked on nuclear rocket propulsion. And I did a couple of papers the first few years at JPL, having to do with neutron reactor theory. And as that died, I didn't particularly worry about it, I just sort of started working more and more in relativity and less and less in nuclear reactors. And the bottom line in those days was that if you could publish respectable papers and do respectable research, then you were funded to do that research. Everything was deemed ultimately irrelevant to the space program. So over the years I survived by doing relativity theory here, And I was fortunate in the fact that at a certain point, I realized that there might be some gravitational wave experimental observational possibilities using spacecraft tracking, which is very precise tracking. And that probably saved my career, JPL, because ultimately money got tighter and tighter, and we had to justify our work by relevance to the space program. And by that time I was, that's a long story, it's probably another story. Kip also was very instrumental in that story in reassuring people here that this was respectable work.

55:00 But we managed to start getting experiments on board interplanetary spacecraft to search at a certain threshold level, which is pretty high. But anyway, to use technology that was available here to search for possible long-period gravitational waves. And that justified the theory I did all those years also, and it all came together and I'm still here. Was the theory that you were working on along connected with gravitational waves, or was there other aspects of that theory? Well, my interest is probably pretty mathematical in the theory, my theoretical interest. and with a close colleague named Hugo Walquist who he and I sort of mutually stimulated one another and he moved into relativity sort of under my influence here and the two of us made our careers here together as colleagues with him we developed I developed mathematical techniques The field equations, after all, are a big, complicated mess of partial differential equations, many, many dependent variables and four independent variables. And with those methods you can do various things, you can specialize and discuss anisotropic cosmologies, you can specialize and discuss certain mathematical problems that are probably theoreticians, presumably you can make a contribution to calculation of gravitational waves or formulation of the wave content of the equations. You always can justify good theoretical work by possible applications, in this case discussing sources and waveforms and so on. The truth is I have not really done much calculating of any waveforms or sources. I've really sort of stayed at the extremely theoretical end of things, but I suppose the other thing to be said is if you do have some relatively experimentation going on at an institution, the institution itself needs somebody that's in the field, that knows other people in the field, and talk with them, and provide the bridge between the engineering technology that's being used

57:30 in the theoretical and research part of the academic world, so I've been very lucky. Meanwhile Bill, well of course you know all this about Bill, but then after he graduated from, got his PhD under Kip, I think he went straight to Santa Cruz. Am I right in that? I'm trying to remember. I'm not sure. Yeah, I know, I don't know if he went straight there. I think he must have done his post-doc at Santa Cruz. That sounds right. I guess I'm not sure anymore. But he was lucky. I guess everybody has to be somewhat lucky at some points in one's life. He was lucky in that the Santa Cruz Physics and Astronomy departments could sort of throw together. They decided they needed one relativist. And for many years he lived as a half-time billet under like observatory aegis and half-time under physics. The impression I get is that he was a brilliant teacher because he had so many wide interests from electromagnetism, optics, relativity, applied math. Yes, I got the impression that he was going to be very well-rounded. The students up there still maintain a webpage in his name, which is a lot of the stuff from his course and little things. It's when you're really up to look at that. I remember looking at his webpage when he was still teaching. I remember looking at it and being impressed by the breath of the teacher. Let me see, since you mentioned the story about the development of projects to look at at low-frequency gravitational waves with Doppler tracking a space car. That's actually a topic that I'm very much interested in because the work that I'm doing now in Cardiff

1:00:00 is really aimed at looking at the connections between theory and experiments and gravitational wave detection. So the influence that the at the moment ever-growing field of gravitational wave detection has had on theorists and then also the impact that theorists have had on the field. interested in learning something about the Doppler tracking side of things, which I know is about at this point. So, you were saying that at some point you realized that this would be a possible means of detecting gravitational waves. When did that come about? Well, it's hard to say. The first important need, you might say, for general activity theory at EPL was in the development of the planetary ephemerides. Yes, I was going to ask about that experience. Tracking, there are several different ways of observing, of tracking spacecraft, the primary, what is called ranging, which is just what it sounds like, it's a close relative of World War II radar. you put out some sort of microwave signal that goes to a distant object and if it's echoed back by that object you measure the elapsed time when it gets back and that's called ranging to the spacecraft around here it's called ranging and if you know Newton's equations for motion of a if you know, roughly speaking, the gravitational field it's in from the Sun and the Earth and maybe a few heavy planets that it might be in the Earth, then you can fit the theory of that to your ranging data and determine the parameters in the theory. So from ranging you can get angular information in the sky and you learn a lot about an orbit just by measuring ranging to the orbit. One of the tricks, then, is to observe how the ranging signal varies as the Earth rotates.

1:02:30 The Earth rotates around, so there's a Doppler shift, but there's also a time delay as the ranging signal arrives earlier or a little late, depending on how the Earth rotates. Meanwhile, it's doing this active ranging. setting up a series of pulses or frequency modulations and getting it back from the spacecraft, you fit the Earth's 24-hour period to that data, and you learn a lot. And this is the way JPL usually navigates a spacecraft, and also then, as a byproduct, refines the ephemeris of the planets. So you can play all kinds of games involving geophysics and studying solar plasma and at some level if you can do things precisely enough you can get terms in the mathematical equations that fit to the data, those terms being of relativistic origin, corrections of order c squared, one over c squared, and the classical three tests of relativity, measuring advance of perihelion, time delay effects, displacement effects, angular displacement effects, propagation of light, all of these things become much more refined and a whole a variety of tests that flow from precise celestial mechanics that verifies general relativity. Well, you can have that pretty well in your head. There was a time when I did help some of the people formulating those orbit determination programs by putting in some extra relativistic terms. There was a time when Brandt-Dickey theory was very popular, And so variants of generativity were at hand, at least at some precision level. Kip then made a big industry out of this in the BPM formalism with advanced parameters, but primarily there's a parameter called beta and called gamma that can be regarded as adjustable parameters in these fits to planetary ephemerides and to spacecraft orbits, and beta and gamma can be measured that way.

1:05:00 This was probably the first relativity that TPL was putting a beta and gamma into the orbit determination programs. I think a lot of people from time to time made off-the-cuff remarks by, hey, someday you might see a gravitational wave, or maybe a gravitational wave would go through. And we never took it seriously because the level of precision wasn't good enough. The gravitational waves, you might talk about a few, I'm not sure at the moment what, millimeters, tenths of millimeters, tiny little effects like that from gravitational waves that were conceivable at least at that time. And that was way below the precision that the JPL orbit determination stuff was doing. So, for many years, it was essentially the so-called solar system tests of static or stationary general relativity was all it was possible to do with our technology. Well, the technology improved. For many years, they had timekeeping standards here for the ranging, which were atomic frequency standards. I think they were called cesium standards, was the best, maybe there was another atomic clock frequency standard. And they turned out they really weren't good enough for navigating spacecraft. And so there was a push on during the 60s and 70s to go to a higher precision frequency standard for navigation purposes. It's just a technological accident. The next thing best, better, the next thing better than a cesian clock is a so-called hydrogen naser clock. But that wasn't just a little bit better. It was like two orders of magnitude better. And so they were sort of driven by the engineering imperatives to improve the timekeeping stability of the deep space net around the globe beyond what they needed. And Walquist and I did become aware that, gee, maybe there were some more high precision games as far as gravity could quite be playable.

1:07:30 But the, finally we got the idea, this idea again was not just with us, this was in the But somebody asked me at one point, what really would be the effect on not the ranging by Doppler, but the ranging of signals to spacecraft, but what would be the effect on the so-called Doppler signal? Because standing in the wings with this other technique, instead of doing radar-type ranging to determine time intervals, the actual microwave signal that is echoed back by a spacecraft is changed in frequency. You set it up with a certain frequency and it comes back with a different frequency because primarily of ordinary Doppler motion effects the spacecraft is moving with respect to the Earth. But somebody, and I don't remember who challenged me to actually write down a formula instead of just waving hands, be the effect on the observed Doppler frequency if a gravitational wave, or wave front, went through the beam while we were doing a Doppler measurement. Unfortunately, sometimes people call it Doppler ranging, which really confuses the terminology. And that's a simple enough matter, but no one had done it before. You set up a space-time diagram, and you put in a so-called null geodesic from the Earth that goes up and intersects the spacecraft, and another null geodesic from the spacecraft that comes back on the Fincher-Hell cone intersects the whirlwind of the Earth, and you assume that you have, on the whirlwind of the Earth, a frequency standard that is itself transported along that whirlwind and so you can measure frequency upon emission and you can measure frequency upon reception and that gives you a Doppler shift which might include gravitational wave there. Actually you don't do it that way what you do is you continually emit signals and you continually receive signals. So really the measurement you make is the instantaneous difference in frequency between what's coming in at that moment, which is admitted in the past,

1:10:00 and what you're sending out in that moment, which would again be received in the future. Same sort of information that's folded into itself, so you get this continuous record. Okay, any relativist knows how to lay out the equations for propagation of frequency along a light curve. actually goes back to Schrodinger Schrodinger in one of his books has a neat little equation for how a four vector is parallel is parallel propagated along a null geodesic a photon is described by by a null geodesic but the four vector and there's a null four vector along the null geodesic but the length of that In any coordinate system, it has a length. Its absolute length is zero. It's a null. It's a null particle. It has zero mass, but it still makes sense to talk about parallel propagation of it, and if you go around the circle, you can compare it when it gets back to the way it went out. Well, you can do the geometry in a gravitational wave metric, the first order metric is rather easily written down. And so I did it. Amusingly enough, there's a neat way of doing it. There's a brute force way, which is to write down coordinates and do parallel propagation, a la the old equations from Einstein and so on. But a so-called plane wave, gravitational wave metric, first order, has killing vectors in it, symmetry directions. And Bill Burke had taught me at one point how neat it was to take advantage of those killing vectors. And so using the killing vectors, you can very quickly derive the equations here instead of doing the root force method. And so I was always sort of tickled that I was able to use that little technique of bills. And we published, Hugo and I published a short paper with the equation. And if you think about it for a while, the results aren't even very surprising.

1:12:30 if you emit let's see how can I say and the hand waving technique that I always use is to say if a gravitational wave comes by the earth it wiggles the earth in some sense it does at least in any coordinate system it does we all know, we relativists all know the crystal equivalence is sitting on the earth we don't know it's wiggling But we're on free fall, and so we don't feel anything. But the Riemann tensor does come past the Earth, and so roughly, for intuition, one can say the Earth wiggles when the radio wave comes by. If at that moment, when the radio wave comes by, you're sending out a precise frequency tone to a distant spacecraft, it'll pick up a Doppler shift. And it's a result of the Riemann tensor coming by. and a round trip light time later that frequency will have gone to the spacecraft will have been transponded back to the Earth again and you will see the wiggle in the Doppler shift when it comes back a round trip light time later and you say well maybe something happened maybe there was some plasma that the microwave went through or maybe the spacecraft wiggled but anyway you'll see a wiggle Of course, when that Riemont tensor first hit the Earth, you were receiving. As I said, you were also continually receiving those things. So the frequency that you were receiving took a wiggle at that time also. So now we have a wiggle at the moment the gravity weight comes by in the Doppler shift that you measure, well, in respect to your hydrogen measure of time-keeping. You also get a wiggle in the spacecraft, a wiggle in the Doppler record at the round-ship lifetime. But there was an intermediate time when the Riemann tensor hit the spacecraft. And it wiggled the spacecraft. Right. So there's another copy of the waveform in the Riemann tensor that came to the Earth, which we could measure as a Doppler ship, in between the first and last ones that I described. So that's the net result is that there are three observed signals in the round-trip Doppler record if a single shock wave or pulse of gravity waves goes by. And I think that's probably one of my original contributions to point that out,

1:15:00 just a three-pulse signal. And we made hay out of it because we said, look, there's no other physical thing that we can think of that would do that. Shaking the spacecraft all by itself or intervening plasma or going out here and kicking the antenna to the goldstone all would give one or two. If there's a clock, if the 100-meter clock suddenly is shocked or gives an anomalous signal, it will be observed then and a round-tripped lifetime later as a two-pulse. So anyway, so we published that and we said, look, maybe we should think, we and NASA should think about actually looking for three pulse signals that we were just at that naive level at that time. When was that published? 1974, maybe. So, you had worked out an obvious signature that a gravitational wave would lead. The three pulses have relative spacing. The overall spacing is the round trip flight time back and forth to the spacecraft. The position of the intermediate pulse depends on the angle in the sky of where this gravity wave propagation vector is to the vector to the spacecraft. So it's dependent on one parameter, theta, in the sky, the spacing of the three pulses, and the relative heights of the three are also dependent only on theta. And there's some neat internal consistency things, the sum of the three pulses has to In some sense, if the pulses overlapped, if you were at an extremely long wavelength gravity wave, so if the period was long compared to your characteristic lifetime back and forth to the spacecraft, in that case it's like the measurement you're trying to make becomes a local measurement if the gravity wave length is long. And we all know local measurements somehow are supposed to go to zero because you can't locally determine where the gravity is going by.

1:17:30 So the principal equivalence says that the sum of the three pulses has to be zero. That's sort of neat. And there's an exception to this, which Kip has pointed out on occasion, which is if instead of a gravity wave pulse coming by, you had a so-called post-it memory this is a bizarre case where you can have a different Minkowski space-time on either side yes certain sense the characteristic scale of the Minkowski space changes size across the pulse in that case my statement about the three pulses adding up to zero is not correct But in all the stuff we've published, we've almost sort of ignored that case. Sum of three pulses are zero, and as I say, there's a relationship between the spacing of the middle pulse and the relative heights. There's really only one parameter that dictates this whole characteristic pattern that comes by, that angle theta. And you asked when I published that. But that did lead us on because we then, within a year or so, we approached the Voyager project. about, hey, you know, you've got, so we are now putting in an experimental basis just at that time, the hydrogen measures in the deep space, and we approached the larger project about somehow getting on the project and scheduling some observing times, and that didn't fly. They were so busy doing their business, which is planetary physics, Yes, but they didn't want extraneous fishing explorations. I do remember a meeting when Kip and I went to talk to a project scientist in the larger mission, one named Ed Stone, who is now well-known at JPL. But we couldn't talk him into it. But I was stimulated to go ahead then and write the first full-scale proposal for a gravity wave search using Galileo, Galileo, starting in about 1976, trying to believe how long ago, was being planned, and the Deep Space Network did have the hydrogen majors in, so I wrote a successful proposal.

1:20:00 Apparently it was a close thing. I've heard rumors about the difficulty that committees had accepting that proposal. But I did get on board Galileo to do an experiment. And I got on board with the explicit agreement that they were not committed to put X-Band on board. Now we're getting into the business of S-band, X-band, K-band, these are successively higher microwave frequencies used for the navigation of spacecraft, navigation and data return of the spacecraft. Oh, where are we here? Yeah, okay, when you asked me the date of publishing that, I was way off. I was thinking of the first work that Hugo and I did with our developing new formalisms and so on. That was in 1964. But the short little paper responding to the idea of what's the response of spacecraft to gravity waves was 1975. That was the epic when they were putting in the hydrogen majors. And that was when the technical possibility was there. That's when it became feasible at a much higher level. Still at a very crude level with respect to what most people thought sources might be in those days. So I guess in 1976 then I did write the Galileo proposal and got on board Galileo and I started agitating for X-band tracking. The higher the microwave frequency that you can use, the less

1:22:30 influenced it is by interplanetary plasma, by the solar wind. And the hydrogen maser timekeeping precision was by an order of magnitude more precise than the S-band microwave link to the spacecraft to that effort would allow. I mean, the fluctuations due to the solar wind were the dominant noise source in trying to do Doppler measurements. And by getting X-band, which is a factor of three higher in frequency, and therefore it turns out a factor of three squared, less influence from the solar wind, by getting X-band tracking on board, we would essentially be able to match the expected frequency fluctuations from solar plasma to the threshold set by the hydrogen maser timekeeping. So that became the game. There's another, there's a lucky happenstance here, which is that hydrogen masers have their best performance over integration times of about a thousand seconds. If you look at the technology of hydrogen meters, they are not very good clocks to measure short things, to measure intervals in the order of a second or a tenth of a second or something like that. And also they're not very good over a period of a day or more because they start to get long-term drifts. they are at their best at around a thousand seconds and a thousand seconds is a typical round trip lifetime to track an interplanetary spacecraft going out to Jupiter in one to two three thousand seconds depending on where it is in the sky so that was again something that played into our hands here making this a sort of feasible technology The corollary is that you can't really do this Doppler tracking very well if you have something going around the Earth or something, even in the inner solar system, because you have much shorter echo time from back and forth to the spacecraft, and the precision

1:25:00 of your timekeeping is degraded. If it's not near a thousand seconds, if it's a hundred seconds, it's quite a bit worse. That's the fact that the inner solar system is full of plasma. So I got on Galileo, Galileo as you probably remember had all sorts of ups and downs in terms of having to be redesigned for various different propulsion options that NASA kept changing its mind about. After they finally got Galileo off, enough time had gone by, the Deep Space Net had fully instrumented all three stations around the globe with X-Band, and I had succeeded with a lot of help from the Deep Space Net in talking the Galileo project into putting on a small X-Band transponder for research purposes. And also for learning how to engineer such things for successive generations of spacecraft. And everything looks great. Of course the terrible thing happened that the large unfoldable antenna onboard Galileo did not unfold. So Galileo has been forced to perform the rest of its mission and incredibly they were able to do it. They've been forced to do it at S-band, which is the old frequency used by Voyager in the preceding generations. They had as a backup on Galileo a small omni antenna, which I visualize as some sort of little thing, like a little cone or something. It's nothing like the big paraboloidal antenna that they were going to use with X-band. But they've succeeded at a very low data rate, getting the data back for a good fraction of the pictures that they intended to take. In any case, they've had a very successful mission, but the X-band that I got on board was only electronically connected to the big antenna. So the Galileo data that we then got, and are still analyzing, was all S-band data, which does not really take advantage of the capability of the BSN timekeeping in the way we hoped.

1:27:30 The hope of the future now is going to be the Cassini mission. The Cassini mission has an official Bradley Wave search experiment on board. the Cassini mission is upgraded, the backup antenna of the Cassini mission is X-Band, but for the purpose of the gravity wave experiment, they have a K-Band transponder on Cassini, and it's another factor, four or so, lower threshold due to solar plasma. So they're going to do a much better gravity wave experiment with Cassini than they've been able to do so far. So the K band is higher frequency? It's another higher frequency. I'm so bad about frequencies. Let me tell you wavelengths. The S band, the Voyager and the Galileo backup had, is around 12 centimeter wavelength. The X band that has now become the standard with the DSN is 3 cm wavelength and the K band is around 1 cm. And the improvement goes as a square of those ratios. Have there been any other missions that did Doppler missions? Yes, yeah. It's been on almost every one now since we got on Galileo. That sort of broke the log can. It really doesn't impact the mission as much. They have to give us a little support to participate and they have to pay for data reduction costs, but the actual onboard mass and power requirements are quite easily swallowed by the spacecraft engineers. It doesn't impact the planetary, the real reason for the mission. The other thing to be said is that, well, it's become politically more

1:30:00 respectable. The growth of the LIGOs around the world, the search for gravitational radiation is not, it's more in the public consciousness, I would say. Yes. The, let's see, the Ulysses mission, which is a joint mission, European Space Agency and JPL for tracking, all these international missions, if they're planetary missions, they usually rely on the JPL Deep Space Net for their data gathering. So we tend to get a piece of the action even though the European Space Agency or somebody else builds a spacecraft. So Ulysses had an official gravity wave experiment with Italian colleagues of ours and Hugo Wellquist as a co-eye. There was a previous mission on which Hugo was going to be the PI and we got on board and everything was fine, it was called. It was to be a twin mission. There was to be a US spacecraft and the European spacecraft to go around the poles of the sun and north and south poles simultaneously. And Hugo was the PI of the gravity wave experiment for the American one, and Hugo, our good friend was B.I. for the one aground the other way. And NASA canceled the one hour. So Hugo is on, Bruno's B.I., Hugo was on Ulysses. The Mars Observer went to Mars about four years ago on an American mission, and our colleague John Armstrong was a gravity wave experimenter on it. All these gravity wave experiments take place during cruise, when you're on your way somewhere. That's the other reason we can get on board, because after they get to Saturn or Mars or wherever, they don't want to fiddle around with the Doppler tracks. the Mars Observer cruised to Mars, and when they attempted to slow it down and go into orbit, something happened, it disappeared.

1:32:30 It was a lost mission at that point. So the only data taken on that mission was the gravity wave taken during cruise that Armstrong is reducing. And there was a nice coincidence in 1992, when all three spacecraft were in cruise, that is to say Galileo, Ulysses, and Mars Observer. And we managed to talk to three projects into cooperating and all turning on and allowing us to track them simultaneously for three weeks. So we got simultaneous data. That's the other thing with gravity waves. If we ever saw something, we wouldn't know whether to believe what we saw or not. If you could have two spacecraft independently and see the same thing, that would have been much nicer. So we had a three-way joint experiment in 1992. Most of the data from that has been reduced now. The bottom line in all of this And so far we haven't seen candidates, candidate events, candidate sine wave things sometimes in the Fourier record. And we usually manage to talk ourselves out of it. In the case, there was a beautiful event in the case of that three spacecraft experiment, which only one spacecraft saw, the other two did. and almost certainly it was a glitch at the ground station. If you're tracking three things in the sky you have to use all three DSN stations at the same time. In fact, they have to be in different parts of the sky. Usually at one station you cannot track two things like that simultaneously. Well, if you're using the hydrogen major and if you're doing open loop tracking. Anyway, for technological reasons it's much better if you can use all three. data. Now Mars Observer has a follow-on mission that is at Mars now called MGS, Mars Global Surveyor. It's very slowly re-entering Mars now. They're doing what they call aerobraking to try to load the orbit down. They're having problems. But during its cruise, Armstrong

1:35:00 again got data. And these missions now, Mars Observer and Mars Global Surveyor are X-band missions. So from now on it's X-band and maybe K-band, as you can see. Well, is there any indication that going to, for instance, K-band might improve the sensitivity sufficiently to put it within the range of what is expected signal? The range of what is expected has always been several orders of magnitude beyond where we've been. people are always thinking up new bizarre sources, and if you've got a couple of ten to six mass, ten to six solar mass black holes orbiting one another, that toward the end of the lifetime of that We'll put out a nice big signal in our band in the 1,000 second period band. So, always we can say there are something that might be out there, but this is a very dangerous thing for scientists to say. Something might be out there so we should look. That's the position we've been in. To some extent LIGO's in the same position, saying we have to start somewhere, we have to start developing technology, we have to start learning how to analyze the data, and we can see some follow-ons coming, and we've had to say that, certainly, in going up from S-band to X-band to K-band. Now, I think we've been honest, and John Armstrong is a very cautious colleague of ours, and he's been at some pains to actually remember and write down and refer back to projections that we've made as to what we might do. And he tells me that we really have been honest. We haven't oversold what we can do. And with the X-band data he's gotten on Mars Reserver, he has shown that our past projections of what X-band can do are just about what we're achieving. But that's still an order of magnitude or so short of reasonable sources, I think. With K-band we'll close that gap by a factor of 3 or 4, we'll get up to almost 1 power

1:37:30 of 10 to 17, maybe 5 times 10 to the minus 16, which isn't probably good enough, but it's close, it's certainly worth doing in our opinion, all of these things have been from NASA's standpoint chief, it's a very small fraction of the cost of the the planetary missions. But also with K-Ben, we may be reaching the limit of what we can do. We don't really see any future technological improvements that are going to get much better. If we could build a deep space net station on the top of Marakea and get above the atmosphere, or put one in orbit above our Earth's atmosphere, I think there's more improvements. But the so-called troposphere or atmosphere density fluctuations are probably going to set the limit for Cassini. The limit won't be set by the timekeeping on the ground anymore, and it won't be set by the solar plasma because it will be clean there. But the Earth's troposphere seems like it's just something we can't do anything about. It certainly gives frequency fluctuations, and it's more or less non-dispersive. So the delta F over F level of troposphere fluctuations is about the same with X band and K band, or anything higher. The next thing in space way off in the future would have to be some interparameters in space. A LIGO in space would be a very nice thing. Right, sure. I guess I gathered that there's a proposal here now for an Omega project. Omega project is a JPL proposal for sort of a scaled down LISA. LISA is the big European cornerstone mission. which would, I guess, trail the Earth. It would be in solar orbit anyway. And my colleague Ron Hellings is pushing the Omega Project, and it's taken various different forms. I believe it's an Earth-orbiting interferometer. So I got it, yes. But I'm not sure. I haven't really been involved much. I'm not going to interview Ron on that. I'm afraid Lisa and Omega both seem awfully far in the future.

1:40:00 Difficult in these times to find big things like that to be dedicated missions, just dedicated to fishing for gravity waves. Right. Well, I was curious as to the people who worked on the Doppler searches for gravitational waves, are the people who work with you mostly theorists like yourself, or do they also sometimes have an experimental background? John Armstrong is a radio astronomer by training. He is not really a theorist. He's a very able radio astronomer who has done all kinds of work with the deep space net, array and so on. He knows the technology of the deep space net. And I should have said in the early days when Hugo and I were pushing this gravity wave idea, we had to turn ourselves into, perhaps not experimentalists, but at least into, we had to make feasibility studies, we had to put numbers in. Yes. And in order to put numbers in, we had extensive interactions with people and engineers in the Deep Space Network. But I would say, above all, we learned about propagation through plasma, through the solar wind, from John Armstrong and his colleague Richard Wu. So those two were, and Armstrong became a member of our team, I mean Hugo and John and I were essentially the team put that on. John knew what we could do and we were all turned on by one another's. So that was the big input I would say, was from Armstrong. It was a, let's see, Bruno Bertotti, it's probably like Hugo and me, he's probably best thought of as a theorist, turned gravity wave experimenter, and not a dyed-in-the-wool experimental scientist to begin with.

1:42:30 So, in this sort of work, you presumably have a fairly small number of people involved, and when you have time to take the measurements, do you sort of go and take them yourselves and then do the data analysis, or how does it...? The Deep Space Net, which is a cast of hundreds, has a group especially called the Radio Science Support Group. It's had various supervisors over the years. The present supervisor is a guy named Sammy Asmar. It's a M-I-A-S-M-A-R. And when you have an approved experiment on a spacecraft, the support group assists you. They assist you in scheduling passes and telling the deep space stations which way to point and which time to turn on and off, what frequencies you want to look at, what data rates you want to take. The radio science support group is absolutely essential for almost any of these solar system tests that you, we talked about, the rating tests to observe things or things are occulted by planets, when distant radio sources or spacecraft are occulted by planets. It's in close, close collaboration with that support group. They have to know what your scientific requirements are and they have to tell you what you can get and what you can't get. And Even though the project has planned something some years in advance, it almost turns out something goes wrong. Some other project wants the time, or some piece of equipment at some station fails. These things are often sort of smoothed over. But my experience has been you get about 50% of what you ask for, for all sorts of reasons. It's a strange way to do an experiment. You're not doing an experiment in a laboratory, which is hands-on. We're doing an experiment with a cast of hundreds and data thinking going on all around the Earth. That data is taken at the stations and then telemeted back and then finally furnished to us as that takes, along with logs of what happened when.

1:45:00 And Armstrong, as a radio astronomer, was very familiar with that whole system and essentially led us by the hand. learning how to work with it. Would one of your group go to one of the stations in order to it? Usually just not out to the stations, but here to the central control rooms at JPL, a few hundred feet north of us. And everything comes back to there? Everything comes back to there. Except sometimes big tapes used to come back by slow mail and arrive five weeks later, but it's getting more automatic all the time. They're using satellites around the Earth to transmit data and so on. One of the interesting things about LIGO is that it seems as if, up to the present moment at any rate, the theorists are going to end up doing a lot of the data analysis. That's the only thing engineers can ever think of theorists as really any use doing But again, Armstrong, Hugo and I were pretty egg-headed, we didn't really know about data analysis, but Armstrong, radio astronomers do, they know about correlators and so on and so forth, John is essential, and he's carrying the ball, he's somewhat younger than Hugo and I, Hugo is now retired, he still comes in, doing theoretical work, but I've sort of been detaching, and Armstrong is the PI on these. later in generation of spacecraft. And he, as you say, had sort of some of his background and data analysis as well. Exactly. He's very, very good at it. Well, you mentioned the, of course, events that turn up that remain unexplained. Is it usually the case that you know, candidate events are usually assigned to a cause that you're able to discover, or is it just as often happening that, you know, you decide that it's not, convince yourself as you say that it's not a gravitational wave, but that it's still not clear what the cause they're doing? Well, once the usual pattern is that John makes a histogram of, for example, candidate

1:47:30 events, or more likely, well, for example, you can take a long free record. It looks like the noisiest, the data just looked terrible. It looks just like total white noise. It's not white, usually turns out to be colored, but anyway, you do a free analysis of that and you get, I don't know, 10,000 frequencies. If you have a long string of data, you can, the 10 second resolving time you get lots of points and so you can get 10,000 frequencies. You make a histogram of those frequencies. How many there are at each, you know, how many at each strength. I mean each of these 10,000 frequencies will have an amplitude associated with the Fourier record. And so you plot the number that have a certain amplitude versus, what am I trying to say? You can use different I.O. You can use different I.O. You plot as an axis of the amplitude of various frequencies that you observe. This is now presuming we're searching for sine waves, from a sine wave source, a sinusoidal source. chirps and other periodic things, or clumps, all sorts of different punitive signals you can search for. But the simplest one to think about, for me at least, is think of sine wave signals. You have a bunch of noisy data. Flop the amplitude of the sine wave this way, and how many of them there are that way. And so you have a very large number of very weak ones, and so on, and there is, based on white noise, a perfectly probabilistic, it's white Gaussian noise, you and it's it's amazing we achieve the theoretical shape that we should which means we really don't have systematic errors we've chopped off the data so the data sample we're looking at is truly random and way down the end for the very strongest ones there will be one or two they sort of look like outliers but you can't quite tell and so we'll look at those try to see this is that frequency

1:50:00 change, can you watch it for the beginning or end of the pass, if it's a three week pass, if the geometry changes during three weeks, you can check whether certain things should have moved in certain ways during the three weeks, and the internal consistency always says, now what we're looking at is just the last one of a Gaussian distribution, and it should be regarded as noise. So the noise is by and large very gassy? There's the occasional large hiccup, and it always turns out somebody threw a switch somewhere in the DSM, they were recording and they went to a different one, or they changed the tape, The station logs are very good for that. We do that sort of painstakingly, but it's very profitless. You always get the answer that, yeah, there's a physical reason for that change in the dump. So you can actually frequently find the cars by checking the logs? And maybe John could quote you some more. Actually, he'd be a good ad for you in an interview. I don't know how much time you have or whatever, but... Unfortunately, that's much in this trip, but hopefully I'll get another chance. If they move something on board the spacecraft... If the people who are controlling the spacecraft feel the need to change something, we'll see it. And we like to tell them what we see because they're always impressed. We can see velocities, what was it John told me, on board the Mars Observer, he could see a velocity of something like a micron per second. The Mars Observer had a very bad design from our standpoint. It was commissioned by JPL from an aircraft company, and they probably took existing designs and modified them. And they put up on that spacecraft an antenna, instead of being right near the center mass of the spacecraft, the X-band antenna for the transponding was on a boom, so it was

1:52:30 not quite a ways off the center of mass, the spacecraft itself had what are called reaction wheels inside it. Instead of using gas to keep trying to orient the spacecraft, it would accumulate angular momentum in these reactions. If you want to turn the spacecraft, you simply turn the wheel the other way. Go like this with the wheels. And when those wheels would turn they weren't perfectly balanced and this boom out here would resonate with them and it was configured in such a way that the boom resonated back and forth like this in the direction of the earth's signal and he would see these huge signals due to that due to the boom the motion of the boom when the reaction was working and he made up a model and he fitted the data, and incidentally we couldn't find, maybe we didn't know where to look, but the system here at JPL was unable to tell us the distance from that antenna to the center of massive. Once it was gone, we didn't know it, so John fitted that into a model. And then weeks later, he succeeded in getting from the system the telemetered data as to what the reaction wheels, and the engineers knew which way they turned and how much and when. All that engineering data gets put on the data stream coming back to the spacecraft. And he verified in about three quarters of his cases that his model fit exactly what had been going on. And it was motions in the order of a micron per second received at an interplanetary distance. Remarkable. V over C, if you can find V over C for a micron per second, you'll get something like one part of 10 to the 14th. That's the precision that we've heard of doing our Doppler measurements with. We don't think it's very good precision, even. So, in any case, you're saying that beyond Cassini, which will be the most sensitive one yet, partly because you'll be limited by the Earth's atmosphere, it's probable that there are no plans at present to sort of push further? No, we will certainly, for future deep space missions, we will certainly propose to continue taking K-band data.

1:55:00 Presumably our probability of success is directly proportional to the number of hours that we're looking. See, that's the other problem. We're not on the air all the time like LIGO. We can only look for a few hours during every pass, and usually there's only one pass a day, at least per station. At the epoch of Cassini there is only planned to be one K-A band transmitting station in the Deep Space Bank. Only here it goes though. The station in Spain and the station in Australia are not readily planned to be implemented in the K-A band. If in the future that would happen, I would think it would, just as the normal upgrading of the ESN goes on, then you could from a future spacecraft get maybe three times as much data in some sense, schedule as many days. But in terms of the frequency of precision, I don't know whether there's much to be done beyond that, short of going above the atmosphere sometimes. If LIGO ever saw something that might give a big impetus to the whole field, then we could sell some more. But it's hard to get scarce dollars to chase unknown things. What type of source are, you mentioned earlier, sort of reasonable sources that might be out there? What type of, do you have a most favored source? Well, yeah, I'm sure. Supermassive, coalescence of supermassive objects. I guess that's going to be the strongest, too. We'd be nice that gamma ray bursts were associated with the same thing, wouldn't it? Then we'd have some idea of source frequency. People are forever challenging us to say, what are the probabilities of success? You know, if we give you a three-week tracking period, what's the chance you'll see something? Guarantee you'll see a gravity wave or, boy, we just run away from questions like that because we are fishing, we're looking under a lamppost. We have a technology here that is capable of us. But the weakest link in the whole thing is the source distributions and event frequencies, astrophysically.

1:57:30 It's very interesting, though. just to go back to the radiation reaction problem maybe we can take a break I'll go to the bathroom down the hall maybe you'd like to stretch your legs I can even think about trying to make tea I'm not sure, I bet you're a tea drinker. No, actually not, but you should mix in a few. Oh no, I haven't made it for you. I have a tea pot in there that I'm sticking to. Okay. Let's just stretch our legs. Yes, good idea. Can you turn this off for a minute?