Interview with Grant Matthews (contd.)

0:00 In this piece, it's hard to picture that there's any more to the problem than just a distorted gravitational potential, whether it's relativistic or not. And this extra piece comes from working out the equations of motion and analyzing what the forces are, and it's there. Unless you impose a special condition that cancels out the velocities. But all we see, I'm repeating again, but all we see is that the stars figure out that they can respond with a certain motion and that their energy goes down. And so they relax to there. We found that no matter how we start the stars out, we can spin them up, we can rigidly co-rotate them. We can set them with zero spin at all in the frame of an inertial observer sitting away from the stars. that it takes them only a few sound-crossing times, and they relax to this unique solution. It's just, you don't anticipate it if you're just thinking about the field, and, you know, some static matter responding, you know, adiabatically to, you know, slightly distorted gravitational potential. It's just, you know, it's a covariate derivative. there's that that extra piece the um does well obviously you're continuing to work on you know well continue to work ahead on the on the same line that you have been does the the reaction to the work that you've done so far kind of tend to influence the way that you proceed? I mean, for instance, in the immediate absence of any kind of attempt to reproduce your work and so that therefore there's still skepticism in various quarters. Well, like I say, right now we've stopped all of our new projects and we've been doing I think all summer we've done nothing but a series of, you know, sort of test bed calculations to try to demonstrate, or at least to see for ourselves what happens if we try to impose, you know, rigid co-rotation, which was this, you know, the Baumgart things.

2:30 And instead of writing the next paper that we wanted to, which is on, you know, development of gamma ray bursts from heating of the stars and so forth, instead we're writing a paper on this is the meaning of the conformally flat approximation, this is why we believe it, this is what happens if the star is linearly translating or rigidly co-rotating. So we're having to do an explanative paper. The last paper we submitted, the referee came back and said, well, here are these six papers that have said that this effect is not real and we can't accept this paper until you tell us why we should not believe six people have looked at this problem. So for us, it's a serious problem. Since right now we're having a hard time getting published we write a paper that explains what I've been explaining to you, what's different than what they've done and what we've done. Because people read them, and the way people write them, it sounds like, oh, well, they've done the same thing, or they've done something better, and in fact they've left out the piece of the physics that we think is causing the effect in an obvious way. Okay, I don't want to voice my frustration. No, but it is an interesting point, certainly from the sociology point of view. I mean, in a key way, the refereeing process sort of obliges you to take a step backward before you take your two steps forward. I mean, to get published, you have to address the other papers, because the referees want you to do that. Yeah, yeah. Well, it seems to make a difference who's the referee, too. If it's someone of a post-Newtonian background, say, then we seem to have more trouble. and if it's someone who's a real numerical relativist who usually has no trouble understanding what we've done. And we can tell from the, you know, the referee reports, you know, we've submitted four papers now, and the first two went to a numerical person, so there's no problem at all. The third one went first to a post-Newtonian type, and then after two rejections, we had to insist that the editor send it to someone who was a real numerical relativist. was no problem getting it published and then the third one

5:00 went to someone who actually i i haven't i'm not sure who they are but they knew enough about the problem to know the existence of these other papers but not enough about the problem to appreciate the difference between what they have done what we have done so uh actually sociology Ideology-wise, this is a peculiar thing, too. Even given that, the two referees at FISREV Letter both accepted it. The second one accepted it only saying you should address these other papers that have come out. And it was the editor that rejected the paper, which I have never seen in my career. I could show you the report. It's the most bizarre thing. So, of course, I'm going to write back to the editor. But before we do that, basically we submitted it way back last spring. Before we do that, we decided, well, let's finish a series of calculations where we're sure we understand rigid co-rotation and why those people didn't see the supply. That's why it delayed us. Why the boundary? Yeah, that paper has caused us some delay. And again, you know, they were things, I think, excessively strong for a paper that does not address the hydrodynamics. I mean, they have their own way of doing hydrostatic equilibrium, but it's imposed a very special hydrostatic equilibrium, namely the killing vector rigid co-rotation. So I suppose, on the face of it then, that, of course, represents a considerable problem since, as you say, it's probably the only real way to satisfy, from a quite realistic point of view, to satisfy the skepticism of others, obviously, is if somebody else reproduces, or to reproduce you as well. and at the same time obviously there's difficulty this creates difficulty for yourselves the fact that there is skepticism out there obviously simply obliges you to go through a lot of justification much more than one would normally have to do with I guess that's inevitable if you're the first person to see some new effect

7:30 everybody who has some ten minute thought on the problem wants to write something about it. And, you know, again, it took us eight years to write this code, so it's going to take a long time for somebody even to reproduce, even trying to reproduce exactly what we did, you know, much less try to do, try to relax the conformal and flat condition, you know, do the real evolution equations. That may even be impossible. I mean, no one that I know of, maybe you know more than I do, but as far as I know, no one has been able to solve, in 3D, the evolution equations of relativity and have them be stable, you know, the k-dot and the gamma-dot terms. I know the Grand Challenge people have had a lot of trouble. I mean, in principle, they could do it, but the things I hear them say is that computers aren't big enough to do it. In fact, as far as I can read from hearing their talks, of course they'll tell you themselves what the story is, and maybe I don't have it right, but my understanding is the only thing they can do is the conformally flat solution, that's their initial value. And if they try to evolve even one grid point from there, my understanding is that the problem goes non-linear. I could be wrong, but that was my understanding from the last talk I heard from those guys. You should get that clarified. So it may ultimately be that conformally flat solution is the only thing we ever have. Talking to Jim York last summer at the Marcel Grossman, he was in Israel this year. He doesn't think you can use ADM to solve the problem new hyperbolic system of equations, but he thinks it's the only way you can solve the evolution exactly in 3D. But I haven't seen anyone yet actually able to solve that set of equations. I mean, they look simpler. What happens is you end up with, I forget the numbers, 30 or 60, or some huge number of differential equations, but they're supposedly better

10:00 I don't know if you know about this new formulation, but I mean he got up and in fact emphatically said this is the only way in the future to be able to solve 3D numerical relativity. But I haven't yet seen that anybody actually could solve a problem using that method. But again, there are other people that know more about it than I do, and when you go to NCSA, they can probably fill you. You should go talk to Jim York, though. Yeah, I hope to, yeah. As a matter of fact, my master's advisor, when I was still in Ireland, was this former student of Jim York's, and I'm hoping to get a chance to go. Who is that? Neil Amarok, who is a student of Jim York's in the early 70s. So, yeah, but I'm obviously hoping there's going to change it off at some point. I don't know if it's my chance, but... But you mentioned that the gamma ray verse people have been quite interested in the results, and so your plan is to produce a paper to directly deal with the... Well, our last paper started to address it, because one of the things, if the stars are are compressing that release binding energy has to go somewhere and at some point stars are compressing faster than stars can radiate them away and so in fact they generate a lot of internal heat now we had assuming that you know there is these motions and shocks that go on that translate the compressional energy into into shock heating if that happens then you can get a that's actually spread over some time. But let me say, first of all, the cosmological model has a lot of observational impetus now because one of the three counterparts, two or three, actually has a redshift that's greater than 0.8 that was an intervening plan. So now we know it's cosmological. If it's cosmological, well, okay, the binary neutron star. Now, there's another group that does binary neutron star newtonian type collisions to try to get a gamma ray burst and they put in the neutrino transport but if you don't have this effect going on the merger happens very short you know it's an orbit

12:30 time scale it's like a millisecond and they're gone you get you know a reasonable neutrino intensity while they're going in but it's over too soon excuse me to drive a burst but if this result is right the stars are more gradually heating up and you get a period of you know seconds or so when one of the stars is getting close to collapse where you can get this fairly large 10 to the fifth fraction of 10 to the 53 years and the tree knows out which is just what you want by the way and then the star goes on and then the fact that there are two stars that will be collapsing at different times will actually give you a kind of a double source going on in time scale of maybe seconds or something like that uh and is that characteristic well i think the generic gamma-ray bursts the models that seem to work actually have multiple spikes they don't tend to well there is this peculiar thing there's a thing called the t90 But if you look at the duration of the burst, T90 is saying, you know, integrating the time from the, you know, when it first gets 10% above background, you know, 10% of its peak down to 90% of its peak, or if you look at 50% of T50, it is bimodal. That distribution, and one of the things I had in mind to work on was whether or not this scenario could explain that bimodality, which there is no model for. But the models that seem to best reproduce burst characteristics right now are sort of developed out of, I think, Mazaros and Ries. And they actually tend to be multiple shockwaves coming out to the interstellar medium. And it's actually, the shockwaves, they're multiple shockwaves, and the shockwaves have to collide with one another. And when they collide, then they produce a burst. So you have shocks from behind catching up with other ones. you know a gamma factor rents you know kind of gamma factor of 100 in order to get the energies right and the details right but i mean gamma rays burst have these uh you know well you know tens of milliseconds to second type multiple bursts i'm saying and you the only way to get that kind of random thing in a model you know the successful ones i've seen steve peran has some nice models with it um so there has to be some more complicated physics sort of like an accretion disc kind of

15:00 thing going on there but again if you have this kind of collapse going on we do get some material floating around there afterwards so not much the neutrinos ablate material of the star so it's not all together clear that we would get that multiple burst kind But it's one of the things we like to work on to see how we could drive that. Jim has a student that's working on a simpler thing, which is, you know, you just get the neutrino transport, then you get para-annihilation. You know, you have these 10 of the 53 ergs and neutrinos, NUNU-BAR annihilations are efficient at about 10% Jim claims seems high to me that that's using a supernova code and adapting it to this problem where he is very careful neutrino transport if you get 10% of that energy they get 10 to 52 ergs and and e plus e minus plasma and and yet he's had the student work on just okay now you have the plasma firewall just expand it you know do the hydrodynamic expansion but haven't even put the gravity in it just a simple thing but the thing that's nice about it is that it in fact becomes optically thin at a point where you have a gamma factor of 100 in the expanding fireball and it has the right time scale and the right energy so it looks a lot like a gamma ray burst so there's a lot of the features of a gamma ray burst that could be there And I imagine the fireball developing with sort of the ram pressure of the residual star and the black hole that's formed still going through it, which is something that I'd like to work on at some point. One may also be able to get this multiple shock kind of structure going out through that fireball. So I think there's the substance of a good gamma ray burst in there. Yeah. But, again, we're diverted from that now. So, well, but is it your plan, I suppose, to go ahead with that as soon as possible?

17:30 I suppose, obviously, there's no immediate prospect of anyone reproducing the result, given the fact that the Grand Challenge people, for instance, have met with fairly limited success so far. So I suppose for the foreseeable future, it's just a question of pressing ahead and dealing with the criticisms that we've come. Yeah, I mean, that's what we have to do. I mean, you know, nothing would make me happier than to settle this one way or the other. I mean, if we could find out something wrong, I would be absolutely delighted to let the world know or if somebody else could find something wrong or even if somebody else did the same calculation you know and and either got the result or didn't it would be most relieving one way or the other but sitting here you know nobody well actually i can't say no some people believe i think so we went down and had a long talk with larry smarr and he pointed out something he said in his neutron star calculations he did with jim a long time ago he remembers that central density those were actually symmetric the central density increased the stars came in and he puzzled about that so that's why i want to have chuck redo the calculation chuck did it did a better resolve And more accurate gravity, subsequent calculations, trying to get Chuck Evans to get us that data. But he seems to have lost the head. So, I told you what I hear from Jim, Jim York's response to it. uh i talked to jim a little bit about it and uh he he doesn't seem real happy well for the reasons i related to you about a sequence of initial conditions as a way to try to approximate the system of course he'd like to see the whole evolution which is the right thing to do uh and of course he he has just gone whole over over this the set of hyperbolic equations So he was telling me we should retool and do it that way.

20:00 In fact, if I get another student who's interested in this problem, because it would take a few years to develop, that's one of the things I'd like to have a student do. And I had Pedro spend the first year of his thesis research trying to develop a perturbation that would recover the off-diagonal pieces that were missing, but it turned out to be a hopelessly complex problem. I mean, it was just equations went on forever. Saturated our machines, trying to run maple to generate the term. Yeah, exactly. Um, so let's see, who else? Sam Finn, I think, is a good numerical person who has a good sense of, he's a guy you should actually talk to. Yeah. He's nearby. Well, unfortunately, he's just gone out to Caltech for sabbatical year. So I just missed him in Chicago. Oh, that's right. I remember he said he was going to do that. So I hope I'll catch him in Caltech the next time I'm there. Yeah, he has a more sensible view in our conversations with him. and he understands that the limitations but also now Chuck Evans has a okay hello he he doesn't he he hasn't he's asked not to be on this project and wait it and see how to say it we asked him to continue and he said he had other things to do but he's he he understands this quite a bit if you're going to uh to north carolina to talk to jim york you ought to talk to chuck so um I guess there was at least one paper which was supportive of, at least the only one I made aware of that was supportive of it by Cook. Yeah, the axisymmetric. It showed that you had, in a different case, that they agreed with you. Yeah, actually, I'm puzzled about that. I think that an axisymmetric calculation should be exact in a conformally flat approximation, but they use a different kind of conformally flat approximation in which it's no longer exact, which is that they impose cylindrical symmetry so that instead of the three-component shift vector, there's only two or one or something like that.

22:30 And that's why they're conformally flat, which isn't the same as our conformally flat, it's different coordinates, was not exactly the answer, but, you know, the difference in their answer was pretty close to numerical noise, I mean, a fraction of a percent. So, although, yeah, I had to study their paper for a while to try to appreciate why they even thought it wasn't exact and it's because they reduced it down to you know two metric coefficients at a three or three instead of four or something like that um so then it became an approximation even then it was pretty good there is another paper which didn't get published because it happened to go to the wrong referee which actually was written in a way that it was critical of us which was by reason Schaefer who did the oh you know you do two-point particles in orbit calculation you're copying the procession and so forth in an expansion and you know metric, an expansion with a, you know, the exact Einstein. And they show it, well, the second order was exactly the same. And then the fourth order, there were some deviations that would begin to come in. Now, if you look at a problem like what you're interested in, you know, a massless particle next to the Schwarzschild, then it was a big correction, the difference between the two. But if you look at a binary where you have almost equal masses. It turns out the difference at V to the fourth was tiny. It was like, again, fractions of a percent. Now, unfortunately, they wrote their paper in a way to exaggerate the difference between the two methods. So they were describing the Schwarzschild test mass kind of problem,

25:00 which we thought was a little unfair but we weren't the referees someone else was the referee I probably shouldn't say who it was it's someone we've discussed already who didn't like the paper I suppose for your continuing work who do you see being the uh the audience for obviously you were saying the gamma ray people are interested in in this um and then on the gravitation way side is it sort of a question of waiting for well assuming that at some point it's going to be decided well the ligo people ought to be yeah yeah i mean if they want a template we'll generate one right you know and people can decide whether or not they want to believe it or not but we'll sure try to publish it Because it will still be better than anything that's available. So that's, yeah, I see that as an important audience. I guess Joan Santrella I think has gone to post Newtonian so far, but I think she plans Yeah. Actually, I'm surprised the way she proceeded, because she knows numerical relativity, but she started by building a Newtonian code. A lot of people call post-Newtonian taking a Newtonian code and then doing the post-Newtonian multiple moment to get the gravity wave. So that sometimes gets confusing. As far as I know, she does not have a post-Newtonian Now, I could be wrong, but I haven't seen anything published by her using that. I have to think of what the most recently that I've seen it from her. The one I know of is purely Newtonian, and the last time I heard her speak it was still Newtonian. I think you're probably right, because I think she— Well, I know that she and Richard Mastner are developing a smooth particle hydro, fully relativistic code, but that's all I've heard about it. has said that she's doing it. I haven't, you know, not that she hasn't had any progress,

27:30 I just haven't seen a talk where she's talked about it. That would be a way to test them. Yeah, so hopefully it's going to come from that. No, I think you're right. I think she only maybe has a Newtonian with some post-Newtonian corrections, because I think she did decide rather than do some post-Newtonian hydro, that should we go directly to the relativistic model since that single area? Well, that's a good choice because if you look at the post-Newtonian hydro equations, they're ridiculously complex as soon as you get beyond first order. It makes much more sense to just do the full relativistic hydro equation and get your metric coefficients from somewhere. Now, what I've always thought people should do is forget about keeping the hydro truncated at some order. Use post-Newtonian just to get the shift and the alpha, which you can do even to solve the metric in post-Newtonian and then plug that into the exact hydro equations. I don't see a problem with that, although purists would probably worry that things weren't truncated at the right order. that would make much more sense to me as a way to proceed because it's much easier. And that's a calculation we've had in mind to do. It turns out it's a simple thing for us to modify our code to do the post-buttonic metric and then just to run regular hydro. We started doing that and then we got sidetracked into all this stuff. But that's one of the other tests we wanted to do was to run the post-buttonic metric although our interest in that is waning. because you would you would you expect how far would you have to go to to put in say the star well as i said i think if you do the first post-newtonian gravitational field but then do the hydro including all the forces based on that post-newtonian metric in principle you could see n effect i don't think it'll be as big but there is a velocity dependent force term and so it should start to show up now actually this there is a pope well again uh nakamura is another guy who is is close to what we're doing in fact i want i'm going to japan in november to try

30:00 to talk to him some about it uh he has a student that's done post natoni but i believe it's not second post tonal and first post plutonium uh in fact i'm not sure it's student or postdoc there is somebody in his group that gave a talk at the marshal goes they don't see the effect in post plutonium hydro but uh i'm not sure what order they've taken it to i don't think they've gone the second order now he he has his own way of solving the neutron star equations and i think he could also he could he is the only one in the world right now that could reproduce this if he wanted to and i don't know why he has them um although uh well maybe he's wrestling with some of the instabilities we dealt with early on too he and you know right But at least according to his papers, he has a code that's very close to being able to test this. So in any case, you're going to visit him? Yeah. He had some interesting thoughts because I talked to him briefly at Marcel Brussman. there is about the circulation and how it generates and if it violates the circulation theorem. And so that's another thing we're trying to address in this paper. We've calculated the circulation of the material. There is a circulation theorem that you have to have a shock or heat or temperature gradient in order to generate a vorticity like that. So just one thing after another well to go back one of the big audiences for your work, Lago which is basically what I'm interested in primarily what's your feeling about But what needs to be done for LIGO, do you feel that the present code that you have can generate the templates? We actually had to do some modification because what we want to do is bring the stars far enough apart

32:30 that we can touch bases with the post-Newtonian women. And, you know, so at least 200 kilometers are. So we had to re-grid the hydro so we could keep it centered around the star and move the field way out. A-series done, and Pedro's worked on it, he's a little bit depressed because he thinks whatever he does won't be getting, can't be published now, but I think he tends to overreact, you know, a student, but we suspended that paper, which we had a draft written and the first calculations done until we can finish this set of testbed demonstrations of what we're doing. It's all right. So that's another example. But what we can provide to LIGO is, at the level of this approximation, a different template for the gravity waveform as a function of equation of state and masses of the stars. So that should be useful. Yeah, sure. There have been different estimates as to exactly how accurate a template is going to be needed, and the numbers have varied quite a bit. But how, I suppose basically how accurate would you estimate the tempests that you could produce our form, basically conforming with that code? Well, um... Yeah, that's tough. I would say we probably couldn't reproduce the exact signal to say 10,000 cycles, which is probably what people want. I mean, if you ask them, that's probably what they want. But I think what we can furnish is a modified power law type function, which would have of parameters that contain the basic physics and would attach to the power law for a post-Newtonian. And so, you know,

35:00 whatever we furnish will be, I think, better than what's available. Now, the reason that it may not matter so much is qualitatively what we see is that, it's just less chirp it's very smooth signal you know the frequency is very slowly rising and it stays very low both of which are good news for LIGO as I mentioned before yeah so I mean that qualitative feature is probably pretty good you know put an estimate on I mean up to the point where the stars collapse say, the typical equation of state that we like, again, the energy in the gravity wave is about a part in 10 to the third. So the validity of our quasi-static approximation is probably put to a part in 10 to the third. But you have to add into that, well, we have a numerical grid, and our stars only have, you know, 100 zones or so, and, you know, so 1% is probably a more reasonable and still optimistic estimate of, you know, how well we could get, say, the frequency for a given orbit separation. Well, there's another way to put it. The gravitational radiation coming out, you know, there's the quadrupole term, it's the dominant term, and then our biggest correction is the slow motion correction in the multiple expansion, which most people don't put in, but it's actually a 10 percent correction already. So, I mean, the standard post-Newtonian things that don't have the slow motion correction are already way off if it's just a quadruple thing, I mean, at the level of 10 percent. Now assuming that we only put in that 10 percent correction, now that we also went to the hexadecapul term, and that's tiny, that's like a part of 10 of the eighths, so it converges very fast. And so we know that the mass moment piece is converged, at least in terms of multiple

37:30 expansion, very well. But the slow motion correction, assuming that the next term was 10% of the first term, is at best 1% accurate and at worst 10% accurate. on the other hand the uh let's see that's the that's the current multiple moment which is also itself well okay well no i said that right that first correction which is a which is a wait now i have to get this clear there are two pieces there's the mass multiple moment and there's the current multiple moment the current multiple moment is again only one percent believe we have that piece off the slow motion correction that's 10% and that is 10% of like the quadruple piece and it diminishes as the opposite side so you're saying that this brain to the shirt that does the opposite yeah the M2 does not rise much I can show you a picture of the kind of thing we see. Sure. I have to find my figure. Thank you. my transparency's got scrambled in my last trip and so I haven't heard them out yet

40:00 about signal-to-noise, this is if you do the Newtonian, and this is as far as we've integrated the 4U transform, that we get a much higher signal-to-noise, around 100 Hz. And that's just a cartoon of the calculation. There's a picture of our chirp up to the time when the stars collapse. Yeah, it's nothing, which is good, I mean, actually, this frequency has been provided by 10, so that you can see anything at all, otherwise it's just a solid black line. Well, yeah, as you say, it gives you a lot more cycles, I don't know. Yeah. It's good for the power spectrum. Well, I suppose, Ben, the next question would be how close do you think we are to understanding sources like neutron starbiner? I mean, what more do you think needs to be done, or are there any more surprises that you think might be learned? Oh, I think there's a lot, because we've hardly touched on MHD yet, and our first little, So, let me show you a figure. Our first little, just barely tickling the problem. what happened I mean this is just a vector potential this time we set up a kind of a dipole field but that's in the plane of the orbit so it's not necessarily realistic thing that shows you know that that

42:30 swirling motion of the fluid yes that's what I was talking to you about here it's like I keep talking about how we get this peculiar motion this is in the frame of an orbit that's going around like this this is the response of the fluid it gets this double vorticity going around it's actually kind of a torus and if there are field lines that were threaded through the star they're connected to the fluid this is how they ramp up and so this a few sound crossing times. So you see, that's a complicated mess. And we haven't put in the back reaction yet. And then, you know, there's a lot about neutron stars you don't understand. I think the basic feature for a gravity waveform we do, but if all this is right. I think there's a lot of calculations to do. I mean, just MHD itself, 3D MHD and relativity is a mess. I mean, we started tackling it, but that's a tough problem. On top of all this other thing, which nobody believes that yet, so this is going to have to wait until our grandchildren are present, right? Yeah. Well, I suppose this has, of course, been a problem. A lot of people keep saying that the binary black hole people aren't going to be ready when LIGO is actually online. So I suppose we may have to just wait for the experimentalists and say they're successful. That's a tough measurement. I mean, you know, So we'll all go hand in hand, but, yeah, you're more optimistic than I am that they'll actually see something. Well, I don't know. My bet is maybe one of the cryogenic bar detectors that's actually tuned for a known pulse-off frequency if they're lucky enough to have a little bump on a neutron star. might have a better chance because there you have a nice stable frequency you know exactly what the frequency is and you know what to look for um so if i had to guess who will see something

45:00 first i probably shouldn't say this that's where i would have invested my money although it's not as as big a deal, a signal like that, I think that's a system we have a chance of understanding better. So you think that there may well be a following, and all this problem could be with LIGO that you sort of can't really extract your signal from the noise unless you understand it beforehand well enough to do so, and then you can't really get the understanding too easily unless you I've got some experiments to put in there. Yeah, well, I mean, we'll have to work our way through that. I think that, I mean, I can be more optimistic. I think we can generate a functional form for the wave form that contains the physics we think has in it, and then you've got everything.