Interview with Doug Swesty

0:00 I had been interested in neutron star mergers actually for quite a while, but actually for reasons that probably a lot of people hadn't thought about, I'm very interested in, among other things now, in how neutron star mergers might result in nucleosynthesis of certain heavy elements, the R-process elements. and that's still something that very much interests me but I actually really wasn't even probably terribly aware of the viability of these things as sources for gravitational waves that might be detected by LIGO at that stage in my career when I was in graduate school but then after I came here I still the appropriate numerical technology existed here to try and begin to start models of these mergers, and again, I was still interested in it for nuclear synthesis. But at that time, the Black Hole Grand Challenge was really just starting to pick up steam here, and Ed Seidel was very heavily involved in that, and I became very interested in what its capabilities were, and this whole Neutron Star Merger Grand Challenge effort kind of evolved out of a conversation that I don't remember exactly where it took place, but probably over the lunch table, because Ed and I used to go to lunch quite a lot, where I said, gee, could you add source terms to your space-time evolution code? And Ed said, yeah, I could. And I said, well, gee, we should think about trying to model neutron star mergers for this. And then Ed said, yeah, we should look at how these things would work as sources of gravitational radiation and so the whole thing was kind of born out of just the everybody being in the right place at the right time here in order to make that happen myself doing dense matter astrophysics and neutron stars and credit neutron stars and supernovae and Ed doing the space-time evolution and the ideas really just took off from there it's really I mean it's become a big part of what I do here I have a major effort going on in trying to numerically model supernovae, but this has taken a large fraction of my time up now. I've probably spent at least half my time working on the neutron star modeling effort. We're just at the point where we now have

2:30 a coupled space-time plus hydrodynamic evolution code. We're just starting to do relativistic evolutions of single neutron stars as a testing effort, and hopefully within the next six months we'll be in a position where we've done a fully relativistic model of a merger. We also have a really big effort going on in post-Newtonian modeling too. If you're interested in talking too, I also have a postdoc and a graduate student over at NCSA. Alan Calder recently from Oak Ridge, and he's really new to the project. He's only been here about a month or so, and he's actually a supernova person by training too, and I have a graduate student, Ed Wang, who is actually technically a graduate student at Washington University in St. Louis, even though he lives here and works with me on this as a thesis project, but if you're interested, you might want to chat with those guys a bit So there right now, we're making some final pushes on a major effort that we've had to do Newtonian and post-Newtonian simulations of these motors, and we're finding some really interesting things about these models that are very important. They're baselines for us to do the relativistic calculations on. It turns out there's a tremendous sensitivity to the numerics in the problem, which makes it very hard to do these simulations correctly, and at least some of the simulations we've seen published so far probably are somewhat in error. So, the Newtonian? Yeah, the Newtonian and the post-Newtonian. It actually makes a big difference whether these things are done in a rotating versus a non-rotating frame. A surprising amount of difference, literally. And that's all just due to numerical difficulties. So we've just been kind of finishing a big effort there. So it's really kind of changed the focus on the problems we want to address, too. I mean, I think LIGO is a really marvelous thing because it's opening a new window on the universe. I mean, I know I'm kind of spouting back, you know, things that Kip has often written about. I feel embarrassed, actually, to do this because to get up here and say things that I've only realized in the past couple of years

5:00 but that Kip's been, you know, pushing for 20 years is, you know, sort of, I feel a little bit like a Johnny-come-lately hopping on the bandwagon here, but it is an interesting problem. I'm sure Kip is happy to have Kip. Well, I hope so. I mean, you know, Kip and people like Reiner Weiss and so on really deserve a lot of credit for this because they've seen this thing through its, you know, everything from intellectual conception to, you know, the instantiation of it that we're now seeing. And that's a marvelous, marvelous thing. You know, it would be wonderful if at some point in my career I could, you know, ride the same wave through the evolution of a project in the way that Kip and a lot of other people have done here. I think it's pretty cool because not only, you know, I'm also interested in this from a supernova standpoint, too. I mean, I have a lot of interest about whether or not you might be able to detect the gravitational wave signals from a galactic supernova. One of the things that I've spent some time doing is to try and predict what the neutrino signals would be from a galactic supernova. And the potential, if there were joint information coming from something like LIGO and from a neutrino detection experiment like Snow or Super Cameo Kanda, it's just really awesome. I mean, you could have direct time-of-flight measurements of neutrino arrival, which could tell you something. It would be a direct measurement of neutrino mass. if you could use LIGO signal to pin down the instant of core bounce or something in the supernova problem I think that has some possibilities we actually have kind of a little small project in the background to look at that right now in conjunction with that side L it's also kind of changing a lot kind of science we're doing And it's made it a requirement for theorists to kind of raise... That's an occupational hazard. Well, you know, proposals are due on the 15th, so I've got a million phone calls back and forth with collaborators right now. I was going to ask, actually, who are the main PIs on the... Oh, on the Neutron Star Merger Grand Challenge? The head PI is Paul Saylor from the Department of Computer Science here.

7:30 He's a computational mathematician and he has worked out really wonderfully with us and we have a lot of interaction with him. Actually a lot of what we can do here we can do because of the fact that we're able to act with people in different disciplines. And that's what makes this whole project possible without parallel computing and without really good advanced numerical technologies we couldn't do what we're doing right now. and myself Mike Norman who unfortunately is on sabbatical here so he won't be able to talk he's on sabbatical this year so he won't be able to talk to him he's at Munich with the Max Punk and Ed Seidel who still maintains a joint appointment here even though he's in Potsdam and let's see then at Washington University in St. Louis There's Wymo Suin, who I think you probably know, Cliff Will. And at Stony Brook is Jim Latimer, who's our main equation of state and neutron star structure expert. And then, that kind of covers the physicists, but we also have a computer scientist, Ian Foster from Argonne National Laboratory, and at Livermore, Steve Ashby, who's another computational mathematician, and he's also director of the Center for Advanced Scientific Computing there. And that's it. So one thing that's kind of different from the Black Hole Grand Challenge is that rather than go out and get everybody who was working on neutron star mergers and put them under one proposal, what we did was assemble a bunch of people all expertise that needed to be brought to bear on the problem, and usually there are no more than, and in this case, almost everyone has a different area of expertise with the exception of maybe WIMO and Ed Seidel, and, you know, it's, I think, made for a little better working

10:00 relationship, given the fact that we didn't have people who were really competing with one another. They were all bringing their own area of expertise to the problem. And that's worked out pretty nicely so far, I have to say. How long has the alliance been working? Well, officially probably a year and three-quarter, unofficially about a year. Or, I'm sorry, officially a year and unofficially about a year and three-quarters. Our funding just turned on as of September 1 last year. mark right now. But we had been doing this for some time beforehand. I mean, we shopped this proposal around for funding to at least two other different sources before we finally hit from the NASA High Performance Computing and Communications Program. We had also pitched the proposal to the NASA Astrophysics Theory Program and to the National Science Foundation as well, their Stellar Astronomy and Astrophysics Program. I was actually a little bit shocked that NASA chose to fund it. You know, given that its focus was on gravitational waves and things that were really vital to LIGO, I kind of thought NASA would honestly have taken a pass on it. But they've been quite excited about it. In fact, we were the only astrophysics proposal that was funded by NASA. Most of them were Earth and space science related or science-related proposals, as I meant to say. Yeah. So it's worked out very nicely. Right. And we're, you know, ahead of where we thought we'd be on some aspects of the problem behind on others. This is usual with science. I mean, we've been uncovering new and strange things that we hadn't really anticipated, and some things have turned out to be harder than others. one aspect of the whole collaboration which is probably a little bit unusual compared to other efforts like the Black Hole Grand Challenges some of our focus is actually on achieving ultimately one of our goals is to deliver a general purpose relativistic hydrodynamics code to the astrophysical community that they can use to model a wide variety of phenomena and as part of that

12:30 we have performance milestones are required to meet from NASA. Technically, what we have is not a grant, it's a contract. We have a contract to deliver a code that works and it performs at such and such speed. And we have to meet those milestones in order to get paid. So it's kind of a new paradigm for doing science a little bit. And it's brought its own difficulties with it. So, and that, the idea, it would be a full GR, ultimately a full GR hydro? Yeah, we do have a full GR hydro right now. Yeah, we're still testing, and, you know, like I said, we're doing simulations with single neutron stars right now to try and understand that before we do the binary systems. But we hope to do that sometime soon. I think the problem is not, I mean, it was more a question of just man hours to do the proper assembly of the code to get that part of it running. the bigger problem is going to be imposing gauge conditions on the space-time and how do we maintain good coordinate control throughout the course of the evolution that we kind of don't know how hard that's going to be yet it may be easier than we thought it may be harder than we thought personally there's some dispute within the collaboration about this and I tend to believe it's going to be easier than most people think But I come from a different background than a moral activist, and I have physical arguments why I think it won't be so difficult. I could be completely wrong about that. I admit that right up front. I do have a wager with Ed Seidel, a six-pack of beer, about whether I'm going to be able to do things in certain ways or not, so we'll see who ends up paying up on that one. So, you eventually have to see that providing, well, presumably, ultimately, waveforms or whatever for LIGO is one big motivation for the project. Presumably, there are other ones then, like maybe gamma reverse? As a matter of fact, yes. I'm working on a proposal right now to NASA Astrophysics Theory Program to look at gamma reverse models in more detail. I think this is a very exciting time for that. recent observations from February 28th and May 8th,

15:00 indicating that it seems likely these things are cosmological now. And it's just my wife's account of astronomers. That's right. Yeah, I understand there have been a couple meetings there about that so far that people have told me about, but I don't know anyone who's been present at them where these things were discussed. But it looks really promising from my standpoint. And I honestly will say that I went into this being very pessimistic about neutron star mergers being the site of gamma ray bursts. But that's swung around a lot. The mechanism people had envisioned with neutrino, anti-neutrino annihilation coming from the merger, I just don't think is right. And that's born out of experience with supernova calculations where we've looked at that same process. It was just very inefficient. but uh you know i think the thing that we need to look at now are other mechanisms for the energy from the the material that's ejected during the merger can be converted into gamma reverse that's going to be a hard and complicated thing because there's a lot of physics we need to add in to be able to treat that right um and yeah that's that's that's a big focus right now it's a rapidly growing focus of what i'm personally trying to do uh and the other aspect of it is One of the two possible sites that we know of in the universe where you could really have a significant amount of R-process material produced is neutron star-neutron star mergers, or neutron star black hole mergers perhaps as well, but the other possibility being supernovae. The problem is the mechanism, as we understand it, for R-process and supernovae, which requires really high entropy and very neutron rich material or very high entries and I should spin neutral material is rare very difficult to achieve now that people doing models and multi-dimensions right now can achieve those kinds of high entropy that we need to have happen to make the thing succeed whereas in the neutron star case if you just eject a blob of neutral-enrich material, there have been a number of calculations that have kind of shown that R-process can occur fairly robustly under those circumstances. The big question is how do you get that R-process material out of the system? And that's something else that we're trying to look at right now, too. We're trying to understand how much material gets ejected

17:30 or how much material is thrown off during the merger and will that material get ejected. And ultimately, I don't think we'll know until, at a minimum, we can do the fully relativistic calculation because you know if you form a large curved black hole in the center of what was formerly a big neutron star how much of that material was sort of in the disk around the coalesced object how much of that escapes is really probably going to depend heavily on the geometry of the space-time there and until we do the I don't think we'll be able to know that. Interesting. So those would be the three big motivations? Well, yes. Actually, there's one more, which is that potentially, and this is fundamentally of interest to me, because this is how I got started in the field at the very beginning, is that the gravitational wave signal may be able to tell us something about the equation of state of dense matter. And we may be able to constrain the behavior of the equation of state of dense matter in these objects based on observables like our process, like gravitational wave signatures and other possible phenomena, timing and energetics of, say, burst signals or something. And that's of fundamental importance both myself and Jim Latimer in this problem. We've tried to do the same thing in neutron star observations and supernovae and so forth. And now this, LIGO is very exciting in that regard. I mean, it potentially could tell us a lot about what's going on, although I think it may be a little more difficult to unravel some of these things than perhaps people have thought. Well, as a graduate student, one of the things I spent a lot of time on in Kitts group was how you would extract equation state information from neutron star merger. That's right. I think that's where I remember. where I first, you know, came across your name is from work that we've done there. And, of course, ultimately we more or less decided we're going to need something like a fully-built mystic code before we do it. That's right. I think you guys were looking at the possibility of doing this analysis in the way that Lindblom suggested in his Zapier paper about getting a radius and a mass and trying to work backwards from that. Yeah, that's where we kind of started off, although it quickly became apparent that it wasn't going to be simple.

20:00 Yeah, I think that that, one, I mean, I wonder about whether you're going to be able to obtain a radius very accurately at all. Because I can show you some movies in a little bit of some simulations we've done at the post-dependent level now, and the objects we're seeing form at the center may not have a very clear radius to them. And the problem is with doing that analysis in the way that Lindblom suggested, is that you can easily come up with very widely different equations of state of radii that may be somewhat similar, but yet the interior structure of the neutron star could be vastly different depending on where you locate phase transitions and so forth. And in some sense that analysis by Bloom-Glong also assumed that the, you know, radius and their density profiles were going to be continuous, which they won't be in the case where you have phase transitions in the star and so I worry about that under those circumstances I mean the problem is yeah if you knew the radius exactly you knew the mass exactly and you could deal with the phase changes and somehow in theory that would work the problem is when you actually factor in uncertainties in the radius and you know assuming the mass could be pinned down very precisely from the first 15,000 orbits I really have a big worry about being able to extract that information that way I don't think we'll be able to do it frankly I think it's going to be more complex than that and there's going to be we'll be able to offer some constraints we won't be able to pin down a lot of things well you know coming at it from another end where we were just looking at signal extraction, you know, learning about what people have done, it was more or less that we had begun to realize that it wasn't going to be a case of being unambiguously able to separate out the radius from any other bits of signal anyway. So it's become apparent that it was going to be even much more subtle. Right. What we see, for example, right now in the post-Newtonian calculations we've done is is that the signal depends more on what's going on in the core of the star, it seems like, than the radius. And it's very interesting, in the post-Dutonian calculations we've done, we see something that sustains itself as a fairly elongated object

22:30 with the very highest densities for some time. And meanwhile, the outer parts of the whole coalesced object are completely circularized. Yet, there's this sort of peanut in the center rapidly whipping around, signals. I'm sorry, I don't have a plot here to show you, actually. This is after the merger? Yeah, we've done a fairly lengthy calculation for about almost five orbits now prior to the merger, you know, and for almost an equally long time, for about 15 milliseconds total now at the post-Newtonian level. And you can still see, you know, a fairly non-spherical object at the center that's maintaining itself for some time. Now, obviously, you know, under many circumstances with a black hole forming, I mean, in the center, this is probably going to be moot. You're going to probably have a fairly spherically symmetric black hole very quickly just due to normal load ringing. Although the one thing that's very interesting, I mean, there's no hard constraint. I mean, you can't say for sure that there's no way to have a 2.8 solar mass neutron star. There's nothing to rule that out at this point. a lot of people would like to have 1.4, 1.5 masses be the maximum mass. There's absolutely no evidence whatsoever to rule out 2.8 solar mass neutron star right now. We just simply don't know. I mean, obviously it's got to be, you know, Rhodes or Phenian limit at 3.2, but between 1.4 and 3.2, I mean, who knows? I mean, it's not probably favored by the equation of state people, which I count myself as one, but we can't say. LIGO, perhaps, is going to tell us. I think that's the most interesting thing about it. I mean, that's the single thing I think that LIGO potentially could tell us in the most unambiguous fashion is whether or not the object formed is a black hole or a neutron star. And, you know, that potentially, in and of itself, would go a long way towards dense matter physics by establishing whether or not an upper limit or a lower limit, perhaps. I shouldn't say lower limit. An upper limit, perhaps, on the neutron star mass, maximum mass. I should say lower limit on the upper limit. Because if you still see a 2.8 solar mass neutron star,

25:00 well, you know the upper limit's between 2.8 and 3.2, but where, we don't know. I mean, I simply don't know what we can say. Well, speaking of the collapse, what do you make of Wilson and Matthews saying that the neutron stars might actually collapse on the way into Merger? Well, as of the beginning of June, when I talked to Grant Matthews at the AAS meeting in Winston-Salem, not all of our systems do that anymore. Yeah, then I'll say that with co-rotation, they don't do that, at least with co-rotation. Oh, I hadn't heard that statement, but Grant told me now that not all systems do that anymore in their calculations. I wasn't quite sure why. Actually, I was very dubious of it, and I continue to be very dubious of it. We had done some analyses to look at, including doing a calculation with fully relativistic hydro, the Newtonian potential for the gravity just to try and see whether the Lorentz contraction effects that they argued were there potentially could enhance the central densities or something. We didn't see that. I mean, we're going to attempt to, you know, to employ their same approximation as well to understand what that is in comparison to the fully relativistic calculation. You know, their conformally flat approximation. Right. But I don't know. Personally, if I had to take a wager on it, not true. I've told Grant that, and he doesn't argue too vociferously with me about it. As a matter of fact, I'm waiting for a phone call back from him right now about something else. My understanding is that results kind of disappeared somewhat. I originally had argued, I had him come down here and give a colloquium about, gee, maybe a year and a half ago. And he'd shown that result there, and I was arguing that, well, their equation of state that they were putting in for their neutron stars was such that the maximum mass was only a little bit above the mass that they were putting in, instead of some small perturbation of the neutron star. As you put the thing on a finite grid, it might have pushed the central density up to the point where it went over the building on it and then in December at the Texas Symposium Grant told me that

27:30 they tried it for even for very high maximum mass stars but like 2.8 or so solar mass I don't know if I don't quite I take that back up to 2.8 it was over to some solar masses but I don't remember exactly where the highest mass when they tried was he told me he still saw the result but then in June two months ago, he told me that they hadn't seen it anymore, so... For the bigger maps? Yeah, they said for the softer equations of state, they still saw it, but for stiffer equations of state, they did. Yeah, I spoke to him earlier in the week. Yeah, there was a definite importance of the equation of state. Yeah, I... bit. I mean, because I was originally arguing with him quite a bit about that, but I now seem to concede that that's true. I don't know. We're, you know, as I mentioned, we're finding things are very sensitive to the numerics, and so I'd be very cautious even about conclusions. You know, we're just pushing on a paper right now where we're going to say that you've got to be very careful during the simulations, period, because things are very sensitive to the numerics, and so So I personally would be very cautious about making any kind of conclusions on this. I tend to be very conservative about that. And I certainly, if I had found something pretty astounding like that, I'd be pretty worried about it. It seems a little funny because I was actually up in, I think April, April 1st, in fact. I remember it was April Fool's Day. I went up to Notre Dame and gave a cloakroom up there. Grant was telling me that they saw things collapsing in the black holes even when they were separated by 50 or 60 kilometers, which I found pretty amazing. Yeah. Yeah, I guess it's surprising. Yeah, I don't know. It's an interesting approximation that they've employed, though. You know, you've probably already talked to Stu. Stu thinks that told me a little bit, at least the last time I talked to him about it, that he thought it was, you know, probably a fairly good approximation.

30:00 I don't know. It's an unknown, and I think until you can compare it to the fully relativistic case, we probably won't know exactly how good. Yeah. Yeah, that seems to be the problem. Of course, once you get a surprising result of the person, you don't know where the difference is. That's right. That's right. So, uh, now we get back to, uh, the, um, the, um, so what kind of time scale do you anticipate with, you know, dealing with the, the binary problem? Like I said, hopefully within six months. Really? Yeah. Yeah, we've learned a lot, actually, from the Newtonian and post-Newtonian simulations we've done. One result, which we're about to push out, actually, which we've done, I mean, there's this tidal instability uncovered by Stu and Fred Rossio a while back in 94, actually in 93, I think, even. You know, even in the Newtonian limit, there was a tidal instability that rips apart two stiff polytropes. We've actually done some work comparing Newtonian and post-Newtonian simulations there whether the radiation reaction effects were more important. I mean, for example, one thing that we were kind of concerned about is that if the tidal instability that actually causes the merger to occur when they get close, as opposed to radiation loss, then you probably have very little hope of determining anything about the equation of state directly out of the coalescence. But we still see a substantial effect from the radiation loss, even just including the 2.5th order radiation reaction term. So that indicates to me that, yeah, it's still an important... The tidal instability is there, but it's still important to actually worry about the radiation loss and potentially that, you know, the signal that we measure from the radiation there can still play a role in determining what the equation of state is or, you know, giving us some information about the structure of neutron stars, which could in turn tell us something about the equation of state. So we've learned a lot about things like that, and that's been very important for us to do the relativistic calculation. As far as time scale, we have the capability, and we could plug results into the code and start running tomorrow. If you believe you could do this using geodesic slicing and no shift,

32:30 we could be running tomorrow. Frankly, I don't think it's going to be that easy, worry about, you know, gauge conditions, and my bet, and it's a bet, and it's based on intuition only, is that we'll do it within six months, some people think that we'll take longer than that, um, I, I argue a bit with the people who have been doing the numerical black hole stuff, because neutron stars are very different, I mean, these guys are dealing with a situation where the space-time curvature increases closer to as you get to the black hole, or to the center of the black hole, whereas in the neutron star case, I mean, you essentially have no gravity at the center. That's right, and you don't have throats to deal with in the way that you deal within black holes. So, I think we'll probably be okay, my guess is, and we can manage things up until the point where a black hole forms in the center, and it may get very difficult beyond that point. that's a guess and we also even though we'll be able to do a simulation we don't even have a technology in place to extract the waveform right now from the relativistic calculation when everything we've been doing so far in Newtonian and post-Newtonian is calculated from the third time derivative in the quadruple moment we haven't even built the equipment into place right now to actually extract the waveform from the we've been too worried about getting codes coupled and tested properly and so forth so we have a way to go on that that would be that would be beyond the six months to get this I don't know it depends on how everything works I mean with now once we've gotten this code coupled that frees a lot of people up, a lot of manpower here, a lot of FTEs to begin to work on this problem in a combined fashion. Mainly the work that we've been doing here has just been purely hydrodynamic simulations developed in the hydrodynamics, the relativistic hydrodynamics code. That's myself and Ed Wang and Alan Calder. With that coupled, we can kind of turn towards other things, and the space-time

35:00 code is now developed and coupled, so people who have been working in the space-time code can now go to work on, you know, waveform extraction and, you know, boundary conditions and coordinate conditions and so forth. It's hard to tell how things are going to work out. The analogy I make is that, you know, imagine someone had proposed doing a magneto-hydrodynamic and nobody had ever tried to solve a system of coupled Maxwell's equations plus hydrodynamic equations before. You have no idea what problems you're going to encounter. And while people have done coupled space-time and hydroevolutions in 1D or in some cases 2D before, there's not really been a lot done in 3D. I mean, Nakamura's done some calculations, Molson and Matthews, and that's it. Yeah. I can't really forecast what we'll encounter. We've already encountered some things in the Newtonian and post-Newtonian simulations that I haven't thought about already that have posed some numerical problems, and that potentially could, you know, the same sort of thing could happen with the relativistic case. So one thing that we've seen that may take longer now is it seems that really to get accurate answers, we're probably going to have to go into a co-rotating frame. which is going to be more difficult, I think, than doing things in a non-co-rotating frame. The hydro, it won't be much of a problem. It may not be a problem for space-time evolution. The extraction of waveforms in a co-rotating frame may be a bigger deal. That I can't say ahead of time. You mentioned the question of when, say, something like the tidal instability sets in and you still also then have a lot of the radiation reaction inspired. Do you have any feeling yet for the dynamical instability from the potential that is the plunge into one of the things that we used to worry about was whether the last stable circular orbit would arrive before many of the hydrodynamic effects were having a big impact on the wave signal.

37:30 So then some sort of plunge would set in? This turns out to be very sensitive to the numerics you do. And we're still sorting through this. That's why I was saying we realize things are very sensitive to numerics. I think there may be even some weak instability even further out than Stu Shapiro and Fred Rossio have found in some cases. We are really fairly worried about that. But, you know, Fred and Stu found this result that basically said the tidal instability, you know, comes in at basically when the separation becomes like three times what the neutron star radii are. We're even seeing a low-level instability further out than that. Now, this is even more complicated because there's a recent result by Kim New and Joel Tolene that said when they went into a co-rotating frame, they don't see an instability in the Newtonian case. However, I can tell you from my own calculations, we have just done a co-rotating frame calculation, a bunch of them actually, and we do see the tidal instability, even in the co-rotating frame. But the results you get are very sensitive to how you do the calculation. So I don't know. The answer to your question is I don't know. I think there are some very tricky things that need to be sorted through numerically in doing this calculation. That's why I think we need to go to the co-rotating frame. It seems to give better answers than the more reliable answers. I'll tell you one thing that's interesting that you should ask about any numerical calculation you see in neutron star mergers, especially if it's done in Newtonian or post-Newtonian limit. You should ask, how well is angular momentum being conserved calculation. And I can tell you, from our own calculations, you have to work very hard to get good angular momentum conservation, unless you're specifically solving the angular momentum conservation equations. Now, and I don't know how much you know about numerical hydrodynamics, but, you know, if you pick up a mechanics book, linear momentum conservation is equivalent to angular momentum conservation. You can transform between frames and show When you numerically find it, when you find the difference between the equations and solve them numerically, if you're solving the linear momentum equations for the gas,

40:00 it's not guaranteed that you're going to get angular momentum conservation. If you do, it's merely an artifact of the fact that you are physically well-representing the underlying system on your grid. And amazingly, no one has looked at how well angular momentum is conserved, or if they haven't looked, they haven't published the results on how well their angular momentum is conserved. And you would think that given you have two bodies orbiting each other in the Newtonian limit, or in the post-Newtonian limit even, you'd want to look at that in the post-Newtonian limit. You can simply calculate the angular momentum loss due to the quadruple moment approximation to make sure that the energy lost is equivalent to the energy you see changing in the energy that's in angular momentum. We've been looking at that very carefully, what we found is that in non-co-rotating frame calculations, there's very poor angular momentum conservation. And that can cause, it causes the system to in-spiral when it probably physically shouldn't. And when you go into the non-co-rotating frame, or any sort of rotating frame where it basically keeps the stars fixed in the, you know, approximately fixed in the rotating frame, you get much better angular momentum conservation as a consequence, and it has a big effect when you do the same calculation from the same configuration in the co-rotating as opposed to the non-co-rotating frame. You see very different results for the time of coalescence. So you have to be very careful about the numerics. You have to be very careful about the resolution, and I don't know that we can say right now where that plunge is going to start. My guess is it's somewhere between when the separations are 3 to 4 times neutron star radius. To be more precise than that, I don't think we can say. And we probably won't be able to for a long time. The thing is, your angular momentum and energy conservation and everything get better in these numerical calculations as you go to higher and higher resolution. There's a limit as to what's practical in these calculations. For example, I have about 60,000 hours of time this year from NSF do these calculations, yet if I tried to do this at a 512 cubed calculation of this, a couple runs would shoot down that 60,000 hours. And, you know, I'd like to be

42:30 able to do it at that high resolution, just simply because I know how good the conservation would be there, and it would be great. But until you can really sort those things out well, you know, there's a limit as to how much we can really save from numerical calculations. If people start quoting things to even one decimal place, I'd be worried. 10 or 20% I think is probably the best that we can do right now. Other people might disagree with me, but I think that's being honest. And people will say one numerical method is better than another, but I very seriously doubt that anybody has got a numerical method that can pin something down in this problem by more than that right now. The problem is so many orders of magnitude are spanned in density in the system you're looking at. There's a limit as to how many zones you can put across a neutron star and how much the density changes from zone to zone, and all those things affect our ability to do accurate calculations. So my guess is the plunge starts when the separations get between 3 and 4 R star, but more precisely than that, I don't think you can say right now. You know, we could probably do a little bit better with a lot of work, but I don't think we'll ever get to the point where we can say, well, the plunge starts exactly when the separation is 3.14159. We have no hope of that in the near future. You mentioned earlier where you thought, for instance, you had an advantage over the experience that the backhaul event challenge people had. In, for instance, having a better mix of people with different specialities as opposed to areas of expertise, as opposed to people with the same background perhaps speaking to each other. So, I suppose, kind of a two-pronged question, whether, on one hand, you feel there are other areas where you've been able to improve on their model, and then also, given that you sort of have the same general idea of an alliance to tackle the problem, whether you feel that their experience has been a positive model? I have never attended a Black Hole Grand Challenge meeting. I only know what I hear coming out of them. And this is more of a sociological comment than anything else.

45:00 My impression is that there's been a lot of friction within that collaboration, and things haven't necessarily gone so smoothly. My impression is that it was due to the fact that they took people who were previously competitors with one another and tried to bring them in under the same effort. And those competitive instincts didn't disappear under those circumstances. in that sense, I think, is more one of the fact that there's less competition and it's easier for us to get along. Also, in many respects, I think the problem we're doing is easier. We don't have to worry about, you know, advecting a horizon across the fixed grid because of the fact that we don't have, you know, a throat in the neutron star that one has to put some horizon-bounded conditions on. I think that's easier. In some ways, it's an easier problem. I mean, frankly, I think we'll probably get neutron star mergers going and more robustly far before they'll get black hole mergers going, even though we started much later. And I think it's just simply due to the fact that it is an easier problem. That's the biggest advantage. Things we've improved on, I don't know. I mean, there's, you know, our collaboration is not complete without friction. And a lot of it has to do with more philosophy than science. I personally do not advocate being attached to any one code. I regularly throw 3D Hydro codes away and start and build a new one from scratch in a week or two. And I think we should be the same way with our space-time codes. In fact, I'm going to do that. I'm building a completely separate space-time code from what other people are doing. And I think these codes should be built in a minimal way. They shouldn't try to do big, grand things. They should try to solve the problem at hand. So, for example, the code I'm working on now, I have no interest in doing anything other than very simple coordinate conditions in it, mainly because it allows me to code the thing a lot simpler, test it in a much simpler way. that's my personal philosophy of how these things should proceed

47:30 not everybody in our collaboration agrees with that I think if you really understand what you're doing well it usually doesn't take you too long to completely throw a code away and rewrite it and work from scratch and do the same thing Thank you Thank you.