Deep divefrom Episode 12Cosmology11 November 202621 min

Oval Orbit or Wobble? Two Giant Black Hole Crashes

A deep dive into one paper: what was known before, what the researchers did, what the numbers say and what they don't.

The paper: Disentangling Spin-induced Precession vs. Eccentricity in GW190521 and GW231123 (arXiv preprint)

Chapters

Transcript

The script the two AI voices read from. The times are worked out from the script, not heard, so a line can start a few seconds early or late.

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Cold open

Host 1You heard the trailer — this is the whole story. Welcome to the Hastrup Review of Science, where artificial intelligence reads real science, so you don't have to pretend you understood the paper.

Host 2Today is one paper, a preprint posted in October by four researchers, three at the Rochester Institute of Technology in New York and one at the University of Calabria in Italy. It goes back to two of the heaviest black hole collisions ever recorded and asks a simple-sounding question: was the orbit oval, or were the black holes wobbling?

Host 1Before we get into it, is the answer different for the two collisions, or do they come out the same?

Host 2Different, and that is the point of the paper. For the collision recorded in May twenty nineteen they find signs of both an oval orbit and a wobble, while for the one recorded in November twenty twenty-three they find a strong wobble and essentially no oval orbit.

Host 1Why would anybody care how two black holes were circling each other before they crashed together?

Host 2Because the shape of the dance is a clue to where the pair came from. A quiet pair that grew up together tends to end up in a neat circle, while a pair thrown together in a crowded cluster of stars can still be on a stretched, lopsided orbit when it merges.

Why anyone listens to colliding black holes

Host 1Let me back up for a second: how do we hear black holes colliding at all, if nothing comes out of a black hole?

Host 2What reaches us is a ripple in space itself, a gravitational wave, made by the two masses swinging around each other. In the wider story of the field, the LIGO detectors in the United States caught the first one in twenty fifteen, and since then LIGO, Virgo in Italy and KAGRA in Japan have together logged hundreds of these events.

Host 1And what does the detector actually record when one of these ripples goes through it?

Host 2A tiny stretching and squeezing of long laser arms, which becomes a wiggly line over time, a rising chirp that ends in a burst. For these two very heavy events the useful part lasts only a fraction of a second.

Host 1So how do scientists get from a wiggly line to the masses and spins of the black holes?

Host 2They compare the line against predicted signals for every plausible kind of binary and see which predictions fit best. The predictions come either from fast approximate formulas, called waveform models, or from full supercomputer simulations of Einstein's equations, called numerical relativity.

Host 1Why not just use the full simulations every time, if they're the real thing?

Host 2Because, as anyone in the field will tell you, a single run can tie up a supercomputer for weeks, so you can't make a fresh one for every guess. The approximate models are quick, but they are tuned against simulations, and where there are few simulations to tune against they can drift.

What was already known

Host 1You said eccentric orbits point to crowded neighbourhoods; what's the usual story for where pairs of black holes come from?

Host 2The paper lays out two broad routes. In the first, two stars live their whole lives as a pair, both collapse, and the orbit has so much time to shrink that it rounds into a circle before the detectors hear it; in the second, black holes meet by chance in dense places like globular clusters, nuclear star clusters or galactic centres, and can merge before the orbit has rounded off.

Host 1And where does the wobble come in, the precession you mentioned?

Host 2Precession is what happens when the black holes spin on axes tilted away from the orbit, so the whole orbital plane wobbles like a slowing spinning top. The paper notes that chance encounters are more likely to produce strongly tilted spins, while pairs that grew up together struggle to make highly precessing systems.

Host 1So both the oval orbit and the wobble point toward the crowded-neighbourhood story, which makes them sound like natural partners.

Host 2They can be partners, but they are also impostors for each other, and that is the core problem. Both effects put extra modulations on the signal, and earlier studies showed that a circular but wobbling binary can be mistaken for an oval, non-wobbling one if your model only allows one of the two.

Host 1What was so special about these two particular collisions?

Host 2Both are extremely heavy, with black holes in a mass range where ordinary stars are not expected to leave black holes behind, roughly sixty to one hundred and thirty times the Sun's mass. The paper says that range points to unusual histories, such as black holes that are themselves the product of earlier mergers, which tend to spin fast, around zero point seven of the maximum possible.

Host 1What had earlier teams already said about the twenty nineteen event?

Host 2One earlier group ran six hundred and eleven targeted simulations and concluded it was best described as highly eccentric and precessing, with an eccentricity near zero point seven at the start of their simulations. Another team modelled it as a near-miss capture on an open, hyperbolic path, and the paper says the studies agree on a chance-encounter origin even if they disagree on the details.

Host 1You keep saying eccentricity as a number; what does a value like zero point seven actually mean?

Host 2It's a measure of how stretched the orbit is: zero is a perfect circle, and values approaching one are long, thin ovals. One catch is that the number shrinks as the pair spirals in, so it only means something if you say at which point in the signal you measured it.

Host 1And the twenty twenty-three event, the newer one, what did people make of it?

Host 2The collaboration's own analysis found very high spins and strong preference for wobble in the statistics, with a precession parameter around zero point seven seven, but a separate measure of how much signal the wobble carries came out at two, below the level where it can be confidently claimed. Other teams using models with eccentricity but no wobble found eccentricity, for example zero point four five at about thirteen hertz, and when one team allowed both effects, the wobble won.

The question they set

Host 1So the open question is really: when you let a model have both an oval orbit and a wobble at the same time, which one does each signal actually want?

Host 2That's exactly it. And the paper's argument is that approximate models that include both effects at once are new, slow and not well tested at these extreme spins, while supercomputer simulations that include both already exist in large numbers.

How they did it

Host 1So what did this team actually do?

Host 2They skipped the approximate models entirely and compared the data directly against a library of finished supercomputer simulations. That library is the fifth release of the Rochester catalog of binary black hole simulations, two thousand one hundred and twenty-nine of them.

Host 1What's in that library, in terms of the kinds of orbits and spins?

Host 2One thousand and twenty-one simulations are on eccentric orbits, of which nine hundred and six don't wobble and one hundred and fifteen do; the rest are circular, six hundred and twenty-five without wobble and four hundred and eighty-three with it. Spins go up to zero point nine seven of the maximum, and mass ratios from equal masses down to one in a hundred and twenty-eight.

Host 1How can a fixed simulation match a real event whose masses nobody knows in advance?

Host 2Here's a convenient fact of gravity: a simulation of two black holes has no built-in size, so the same run describes a pair of ten Suns or a pair of a hundred, just stretched in time. So each simulation can be slid along in total mass until it fits best, while its mass ratio, spins and eccentricity stay fixed.

Host 1And the fitting itself, how do they score whether a simulation matches?

Host 2They use a method called RIFT, short for rapid iterative fitting, which works in two stages. First, for each simulation, it averages over everything about where the source sits and how it's oriented, such as sky position, distance and tilt, to get one score of how well that simulation explains the data; then it fits a smooth surface through those scores to build the full spread of plausible answers.

Host 1When you say score, is that the likelihood numbers I've seen in these papers?

Host 2Yes, they report the natural logarithm of the likelihood. The useful rule of thumb is that the scale is logarithmic, so a gap of one between two simulations means one fits about two point seven times better, and a gap of ten is a factor of over twenty thousand.

Host 1What data did they feed in for each event?

Host 2Public data: both LIGO detectors plus Virgo for the twenty nineteen event, and just the two LIGO detectors for the twenty twenty-three event. They started the analysis at twenty hertz for both, and for the newer event also ran a second version starting at ten hertz.

Host 1Why does the starting frequency matter so much?

Host 2Because eccentricity is quoted at a particular frequency, and since it decays, the value at ten hertz is larger than at twenty. They converted each simulation's eccentricity to twenty hertz with a simple, lowest-order formula that the paper notes is only valid for small eccentricities.

Host 1Did they make any choices up front that could tilt the results?

Host 2A few, and they tested one deliberately. They ran every analysis three times, with spins along the orbit capped at zero point five, zero point nine and zero point nine nine, to see what happens when high-spin simulations are left out; eccentricity got a flat prior from zero to zero point nine.

Host 1And how do they decide whether there's evidence for an oval orbit or a wobble, rather than just a best fit?

Host 2With a Bayes factor, which compares how well two hypotheses explain the data, here reported as a power of ten. For eccentricity they used a shortcut that looks at how much the evidence moves away from zero eccentricity; for precession the shortcut breaks down, so they directly compared the total evidence with and without wobbling simulations.

Host 1So a Bayes factor reported as one would mean the data favour one idea ten to one?

Host 2Right, one means ten to one, two means a hundred to one, and a value like zero point two four is less than two to one. Negative values point the other way.

Host 1Was there anything else they ran each comparison twice for?

Host 2Yes, every event was analysed twice: once with only the non-wobbling simulations, about fifteen hundred of them, and once with the wobbling ones added, about twenty-one hundred. That lets them see directly what happens to the eccentricity when the model is allowed to wobble.

A word from our sponsor

Host 2This episode is brought to you by the Longway hula hoop, the only hoop with a guaranteed eccentric orbit around your waist.

Host 1I've used mine since spring. It never comes back to the same spot, it swings a little further round each time.

Host 2That is the eccentricity. Longway: settles at zero point two at your hips, plus or minus most of your hips.

Host 1Our lab looked at it and says it's actually precession. It is currently orbiting my neighbour.

Host 2Each Longway leaves your waist with a final kick of four thousand kilometres a second. Longway. It is already outside the galaxy.

What they found

Host 1Let's start with the twenty nineteen event: what came out when only non-wobbling simulations were allowed?

Host 2The best fits were mildly eccentric, with eccentricity at twenty hertz between zero point one four and zero point two, mostly equal masses. The single best was a simulation with equal masses, spins along the orbit and eccentricity zero point one six, with a log-likelihood score of about ninety-two point four.

Host 1And when the wobbling simulations were added in?

Host 2The best score rose to ninety-five point one, a gap of almost three, so roughly a factor of fifteen in how well it fits. That top simulation has equal masses, both spins at zero point nine seven, strongly tilted, and still an eccentricity of about zero point one four at twenty hertz.

Host 1So for the older event, adding the wobble improved the fit but didn't make the oval orbit go away?

Host 2Correct. In their preferred run, with spins allowed up to zero point nine nine, eccentricity at twenty hertz comes out at about zero point two one, with a ninety percent range from roughly zero point zero six to zero point four, and the in-plane spin of the bigger black hole at about zero point six eight.

Host 1How strong is the evidence behind those two claims?

Host 2Very uneven. The precession Bayes factor is about three point seven, so thousands to one in favour of wobble, but the eccentricity Bayes factor is only zero point two four, less than two to one, which is a weak lean rather than a detection.

Host 1If someone reads the short summary at the top of the paper, will they see those same spin numbers?

Host 2Not quite, and it looks like a slip. The summary gives zero point seven one seven for the older event and zero point six seven eight for the newer one, while the paper's own tables give them the other way round, so we're going by the tables.

Host 1Now the twenty twenty-three event: did the same pattern repeat?

Host 2Only half of it. With non-wobbling simulations alone, the best single fit had an eccentricity of zero point one four and the smoothed estimates landed around zero point one five to zero point one nine, but the evidence for eccentricity was already negative, a Bayes factor around minus zero point six to minus zero point nine.

Host 1And what happened once the wobble was allowed?

Host 2The best simulation jumped to a score of two hundred and twenty point seven, more than ten above the best non-wobbling one, and all of the top ten wobbling runs beat every non-wobbling run. That winner is a circular orbit with no eccentricity, masses in a ratio of about zero point seven three, and a big black hole spinning at zero point nine five, tilted hard.

Host 1So the oval orbit that showed up before was really the wobble in disguise?

Host 2That's the paper's reading, and it matches what earlier injection tests predicted: a wobbling circular signal fitted with a model that can't wobble gets misread as eccentric. In the preferred run eccentricity at twenty hertz drops to about zero point zero six, with a ninety percent range from about zero point zero one to zero point one two.

Host 1How lopsided is the evidence for the wobble in this case?

Host 2Very. The precession Bayes factor is about eleven, close to a hundred billion to one, the eccentricity Bayes factor is minus zero point six four, and the in-plane spin of the bigger black hole comes out at about zero point seven two.

Host 1Did starting at ten hertz instead of twenty change that picture?

Host 2Hardly. The top scores barely moved, eccentricity at ten hertz came out near zero point one with negative evidence for it, and the precession evidence stayed around eleven to twelve; the twenty hertz run actually scored slightly higher.

Host 1Is there a single picture that shows the fit is real, rather than just a number in a table?

Host 2They overlay the winning simulation on the cleaned-up detector data from both LIGO sites, with the spread from about a hundred and fifty to a hundred and ninety random draws of orientation and distance. The authors say the match is good in both amplitude and timing for each event.

Host 1And did the high-spin cap you mentioned make a difference?

Host 2A clear one. With spins along the orbit capped at zero point five, the newer event's in-plane spin estimate fell to zero point four and was visibly pressed against the edge of what the prior allowed, which is why the authors prefer the least restrictive setting; their best fits all involve spins above zero point nine.

Host 1Where do the newer event's numbers land compared with what other teams found?

Host 2Some agree and some don't. The in-plane spin is close to the collaboration's value, zero point seven two against zero point seven four, but this paper finds a mass ratio nearer equal, zero point nine five against zero point seven four, and a much higher chirp mass, about one hundred and seventy-six Suns against one hundred and thirty-seven in the detector frame; their eccentricity is closest to the one team that also allowed both effects.

Host 1The summary also mentioned a recoil, with numbers in the thousands of kilometres per second; what's recoiling?

Host 2The single black hole left after the merger. When the spins are lopsided, the gravitational waves come out more in one direction, and the remnant gets kicked the other way; the best simulations imply about three thousand nine hundred and sixty-five kilometres per second for the older event and two thousand and fifty-nine for the newer one.

Host 1Is that fast by space standards?

Host 2As a wider point of comparison, the escape speed from even big galaxies is usually reckoned in the hundreds to a couple of thousand kilometres per second, so kicks like these could throw a remnant out. But the paper is careful: these are properties of single best-fit simulations, not measured spreads, and they stand above the runners-up only by about two standard deviations.

Why it matters

Host 1So if I zoom out, what's the principle this paper is pushing?

Host 2That you can't ask a signal whether it was eccentric unless your model is also allowed to wobble, because one effect will impersonate the other. Using real simulations that contain both, the authors say they can tell the two apart in current data, and get opposite answers for two events that looked similar.

Host 1Who actually changes what they do because of this?

Host 2Mainly people inferring where black holes come from. If eccentricity claims built on models without wobble can evaporate, as here for the newer event, then population studies that count eccentric events as proof of chance encounters need to be careful which analyses they count.

Host 1And for someone who isn't an astrophysicist, is there anything in this for us?

Host 2Honestly, nothing practical. It's a careful step in reading the history of very distant objects, and the main lesson travels: if your toolkit can only explain things one way, it will find that one way.

Host 1Can I say this proves the older event came from a crowded star cluster?

Host 2No. It's consistent with that story, and the wobble evidence is strong, but the eccentricity evidence for that event is weak, and the paper itself doesn't run any formation model.

The honest caveats

Host 1What should a listener be cautious about before taking these numbers home?

Host 2First, the library is lumpy: the authors themselves warn that parameter space is not evenly covered and some regions have few simulations, which can shape the results. The analysis can only slide each run in total mass; every other property is restricted to whatever simulations happen to exist.

Host 1Does that mean the very best answer could simply be missing from the library?

Host 2It could be, yes. The smooth surface they fit fills in between runs, but where runs are sparse that filling is guesswork, and the authors show how much the answers shift when high-spin runs are dropped.

Host 1Anything else besides the gaps in the library?

Host 2The eccentricity conversion uses a simple formula valid for small eccentricities, so the exact numbers depend on that choice, and they can't be compared directly with earlier figures quoted at other frequencies or assumed masses. Some of the newer event's numbers also disagree substantially with other analyses, and it's a single preprint that, as far as the text shows, has not yet been through peer review.

Host 1And the recoil numbers, how much weight should they carry?

Host 2Treat them as illustrations. They come from one top simulation per event, and the paper says so directly.

What to watch next

Host 1What would you watch for next, to know whether this holds up?

Host 2First, whether independent teams, using the newer approximate models that include eccentricity and wobble together, reach the same split between the two events. Second, whether the simulation library gets filled in at very high spins, where both top fits live.

Host 1Is there anything coming from the detectors themselves that could settle it faster?

Host 2New events, more than anything. The authors list several other candidates that have been flagged as possibly eccentric, and the method only becomes convincing if it keeps sorting real oval orbits from wobbles case after case.

Sign-off

Host 1That's the deep dive. Every weekend this same feed carries the roundup, the week's new papers in one short episode, with eccentricity measured at twenty hertz.

Host 2Thanks for listening to the Hastrup Review of Science.