Papers

Our worst nightmare in the gravitational-wave population buisiness is \(p_{\rm det}\), the detection probability. That such a crucial aspect that we spend entire discussion sessions at conferences trying to get it right. Selection effects are usually removed, i.e. one goes from a set of observed data to the intrinsic distribution of sources. Wouldn’t it be easier to just model the observed distribution instead? Well, it’s not that trivial, and indeed people thought it was not possibile without biasing your results. It turns out it is possible, but one still needs to model \(p_{\rm det}\). But then, we argue, the comparison between gravitational-wave data and astrophysical models becomes much cleaner.

A. Toubiana, D. Gerosa, M. Mould, S. Rinaldi, M. Arca Sedda, T. Bruel, R. Buscicchio, J. Gair, L. Paiella, F. Santoliquido, R. Tenorio, C. Ugolini.
arXiv:2507.13249 [gr-qc].

A few of us met at the GWsnowballs workshop earlier this year, and during a scientific discussion, I ended up asking: “What’s the current gravitational-wave event with signs of eccentricity that are the least ambiguous?” I argued against the usual suspect, GW190521, because that signal is too short—and short makes it ambiguous. Then we looked at two analyses that searched for eccentricity in the current gravitational-wave catalog. They flagged several events, but only one appeared in both. The “telephone number” of that event is GW200208_222617, and that discussion eventually led to this paper.

I. Romero-Shaw, J. Stegmann, H. Tagawa, D. Gerosa, J. Samsing, N. Gupte, S. R. Green.
arXiv:2506.17105 [astro-ph.HE].

Now, there are a lot of black holes out there. So many that their gravitational-wave signals won’t even be separable, all piling up on top of each other (if/when we’ll have a detector to pick that up). Analyzing this stochastic background can tell us about the details of those black holes; that’s the good old “population” problem in GW astronomy, here tackled in a different way. And, why not, let’s throw in a neural network.

G. Giarda, A. I. Renzini, C. Pacilio, D. Gerosa.
arXiv:2506.12572 [gr-qc].

I started collaborating with some galaxy folks here at my institution, which is just great. Their problem is that of estimating the luminosity function of some objects, with the complication that the survey is flux limited. They’ve been referring to this as a “completeness function”. We looked into the stats togehter, and realized that is exactly the same problem we GW people solve with hierarchical Bayesian analysis, and that completeness function is nothing but our \(p_{\rm det}\) with some weird astro units.

D. Tornotti, M. Fossati, M. Fumagalli, D. Gerosa, L. Pizzuti, F. Arrigoni Battaia.
arXiv:2506.10083 [astro-ph.GA].

Welcome to the beautiful world of SBI, with this terrific piece of work by Pippa Cole. Here we’re looking at extreme mass-ratio inspirals (EMRIs), that is, a small black hole orbiting a big black hole, which will be (one day) detected by LISA. These signals are nasty (long and of a very complicated morphology). We’re trying something new here – a deep learning called “truncated marginal neural ratio estimation” that does not even require writing down the likelihood of the problem. Just simulate all you can. The answer, this thing is great for narrowing down the parameter space where EMRIs will be, kind of like searches do with current gravitational-wave data, but in a very different way.

P. S. Cole, J. Alvey, L. Speri, C. Weniger, U. Bhardwaj, D. Gerosa, G. Bertone.
arXiv:2505.16795 [gr-qc].

This paper came out of some discussions from our “Gravitational-wave snowballs” workshop in Sexten (Italy). We were discussing the good old problem of separating black-hole binary formation channels with spin measurements. Usually one says “aligned=isolated”, “isotropic=dynamical”. But then, some binaries that formed dynamically should also be eccentric. What we then realized is that, for those eccentric binaries and only for those, spin measurements can actually tell which of the dynamical channel (because there are many…) is at play.

J. Stegmann, D. Gerosa, I. Romero-Shaw, G. Fumagalli, H. Tagawa, L. Zwick.
arXiv:2505.13589 [astro-ph.HE].

We’re back to predicting the excitation amplitude of black hole merger ringdowns. We already looked into the simpler case of binaries with aligned spins, and now tried to study the full problem of binaries with misaligned (i.e. processing) spins. Well, this is a hard problem! It’s not even clear which mode is the stronger one anymore, and finding suitable coordinates is not at all trivial. While this is just a first exploration, there’s so much interesting phenomenology here! Do it yourself with the postmerger package.

F. Nobili, S. Bhagwat, C. Pacilio, D. Gerosa.
arXiv:2504.17021 [gr-qc].

Great paper led by our former MSc student Alessandro Pedrotti today! This is about combining the distributions of gravitational waves and galaxies to do cosmology. These two probes measure different things (distance and redshift, respectively), so their distributions will “match” only if the cosmological model is right. You can actually use this to measure the cosmological model itself. Short answer: putting together 3G detectors and Euclid is a great idea.

A. Pedrotti, M. Mancarella, J. Bel, D. Gerosa.
arXiv:2504.10482 [astro-ph.CO].

Long gravitational-wave signals are, well, long. And long often means painful, as more data need to be stored and processed. Kind of intuitively, the solution might be that of cutting things into chunks, so that long becomes short. Here we apply this idea to the popular inner product entering all gravitational-wave pipelines; this is a key building block of everything we do. The answer is that using SFTs, “Short-time Fourier Transforms”, can make things faster by more than 3 orders of magnitudes, sometimes 5. We think this is the solution to future gravitational-wave data analysis problems (think LISA and 3G…).

R. Tenorio, D. Gerosa.
Physical Review D 111 (2025) 104044. arXiv:2502.11823 [gr-qc].

When inferring black holes from gravitational-wave data, we tend to do two things, one after the other. First, we consider each event individually and measure its parameters (masses, spins, etc). Then we consider all the events together and measure the population properties. This is what we do all the time, but, actually, if objects are now part of a population, those parameters should be looked at again in light of all the others. This full problem (all parameters of all the events plus the population parameters) is daunting, and in the past we used an indirect and somewhat convoluted approach. We got back to it now, and this time, we managed to do it head-on. Let me introduce this giant 500-dimensional sampling of the full population problem!

M. Mancarella, D. Gerosa.
Physical Review D 111 (2025) 103012. arXiv:2502.12156 [gr-qc].

General relativity has this beautiful property that coordinates are meaningless. You can change them at will, which means they don’t contain any physics. And, believe it or not, some of the popular formulations we use to write down the dynamics of eccentric binary black holes still have coordinates in them. They go away if you take an average of an orbit (Peters, the man!) but that’s killing some information. In this paper we go back to those old results and show how those gauges can actually be absorbed into the formulation itself. The paper is on the maths-heavy side of things, but the results are great. Peters, you were basically right, but not quite.

G. Fumagalli, N. Loutrel, D. Gerosa, M. Boschini.
Physical Review D 112 (2025) 024012. arXiv:2502.06952 [gr-qc].

Quasar 3C 186 strikes back! Matteo and I got interested in this funny quasar last year (see this one). When our paper hit the arxiv, we got contacted by the real astronomers who take actual data, who told us they had even more beautiful data. We ended up contributing with our relativistic model and… well… everything seems to work. 3C 186 is indeed a recoiling black hole (it might be a rare one, but we’ve observed it nonetheless). The abstract says “decisive,” and this is indeed the right word.

M. Chiaberge, T. Morishita, M. Boschini, S. Bianchi, A. Capetti, G. Castignani, D. Gerosa, M. Konishi, S. Koyama, K. Kushibiki, E. Lambrides, E. T. Meyer, K. Motohara, M. Stiavelli, H. Takahashi, G. R. Tremblay, C. Norman.
arXiv:2501.18730 [astro-ph.GA].

Gravitational-wave population people talk all the time about parametric vs non-parametric methods. Parametric methods mean imposing our astrophysical knowledge on how we look at GW data. This is great, we do want to extract astrophysical knowledge, but what if we don’t know what to look for? The statisticians tell us to go non-parametric, which means using a flexible model that can fit whatever you want. That’s great, but what do we learn then? In other words, where’s the boundary between flexibility and interpretability? Today’s paper shows that one can conceptually separate these two processes and extract parametric results from non-parametric fits. I’m very proud of this piece of work, which was Cecilia Fabbri‘s MSc thesis project and was actually kickstarted by one of my previous students, Alessandro Santini. We even wrote a poem about this!

C. M. Fabbri, D. Gerosa, A. Santini, M. Mould, A. Toubiana, J. Gair.
Physical Review D 111 (2025) 104053. arXiv:2501.17233 [astro-ph.HE].

Black holes on eccentric orbits… what does it even mean? The hard (but fun) thing is that we work in General Relativity, where coordinates don’t have a physics inside. One can always change the coordinates as they want, so they can’t be used to define observables. The eccentricity of an orbit has to do, indeed, with the shape of the orbit itself, and that can be transformed away with suitable coordinates. So, does it even sense to measure the orbital eccentricity of black-hole binaries? The one thing we are allowed to do is to find a coordinate-free estimator in General Relativity that reduces to the eccentricity we all know and love in the Newtonian limit. This is possible! The right mathematical framework for this is something called “catastrophe theory”, a funny name, but Nick likes it.

M. Boschini, N. Loutrel, D. Gerosa, G. Fumagalli.
Physical Review D 111 (2025) 024008. arXiv:2411.00098 [gr-qc].

Our “popfisher” paper is finally out! (and now Viola can submit her PhD thesis). This is about next-generation (aka 3G) gravitational wave detectors. Those beasts will measure millions of black holes… and with so many of them who cares about each source individually. The important thing will be the population of objects, i.e. how those black holes are distributed as a whole. Measuring populations is an interesting but convoluted statistical problem. Here we implement a quick shortcut (the Fisher matrix) and show that yes, 3G detectors will be amazing… but more amazing for some things than for others.

V. De Renzis, F. Iacovelli, D. Gerosa, M. Mancarella, C. Pacilio.
Physical Review D 111 (2025) 044048. arXiv:2410.17325 [astro-ph.HE].

LISA will see a gazillion white dwarfs, but we won’t, or at least not individually. Those signals will actually pile up together in a mashed potato thing called foreground. But this mashed potato won’t be smooth (translate: the gravitational-wave signal won’t be stationary and Gaussian) and this structure can indeed be precious for extracting more information from LISA. But first, let’s taste this with today’s paper, i.e. characterize the foreground.

R. Buscicchio, A. Klein, V. Korol, F. Di Renzo, C. J. Moore, D. Gerosa, A. Carzaniga.
arXiv:2410.08263 [astro-ph.HE].

This is a fun IMBH story we worked out when Kostas and Luca were visiting last summer from JHU. What if (one day, who knows) we observe a highly spinning intermediate-mass black hole? If that happens, is going to be puzzling because IMBH that grow in clusters by mergers of smaller black holes tend to spin down, not up. This is a funny property of black holes, namely that extracting spins is easier than putting it in, so on average black holes slow down after they have merged many times. So if we see an IMBH with large spins, the spin must come from somewhere else. Where? Maybe gas. The argument then is that one can actually convert an IMBH spin measurement into the minimum amount of gas that must have been accreted to get that spin.

K. Kritos, L. Reali, D. Gerosa, E. Berti.
Physical Review D 110 (2024) 123017. arXiv:2409.15439 [astro-ph.HE].

To Stars or to gas, that is the question.
Whether ’tis nobler in the hardening to suffer
The slings and arrows of passing stars,
Or to dissipate against a sea of gas
And by disk end them. To inspiral — to merge,
No more; and by LISA to say we end
The models and the thousand PE samples
That gravity is heir to.

A. Spadaro, R. Buscicchio, D. Izquierdo-Villalba, D. Gerosa, A. Klein, G. Pratten.
Physical Review D 111 (2025) 023004 . arXiv:2409.13011 [astro-ph.HE].

All right I think this is great (but it took me a long time to convince myself and the others that’s the case!) In gravitational-wave astronomy we measure binaries, that is, pairs of two objects. Our signals have information about the pair as a whole. At the same time, we care very much about separating those two objects and measuring the properties of individual black holes and neutron stars. We always do that operation without thinking twice, just say that for each posterior sample object “1” is that with the larger mass and object “2” is that with the lower mass. But is that ok? Surely it’s a choice, but is it the best one? What does it even mean to pick the “best” labels? I think machine learning can help us here and that this problem can be framed using the language of semi-supervised clustering. The results? Well, they seem very significant. Measurements of the black-hole spins are more accurate, you can tell more easily if that’s a black hole or a neutron star, and overall the posterior distributions just look nicer (go away nasty multimodalities and non-Gaussianities!).

D. Gerosa, V. De Renzis, F. Tettoni, M. Mould, A. Vecchio, C. Pacilio.
Physical Review Letters 134 (2025) 121402. arXiv:2409.07519 [astro-ph.HE].
PRL Editors’ Suggestion. Covered by press release.

Press release : Milano-Bicocca.
Other press coverage: ilgiorno, lescienze, ansa.it, adnkronos (1), adnkronos (2), 30science, agenparl.eu, cagliarilivemagazine, ilcentrotirreno, ilgiornaleditalia, laragione, lospecialegiornale, meteoweb, msn.com, occhioche, padovanews, prpchannel, sardegnalive, smartphonology, tgabruzzo24, vetrinatv, unicaradio, altoadige, ecodibergamo, roboreporter, saluteh24, salutedomani.

The ringdown is the final bit of a gravitational-wave signal, after the two black holes have merged. It’s nice because it’s clean; GR is so powerful that all that comes out after a black hole merger has specific frequencies, the fantastic “quasi-normal modes.” While the frequencies only depend on that final BH (thanks Kerr!), the excitations of those frequencies depend on all that happened before, i.e. the merger process itself. In this summer paper by Costantino and the rest of us, we present a new accurate approximant to those amplitudes. Now go home and test GR using postmerger.

C. Pacilio, S. Bhagwat, F. Nobili, D. Gerosa.
Physical Review D 110 (2024) 103037. arXiv:2408.05276 [gr-qc].

The orbits of binary black holes could be eccentric, but in practice they’re not. At least when we observe them, and that’s because of a relativistic effect that circularizes the orbit. Even if astrophysics formed black holes eccentric, relativity makes them circular when we observe them with gravitational-wave interferometers. But we’re interested in the astrophysics back then! What we find here is that the tiny residual eccentricity at detection can be crucial. Even eccentricities that are so small that we cannot tell them apart from circular can mess up the astrophysical inference. Unfortunately, this is a new systematic error that needs to be taken into account: inferring the “formation channel” of binary black holes might be even harder than we thought.

G. Fumagalli, I. Romero-Shaw, D. Gerosa, V. De Renzis, K. Kritos, A. Olejak.
Physical Review D 110 (2024) 063012. arXiv:2405.14945 [astro-ph.HE].

… and we’re back to selection effects. That means modeling what you cannot see. The black holes that gravitational-wave detectors observe are not representative of those that are out there in the Universe. Some are easier to see, some are harder. Quantifying how much easier and harder is crucial to properly understand the underlying astrophysics. In this paper (which came out of Malvina’s BSc student project!), we go back to the basics and work out gravitational-wave selection effects one step after the other, using and refining the most common approximation. Two things to remember: including noise fluctuations is easy, and a signal-to-noise ratio threshold of 11 is probably ok.

D. Gerosa, M. Bellotti.
Classical and Quantum Gravity 41 (2024) 125002. arXiv:2404.16930 [astro-ph.HE].

Population 3 stars are like “the original” stars. Those formed with material that comes straight from the Big Bang. It would be very (like, a lot!) cool to see them with gravitational-wave detectors. But can we tell them apart? Or do they look like all the other stars? Here is an attempt with a fancy machine-learning classifier.

F. Santoliquido, U. Dupletsa, J. Tissino, M. Branchesi, F. Iacovelli, G. Iorio, M. Mapelli, D. Gerosa, J. Harms, M. Pasquato.
Astronomy & Astrophysics 690 (2024) A362. arXiv:2404.10048 [astro-ph.HE].

This is the first of two papers on the arxiv today: it’s fun when two long, very different projects by different people just happen to be done on the same day! This paper is by my former colleague Nate Steinle (now a postdoc in Manitoba, Canada). Here we connect the dynamics of jets in AGN disks to the spin of black holes observable by LISA. And show the latter is a diagnostic of the former! And it’s nice to see my disk-binary code being used for something I didn’t think of when I wrote it.

N. Steinle, D. Gerosa, M. G. H. Krause.
Physical Review D 110 (2024) 123034. arXiv:2403.00066 [astro-ph.HE].

And the second paper on the arxiv today is Daria’s masterpiece! pAGN (which Daria says you should read “pagan”) is a brand new, super cool code that implements the hydrodynamics of AGN disks, at least in their most popular one-dimensional fashion. Those solutions have been around for a long time but their details were, well, let’s say unclear. Daria went through everything from beginning to end, coming up with the “one-stop solution for your AGN disc needs” (that was actually the working title of the paper…). So pip install pAGN and have fun.

D. Gangardt, A. A. Trani, C. Bonnerot, D. Gerosa.
Monthly Notices of the Royal Astronomical Society 530 (2024) 3986–3997. arXiv:2403.00060 [astro-ph.HE].
Open source code.

Not sure what happened here, how the hell did I end up writing a paper with actual radio data that needed to be reduced … Call me an ambulance.

The guy here is 3C186 which is not a postcode but a quasar. A funny one because it’s not centered on the galaxy (it’s a bit off) and it’s also going at another velocity (ciao ciao). One of the leading explanations is that 3C186 is a recoiling black hole, the remnant of black-hole merger is being kicked away (yeah these things can happen). 3C186 also has a radio jet, and that should point in the direction of the black-hole spin. The funny thing is that spin and the kick appear perpendicular to each other, and this is fun because theory says they should actually be parallel. We looked into this a bit carefully and discovered it’s all a lie! The spin and the kick both point along the line of sight and appear perpendicular only because of a super strong projection effect. If this is true, the radio jet should also point straight to us! We then tried to test this with whatever ratio data we could grab (where is that ambulance) and found that… mmh, well, it’s a maybe.

M. Boschini, D. Gerosa, O. S. Salafia, M. Dotti.
Astronomy & Astrophysics 686 (2024) A245. arXiv:2402.08740 [astro-ph.GA].

In the gravitational-wave world, we usually say a binary merger is detected if it has a sufficiently large SNR (signal-to-noise ratio). But is that true? Detection pipelines are far more complicated than that. Here we try to figure out a section threshold from what’s detected. That is: (some) people agree that these guys are GWs, so what’s your SNR threshold for detectability? It’s like reading in the minds of a GW data analyst…

M. Mould, C. J. Moore, D. Gerosa.
Physical Review D 109 (2024) 063013. arXiv:2311.12117 [gr-qc].

I’m obsessed with spinning black-hole binaries but, guys, spinning and eccentric black holes are even better! This is the first first-author paper by Giulia, who is not only a rising GW astronomer but also a semi-professional baker… So take two spoons of black holes, one spoon of spin dynamics, some eccentricity (but less than 0.6 ounces), and a pinch of maths. Put this in a bowl, mix it thoroughly with numerical integrations …and the result is very tasty! Spins and eccentricity shape the dynamics of black-hole binaries together , which means one can hope to measure eccentricity indirectly from the spins, but also that if you forget about eccentricity then your spin inference will be crap. Buon appetito.

G. Fumagalli, D. Gerosa.
Physical Review D 108 (2023) 124055. arXiv:2310.16893 [gr-qc].

…and we’re back to testing GR. We’ve got many gravitational-wave events and would like to use them all together to figure out if our equations for gravity are correct. And here is the issue: there’s only one set (aka catalog) of black holes that contains all the black holes we’ve observed. Now that’s obvious you’d say, and you would be right!, much like we have a single Universe to observe (I’m not a language guy but indeed “Universe” means like “the whole thing”). This effect is known in cosmology (think those low-order multiples in the usual CMB plot), so we called it “the catalog variance of testing GR”. It’s bad, but the Baron Munchauseen tells us we can bootstrap.

C. Pacilio, D. Gerosa, S. Bhagwat.
Physical Review D 109 (2024) L081302. arXiv:2310.03811 [gr-qc].

Gravitational-wave data keep on giving us surprises. The most outstanding one IMO is an observed correlation between mass ratios and spins of the black holes, which was first found by Tom Callister and friends. That is so, so weird… to the point that virtually zero astrophysical models so far can explain it fully and consistently. Well, we can’t either (at least not fully and consistently) but we think this paper is a nice attempt. The secret seems to be the symmetry of the astrophysical environment one considers, and data tends to prefer black holes assembled in cylindrical symmetry. That’s also weird to be honest, but there’s a candidate for this setup, namely accretion disks and their migration traps. Who knows, more data will tell.

… and huge congrats to my MSc student Alessandro who managed to publish a paper even before graduating!

A. Santini, D. Gerosa, R. Cotesta, E. Berti.
Physical Review D 108 (2023) 083033. arXiv:2308.12998 [astro-ph.HE].

Other press coverage: astrobites.

New paper from a new student! Here is Matteo Boschini’s first piece of work, where we look at predictions for the final mass and spins of black-hole remnants. That is, after two black hole merge, what’s the mass and spin of the guy they left behind? These predictions are typically done by fitting (in various ways) outputs from numerical-relativity simulations but those, unfortunately, can only handle black holes of similar masses. On the other hand, black holes with masses that are very different from each other can be handled analytically. Here we show how to put the two together with a single machine-learning fit.

M. Boschini, D. Gerosa, V. Varma, C. Armaza, M. Boyle, M. S. Bonilla, A. Ceja, Y. Chen, N. Deppe, M. Giesler, L. E. Kidder, G. Lara, O. Long, S. Ma, K. Mitman, P. J. Nee, H. P. Pfeiffer, A. Ramos-Buades, M. A. Scheel, N. L. Vu, J. Yoo.
Physical Review D 108 (2023) 084015. arXiv:2307.03435 [gr-qc].

All right, this is kind of far from my day-to-day topics but working on this paper with Alice and Riccardo was super fun. Think LISA and supermassive binary black holes. And… the detector does what it wants. That’s not true of course because the experimentalists are amazing, but there will be noise transients: unexpected blips when the gravitational-wave signal will be corrupted. Here we look at what would happen in a realistic setting when a LISA glitch happens on top of a gravitational wave from a supermassive black hole.

A. Spadaro, R. Buscicchio, D. Vetrugno, A. Klein, D. Gerosa, S. Vitale, R. Dolesi, W. J. Weber, M. Colpi.
Physical Review D 108 (2023) 123029. arXiv:2306.03923 [gr-qc].

We do population analysis in gravitational waves all the time now. That is: we compare many observations from GW experiments against many simulated datapoints from simulations. But what if you only have one observation? That could be a LIGO guy that is kind of an outlier (think GW190521) or maybe a datapoint from a future detector (think LISA) that feels lonely in his parameter space. Don’t look further, this is stats for you (and Matt’s last paper as a grad student…)

M. Mould, D. Gerosa, M. Dall’Amico, M. Mapelli.
Monthly Notices of the Royal Astronomical Society 525 (2023) 3986–3997. arXiv:2305.18539 [astro-ph.HE].

This paper is episode four in the up-down instability series. We first figured out the instability exists (episode 1), then computed when binaries go after the instability (i.e. the endpoint, episode 2), and also checked binaries are really unstable in numerical relativity (episode 3). Now we look at the inference problem with LIGO/Virgo: if unstable up-down binaries enter the sensitivity window of the detector, will we be able to tell? We phrased the problem with some fancy stats using the so-called Savage Dickey density ratio, which is the right tool to answer this question. As is too often the case, current data are not informative enough but the future is bright and loud.

V. De Renzis, D. Gerosa, M. Mould, R. Buscicchio, L. Zanga.
Physical Review D 108 (2023) 024024. arXiv:2304.13063 [gr-qc].

It’s out! The notorious (ask my students…) “ precession v2 ” paper is finally out! This took a veeeery long time; we checked and the first commit for this paper is from May 2020 (!). But the result is an exhilarating tour of spin precession at 2PN with 27 pages and 183 (!!!) numbered equations. We rewrote the entire formalism, change how we parametrize things, compute all we could in closed forms, and speed up the computational implementation. It’s cool, now performing a precession-averaged evolution is a <0.1s operation. If you’re into BH binary spin precession, this is the paper for you. All of this is now part v2 of our PRECESSION python module. So long, and thanks for all the spin.

D. Gerosa, G. Fumagalli, M. Mould, G. Cavallotto, D. Padilla Monroy, D. Gangardt, V. De Renzis.
Physical Review D 108 (2023) 024042. arXiv:2304.04801 [gr-qc].
Open source code.

Third-generation gravitational wave detectors are going to see all stellar-mass black-hole mergers in the Universe. Wooooooooo. But hang on, is this enough? Observing the sources is great, but then we need to measure them. Here we try to focus on the latter and quantify how well we will be able to measure the distance of black holes. Read the paper now, but the short answer is that 3G detectors are going to be awesome but not that awesome…

M. Mancarella, F. Iacovelli, D. Gerosa.
Physical Review D 107 (2023) L101302. arXiv:2303.16323 [gr-qc].

We want more! With gravitational-wave data, some quantities like the masses of the black holes are much easier to see than others. But those others are very interesting, notably spins that process and orbits that are eccentric, because they would tell us how black hole binaries came to be in the first place. So while it would be great to see those, it’s also being very hard. Some tentative claims have been made with current data, but nothing unambiguous so far. In this paper led by Isobel from Cambridge, we show that (surprise surprise…) the signals needs to be long enough before one can tell eccentricity and spin precession apart.

I. Romero-Shaw, D. Gerosa, N. Loutrel.
Monthly Notices of the Royal Astronomical Society 519 (2023) 5352–5357. arXiv:2211.07528 [astro-ph.HE].

Together with my postdoc Nate, we’re proceeding our investigations on supermassive, spinning binary black holes surrounded by accretion disks (that is: a ton of gas around big monsters at the center of galaxies!). In today’s paper, we dig a bit deeper into what happens when the disk breaks. That presumably stops the interactions between the gas and the black-hole spins which could make all this funky astrophysics (spins that moves, disks that breaks, etc) actually observable with future gravitational-wave detectors. More needs to be done of course, but here we are.

N. Steinle, D. Gerosa.
Monthly Notices of the Royal Astronomical Society 519 (2023) 5031–5042. arXiv:2211.00044 [astro-ph.HE].

Lots of “firsts” today! My first -year PhD student Viola just put out her first first -author paper. This is about measuring black holes with not one, but two precessing spins. People have been trying to figure out how to tell if at least one of the two spins of a merging black-hole binary is precessing for quite some time now. And maybe we’ve even done it already for one or two of the current LIGO-Virgo events. But here I must quote that epic Italian commercial from the 90s: “two gust is megl che one” (which is a terrible Italian-English mishmash on a terrible joke to say that when you eat a Maxibon “two flavors are better than one”). In this paper we propose a strategy to identify sources that have the strongest evidence of two processing spins. Viola has been putting together simulated data for the next LIGO/Virgo data-taking period, and the result is pretty cool. If these binaries are out there in the Universe, we will be able to tell they have two spins going around!

V. De Renzis, D. Gerosa, G. Pratten, P. Schmidt, M. Mould.
Physical Review D 106 (2022) 084040. arXiv:2207.00030 [gr-qc].

Big stars burn everything they have, die fast, and produce big black holes. So when you see two black holes together, it’s likely that the big black hole comes from the big star. Or maybe not? Before dying, the big star can drop some mass onto the other guy, making it bigger! So now, the initially big star still produces the first black hole, but, at the end of the day, that might not be the more massive black hole anymore! This scenario is called “mass-ratio reversal” and our astrophysics friends have put together many models out there showing this is indeed possible for a good fraction of the black holes that produce gravitational-wave events. So here we ask the data: given the events LIGO and Virgo have seen so far, what’s the evidence for mass-ratio reversal in binary stars? Read Matt’s paper to find out.

M. Mould, D. Gerosa, F. S. Broekgaarden, N. Steinle.
Monthly Notices of the Royal Astronomical Society 517 (2022) 2738–2745. arXiv:2205.12329 [astro-ph.HE].

Observing gravitational waves from the ground (i.e. LIGO, Virgo, etc) give us a unique view on “the last three minutes” of the life of compact objects before they merge with each other. Going to space (I’m talking to you, LISA!) will instead give us “the last three years”. Completed together with the rest of the Birmingham crowd, this paper provides a realistic view of this truly amazing landscape. LISA observations at low frequencies in the 2030s will be paired with high-frequency data from LIGO’s successors (the so-called 3rd generation detectors). Together (and that’s crucial, together!) LISA and 3g detectors will tell us the full story of the life of merging black holes. LIGO alone is like catching up with a movie because you were late at the theatre, LISA alone is like a huge cliffhanger before the series finale… multiband observations are a bingewatching experience!

A. Klein, G. Pratten, R. Buscicchio, P. Schmidt, C. J. Moore, E. Finch, A. Bonino, L. M. Thomas, N. Williams, D. Gerosa, S. McGee, M. Nicholl, A. Vecchio.
arXiv:2204.03423 [gr-qc].

Daria’s new paper is out! (With key contributions from others in the group… This is also Viola’s first paper!).

Here we look at sub-dominant black-hole spin effects in current data from LIGO and Virgo (yeah sorry guys… our black-hole spin obsession goes on). People have looked at spin precession before, but we’re interested in even more subtle things, namely disentangling precession and nutation. This is a tricky business, which is made complicated by the fact that this piece of information is hidden behind other parameters that are easier to measure (say the masses of the two black holes). Our paper is an attempt to formulate and systematically exploit something we called “sequential prior conditioning” (which is: mix&match priors and posteriors in Bayesian stats…). Results are weak today but strong tomorrow.

D. Gangardt, D. Gerosa, M. Kesden, V. De Renzis, N. Steinle.
Physical Review D 106 (2022) 024019. Erratum: 107 (2023) 109901. arXiv:2204.00026 [gr-qc].

It took a while (so many technical challenges…) but we made it! Matt‘s monster paper is finally out!

Let me introduce a fully-fledged pipeline to study populations of gravitational-wave events with deep learning. If it sounds cool, well, it is cool (just look at the flowchart in Figure 1!). We can now perform a hierarchical Bayesian analysis on GW data but, unlike current state-of-the-art applications that rely on simple functional form, we can use populations inferred from numerical simulations. This might sound like a detail but it’s not: it’s necessary to compare GW data directly against stellar physics. While we don’t do that yet here (our simulations are admittedly too simple), there’s a ton of astrophysics already in this paper. Whether you care about neural networks or hierarchical black-hole mergers (or, why not, both!), sit tight, fasten your seatbelt, and read Matt’s paper.

M. Mould, D. Gerosa, S. R. Taylor.
Physical Review D 106 (2022) 103013. arXiv:2203.03651 [astro-ph.HE].

Spinning black holes are weird (well, all black holes are weird but those that spin are the worse!). They have a funny thing called ergoregion where orbiting particles can have negative energy. Penrose was the first to realize that this can be exploited to extract energy from the black hole itself. The thing is, even if you figure out how to do it, you’re inevitably going to spin the black hole down. At the end of the day, you’re left with a fossil black hole that does not have any spin. The mass of that leftover black hole (“ What’s for lunch dear? Fancy some sushi or prefer a black hole?”) is called irreducible mass. Hawking (another giant!) figured out this has to do with thermodynamics.

Long story short, in this paper we compute the irreducible mass of the black holes detected in gravitational waves by LIGO. It was funny to re-discover that gravitational wave detection was indeed the motivation behind Hawking original proof of the area theorem (he had Weber‘s claimed detection in mind at the time). The story behind our paper starts as a toy calculation with my undergraduate student Cecilia and ended up in a neat, hopefully informative exploitation of LIGO data. We reparametrized LIGO’s black-hole properties using the rotational and rotational contributions to their total energy, we ranked current gravitational-wave events according to their “irreversibility”, and we compute a sort of population version of the area law. Enjoy!

D. Gerosa, C. M. Fabbri, U. Sperhake.
Classical and Quantum Gravity 39 (2022) 175008. arXiv:2202.08848 [gr-qc].

Breaking things is fun! In the previous paper of this series, we looked at accretion disks around massive black-hole binaries and found things were going awry. We kept on finding configurations that our implementation could not handle… And now we know this is real! Finding disk solutions when the spin of the black hole has a large misalignment is just not possible! And that’s because the disk really breaks into different sections. We’ve now checked it with state-of-the-art hydrodynamical numerical simulations that not only confirm what we suspected but also show some funny things (like breaking being prevented by disk spirals, etc). I was serious, breaking things is real fun!

Check out Rebecca’s beautiful movies!

R. Nealon, E. Ragusa, D. Gerosa, G. Rosotti, R. Barbieri.
Monthly Notices of the Royal Astronomical Society 509 (2022) 5608–5621. arXiv:2111.08065 [astro-ph.HE].

Great Scott, a new paper! When analyzing gravitational-wave data, looking at one black hole at a time is not enough anymore, the fun part is looking at them all together. The issue Matt and I are tackling here is that one needs to be consistent with putting together different events when fitting the entire population. This is obvious for things that do not change (say the masses of the black holes, those are what they are), but becomes a very tricky business for varying quantities (say the spin directions, which is what we look at here). In that case, it’s dangerous to put together events taken at different stages of their evolution. And the solution to this problem is…. time travel! We show that but propagating binaries backward in time, one can put all sources on the same footing. After that, estimating the impact of the detector requires traveling forward in time, so going “back to the future”. After all, we all know that post-Newtonian black-hole binary integrations look like this:

ps. The v1 title on the arxiv was more explicit… too bad they took it away.

M. Mould, D. Gerosa.
Physical Review D 105 (2022) 024076. arXiv:2110.05507 [astro-ph.HE].

No black hole is an island entire of itself.

We’ve got many gravitational wave events now. One can look at each of them individually (aka “parameter estimation”), all of them together (aka “population”), or each of them individually while they’re together. That’s what we do in this paper: we look at the properties of individual gravitational-wave events in light of the rest of the observed population. The nice thing is that all of these different ways of looking at the data are part of the same statistical tool, which is a hierarchical Bayesian scheme. Careful, heavy stats inside, don’t do this at home.

C. J. Moore, D. Gerosa.
Physical Review D 104 (2021) 083008. arXiv:2108.02462 [gr-qc].

Today we go deep into the perilous world of binary population synthesis! Using Nicola’s code MOBSE, our master student Maciej has implemented some new prescriptions for how supernovae explode and produce compact objects. In practice, we use the compactness (that’s mass over radius) of the stellar core before the explosion to decide if that specific star will form a neutron star or a black hole. This now needs to be compared carefully with gravitational-wave data, but we suggest that there are two key signatures one should look for: the lowest black hole masses and the relative merger rates between black holes and neutron stars.

M. Dabrowny, N. Giacobbo, D. Gerosa.
Rendiconti Lincei 32 (2021) 665–673. arXiv:2106.12541 [astro-ph.HE].

LISA is going to be great and will detect stuff from white dwarfs to those supermassive black-hole that live at the center of galaxies. If we’re lucky (yeah, who knows how many of these we will see), LISA might also detect some smaller black holes, similar to those that LIGO now sees all the time, but at a much earlier stage of their lives. But if we’re indeed lucky, the science we would take home is outstanding. Using simulated data from the LISA Data Challenge we unleash the new amazing parameter-estimation code Balrog (don’t ask what it means, it’s just a name, not one of those surreal astronomy acronyms) at this problem. Dive into the paper for some real data-analysis fun!

R. Buscicchio, A. Klein, E. Roebber, C. J. Moore, D. Gerosa, E. Finch, A. Vecchio.
Physical Review D 104 (2021) 044065. arXiv:2106.05259 [astro-ph.HE].

Who are the parents of LIGO’s black holes? Stars, most likely. Things like those we see in the sky at night will eventually surrender to gravity and collapse. Some of them will form black holes. Some of them will form binary black holes. Some of them will merge. Some of them will be observed by LIGO. That’s the vanilla story at least, but it might not apply to all of the black holes that LIGO sees. For some of those, stars might be the grandparents or the great grandparents. And the parents are … just other black holes! This is today’s paper lead by Vishal Baibhav. Instead of just measuring the properties of the black holes that LIGO observes, we show we can also say something about the features of the black hole parents. Read on to explore the black-hole family tree.

V. Baibhav, E. Berti, D. Gerosa, M. Mould, K. W. K. Wong.
Physical Review D 104 (2021) 084002. arXiv:2105.12140 [gr-qc].

The quest of finding their astrophysical origin of merging black-hole binaries is now a key open problem in modern astrophysics. Stars are the natural progenitor of black holes: at the end of their lives, the core collapses and leaves behind a compact object. But once those “first-generation” black holes are around, they can potentially meet again and form “second generation” LIGO events. I first got interested in this problem in 2017 and, together with many many others researchers in the community, we explored the consequences of this “hierarchical merger” scenario in terms of both gravitational-wave physics and astrophysical environments. In this Nature Astronomy review article, Maya and I tried to condense all this body of work into a few pages. The result is (we hope) a broad and informed overview of this emerging research strand, with a whopping number of more than 270 citations! Hope you like it.

D. Gerosa, M. Fishbach.
Nature Astronomy 5 (2021) 749-760. arXiv:2105.03439 [gr-qc].
Review article. Covered by press release.

Hierarchical mergers are the new black. LIGO is seeing black holes that are just too big to be there. The reason is that stars, which collapse and produce black holes, do some funny things when they get too massive. Notably, they start to spontaneously produce positrons and electrons instead of keeping their own photons. Long story short: those missing photons make the temperature go up, ignite an explosion that disrupts the core and prevents black-hole formation. This “mass gap” is a solid prediction from our astrophysics friends. In some previous papers, we and other groups pointed out that one can bypass stars and form black holes from previous black holes (and goodbye my dear maximum mass limit!). But now our astrophysics friends are telling us they can also evade the limit with some more elaborate astro-magic (winds, rotation, dredge-up, reaction rates, accretion). Today’s paper is about telling the two apart, with a key prediction: a black hole with large mass but low spin would raise a glass to the astro-wizards.

D. Gerosa, N. Giacobbo, A. Vecchio.
Astrophysical Journal 915 (2021) 56. arXiv:2104.11247 [astro-ph.HE].

General Relativity works well. But we still want to test it, and I guess that’s because it actually works too well (you know, all those quantum things that don’t really fit, etc). And we want to test it with gravitational-wave data, and not just because it’s the new cool thing to do (though it is!) but also because they gravitational waves give us insight into the strong-field regime of gravity where new things, if they are there at all, should show up. Now, all of this sounds great but, in practice, one has to deal with the actual model used to analyze the data. Errors in these signal models (aka waveforms), which are somewhat inevitable, can trick us into thinking we have seen a deviation from General Relativity. So, before you go out on the street and shout that Einstein was wrong, keep calm and mind your waveform.

ps. The codename for this paper was SANITY: S ystemA tics usiN g populatI ons to T est general relativitY.

C. J. Moore, E. Finch, R. Buscicchio, D. Gerosa.
iScience 24 (2021) 102577. arXiv:2103.16486 [gr-qc].

Other press coverage: indiescience, sciencedaily, phys.org, astronomy.com, physicsworld.

Here is the latest in our (by now long) series of papers on black-hole binaries spin precession. This work was is championed by two outstanding PhD students, Daria (in my group) and Nate (UT Dallas). The key idea behind this paper is that, for black-hole spins, one cannot really talk about precession without talking about nutation (although we only say “precession” all the time…). The spin of, say, the Earth also does both precession (azimuthal motion) and nutation (polar motion). But, unlike in the Earth problem, for black-hole spins the two motions happen on roughly the same timescale meaning that you cannot really take them apart. Or can you? We stress the role of five parameters that characterize the combined phenomenology of precession and nutation. The hope is now to use them as building blocks for future waveforms… stay tuned!

ps. Stupid autocorrect! It’s nutation, not mutation.

D. Gangardt, N. Steinle, M. Kesden, D. Gerosa, E. Stoikos.
Physical Review D 103 (2021) 124026. arXiv:2103.03894 [gr-qc].

Orbital eccentricity in gravitational-wave observations has been long neglected. And with good reasons! Gravitation-wave emission tends to circularize sources. By the time black holes are detectable by LIGO/Virgo/LISA/whatever, they should have had ample time to become circular. Unless something exciting goes on in their formation, things like clusters, triples, Kozai-Lidov oscillations, etc. And if that happens, we want to see it! This paper contains the first model for gravitational waveforms and black-hole remnants (final mass, spin) trained directly on eccentric numerical relativity simulations. Because eccentric is the new circular.

T. Islam, V. Varma, J. Lodman, S. E. Field, G. Khanna, M. A. Scheel, H. P. Pfeiffer, D. Gerosa, L. E. Kidder.
Physical Review D 103 (2021) 064022. arXiv:2101.11798 [gr-qc].

Up-down instability S01-E03.
“Previously on the up-down instability. After finding out that the instability exists (S01-E01) and calculating its analytic endpoint (S01-E02), one terrifying prospect remains. What if it’s just PN? Can all of this disappear in the strong-field regime? This challenge now needs to be faced”.

Today’s paper is the latest in our investigations of the up-down instability in binary black holes. If the primary black hole is aligned and the secondary is anti-aligned to the orbital angular momentum, the entire system is unstable to spin precession. We found this funny thing using a post-Newtonian (read: approximate) treatment but we couldn’t be 100% sure that this would still be true when the black holes merge and our approximation fails. So, we got our outstanding SXS friends on board and ask them if they could see the same effect with their numerical relativity (read: the real deal!) code. And the answer is… yes! The instability is really there! And by the way, these are among the longest numerical relativity simulations ever done.

V. Varma, M. Mould, D. Gerosa, M. A. Scheel, L. E. Kidder, H. P. Pfeiffer.
Physical Review D 103 (2021) 064003. arXiv:2012.07147 [gr-qc].

Spin precession is cool, and we want to measure it. In General Relativity, the orbital plane of a binary is not fixed but moves around. This effect is related to the spin of the orbiting black holes and contains a ton of astrophysical information. The question we try to address in this paper is the following: how does one quantify “how much” precession a system has? This is typically done by condensing information into a parameter called \(\chi_{\rm p}\), which is here generalize to include two- spin effects. There are two black holes in a binary and we received numerous complaints from the secondaries: they want to join the gravitational-wave fun!

D. Gerosa, M. Mould, D. Gangardt, P. Schmidt, G. Pratten, L. M. Thomas.
Physical Review D 103 (2021) 064067. arXiv:2011.11948 [gr-qc].

And here is the latest episode in the series of our massive scalar-tensor gravity papers… After stellar collapse, we now look at how neutron stars look like in this strange theory of gravity (recap: “massive scalar-tensor” means that gravity is mediated by the usual metric plus a scalar field which as a mass). Result: not only the theory is strange, stars are strange too! If you want to get a neutron star of 40 solar masses, look no further, massive scalar-tensor is the theory for you. More seriously, we explore all the different families of static solutions, highlighting a remarkable phenomenology. This is the kind of predictions we need to test gravity with astrophysical sources!

R. Rosca-Mead, C. J. Moore, U. Sperhake, M. Agathos, D. Gerosa.
Symmetry 12 (2020) 1384. arXiv:2007.14429 [gr-qc].

And here is my latest lockdown effort: some experiments in the wonderful and perilous world of machine learning. The idea of this paper is to teach a computer to figure out by itself if a gravitational-wave signal will be detectable or not. The problem is very similar to that of image recognition: much like classifying if an image is more likely to contain a dog or a cat, here we classify black-hole mergers based on the imprints they have in the LIGO and Virgo detectors. This is important to quantify the so-called “selection effects”: in order to figure out what the Universe does based on what we observe, we need to know very well “how” we observe and thus what we are going to miss. Our code is built using Google’s TensorFlow and it is public on Github, feel free to play with it!

D. Gerosa, G. Pratten, A. Vecchio.
Physical Review D 102 (2020) 103020. arXiv:2007.06585 [astro-ph.HE].

Supermassive black hole inspiral and spin evolution are deeply connected. In the early stages when black holes are brought together by star scattering and accretion, spin orientations can change because of interactions with the environment. Later on, when gravitational waves are driving the mergers, spins change because of relativistic couplings. In this paper we try to follow this complicated evolution in a full cosmological framework, using products of the Illustris simulation suite, a new sub-resolution model, and post-Newtonian integrations.

M. Sayeb, L. Blecha, L. Z. Kelley, D. Gerosa, M. Kesden, J. Thomas.
Monthly Notices of the Royal Astronomical Society 501 (2021) 2531-2546. arXiv:2006.06647 [astro-ph.GA].

If General Relativity is too boring, couple it to something else. In this paper we study what happens to stellar collapse and supernova explosions if gravity is transmitted not only with the usual metric of Einstein’s theory (aka the graviton) but also an additional quantity. If this extra scalar field has a mass, it dramatically impacts the emitted gravitational waves… Which means that maybe, one day, one can use gravitational-wave data to figure out if scalar fields are coupled to gravity. Here we try to explore all the related phenomenology of stellar collapse with a large set of simulations covering the parameter space. And the overall picture is remarkably neat and simple!

R. Rosca-Mead, U. Sperhake, C. J. Moore, M. Agathos, D. Gerosa, C. D. Ott.
Physical Review D 102 (2020) 044010. arXiv:2005.09728 [gr-qc].

The latest news from our LIGO/Virgo friends (including some colleagues here in Birmingham) was an astrophysical surprise. The black-hole binary GW190412 is just different from every other one we have had so far. One of the two black holes is about three times larger than the other one, it’s spinning relatively fast, and that spin might even be misaligned with respect to the binary axis. That’s a lot of new things, which makes this event very challenging (but we like challenges!) to be explained with a coherent astrophysical setup. That’s what I meant by an astrophysical surprise. Today’s paper is our attempt to, first of all, quantify that GW190412 is indeed very unusual. Maybe it comes from a second-generation merger (that is, an event where one of the two black holes is the result of a previous merger). This might explain its features, but then the astrophysical host must be very unusual. So, yet another challenge.

D. Gerosa, S. Vitale, E. Berti.
Physical Review Letters 125 (2020) 101103. arXiv:2005.04243 [astro-ph.HE].
Covered by press release.

Press release : Birmingham, MIT.
Other press coverage: International Business Times, SciTechDaily, VRT, notimerica, allnewsbuzz, canaltech.

A black-hole binary starts its life as two single black holes, and finish it as a single black hole. In between there’s all the complicated dynamics predicted by General Relativity: many orbits, dissipation of energy via gravitational waves, spins that complicate the whole business, and finally the merger which leaves behind a remnant. In this paper we put together different techniques to map this entire story beginning to end, connecting the two asymptotic conditions of a black-hole binary. This work started as a summer project of my student Luca: well done!

L. Reali, M. Mould, D. Gerosa, V. Varma.
Classical and Quantum Gravity 37 (2020) 225005. arXiv:2005.01747 [gr-qc].

New paper today! We’ve been working on this for a very long time but three weeks of lockdown forced us to finish it. It’s about distorted (aka warped) accretion discs surrounding black holes. If the black hole is spinning and part of a binary system, the disc behaves in a funny way. First, it’s not planar but warped to accomodate these external disturbances. Second, disc and black hole interacts and tend to reach some mutual agreement where the disc is flat and the black-hole spin is aligned. We find it’s not that easy and things are actually much more complicated: read the paper to know more about non-linear fluid viscosities, critical obliquity, mass depletion, etc.

ps. Here is a Twitter thread by P. Armitage.

D. Gerosa, G. Rosotti, R. Barbieri.
Monthly Notices of the Royal Astronomical Society 496 (2020) 3060-3075. arXiv:2004.02894 [astro-ph.GA].

We’ve been knowing about the mass gap for a while, but I bet “spin gap” sounds new to you, uh? The gap in the spectrum of binary black hole masses is due to pair-instability supernovae (i.e. what happens if a giant ball of carbon and oxygen burns all at the same time). As for the spin gap, it might be that stars collapse into black holes which have a tiny tiny spin. But that’s only for black holes that come from stars: those come out of the merger of other black holes, on the other hand, are very rapidly rotating. So, there’s a gap between these two populations. Our paper today shows that, together, mass gap and spin gap are powerful tools to figure out where black holes come from. Cluster or field? Gaps will tell.

V. Baibhav, D. Gerosa, E. Berti, K. W. K. Wong, T. Helfer, M. Mould.
Physical Review D 102 (2020) 043002. arXiv:2004.00650 [gr-qc].

Sometimes you have to look into things twice. We found the up-down instability back in 2015 and still did not really understand what was going on. Three out of four black hole binaries with spins aligned to the orbital angular momentum are stable (in the sense that the spins stay aligned), but one is not. The impostors are the “up-down” black holes –binaries where the spin of the big black holes is aligned and the spin of the small black hole is antialigned. These guys are unstable to spin precession: small perturbation will trigger large precession cycles. Matt’s paper today figures out what’s the fate of these runaways. We find that these binaries become detectable in LIGO and LISA with very specific spin configurations: the two spins are aligned with each other and equally misaligned with the orbital angular momentum. There’s a lot of interesting maths in this draft (my first paper with a proof by contradiction!) as well as some astrophysics (for you, AGN disks lover).

M. Mould, D. Gerosa.
Physical Review D 101 (2020) 124037. arXiv:2003.02281 [gr-qc].

The Milky Way, our own Galaxy, is not alone. We’re part of a galaxy cluster, but closer in we have some satellites. The bigger ones are the Large and Small Magellanic Clouds (which unfortunately I’ve never seen because they are in the southern hemisphere) but also other smaller ones: faint groups of stars in the outskirts of the Milky Way. Much like all galaxies, these faint satellites will have white dwarfs, those white dwarf will form binaries, which will be observable by LISA. There’s a new population of gravitational-wave sources there waiting to be discovered!

ps. The second half of the story is here.

V. Korol, S. Toonen, A. Klein, V. Belokurov, F. Vincenzo, R. Buscicchio, D. Gerosa, C. J. Moore, E. Roebber, E. M. Rossi, A. Vecchio.
Astronomy & Astrophysics 638 (2020) A153. arXiv:2002.10462 [astro-ph.GA].

The LISA data analysis problem is going to be massive: tons of simultaneous sources all together at the same time. In Birmingham we are developing a new scheme to tackle the problem, and here are the first outcomes. We populate satellite galaxies of the Milky Way with double white dwarfs and show that LISA… can actually do it! LISA will detect these guys, tell us which galaxies they come from, etc. It might even discover new small galaxies orbiting the Milky Way! Surprise, surprise, LISA is going to be amazing…

ps. Here is the first half of the story.

ps2. The code still needs a name. Suggestions?

E. Roebber, R. Buscicchio, A. Vecchio, C. J. Moore, A. Klein, V. Korol, S. Toonen, D. Gerosa, J. Goldstein, S. M. Gaebel, T. E. Woods.
Astrophysical Journal 894 (2020) L15. arXiv:2002.10465 [astro-ph.GA].

LISA is going to be cool. And not just for your astro-related dreams. Theoretical physicists can have fun too! This community-wide manifesto illustrates just how cool things are going to be with LISA. LISA will constitute a major milestone to test gravity, cosmology, the nature of black holes, etc. A big thanks to all those involved.

E. Barausse, et al. (320 authors incl. D. Gerosa).
General Relativity and Gravitation 52 (2020) 8, 81. arXiv:2001.09793 [gr-qc].

Today’s paper is about superkicks. These are extreme configurations of black hole binaries which receive a large recoil. Black hole recoils work much like those of, say, a cannon. As the cannonball flies, the cannon recoils backwards. Here the binary is shooting gravitational waves: as they are emitted, the system recoils in the opposite direction. In this paper we show that superkicks might be up to 25% larger if the binary is mildly eccentric. This means it’s a bit easier to kick black holes out of stellar clusters and galaxies.

U. Sperhake, R. Rosca-Mead, D. Gerosa, E. Berti.
Physical Review D 101 (2020) 024044. arXiv:1910.01598 [gr-qc].

Gravitational-wave astronomy is, seems obvious to say, about doing astronomy with gravitational waves. One has gravitational-wave observations (thanks LIGO and Virgo!) on hand and astrophysical models on the other hand. The more closely these two sides interact, the more we can hope to use gravitational-wave data to learn about the astrophysics of the sources. Today’s paper with JHU student Kaze Wong tries to further stimulate this dialog. And, well, one needs to throw some artificial intelligence in the game. There are three players now (astrophysics, gravitational waves, and machine learning) and things get even more interesting.

ps. The nickname of this project was sigmaspops

K. W. K. Wong, D. Gerosa.
Physical Review D 100 (2019) 083015. arXiv:1909.06373 [astro-ph.HE].

What’s in between neutron stars and black holes? It looks like neutron stars have a maximum mass of about 2 solar masses while black holes have a minimum mass of about 5. So what’s in between? That’s the popular issue of the ‘low mass gap’. Actually, now we know something must be in there. LIGO and Virgo have seen GW170817, a merger of two neutron stars, which merged in to a black hole with the right mass to populate the gap. Can this population be seen directly with (future) gravitational-wave detectors? That’s today’s paper.

A. Gupta, D. Gerosa, K. G. Arun, E. Berti, W. Farr, B. S. Sathyaprakash.
Physical Review D 101 (2020) 103036. arXiv:1909.05804 [gr-qc].

Funny things happen in supernova explosions. Funny and complicated. If the star is too massive, the explosion is unstable. The black hole it formed it not as massive as it could have been. In gravitational-wave astronomy, this means that we should not observe black holes heavier than about 50 solar masses. This does not apply, of course, to black holes that are not formed from stars, but from other black holes (yes! more black holes!). If black holes resulting from older gravitational wave events somehow stick around, they could be recycled in other generations of mergers. We point out that this can work only if their astrophysical environment is dense enough. Can we measure the escape speed of black holes “nurseries” using gravitational-wave events that should not be there because of supernova instabilities?

D. Gerosa, E. Berti.
Physical Review D 100 (2019) 041301R. arXiv:1906.05295 [astro-ph.HE].
Covered by press release.

Press release : Birmingham.
Other press coverage: Scientific American, astrobites, interestingengineering, metro.co.uk, Media INAF, Great Lakes Ledger, sciencealert, sciencetimes, mic.com.

LIGO and Virgo are up and running like crazy. They started their third observing run (O3) and in just a few months doubled the catalogs of observing events. And there’s so much more coming! In this paper we try to work out “how much” using our astrophysical models. Figure 4 is kind of shocking: we’re talking about thousands of black holes in a few years, and millions of them in 20 years. Need to figure out what to do with them…

V. Baibhav, E. Berti, D. Gerosa, M. Mapelli, N. Giacobbo, Y. Bouffanais, U. N. Di Carlo.
Physical Review D 100 (2019) 064060. arXiv:1906.04197 [gr-qc].

Spoiler alert: this paper is a bit sad.

Stellar-mass black-hole binaries are now detected by LIGO on a weekly basis. It would be really cool if LISA (a future space mission targeting low-frequencies gravitational waves) could see them as well. We could do a lot of cool stuff, in both the astro and the theory side of things. In today’s paper, we try to figure out how easy or hard it will be to extract these signals from the LISA noise. Well, it’s hard. In terms of the minimum signal-to-noise ratio required, we find that this is as high as 15. The number of expected detection becomes discouragingly low unless the detector behaves a bit better at high frequencies or black holes with 100 solar masses start floating around.

C. J. Moore, D. Gerosa, A. Klein.
Monthly Notices of the Royal Astronomical Society 488 (2019) L94-L98. arXiv:1905.11998 [astro-ph.HE].

Where do black holes come from? Sounds like a scify book title, but it’s real. These days, that’s actually the million dollar question in gravitational-wave astronomy. LIGO sees (lots of!) black holes in binaries, and those data encode information on how their stellar progenitors behave, what they like or did not like to do. This is paper is the latest attempt to understand if black holes formed alone (i.e. a single binary star forms a single binary black hole) or together (i.e. many stars exchange pairs in dense stellar environments).

Y. Bouffanais, M. Mapelli, D. Gerosa, U. N. Di Carlo, N. Giacobbo, E. Berti, V. Baibhav.
Astrophysical Journal 886 (2019) 25. arXiv:1905.11054 [astro-ph.HE].

Surrogate models are the best of both worlds. Numerical-relativity simulations are accurate but take forever. Waveform models have larger errors but can be computed cheaply, which means they can be used in the real world and compared with data. Surrogates are as fast as the approximate waform models, but as accurate as the numerical-relativity simulations they are trained on. Don’t believe me? I don’t blame you, this does sound impossible. Check out our new paper, where we pushed this effort to binaries with spins and more unequal masses.

V. Varma, S. E. Field, M. A. Scheel, J. Blackman, D. Gerosa, L. C. Stein, L. E. Kidder, H. P. Pfeiffer.
Physical Review Research 1 (2019) 033015. arXiv:1905.09300 [gr-qc].

The prospect of multiband gravitational-wave astronomy is so so so exciting (I mean, really!). So exciting that we want to make sure once again it’s true; and this is today’s paper. Multiband means seeing the same black hole binary with both LIGO at high frequencies and LISA at low frequencies. LISA observations can serve as precursors for the LIGO mergers, and you can a whole lot of new science (astrophysics, tests of GR, smart data analysis, cosmology, etc). Here we have a new semi-analytic way to estimate the rate (i.e. how many) of multiband events, and we also explore some of the stellar physics one could constraint with them. Enjoy!

D. Gerosa, S. Ma, K. W. K. Wong, E. Berti, R. O’Shaughnessy, Y. Chen, K. Belczynski.
Physical Review D 99 (2019) 103004. arXiv:1902.00021 [astro-ph.HE].

As you can imagine, I’m kind of obsessed with black hole binaries. So easy (let’s face it, a black hole is easy! Just mass and spin), but at the same time so terribly complicated… Happy to present our attempt to see the binary dynamics in real time. Technical blah blah: we attach a visualization tool to a numerical relativity surrogate model. Are you ready to be a binary black hole explorer? Here!

ps. Folks are having fun with this! From mikesmathpage.

V. Varma, L. C. Stein, D. Gerosa.
Classical and Quantum Gravity 36 (2019) 095007. arXiv:1811.06552 [astro-ph.HE].

Latest in the series of our spin-precession papers, here we found a thing that was worthy of a new name: wide nutation(we had wide precession before, but this is better). These are black-hole binary configurations where the angle between any of the two spins and the orbital angular momentum changes a lot. Can’t change more actually: spins goes from full alignment to full anti-alignment. And they do it many times.

We found this wide precession during Alicia’s SURF undergraduate summer project at Caltech!

D. Gerosa, A. Lima, E. Berti, U. Sperhake, M. Kesden, R. O’Shaughnessy.
Classical and Quantum Gravity 36 (2019) 105003. arXiv:1811.05979 [gr-qc].

Black hole mergers are like a scattering problem. Two black holes come in, and one black hole comes out. The difference is a bunch of gravitational waves. Those are nice, of course, but the remnant black hole is important too! Here we provide accurate predictions of the mass, spin and kick of this remnant given the properties of the two merging black holes. If you need those numbers (want to build a waveform family? or test GR perhaps?) just use our python module surfinBH!

And what if you collide ducks instead of black holes?

V. Varma, D. Gerosa, L. C. Stein, F. H’ebert, H. Zhang.
Physical Review Letters 122 (2019) 011101. arXiv:1809.091259 [gr-qc].\

Press release: Caltech, Ole Miss.
Other press coverage: Space Daily, phys.org, longroom, tasnim, europapress (Spanish), Media INAF (video in Italian).

We all know Doppler shifts, right? That’s like the biibouuubiiiiboouuuuuu of an ambulance. That happens to gravitational waves as well. Suppose you have a merging binary which is emitting gravitational waves (bibooou). If that binary is going somewhere (say it’s falling into the gravitational potential of a third body), much like the ambulance, the emitted signal will be Doppler shifted. This paper shows a very nice calculation to incorporate Doppler shifts into gravitational waves.

This started out as Katie’s undergraduate summer project at Caltech. Congrats Katie!

K. Chamberlain, C. J. Moore, D. Gerosa, N. Yunes.
Physical Review D 99 (2019) 024025. arXiv:1809.04799 [gr-qc].

Today’s paper celebrates the wedding of startrack and precession (the nickname for this project was pretrack 😉 ). We use population synthesis evolution from startrack to predict the parameters of spinning black-hole binaries observed by LIGO. The spin distribution is then propagated from formation to detection using post-Newtonian evolutions from my precession code. The bottom line is that spin measurements can be used to truly reconstruct the binary formation channels, and some specific mechanisms (like mass transfers, tides, natal kicks, supernova’s instabilities etc.). Our database is publicly available (play with it!), as well as a little code to compute gravitational-wave detectabilities.

Update : I think this is my 25th published paper!

D. Gerosa, E. Berti, R. O’Shaughnessy, K. Belczynski, M. Kesden, D. Wysocki, W. Gladysz.
Physical Review D 98 (2018) 084036. arXiv:1808.02491 [astro-ph.HE].

LISA is going to be amazing: supermassive black-holes, galactic white dwarfs, EMRIs… Besides all of that, LISA can help us doing LIGO’s science better. Some LIGO sources (notably, things like GW150914) will show up in LISA years in advance. LISA is going to tell us when (in time) and where (in frequency) LIGO will see these sources. In this paper, we explore the idea of adapting the LIGO noise curve if one knows that a source is coming in (because LISA told us). We apply this idea to ringdown tests of GR, and show how powerful they become.

R. Tso, D. Gerosa, Y. Chen.
Physical Review D 99 (2019) 124043. arXiv:1807.00075 [gr-qc].

Other press coverage: astrobites.

Gravitational-wave astronomy is moving. Quickly. In a few years we are going to have large catalogs of many detections, and a whole lot of information to extract from them. Instead of focussing on parameters (masses, spins, redshifts) of single sources, we will want to extract hyperparameters describing physical features of the population (metallicity, natal kicks, common envelope, stellar winds, etc). Here we show how to do this in practice: read our new paper for an amazing journey through hyperlateral cubes, Gaussian process emulators, selection biases, hierarchical modeling and more.

Our tools are publicly available! Here is Steve’s Webpage and our public code.

S. R. Taylor, D. Gerosa.
Physical Review D 98 (2018) 083017. arXiv:1806.08365 [astro-ph.HE].

Editor’s coverage in APS’s Kaleidoscope.

This is a massive review born out of the European COST Action CA16104 Gravitational waves, black holes and fundamental physics (GWverse). We summarize the status of the field of gravitational-wave astronomy and lie down a roadmap for the immediate future.

L. Barack, et al. (199 authors incl. D. Gerosa).
Classical and Quantum Gravity 36 (2019) 143001. arXiv:1806.05195 [gr-qc].

Editor’s coverage in physicsworld.com.

LIGO can measure spins. Well, effective spins actually. These are special combinations of the two spins (magnitude and direction) and the binary mass ratio. There’s a ton of astrophysics that can be done just with this quantity, but one should always be careful. Today’s paper points out a few important shortcomings when dealing with effective spin measurements. Want to know more about asymmetries and selection biases?

ps. You can hardly find a better day to post a paper on the arxiv than May 4th

K. K. Y. Ng, S. Vitale, A. Zimmerman, K. Chatziioannou, D. Gerosa, C.-J. Haster.
Physical Review D 98 (2018) 083007. arXiv:1805.03046 [gr-qc].

Surrogate models are fancy interpolation schemes developed to provide accurate (well, really accurate) waveforms directly from numerical relativity simulations. The first surrogate able to model fully precessing systems came up recently (and it’s really an amazing piece work!). Here we exploit these advances to explore how linear momentum is emitted in generic black-hole mergers, and well as its back-reaction. Black holes get kicked!

D. Gerosa, F. H’ebert, L. C. Stein.
Physical Review D 97 (2018) 104049. arXiv:1802.04276 [gr-qc].

Natal kicks imparted to neutron stars and black holes at birth can be constrained using LIGO data. Kicks cause misalignments between the spins and the orbital angular momentum. Here we compare large banks of population synthesis simulations to LIGO data using hierarchical Bayesian statistics and show that (already with 4 events!) natal kicks are constrained from both above and below. Simulated binaries are produced merging Startrack evolutions to my precession code. More on this very soon…

Update : here it is!

D. Wysocki, D. Gerosa, R. O’Shaughnessy, K. Belczynski, W. Gladysz, E. Berti, M. Kesden, D. Holz.
Physical Review D 97 (2018) 043014. arXiv:1709.01943 [astro-ph.HE].

Supernova can be used to test gravity! …and if there’s a massive scalar field around, things get terribly interesting. Here we generalize arXiv:1602.06952 to study stellar collapse in massive scalar-tensor theories of gravity (that is, the graviton is coupled to a massive scalar field) with numerical simulations. The scalar-field mass introduces a dispersion relation, and different GW frequencies travel at different speeds. It might even make sense to target historic supernovae: maybe the tail of the signal is still coming to us!

U. Sperhake, C. J. Moore, R. Rosca, M. Agathos, D. Gerosa, C. D. Ott.
Physical Review Letters 119 (2017) 201103. arXiv:1708.03651 [gr-qc].

Bayesian statistics is really cool. It lets you specify clearly and openly all the assumptions that enter an analysis. What’s the effect of these prior assumptions on current inference with gravitational-wave data from black-hole binaries? Here we tackle this question head-on, and perform parameter estimation runs on LIGO data with many (astrophysically motivated!) prior assumptions. Some parameters (like chirp mass) do not suffer from prior choices but others (like the effective spin) do! Specifying the astrophysics as priors is a powerful tool to extract more science from GW data

Update : at the time of publication, this was the first independent reanalysis of any GW data! (There are many more now…). Also, use our data for your research!

S. Vitale, D. Gerosa, C.-J. Haster, K. Chatziioannou, A. Zimmerman.
Physical Review Letters 119 (2017) 251103. arXiv:1707.04637 [gr-qc].

Looks like some of the LIGO black holes have low spins (better, low effective spins). In this paper we show these values can be accommodated with standard “field binaries”, i.e. formation channels where binary black holes form from binary stars.

K. Belczynski, J. Klencki, C. E. Fields, A. Olejak, E. Berti, G. Meynet, C. L. Fryer, D. E. Holz, R. O’Shaughnessy, D. A. Brown, T. Bulik, S. C. Leung, K. Nomoto, P. Madau, R, Hirschi, E. Kaiser, S. Jones, S. Mondal, M. Chruslinska, P. Drozda, D. Gerosa, Z. Doctor, M. Giersz, S. Ekstr:om, C. Georgy, A. Askar, V. Baibhav, D. Wysocki, T. Natan, W. M. Farr, G. Wiktorowicz, M. C. Miller, B. Farr, J.-P. Lasota.
Astronomy & Astrophysics 636 (2020) A104. arXiv:1706.07053 [astro-ph.HE].

Part of our series of spin precession papers, here we study nutational resonances. Those are configurations where the precession of L about J, and that of the two spins are in resonance with each other. These configurations are very generic (virtually every binary will go through resonances), but their effect on the dynamics seems to be small, unless… unless you end up in transitional precession! Transitional precession (great paper!) turns out to be a very special nutational resonance.

X. Zhao, M. Kesden, D. Gerosa.
Physical Review D 96 (2017) 024007. arXiv:1705.02369 [gr-qc].

Black-hole data can be used to probe the lives of stars. That’s the promise of gravitational-wave astronomy, right? Here we give it a go. We present a (admittedly) very simple model showing that the misalignment of GW151226 can be easily explained with large natal kicks. I like simple things…

R. O’Shaughnessy, D. Gerosa, D. Wysocki.
Physical Review Letters 119 (2017) 011101. arXiv:1704.03879 [gr-qc].
APS Editor’s choice (physics.aps.org). Covered by press release.

Press release : Rochester Institute of Technology, Caltech’s tweet.
Editor’s coverage in physics.aps.org.
Other press coverage: IOP’s physicsworld.com, Science Daily, Phys.org, astronomy.com, sciencenews, iflscience.

What if the black holes LIGO sees are the results of a merger? I mean, we see mergers, but maybe those are second-generation ones, and the two merging black holes come from first-generation mergers. Or (more likely…) stellar mass black holes form from stars and only merge once…

D. Gerosa, E. Berti.
Physical Review D 95 (2017) 124046. arXiv:1703.06223 [gr-qc].
PRD Editors’ Suggestion.

Other press coverage: Ars Technica.

Equal-mass binaries correspond to a discontinuous limit in the spin precession equations. A new constant of motion pops up, which can be exploited to study the dynamics. This is a really neat calculation done with Jakub, a Cambridge undergraduate student. Also, my first paper at Caltech!

D. Gerosa, U. Sperhake, J. Vosmera.
Classical and Quantum Gravity 34 (2017) 064004. arXiv:1612.05263 [gr-qc].

Black hole kicks are cool: powerful (up to thousands of km/s!) recoils that black holes receive following a merger. Here we show these events might leave an imprint on the emitted gravitational waves, which is potentially detectable by future interferometers.

D. Gerosa, C. J. Moore.
Physical Review Letters 117 (2016) 011101. arXiv:1606.04226 [gr-qc].
PRL Editors’ Suggestion. Covered by press release.

Press release : Cambridge University, Cambridge Center for Theoretical Cosmology
Other press coverage: astrobites, particlebites, Daily Mail, phys.org, Particle Bites, egno.gr, Daily Galaxy, Register, Media INAF, IneffableIsland, AstronomyNow, Accademia delle Stelle, noticiasdelaciencia, Cambridge TV.

Here we present my numerical code precession, which implements our multi-timescale way to look at spinning black-hole binaries. The paper has a detailed description of the various functions as well as lots of examples.

D. Gerosa, M. Kesden.
Physical Review D 93 (2016) 124066. arXiv:1605.01067 [astro-ph.HE].
Open source code.

Here we present 1+1 numerical-relativity simulation of stellar collapse in scalar-tensor theories, where gravity is mediated by the usual metric coupled to an additional scalar field. Bottom line: you can test General Relativity with supernovae explosions!

D. Gerosa, U. Sperhake, C. D. Ott.
Classical and Quantum Gravity 33 (2016) 135002. arXiv:1602.06952 [gr-qc].

This is a follow up of arXiv:1403.7147, just done better. Instead of overlaps, we do real injections in LIGO parameter-estimation codes to show that spin-orbit resonances are indeed detectable.

D. Trifiro’, R. O’Shaughnessy, D. Gerosa, E. Berti, M. Kesden, T. Littenberg, U. Sperhake.
Physical Review D 93 (2016) 044071. arXiv:1507.05587 [gr-qc].

Here we study the stability of black-hole binaries with spins (anti)aligned with the orbital angular momentum. Aligned configurations are points of equilibrium, but are they stable? If the heavier black-hole is aligned and the lighter one is anti-aligned, this turns out to be unstable! And the onset of this instability can be in the LIGO or LISA band!

D. Gerosa, M. Kesden, R. O’Shaughnessy, A. Klein, E. Berti, U. Sperhake, D. Trifiro’.
Physical Review Letters 115 (2015) 141102. arXiv:1506.09116 [gr-qc].
PRL Editors’ Suggestion.

Detailed analysis of 2PN black-hole binary spin precession using multi-timescale methods. Follow-up of the Letter arXiv:1411.0674, this paper contains the full calculation and the description of the underlying phenomenology.

D. Gerosa, M. Kesden, U. Sperhake, E. Berti, R. O’Shaughnessy.
Physical Review D 92 (2015) 064016. arXiv:1506.03492 [gr-qc].

What happens if you throw a scalar field into General Relativity? And if you throw more than one? Here is a paper on the phenomenology of neutron stars in theories with more than one scalar field coupled to gravity.

M. Horbatsch, H. O. Silva, D. Gerosa, P. Pani, E. Berti, L. Gualtieri, U. Sperhake.
Classical and Quantum Gravity 32 (2015) 204001. arXiv:1505.07462 [gr-qc].
IoP Editor’s choice (CQG++, IOPselect).

Supermassive black holes in binaries and their accretion discs… Spins align on some timescale, but migration also takes place. Do gas discs have enough time to align the spins? Well, the secret is the mass ratio: light secondaries might prevent primaries from aligning. A great collaboration between gravitational-wave and planet researchers!

D. Gerosa, B. Veronesi, G. Lodato, G. Rosotti.
Monthly Notices of the Royal Astronomical Society 451 (2015) 3941-3954. arXiv:1503.06807 [astro-ph.GA].

A massive review on testing gravity, which came out of a nice meeting we had at University of Mississippi in January 2014. See the numbers.

E. Berti, et al. (53 authors incl. D. Gerosa).
Classical and Quantum Gravity 32 (2015) 243001. Topical Review. arXiv:1501.07274 [gr-qc].

2PN black-hole binary spin precession works exactly like Kepler’s two-body problem. Not kidding: just define effective potentials and divide the phase space into morphologies. The only things you need are a few timescales to play with.

M. Kesden, D. Gerosa, R. O’Shaughnessy, E. Berti, U. Sperhake.
Physical Review Letters 114 (2015) 081103. arXiv:1411.0674 [gr-qc].
Covered by press release.

Press release : Cambridge University, Cambridge Center for Theoretical Cosmology, Ole Miss, UT Dallas.
Other press coverage: Science Daily, phys.org, phys.org (2), Media INAF, Astroblogs, RIA, Daily News, Science World Report, Tech Times, Tech Times (2), SpaceRef, Space Daily, ECN, R&D, Daily Galaxy, scitechdaily, nanowerk.

Black-hole kicks are powerful. I mean, really powerful. They can even eject supermassive black holes from the heavier galaxies in our Universe. And then these galaxies are left “empty”.

D. Gerosa, A. Sesana.
Monthly Notices of the Royal Astronomical Society 446 (2015) 38-55. arXiv:1405.2072 [astro-ph.GA].

Spinning black-hole binaries might belong to two spin-orbit resonances, or families. Can you tell them apart using gravitational-wave observations? Spoiler: yes!

Bonus note: check out the title in v1 on the arxiv…

D. Gerosa, R. O’Shaughnessy, M. Kesden, E. Berti, U. Sperhake.
Physical Review D 89 (2014) 124025. arXiv:1403.7147 [gr-qc].

Spin precession in stellar-mass black hole binaries encodes information on specific formation mechanisms like tides and mass transfers. My first paper on spin precession…

D. Gerosa, M. Kesden, E. Berti, R. O’Shaughnessy, U. Sperhake.
Physical Review D 87 (2013) 10, 104028. arXiv:1302.4442 [gr-qc].

My very first paper was on alignment between supermassive black holes and their accretion disks. Maybe it takes a bit longer…

G. Lodato, D. Gerosa.
Monthly Notices of the Royal Astronomical Society 429 (2013) L30-L34. arXiv:1211.0284 [astro-ph.CO].