From summer 2022 to summer 2023, I will be taking a sabbatical leave from RIT to focus more fully on research. The Simons Foundation's Simons Fellow program generously is providing support to extend to a full year's sabbatical. I look forward to visiting colleagues in California and New York, and to focus fully
on research directions afforded by impending gravitational wave and multimessenger observations.

LIGO, Virgo, and KAGRA provide a comprehensive report and discussion of the compact binaries found during the third observing run.
We've found a lot this run: neutron star black hole binaries (GW200105 and 200115); big black holes (GW190521); and several binaries likely containing neutron stars. We've learned a lot about what nature produces in our local universe, and even a little about how the faraway universe looks somewhat different than the universe nearby. (Short version: more mergers as we go back in time, so far.)

This carefully conducted census of merging objects in the nearby universe reveals some interesting surprises. We find neutron stars in merging binaries can have a wide range of masses, unlike the neutron stars in merging binaries in our own galaxy. Conversely, we find certain types of binary black holes are more likely than others with comparable masses. We're able to measure the merger rate versus mass over the whole mass plane LIGO's sensitive to, letting us paint a single picture of merging objects from neutron stars up to the most massive black holes we've seen. In that picture, we see hints of some gaps, for example between black hole and neutron star masses.

For experts:Why should you care? Black hole masses seem to cluster, but without a corresponding signature in the spin distribution that you'd expect from hierarchical grown. Observed black hole spins are mostly small, being particularly well constrained to be near zero at low mass (and for the most asymmetric binaries); conversely, some very large black holes are likely spinning. We still stand by our previous claims that the black hole population shows signs of precession, after carefully considering counterproposals in the literature. We hadn't fully appreciated how much modeling systematics impacted some of our merger rate estimates, notably for BNS, so our error bars can be more conservative than before.

You can find all of the papers which LIGO and Virgo released this week at papers.ligo.org.

RIFT and the O3 catalog: Our parameter inference code RIFT was once again widely used in GWTC-3

PopModels and the O3 population: RIT-developed PopModels was one of the tools used to infer the population of merging binaries.

Activity on: 2021-11

r-proess EOS

Neutron star mergers eject radioactive material that eventually decays into heavy elements like gold and uranium. But not all mergers are the same: some are heavier, others more asymmetric, and the amount (and properties) of the ejected material changes depending on the merger. Surveys of ancient stars likely contaminated by a single merger event give us an idea of the range of outcomes from these mergers. These outcomes also depend on what neutron stars are made of, as that governs how they are torn apart and thus how much material is ejected.

Recent RIT postdoc Erika Holmbeck just led a novel investigation to use the observed abundances of these ancient stars to constrain the nuclear equation of state. We found a nuclear equation of state that's surprisingly consistent with other observational avenues, despite using no information from those other channels.

Erika has recently moved on to a Hubble Fellowship at Carnegie observatories in Pasadena.

For the first time, LIGO has discovered a neutron star merging with a black hole. RIT studen Anjali Yelikar worked hard on part of the analysis, to characterize the properties of the merging binary.

For experts Yes, we can only infer the companion objects are neutron stars from their masses. Both are consistent with zero-spin BHs once again, like 190814. Combined with previous observations (e.g., 190426 and 190425), GW-derived NS masses generally don't seem to resemble the galactic pulsar distribution, extending to higher masses more frequently. Interesting times for formation modeling ahead!

LIGO has discovered surprisingly massive black holes before, notably GW190521. Now, we report the results of analyses focused on these unusually high masses: 100 to 10^5 times the mass of our sun. With these independent and focused reanalyses, we are even more confident that 190521 is real. We also find a few marginal but tanalizing things.

For expertsIn this work, the RIT-developed RIFT parameter inference pipeline was heavily used to characterize the sometimes puzzling features of the most massive black holes. RIT students Anjali Yelikar and Aasim Jan worked hard on this work. The RIT numerical relativity team of C. Lousto and J. Healy provided numerical relativity models for searches to use as synthetic targets, to characterize how far these dedicated searches could find IMBH.

Merging neutron stars eject hot, radioactive material asymmetrically. The light this material emits can provide critical clues into just how much material came out (and what types, and in what direction, and how far away). But the light emitted by this material is complicated, not least because it passes through material whose interactions with light aren't as familiar as most elements. So detailed simulations of these ``kilonova light curves" are essential to provide a reliable benchmark against which to interpret real observations.

The Los Alamos group (led by R. Wollaeger) has put out a new state-of-the-art library of simulations of these kilonova light curves. RIT graduate student Marko Ristic has been helping target these simulations, interfacing with parameter inference code developed by RIT undergraduate Ben Champion; more on that soon.

Gravitational wave astronomy relies on comparing detector data to our best estimates for the solutions to Einstein's equations. At root, these estimates all derive from supercomputer-based simulations of these equations: numerical relativity (NR). Due to their high cost, they're relatively rare, and various approximations have been developed to mimic them or interpolate between them with some level of fidelity. We've previously pioneered methods to interpret GW data by directly comparing to NR, circumventing these intermediate approximations. With a new paper, we demonstrate this comparison technique systematically, characterizing the most significant reported GW observations from the first two ``observing runs" of current GW detectors.

For experts: We demonstrate PE based only on comparison to NR works on O1O2. If we use the same priors, we get essentially the same answers as model-based methods. This demonstrates that simulation sparseness is not a significant obstacle, and shows our method can be applied effectively to paraeters (like eccentricity) which haven't yet been modeled as thoroughly.

For more information, see the links below, and prior posts

LIGO and Virgo report on all the compact binaries found in the first half of the latest observing run (O3a): GWTC-2..
We find a few pretty massive binary BHs, like GW190521; a few fairly massive BH that are significantly spinning, like GW190517; a few asymmetric binaries, like the previously-reported GW190814 and GW190412; and a few binaries with one or more object below 3 times the mass of our sun, and therefore potentially neutron stars.

One interesting find was a marginal NSBH candidate (false alarm rate of order 1/yr) GW190426. This event was followed up extensively with optical telescopes. For marginal events like this, we have a hard time corroborating the nature of either component -- the GW signature of matter is easier to discern for two neutron stars, with a loud signal.

Last but not least, we find tantalizing suggestions of precession, though we don't see compelling evidence for spin from any one event.

For experts:Why should you care? More events like GW190521 suggest it isn't an outlier, but part of a population of larger BH that challenge the traditional "mass gap" boundary. Large spins on objects like GW190517 challenge natal spin models for isolated binaries, which must both explain a preponderance of events near zero at all masses and a few high-mass events with large spin. Support for precession from measuring chi_eff (some definitely can be negative) and chi_p (some have nonzero values) suggests at least some events are strongly precessing.

You can find all of the papers which LIGO and Virgo released this week at papers.ligo.org.

RIFT and the O3a catalog: Our parameter inference code RIFT was used to compare gravitational wave observations to the data. Jake's thesis (under embargo until Dec 1) included some of the O3a PE.

Activity on: 2020-10

New PhDs awarded

My first two graduate students at RIT are graduating!

Jacob Lange developed RIFT, an algorithm to perform iterative inference on marginalized likelihoods; directly compared GW observations to numerical relativity simulations and other cutting-edge models to explore waveform systematics; and did an enormous amount of work helping to produce LIGO results, for O3a particularly. Jake will be moving to ICERM and then UT Austin for postdocs.

Dan Wysocki developed PopModels, a general framework for bayesian hierarchial inference for GW source populations. He's most well known for his work on the LIGO O2 populations paper. He'll be starting a postdoc at UW-Milwaukee.

Activity on: 2020-08

Coagulating BHs

In dense environments, compact binaries can repeatedly coalesce. Like blobs in a lava lamp, the compact binaries coagulate into large and larger objects. The details, however, depend on the interacting environment that forces the bodies together; different environments like AGN disks or globular clusters have very different physics. In a new study led by Z. Doctor and RIT student D. Wysocki, we describe a generic framework to BH coagulation. We show how BH masses and spins grow with time, for different interaction choices. And we explain how to constrain these parameters, and the natal BH population, via comparison with observations.

For experts:Why should you care? Hierarchical BH-BH formation scenarios make strong predictions connecting the mass and spin distributions at different mass scales. Our framework shows how to stringently constrain these models via GW observations, allowing for arbitrary complexity in the natal BH distribution. We explore realistic BH natal mass and spin distributions, allow for physical recoil kicks from a realistic confining potential, and show how to constrain our physically-parameterized phenomenological model via comparison to GW observations.

Closely related: our group's recent work on AGN disks (McKernan et al 2019; Yang et al PRL 2019) describes a new mechanism by which BH can form hierarchically.

PopModels and the BBH merger rate: Daniel Wysocki's population code PopModels is one of the methods used to compare gravitational wave observations to different candidate populations of binary black holes. This is the first code which can handle generic generative models (i.e., the output of Monte Carlo procedures to produce synthetic binaries, a typical method that theorists use to characterize their formation scenarios).

Activity on: 2019-11

LIGO's catalog of compact binaries from O1 and O2

LIGO and Virgo report on all the compact binaries found in their most recent observing run (O2). We report on a few new binary black holes (BHs) and their properties; reassess our inference about previously-reported binaries; and infer how often that different kinds of compact binary coalesce. We find no very massive BHs, suggesting an upper mass limit as would be expected from stellar evolution. We find that BH spins are unlikely to be large. Unfortunately, given small BH spins, we can't tell much about BH spin-orbit (mis)-alignment, yet.

For experts:Why should you care? The universe provides a symphony of mergers and, by listening to it, we're learning more about how the chorus is assembled. We don't hear loud, deep voices (BHs) in this chorus, beyond a certain size. Because that mass cutoff resembled a boundary set by pair-instability SN, which we expected to be visible in GW observations, we might be seeing hints of a characteristic feature of stellar evolution in our data, for the first time. Unfortunately, we can't distinguish between cluster and field formation yet using spin-orbit orientations, as I proposed a decade ago, but we should be able to soon. And more broadly we can begin to compare the detailed predictions for the mass and spin distribution produced by formation scenarios like those I've worked on to what we see.

A personal note: We had dreams a decade ago that results like these would be possible (see eg slides 21,22, and 27 in a talk of mine from 2009). It's incredibly exciting and satisfying to see these dreams being realized.

You can find all of the papers which LIGO and Virgo released this week at papers.ligo.org.

RIFT and the O2 catalog: Our parameter inference code RIFT was used to compare gravitational wave observations to a few expensive but state-of-the-art models for compact binaries, notably including direct comparison to numerical relativity.

PopModels and the BBH merger rate: Daniel Wysocki's population code PopModels is one of the methods used to compare gravitational wave observations to different candidate populations of binary black holes. We used this to tell how often different kinds of BH binaries merged, extending our previous demonstration and preliminary results. (Dan is helping present these LVC results at the conference where they're being introduced.)

Activity on: 2018-12

GW170817: Measuring the tidal distortion and equation of state of merging NSs

Using better waveform models and more comprehensive physics, we (the LVC) have reanalyzed gravitational waves from the coalescing neutron star binary GW170817. In the revised analysis, we could more sharply constrain how the two neutron stars (NS) deform due to their mutual self gravity. These constraints allow us to constrain the size of the two neutron stars, and hence the nature of ultra-high-density matter.

RIFT and GW170817: Our parameter inference code RIFT was used to compare gravitational wave observations to a few expensive but state-of-the-art models for the inspiral and merger of binary neutron stars.

Activity on: 2018-05

RIFT: Iterative fitting for parameter inference

RIFT is an algorithm to perform Rapid parameter Inference on gravitational wave sources via Iterative Fitting. In short, we fit the likelihood as a function of parameters; then, we use the fitted likelihood to infer source parameters. RIFT provides unique capabilities to use the best available models. Also, RIFT shares technical roots with a closely related code, to infer BBH parameters via direct comparison with NR simulations. As we'll demonstrate soon, this investigation corroborates the tools used by and complements the results of direct comparison with NR.

For experts: Building off the rapid_pe approach introduced in Pankow et al 2015, RIFT adds a concrete fitting and iteration strategy, enabling it to operate robustly.
Due to its structure (inherited from the rapid_pe approach of Pankow et al 2015, used extensively in comparisons to NR), this method inherits unique technical capabilities to employ costly but accurate waveforms; to assess model systematics; and to enable unique calculations enabled by direct access to the marginalized likelihood, such as constraints on the equation of state. We first demonstrate the code using aligned and precessing binary black holes, including GW150914, and synthetic binary neutron stars. Then we show how to use RIFT to identify differences between models; employ a patchwork of models; and constrain the nuclear equation of state.

For more information, see

Lange, O'Shaughnessy, and Rizzo Rapid and accurate parameter inference for coalescing, precessing compact binaries, available at arxiv.org (LIGO DCC P1800084)

Activity on: 2018-05

The population of binary black holes

We show how to simultaneously infer the compact binary rate versus mass and other parameters, for compact binaries observed via gravitational waves. For example, we infer the merger rate, mass distribution, spin distribution, and spin misalignment distribution for merging binary black holes, accounting for selection bias and measurement error.

This phenomenological framework lets us characterize the compact binary population, without adopting strong assumptions about the underlying physics. Such model-neutral inferences can be important to infer the underlying formation channel for binary black holes (see, e.g,, Mandel and O'Shaughnessy (2010)), as well as to identify how massive stars end their life (e.g., through BH natal masses and spins; see, e.g., Wysocki et al 2018).

For experts: Using synthetic data, we demonstrate how to reconstruct the merger rate versus parameters for binary neutron stars and black holes, and how these inferences improve our ability to constrain future observations like NS tides. Using both real observations (O1 and O2) and synthetic data, we emphasize that the merger rate and mass distribution are correlated: any conclusions about the merger rate must now propagate systematic uncertainty in the mass distribution into their results. Finally, reproducing previously discussed results, we show that current observations are consistent with small BH natal spins, strongly disfavoring a population with large spins; consistent with a deficit of very massive BHs, above the pair-instability cutoff; and do not yet appear to constrain the BH spin-orbit misalignment distribution.

For more information, see

Wysocki et al Reconstructing phenomenological distributions of compact binaries via gravitational wave observations, available at arxiv.org (1805.06442)

Activity on: 2018-05

GW170608: Another low-mass binary black hole

Back in June 2017, another binary black hole was detected: GW170608.

Comparing GW170608 to numerical relativity: This merger is similar to GW1511226: a fairly low mass merger, spiralling slowly through the emission of gravitational radiation and thus producing a long signal in the LIGO instruments. While NR simulations aren't long enough to capture the full inspiral, we can hybridize these simulations with analytic models, and compare the hybrids with our data. This paper is the first time LIGO data was compared with these hybrids. The following graphic compares the reconstructed GW signal from model-based PE (blue) with NR reconstructions generated using several best-fitting simulations. To highlight the brevity of these simulations, we have not hybridized them in this graphic. [Image credit: LSC/Sudarshan Ghonge]

Activity on: 2017-11

Multimessenger observation of a binary neutron star merger

LIGO and Virgo found a merging binary neutron star; told astronomer colleagues where to point their telescopes; and those colleagues found a flash of light, consistent with what we'd expect from such a merger: a radiation from a small amount of hot, cooling radioactive material ejected at high speed. And a (very faint) gamma ray burst, with an X-ray and radio afterglow.

Superlatives fail. This event the Rosetta stone we've been waiting for. Now we can connect the investigations conducted over decades in many mostly-independent fields of astrophysics. And it's a triumphant beginning to the era of multimessenger astronomy. We expect to find many more events like this, soon. Using the census of events we obtain, we'll know how these cosmic explosions work (e.g., some will be bright, some not, depending on whether they 'point' towards us or not and just what kinds of NS take part in the merger). Combined (let us not forget!) with our growing census of black holes, we will be able to deduce how these objects can be formed from the lives and deaths of massive stars.

For those keeping score at home, let's count how many discoveries are wrapped into one:

Discovering gravitational waves from a merging neutron star: Neutron stars (and even pairs of neutron stars that will eventually merge) have been seen many times before. A Nobel prize was even already awarded for observing the (slow!) inspiral of a galactic neutron star binary. But this is the first time we've seen the waves directly, over about 100 seconds of rapidly-accelerating inspiral and finally merger.

Discovering (faint) gamma ray burst from a (close by!) merging neutron star: Now we know NS mergers are responsible for (at least some) short gamma ray bursts. Despite being so close -- the closest ever found by far -- it is also weak (as a gamma-ray burst). Followup observations by our EM partners (e.g., the X-ray and radio emission) suggest we're seeing it off-axis. We're finally getting the opportunity to test these burst models in detail.

Nuclear physics: We can't (yet) use GW alone to confirm matter is present, but we can rule out a few equations of state. We can estimate how much of that radioactive material is ejected quickly and forms gold and other heavy (r-process) elements. Based on how often these occur, we expect NS mergers can form most of these elements.

Cosmology: Gravitational wave sources are "standard candles", with known (but orientation-dependent) brightness. We can use this standard candle to measure the distance to the source and hence the expansion of the universe, independently checking a century of work going back to Edwin Hubble!

Astrophysics: By finding it, we know they occur fairly often: at least as often as we expected from our own galaxy, possibly more. EM partners found it near an old galaxy (as has been seen before with GRBs), suggesting it was born long ago and may have received a large "natal kick" when the star exploded.

For experts: Plans are useless but planning is essential. In low latency, search and sky-localization experts handled a strong glitch 1.1s before coalescence with aplomb, combining tools to provide a skymap quickly, when it mattered. That said, handling a loud glitch like this was still a pretty novel challenge for parameter inference, let alone on this timescale, and we're not done with this event by far. In my personal opinion, I expect we (the LVC) will publish mildly refined parameter estimates and new tests of GR soon, when we have better control over systematics (e.g., a careful study of glitch subtraction and measuring tides in the strong field and modifications to gravity), but we can only do so much in 2 months.

Recently another binary black hole was detected: GW170814. This was observed not only by LIGO, but with Virgo -- a gravitational wave detector in Pisa. Working together, the network was able to more precisely identify where the source came from. Our astronomer colleagues pointed their telescopes at this small location quickly, looking for hints of light.

We didn't expect a flash of light from merging black holes, but LIGO is sensitive to other sources that could radiate, like exploding stars (supernova). Precision pointing makes multimessenger astronomy possible.

Comparing GW170814 to numerical relativity: This merger is similar to GW150914 and GW170104, and can be modeled well using many of the same NR simulations. Following a figure in the GW170814 discovery paper, The following graphic compares GW170814 to a few best-fitting NR simulations. RIT student Jacob Lange made the reconstructed solid curves on this figure, using simulations of binary black holes provided by RIT; see also similar figures using simulations provided by SXS and Georgia Tech. [Image credit: LSC/Sudarshan Ghonge]

Activity on: 2017-09

Model systematics and inference about precessing black hole binaries

LIGO has detected heavy binary black holes. By measuring the BH masses and spins, we get clues into how massive stars evolve, interact, and end their lives.
These clues rely on inferences about the BH binary from the observed GW signal, obtained by comparing models for the signal to the observed data. Because of the difficulty in solving GR exactly, these models are approximations, and these inferences imperfect

How reliable are our conclusions? In a new paper, we try to demonstrate the potential effect of systematic modeling error. We first compare two such models to one another, finding not-infrequent disagreement. We generate synthetic signals, and draw distinctly different conclusions depending on which model we use to interpret our data. So, we show by concrete example that under suitable circumstances, inferences drawn from any one model can be biased.

For experts We compare SEOBNRv3 and IMRPv2 on the posteriors of real and synthetic events. We find significant disagreement between the two models, particularly for high spin. For GW151226, disagreements are substantial and frequent.

For more information, see

Williamson et al Systematic challenges for future gravitational wave measurements of precessing binary black holes , available at arxiv.org

Activity on: 2017-09

Isolated evolution with BH natal kicks can explain LIGO's reported observations

LIGO has detected and inferred the parameters of several binary black holes. Using these inferences, we can compare LIGO's observations to the predictions of detailed formation models. These models attempt to explain the number of sources LIGO detects, and the likely properties (masses, spins) of each event. In a recent series of papers, we perform these comparisons, between LIGO's first four observations (GW150914, GW151226,GW170104, and LVT151012) and detailed models for BH-BH formation from isolated pairs of stars.

Most successful formation scenarios can reproduce the correct number and even approximate mass distribution of sources LIGO observes. As I explained years ago in severaltalks and in Mandel and O'Shaughnessy (2010), to distinguish between formation channels, we must use the observed BH spins, whose magnitude and (critically) misalignment can provide clues about how each pair of BHs formed.

We find LIGO's observations can be easily explained by isolated binary evolution, by adopting one of two simple possibilities. One possibility, as described in Belczynski et al 2017, is that massive BHs may have small spins. Most of LIGO's observations to date are consistent with zero spin; only one binary black hole, the lightest, has definite evidence for at least one nonzer spin. Another possibility is that BHs, at birth, are ``kicked", tilting the orbit and reducing the net aligned spin to which LIGO is sensitive.

For experts: We compare the inferred masses and spins of LIGO's observed black holes to models for isolated binary evolution, systematically exploring the impact of BH natal kicks. We consider a wide range of BH natal spin distributions. Isolated binary evolution can easily reproduce LIGO's observations, even when allowing a significant chance of large natal spin, simply by adopting very modest BH natal kicks. Conversely, as seen in other studies, LIGO's observations suggest that BH natal spins are likely small. This study generalizes the work of ROS, Gerosa and Wysocki, by applying detailed binary evolution models.

For more information, see

Wysocki et al Explaining LIGO's observations via isolated binary evolution with natal kicks, available at arxiv.org

Belczynski et al
GW170104 and the origin of heavy, low-spin binary black holes via classical isolated binary evolution, available at arxiv.org

GW170104: another binary black hole detected by gravitational waves

Advanced LIGO has detected another coalescing binary black hole (BBH). The new object (GW170104) was slightly less massive than the first-discovered BBH (GW150915). Both it and GW150914 share a common property: a quantity that measures the "net spin perpendicular to the orbit" (for short, the "net aligned spin") is consistent with zero. This time, it's less likely to be positive.

Now that we have observed two similar ``heavy" binary black holes, we are modestly more confident that these heavy black holes cannot be born with large, exactly parallel spins. (Some people had argued just that before Feb 2016, based on observations of smaller black holes made previously, with X-rays.) The LIGO team suspects that heavy black holes either (a) are individually born with small spins or (b) when they occur in binaries, have tilted spins so the ``net aligned spin" is small.

At RIT, our group also compared this data to supercomputer simulations, to assess the reliability of our inferences. We helped coordinate followup simulations to further corroborate our answers.

Inferring parameters If, however, nature provides many strongly precessing binary black holes, then our previous work suggests the models we've used for parameter inference might not reliable enough. (Modeling strongly precessing black holes with analytic approximations is hard!) So far these models (and LIGO's inferences) have been done by making several approximations. We check these answers by performing followup simulations and by direct comparison of LIGO data to numerical relativity

Comparing GW170104 to numerical relativity Left: The following graphic compares GW170104 to 10 best-fitting NR simulations. RIT student Jacob Lange made the reconstructed yellow curves on this figure, using simulations of binary black holes provided by RIT (6), SXS (2), BAM (1), and Georgia Tech (1). The solid blue region is the inferred parameter range reconstructed by LIGO's modeled inference [Image credit: LSC/James Clark]. Right: This movie compares the LIGO observations (shown in yellow and blue) to the expected response according to specific RIT simulations of binary black holes (shown in black). The inset in the upper left illustrates the properties of the black holes in each simulation. [Image credit: LSC/Andrew Williamson]

For experts: My personal perspective : LIGO observations are now making reality a project I've worked on and proselytized about for the last decade: astrophysics enabled by measuring (precessing) binary black hole spins.

We've known for years that different formation models (clusters vs field binaries) made very different predictions for spin orientations (isotropic vs modestly misaligned). Since those predictions are so different, we can quickly distinguish between formation models so long as each observation provides some information about spin magnitudes and misalignments. [How? Statistics 101 methods on any parameter work fine eventually, though sharper methods yield robust results sooner.] The challenge is getting the data; making precise measurements of misalignments; and connecting those observed misalignments to astrophysical parameters.

Connecting the spins LIGO sees now and the spin misalignments billions of years ago, when the BH was first formed (e.g., Gerosa et al 2015 ). [Since black hole spins evolve substantially over billions of years, this work is particularly critical for interpreting LIGO measurements for astrophysics. We show how to evolve systems in time, emphasizing the role of the "net aligned spin" as a conserved constant.]

Inferring binary black hole parameters with numerical relativity

In a new paper, my RIT graduate student Jacob Lange provides detailed demonstrations and descriptions of a new method to infer the properties of binary black holes: by direct comparison to solutions of Einstein's equations. As part of the LIGO Scientific Collaboration, we used this method to infer the properties of the first detected binary black hole (GW150914).

Why does this matter? Observations of binary black holes can tell us about the lives and deaths of massive stars. But only if we can confidently infer the binary's properties. For example, LIGO measurements could begin to differentiate between strongly precessing binaries (probably made in dynamical environments) from stellar siblings (born in isolated pairs). But inferring the properties of precessing binaries is hard.

Some of our earlier inferences have been made using approximations to solutions to Einstein's equations. These approximations are well-known to be omitting a lot of physics present in real solutions, most particularly for precessing mergers. By contrast, numerical solutions of Einstein's equations always include all available physics. So this method lets us make more precise inferences, without bias.

For experts: This methods paper describes the underpinnings and validation studies for the method used in our LVC-all paper comparing numerical solutions of Einstein's equations to GW150914. We describe and validate our one-step extraction procedure, applied to most simulations by default. We show most sources of systematic error are under control. We demonstrate our method using a variety of sources.

Abbott et al, Directly comparing GW150914 with numerical solutions of Einstein's equations for binary black hole coalescence, available here (summary on this article here)

Activity on: 2017-05

Measuring BH natal kicks with GW

One of the coalescing binary black holes discovered by LIGO (GW151226 or "Boxing Day") is consistent with a scenario where the more massive black hole is spinning, with its spin misaligned with the orbital angular momentum. If true, some event or process must have imparted this misalignment. In one way the binary might have formed, this misalignment would arise when the biggest star ends its life and forms a black hole, via a "natal kick" imparted to the newborn BH. These natal kicks are known to be imparted to newborn black holes; some observations suggest they may also be imparted to BHs.

In a new paper, my collaborators and I tried to constrain the strength of these natal kicks, based on GW151226. Working under the assumption they formed from isolated pairs of stars, we found strong natal BH kicks were required.

For experts:
We show how current gravitational wave observations provide new insight into how black holes form in stellar collapse. This paper is the first study to attempt to extract information about concrete astrophysical properties of supernova explosions from gravitational wave observations. It provides an easily-understoond and -generalized framework to enable the interpretation of future events. With just one event, our results begin to challenge standard supernova theory and black-hole binary formation models.

The detection of gravitational waves from massive binary black holes poses a theoretical challenge. Numerical relativity, the only accurate method to solve Einstein's equations for binary black holes, is slow, limiting the number of followup simulations that can be carried out to mimic new events. These highly-accurate solutions are also required: they include physics not incorporated in phenomenological models. Fortunately, NR solutions can be bridged by surrogate methods, which reliably interpolate between these solutions.

In a new paper, we introduce a fast method to compare the data to these NR surrogates. We demonstrate that physics uniquely available to NR or NR-surrogates significantly influences our interpretation of the gravitational wave data.

For experts: We introduce several technical improvements of use for GW parameter estimation. Our method circumvents ILE's previous need to use a discrete grid, enabling embarassingly-parallel PE for generic sources. Too, our extensions now mean ILE can use very accurate models anywhere in parameter space, being limited neither by systematic limitations of models nor discrete placement of NR simulations.

Too, we extended the gwsurrogate interface to provide direct access to the basis functions; developed tools to ``re-ROM" existing surrogates into the necessary linear basis; and built a new basis for an NR surrogate.

Most interesting, however, are the prospects for the future: this approach is very fast, scalable, accurate, and generic. With tighter integration (e.g., pre-filtering the data against a ROM basis) and GPU integration, this approach could enable streaming PE, providing the best parameter estimates in real time!

For more information, see

ROS et al, An architecture for efficient multimodal parameter estimation with linear surrogate models, available at CQG

gwsurrogate, a surrogate waveform package used and extended for this work.

Activity on: 2017-01

Do similar-looking galaxies host similar compact binary populations?

Epochs of low-metallicity star formation massively overproduce binary black holes. In any galaxy, most coalescing binary black holes often come from epochs of low-metallicity star formation, that occurred early in its lifetime. Low-mass galaxies, which are naturaly low-metallicity, will produce many more coalescing binary black holes per unit mass

The assembly history of galaxies can differ: galaxies with the same present-day properties will generally have different histories. I had guessed (incorrectly, it turns out) that this strong sensitivity meant that galaxies with similar present-day properties could host very differnt BBH properties. Using full galaxy assembly calculations, we found the opposite result: the star formation rate and metallicity vary in opposition, so the present-day BBH population is surprisingly stable to changes in the evolutionary trajectory.

For more information, see the links below, and prior posts

The origin of GW150914 via isolated binary evolution

In a paper appearing in Nature, my collaborators and I present a state-of-the-art synthetic universe (StarTrack) calculation, carefully accounting for the intrinsically rare but critical low-metallicity star-forming environments which produce binary black holes. This calculation shows how GW150914 could have formed from isolated stellar evolution. It introduces a framework with which to predict and interpret subsequent binary black hole gravitational wave events.

For context, this approach explains and produces all of the gravitational wave events and candidates seen to date, including the recently-announced GW151226. This model is being widely and rapidly adopted to prototype the future of gravitational wave astronomy.
[For nonexperts, a short
National Geographic article does a good job summarizing the current discussion among astrophysicists.]

For more information, see the links below, and prior posts

GW151226: a binary black hole detected via gravitational waves

Advanced LIGO has detected gravitational waves from the coalescence of two black holes, again. The new event, denoted GW151226, occurred on Dec 25th (US time).

What did we see?This event reveals another population of coalescing black holes. This time, the coalescing black holes were more similar in mass to black holes detected by other means (i.e., telescopes). Also, This coalesence of two smaller black holes

With two highly signifiant events, we can only begin to sketch the relative probabilities at which different binaries form...and only in the region we're reporting on so far.

Masses: GW151226 was smaller and probably had one member bigger than another.
Based on how far we can see sources like GW151226 versus GW150914, we can figure out how frequently the two objects occur. The lower mass object (GW151226) is most likely more frequent than the more massive one (GW150914). So, keeping in mind considerable uncertainty, the event rate is roughly consistent a population of more frequent binary mergers at lower mass, and somewhat fewer at higher mass.

Spins: The new coalescing binary had at least one spinning black hole in it. But like before, the net effect of spin is small. And like before, we can't tell if the binary is precessing or not.

Fundamental physics: The coalescence is still consistent with GR, as demonstrated by comparison with models and several NR similations.

What does it mean? (for experts) Personally, I think the low net aligned spins of GW150914 and GW151226, combined with the low mass of GW151226, place serious constraints on isolated chemical eveolution. Globular cluster models too are harder to reconcile with the low (and uneven) mass of GW151226.

For more information, see the links below, and prior posts

papers.ligo.org: a one-stop location for the latest results!

Directly comparing GW150914 to numerical relativity

GW150914 was produced by the coalescence of two black holes, in good agreement with the predictions of general relativity, as estimated by full numerical simulations of Einstein's equations. To infer the properties of GW150914, however, the LIGO Scientific Collaboration previously made systematic comparisons between the data and semianalytic models, tuned to these full numerical simulations. In a new paper, GW150914 is compared directly against a large suite of numerical simulations of Einstein's equations. These comparisons enable a completely independent reconstruction of GW150914's properties, without recourse to these approximations. Though these simulations include new physics not previously incorporated in our analysis, we find reassuringly similar conclusions regarding the source properties.

For nonexperts:
The process of solving Einstein's equations on a supercomputer is called
numerical relativity. All the understanding we have
about the coalescence of binary black holes comes, in the end, from numerical relativity simulations. However, these
simulations are notoriously challenging, requiring weeks to months of time on the world's fastest supercomputers.
Working with four teams of experts in numerical relativity, including my RIT colleagues, we assembled a large
collection of more than one thousand of their simulations of binary black holes.

Fortunately, because Einstein's theory of gravity works the same way for all objects, no matter their mass, we can scale
each simulation to larger or smaller black holes. In other words, for every simulation, we can pick any total binary
mass we want. Still, we only have one thousand simulations to cover all the other parameters needed to describe a
binary black hole: the ratio between the two black hole masses, and any other intrinsic properties (spin) the black
holes have.

The problem of reconstructing the black hole's properties turns into a jigsaw puzzle: we have only some of
the pieces, but from experience we know the picture was drawn with a broad brush. We can boil the comparison between
the data and a particular simulation and mass down to one number. This number (the marginalized likelihood) tells us the color of each piece of the puzzle. For an object like GW150914,
with very few gravitational wave cycles, the colors of neighboring pieces of the puzzle are necessarily similar. So
even though we're missing most of the pieces, we can still figure out what the whole puzzle looked like. Or, at least,
the most important part of the puzzle: the part that describes black holes most like GW150914.

In our original analysis, which you can read
about here, we were excited to identify the
masses and spins of the two black holes. These provide pieces of another jigsaw puzzle: how do we make binary black
holes in the first place? Our new analysis teased out a little more information about the two black holes that merged
to form GW150914, using information uniquely available from numerical relativity simulations.

Perhaps most important, however, we found similar conclusions using an independent analysis that
incorporated simulations of binary black hole coalescence.

This work also more explicitly illustrated a result we learned in our
initial interpretation of GW150914: how binary black holes with very different dynamics can, under
suitable circumstances, produce gravitational waves like GW150914. Some of the simulations which fit the data were
simple, with the inspiral occurring entirely within one plane. In others, the orbital plane slews strongly (precesses)
through the merger. The movies below illustrate the range of possible sources of GW150914.

Finally, by measuring how similar each simulation was to this event, we can now figure out where new simulations would
fill in the gaps, for this and future events.

For experts: When higher harmonics are included (l=3), we can place tighter constraints on the mass ratio.

For more information, see the links below, and prior posts

Advanced LIGO has detected gravitational waves from the coalescence of two ``heavy" black holes -- source frame masses 36+29 solar masses. This amounts to three discoveries in one:

This report only covers some of the first science run -- the LIGO Scientific Collaboration continues to analyze the remaining O1 data, and prepare for O2. Based on this event, we expect many more detections over the next year.

For more information, see the links below, and prior posts

papers.ligo.org: a one-stop location for the latest results!

My collaborators and I have claimed for years that advanced LIGO would frequently detect coalescing "heavy" binary black holes, most recently at the start of O1. GW150914 is consistent with our expectations, both recent and soon to be updated. Our predictions have been completely vindicated.

What's next? In our model, the binary black holes form from prompt collapse of massive stars. In this scenario, I personally expect their spins to be strictly and positively aligned with their orbital angular momentum. If GW150914 formed this way, however, LIGO data requires both black holes have surprisingly low spins.

Will future binary black hole observations support aligned spins? low spin magnitudes at birth? precessing spins? Eccentricity? A mixture of all of the above? All these options favor or disfavor different formation scenarios. Soon, LIGO observations will discriminate between them, converting a theorists' playground into an observer's paradise. Let the data decide!

For more information, see the links below, and prior posts

Now that gravitational waves have been detected, what's next? We transform gravitational waves into a tool for astronomical discovery!

The unexpected: Einstein's theory says any time-varying mass (quadrupole) radiates gravitational waves...so the universe is full of sources, some of which we may not have imagined.

Coalescing binary black holes: LIGO will detect many more, soon, and measure their properties equally if not more precisely. We can build a large census of "heavy" black holes in the local universe -- a census we can correlate against other experience. We know how stars evolve; we see similar black holes (and their progenitors) in our own galaxy; and new large-scale surveys will complement insights from LIGO into binary star evolution. (We'll make a census of binaries including neutron stars too.)

Simultaneously seeing and hearing explosions: Multimessenger astronomy: The inspiral and merger of neutron stars, if sufficiently close by, can be detected via their gravitational waves too. But this merger often tears the neutron star apart, throwing highly radioactive material to large distances while releasing an enormous amount of gravitational energy. So we should be able to see it with telescope...and probably have: short gamma ray bursts and kilonovae.

In other words, nature's provided us with a cosmic collider, throwing neutron stars onto other compact objects. Gravitational waves can tell telescopes where to look and identify what happened, particularly the inputs to the coalescence; electromagnetic observations tell us what comes out. Using these two probes, we'll be able to disassemble and reassemble the physics underlying these two longstanding cosmic mysteries, in a controlled fashion. And we'll learn quite a bit about nuclear physics, too.

Neutron stars as a source and detector of gravitational waves: With roughly one billion in our galaxy, the closest and most persistent relics of stellar death are neutron stars, which uniquely are useful both as sources and detectors of gravitational waves:

Neutron stars as souces:
If neutron stars irregular enough -- and all calculations suggest they could and indeed should be -- then we'll be able to detect these steady-state sources too. The strength of their gravitational wave signal will provide another perspective into nuclear physics.

The Milky Way as a detector? Neutron stars are often periodic radio sources: pulsars. The regular arrival time of these pulses can be distorted by an intervening gravitational wave. So, by timing sources, we can tell if nearby galaxies contain hidden supermassive black hole binaries: if so, we'll see distinctive patterns in their radiation.

Activity on: 2016-02

Understanding parameter estimation for BH-NS binaries

What will gravitational waves tell us about merging compact binaries and why? For a theorist, that question can be easily albeit approximately answered by the Fisher matrix. Until recently surpassed by even-more-accurate (but slow) full Bayesian parameter estimation strategies like lalinference and ILE, the Fisher matrix has been the workhorse of gravitational wave astronomy for decades, allowing theorists to quickly calculate whether compact objects masses and spins; the nuclear equation of state; and even modifications to general relativity itself will be observationally accessible.

For nonprecesing binaries, the Fisher matrix is easily calculated from derivatives of the predicted GW signal. For precessing binaries, the intermediate quantities needed to compute the Fisher matrix were believed to be analytically intractable. (And, in many practical cases, numerically unstable.) In recent work, my collaborators and I showed how to carry out this calculation. Our extremely simple expressions agree well with the measurement accuracies found by detailed Bayesian calculations. Our estimates can be use to quickly and efficiently assess what parameters can be measured and why in astrophysically plausible sources.

For experts By expanding the spin-weighted harmonics using a corotating frame, we could perform the stationary-phase approximation term by term. If sufficiently many precession cycles occur in band, each term has a unique time-frequency trajectory and is effectively orthogonal to all others. Hence, at leading order the Fisher matrix separates into contributions from each harmonic, weighted by the power in each mode. Critically, each mode's contribution is as if from a nonprecessing binary, in a familiar and tractable form. Though our result formally applies to black hole-neutron star binaries, the a priori rarity of comparable spins implies our conclusions will be broadly applicable.

Advanced LIGO begins operations this week (September 18th), after 7 long years of enhancement.
In O1 ("observing run 1") instruments will finally begin to confront the most optimistic predictions for how often compact binaries coalesce.

For more information, see the links below, and prior posts

Precessing binary black holes produce a complicated waveform, reflecting their time-dependent spins and the line of sight. As discussed below in ``Reliable parameter estimation with SpinTaylorF2" , particularly at high mass ratio the precession of two spinning black holes can be reasonably approximated as if the smaller body had no spin. To the extent this approximation holds, then, GW observatories would have no access to the smaller spin, and hence to unique strong-field effects associated with spin-spin interactions.

In a study led by Daniele Trifiro (Pisa), my collaborators and I demonstrate that if suitable sources occur, advanced LIGO can directly and robustly identify effects from both black hole spins in BH-BH binaries. These effects are not subtle; can be identified over a broad range of astrophysically plausible signal amplitudes and source orientations; and include the signature of conserved constants that reflect properties at compact binary birth.

For experts Using sources known to lie on one or the other post-Newtonian resonance, we construct posterior parameter distributions, each point in which can be classified as belonging to one of three classes. These classes are reliably measured.
More broadly, as implied by our prior work, observationally-accessible properties of the nonlinear dynamics at merger encode conserved properties reflecting the compact binary's asymptotic initial conditions.

Binary black holes with exactly aligned spins remain aligned for all time. My collaborators and I have just discovered an instability: if more massive black hole has spin up (parallel to L) and the less massive black hole has spin down (antiparallel to L), then certain binaries will inevitably become unstable to spin precession, rapidly evolving to large misalignment. This instability could occur in observationally accessible astrophysical compact binaries, including supermassive binary black holes, with significant impact on the light and gravitational waves such an object would emit.

For experts
Both analytically and via direct integration of the orbit-averaged 2PN spin precession equations, we have demonstrated that the up/down spin configuration is unstable; that the instability's nonlinear evolution can be understood analytically, via our previously-described nonlinear spin precession solution; that it occurs for a wide range of masses, spins, and mass ratios; and that, if nature creates up/down binaries, evidence of the instability will be present in the sensitive band of existing and future gravitational wave detectors like LIGO, LISA, and pulsar timing arrays.

Multimessenger astronomy with gravitational waves relies on rapid decisions, as astronomers search for some type of transient afterglow left behind after compact binary mergers. Given limited telescope time, astronomers want to know where, when, and critically whether to point their telescopes. Astronomers in particular want to follow up mergers involving neutron stars, as these could be candidate gamma ray burst sources. Unfortunately, LIGO does not directly measure the components masses (let alone composition) via detected gravitational waves. Instead, these source parameters must be inferred by a process of systematically comparing all possible sources with the data. These exhaustive comparisons can be slow -- days to produce a reliable answer.

In a study led by Brandon Miller and I at RIT, building upon investigations started by my longstanding collaborators from the Chicago metro area, we demonstrated that a fast but approximate method for parameter estimation produces reliable answers to astrophysical questions. This method's speed advantage comes from simplified physics (ignoring the smaller object's spin) and, critically, a fast and accurate waveform model that Andy Lundgren and I introduced in 2013. Using existing codes and algorithms, this approach produces rapid and reliable-enough parameter estimates, often within an hour.
Our approach shows LIGO can rapidly estimate the posterior probability that some gravitational wave data is consistent with a tidal disruption event, beamed towards us, and therefore a good candidate for followup with large electromagnetic telescopes.

For experts Using a fixed set of sources produced with SpinTaylorT2, we compare the performance of parameter estimation using several different approximants and physics, including SpinTaylorF2 (a single spin model); double-spin SpinTaylorT2; and single-spin SpinTaylorT2 and T4. Given the still-large systematic uncertainties in precessing waveform models, these approximations produce consistent predictions for posterior parameter distributions and astrophysically-motivated questions.

As binary black holes (BBHs) spiral inward towards merger, both spin angular momenta precess, according to equations first solved analytically by my collaborators and I in 2014. In a followup to our breakthrough solution, we use our solution to understand how binary black holes precess and inspiral. We can efficiently predict and explain how spin orientations at infinity evolve into other spin configurations just prior to merger, an ingredient essential to many astrophysical processes (e.g., the evolution of supermassive black holes).

For experts
In this work, we introduce a new way to describe precessing binaries that better respects the natural hierarchy of timescales of the problem; explain how these hierarchical coordinates evolve with time; and develop an extraordinarily efficient precession-averaged mechanism for evolving an ensemble of precessing binaries forward in time, treating the specific precession phase as a random variable. This exceptionally efficient approach can evolve precessing binaries from astrophysical seperations to the strong-field regime.

For more information, see ``Solving double-spin evolution" below, and

This year marks 100 years since Einstein formulated his theory of general relativity. As one of our contributions to celebrating this event, the CCRG collaborated with APS TV to put together this short film about our research. At the Center for Computational Relativity and Gravitation, we are acutely aware of the enduring impact of Einstein's theory to relativistic astrophysics; to the burgoning field of gravitaitonal wave and multimessenger astronomy; and to cosmology and physics as a whole.

This film will be shown at the APS meetings in March and April, and has been featured on NSF's Science 360

Activity on: 2015-02

ILE: an alternative architecture for parameter estimation

As noted below about lalinference, gravitational wave astronomy begins with inference : figuring out what kind of astrophysical source was responsible for the implausible event in our data. One conventional, robust, and easily generalized approach is Markov Chain Monte Carlo, where detector data is serially compared with a sequence of proposed model waveforms. For any ``reasonable" way of choosing these sequences (i.e., for any reasonable "jump proposal"), due to detailed balance, random samples from Markov Chain Monte Carlo asymptotically converge in distribution to the posterior parameter distribution. Like any Markov Chain Monte Carlo analysis, the challenge for gravitational wave parameter estimation is efficiency, scalability, and confidence in one's results, particularly given systematic errors and multiple secondary posterior maxima. Rapid and highly accurate parameter estimation is particularly important for:

EM followup: Anyone wanting to point a telescope at a LIGO event immediately wants to know where to point and what to expect (e.g., binary black hole).

Waveform systematics: When estimating source parameters of detected gravitational waves, the most accurate and comprehensive multimodal gravitational wave signal models are expensive to simulate and include.

In a recent work with colleagues from UWM, we proposed an alternative: the ILE architecture, short for integrate_likelihood_extrinsic. For each set of intrinsic parameters -- the parameters which specify a physically distinct binary, like component masses and spins -- our algorithm fully explores and properly weights all extrinsic parameters -- the parameters like distance, source orientation, and sky locations, which only influence how the binary appears in our instruments. Critically, our approach employs brute-force Monte Carlo integration of a low-cost likelihood function, enabling rapid processing with controlled statistical errors, even for expensive-to-compute waveforms.

For experts : By carefully reorganizing and caching waveform calculations that are used to compute the likelihood, we can efficiently marginalize over all extrinsic parameters by brute-force Monte Carlo. To further accelerate convergence, we use an adaptive Monte Carlo scheme that exploits information from the search (for sky location) and explicitly marginalize in time. With extremely low cost per likelihood, our method provides a useful complement to reduced-order methods for nonprecessing systems. However, further investigations are needed to extend this approach to explore more intrinsic dimensions, notably spin precession.

As binary black holes (BBHs) spiral inward towards merger, both spin angular momenta precess. This problem has long been simulated and explored numerically, and even solved when only one object has significant spin. When both objects have significant spin, however, the coupled nonlinear ODEs had been analytically intractable.

Astronomers and gravitational wave physicsts are deeply and broadly interested in carefully modeling how BBH spins precess

Gravitational wave astronomers want to understand how to interpret the rich signal produced by the precession of stellar-mass BBHs' spins during the late stages of inspiral

Extragalactic astronomers want to model the evolution of supermassive black holes, which merge repeatedly with companions as their host galaxies collide. At merger, the supermassive binary black hole radiates gravitational waves generally asymmetrically, causing recoil. Though the recoil strength depends precisely on the spin orientations at merger, occasionally the recoil can be strong enough to eject the remnant from its host galaxy.

In a recent study, we found a new semianalytic solution to this problem, providing new insight and faster computation for long-term spin evolution.

For experts : For relativists, our paper uses a known constant of motion of the 2PN orbit-averaged spin precession equations to solve for conservative motion, then combines that solution with a geometric ansatz for how the angular momenta evolve on radiation reaction timescales.

LALInference: identifying sources of gravitational waves

Gravitational wave astronomy begins with inference : figuring out what kind of astrophysical source was responsible for the implausible event in our data. By exhaustively comparing that data against all candidate signals, we can reconstruct how consistent with that data any any proposed source is. In other words, we can use gravitational waves to measure the properties of the sources responsible for each gravitational wave signal we detect!
These measurements will tell us how often different types of compact objects mege throughout the universe, revolutionizing our understanding of how stars and stellar systems evolve to produce these exotic binaries. And might also let us probe the nature of nuclear matter; resolve longstanding astrophysical mysteries like short gamma ray bursts; and even challenge our understanding of gravity itself.

Through the persistent efforts of several key colleagues (notably John Veitch; Vivien Raymond; and Ben and Will Farr), a subset of the LIGO Scientific Collaboration has consolidated its expertise in gravitational wave parameter estimation into a single authoritative library, lalinference.

For experts: LALInference provides a general library for accessing data and waveform libraries; evaluating the likelihood of the data, assuming gaussian noise; exploring the likelihood surface, via Markov Chain Monte Carlo or nested sampling; transforming the results of that exploration into robust statements about the posterior distribution of source parameters, given a model; and ranking different models, via their evidence.
Though systematically limited by the accuracy of approximations to strong field binary motion and by ideosyncratic correlations unique to gravitational physics, gravitational wave measurements will constrain compact object masses and spins to a previously unattainable accuracy.

Do you want to try to find a gravitational wave? LIGO has publicly released two years of data taken by the three LIGO gravitational wave detectors during ``S5", an observing epoch from 2005-2007, along with all the tools and information needed to analyze it.

For more information, see

The LIGO Open Science Center, a service of LIGO Laboratory and the LIGO Scientific Collaboration. LIGO is funded by the United States National Science Foundation.

Activity on: 2014-09

Gravitational waves from eccentric binaries

Once a pair of compact objects are mutually gravitationally bound, they begin to lose energy and angular momentum to gravitational waves, a process that relatively rapidly circularizes their orbit. Over time, the orbit period decreases, until eventually the binary orbits tens to hundreds of times a second, the frequency range to which ground based gravitational wave detectors are sensitive. Since compact object binaries usually form in relatively wide orbits, with closest approach (perihelion) within a few orders of magnitude of a solar radius and hence orbital periods of minutes to days, by the time these binaries reach this sensitive band, they're almost exactly circular. But not always.

Even a slight eccentricity in the sensitive band of ground-based detectors produces a measurable impact. This impact will only impair our ability to detect gravitational waves if the eccentricity was truly extreme (e>0.4 at orbital frequency 5Hz). But eccentricity can complicate our ability to measure astrophysical parameters.

In this paper, Eliu Huerta at West Virginia University and his collaborators (myself included) introduce a simple, fast model for gravitational waves from eccentric binaries. This model will help quantify how much eccentricity matters, as well as contribute to strategies to detect eccentric sources.

The next gravitational wave detectors should soon operate at design sensitivity, frequently detecting gravitational waves.
What will we see? What might we learn? Particularly when advanced detectors can see massive binaries out to significant redshift? In a recent paper, my collaborators and I try to figure that out.

LIGO and similar gravitational wave detectors are more sensitive to bigger (more massive) binaries. In previous work (Domink et al 2013), we showed ancient, low-metallicity star formation preferentially produced high-mass binaries at a high rate. In this work, we map out what we might detect and why:

LIGO ought to preferentially detect more BH-BH binaries than anything else

The detected mass distribution should be broad, including relatively massive objects.

Detected binary black holes were formed in the early unverse. Detected double neutron star (NS-NS) binaries are formed recently.

The detected (chirp) mass distribution for NS-NS and double black hole (BH-BH) varies significantly and on physical grounds as we change our assumptions.

For experts:
For relativists, our detection rate calculations include high-mass black hole binaries, with realistic spin-dependent merger waveforms; sources at cosmologically significant distances and time-dependent merger rates; and reasonable corrections for beaming and multi-instrument sensitivity.
We predict a high BH-BH merger and hence detection rate because we include the significant contribution from low-metallicity star-forming gas, integrated over all cosmic time.

Previously, my collaborators and I argued (a) that the spin and orbit orientations at birth reflect the processes that formed the binary, notably supernova, which misalign the spin and orbital plane; and (b) that some information about these orientations was preserved as the binary spiralled inwards for millions to billions of years until merger. Specifically, we claimed the relative spin orientations at merger may encode the birth order.

In a recent study, varying a limited set of parameters, we argue that the two resonant families seem to produce distinguishable gravitational waves.
In other words, gravitational wave measurements might be able to identify which member of the binary was formed first.

We haven't performed an exhaustive study ("parameter estimation"); followup work is underway. But our results are a promising beginning.

For experts : For relativists, our paper uses two arguments to suggest that members of the twin resonant families can be distinguished using their gravitational waves. First, we argue based on dynamics: one resonance has both spins on the same side of J as the orbital angular momentum; the other has both spins opposite one another. In the first case, the orbital plane precesses little. In the second, it precesses a lot.
Second, using a pessimistic choice of viewing direction (along J) for both source and template, minimizing precession-induced modulations, we calculate a fitting factor that is significantly different from unity.

Precessing black hole-neutron star binaries produce a complicated and particularly informative gravitational wave signal, encoding information in two complementary channels. On the one hand, the orbit shrinks via gravitational radiation; on the other, the orbital plane wobbles, because the orbital angular momentum (and spins) precess through spin-orbit coupling.

The gravitational wave signal reflects these two complementary physical processes in two largely decoupled scales: a high-frequency, slowly-changing "carrier" signal, reflecting the slowly-shrinking orbit; and a low-frequency modulation in amplitude, phase, and polarization.

Gravitational wave detectors can constrain both processes independently, letting us measure the orbital plane and three-dimensional BH spin. Moreover, using simple estimates of how many orbits the binary makes and how much the orbit precesses, we can understand how well the binary's spins and masses can be measured.

For experts:

Our analysis suggests simple Fisher-matrix-like studies can estimate how well detailed parameter-estimation calculations perform, even for precessing binaries.

We found an example demonstrating that even for precessing binaries, higher harmonics can break degeneracies and rule out a significant subset of parameters.

Our collaborators developed the currently-used-in-LIGO MCMC parameter estimation strategies for precessing binaries. Our analysis and companion studies were part of the calibration process, to gain confidence that we understood our simulations' results and hence how well parameters could be estimated.

Recent work by the Montana State group (1402.3581) uses a different code and waveform model to assess parameter estimation of low-mass binaries, including double neutron stars.

Activity on: 2014-03

Better coordinates for parameter estimation of precessing binaries

To draw inferences about gravitational waves from data, one must systematically compare models against data. The usual methods for doing so (Markov Chain Monte Carlo and nested sampling) wander through the parameter space, often nearby, to identify the next model to try. These methods are therefore invariably sensitive to the choice of coordinates on the set of models.

In this paper, we introduced coordinates defined the detector is sensitive, using angles relative to a conserved constant (J). These coordinates both reflect what's best-constrained by measurements and enable faster parameter estimation, by roughly an order of magnitude.

UWM recently hosted the 23rd Midwest Relativity Meeting, with a satellite Compact Objects Meeting With more than 70 participants over three days, talks covered everything from gravitational theory to observations and astrophysics of compact binaries, showcasing the breadth of modern gravitational physics.

Measuring parameters of BH-NS binaries with gravitational waves

Gravitational waves encode the properties of the source that emit them. But how, and how much? What information will gravitational waves provide to constrain the central engines of astrophysical processes (e.g., short gamma ray bursts)?

For nonexperts, our paper provides a concrete, end-to-end, and pedagogically-accessible illustration of how well existing gravitational wave detectors would do at measuring one specific source: a BH-NS binary. (Future detectors will do better, having better low-frequency sensitivity.) More important, our procedure shows that very simple approximations do a pretty good job at explaining the information gravitational waves provide.

For experts: Our paper shows that our effective Fisher matrix approximation adequately characterizes the performance of parameter estimation. Contrary to older work and in agreement with our earlier analytic study, we show that higher harmoncs provide relatively little astrophysically interesting information for typical nonprecessing BH-NS binaries. Using the output of our Markov-Chain Monte Carlo, we provide a method to quantify the number of degrees of freedom that gravitational wave measurements constrain.

Previous calculations suggest star-forming environments very unlike our own ("low metallicity") formed very massive binary black holes exceptionally frequently. Because short GRBs and gravitational waves are detectable over vast distances, a careful prediction for mergers over cosmic time must include this trend.

We created a few plausible synthetic universes and populated them with merging binaries, accounting for when and where each was born; how long each binary lasts; and time-dependent star forming conditions. Because the rate at which stars form decreases and the composition of the universe gradually changes as stars produce more heavy elements, the intrinsic merger rate per unit volume increases rapidly with redshift out to the era of peak star formation (Domink et al 2013). In other words, rare ancient star formation matters.

For experts: The eight fiducial synthetic universes constructed here are used later to predict compact binary detection rates.
Our calculations should also be useful when interpreting compact binary merger populations over cosmic time, including reconciling short GRB event rates and redshift distributions with galactic and (soon) LIGO constraints.

Binary black holes spiral in very slowly through the emission of gravitational radiation; most mergers should occur millions to billions of years after the binary's birth. During this slow inspiral, coupling between angular momenta has been thought to scramble their relative orientations. That's unfortunate: the spin and orbit orientations at birth reflect the processes that formed the binary, notably supernova, which misalign the spin and orbital plane.

In Gerosa et al (2013), my collaborators and I suggest that the relative spin orientations are significantly less scrambled than previously assumed. In particular, we suggest the relative spin orientations may encode the birth order, potentially allowing gravitational wave measurements to identify which member of the binary was formed first.

For experts: For relativists, our paper demonstrates post-Newtonian resonances can be populated over a wide range of angles. For astrophysicists, our cartoon model of binary evolution proposes an alternative approach to spin alignment in binary evolution codes: tidal alignment during the Herzprung gap, prior to the common envelope phase.

A single-spin gravitational wave signal in closed form

In coming years, gravitational wave detectors should find black hole-neutron star
binaries, potentially coincident with astronomical phenomena like short GRBs. These binaries are expected to precess.
Precessing black hole binaries produce a complicated signal, different in each direction, that reflects how the orbital plane precesses and the relative orientation of the line of sight and that precessing plane.
Gravitational wave science requires a tractable model for precessing binaries, to disentangle precession physics from other
phenomena like modified strong field gravity, tidal deformability, or Hubble flow; and to measure compact object
masses, spins, and alignments.
Moreover, current searches for gravitational waves from compact binaries use templates where the binary does not
precess and are ill-suited for detection of generic precessing sources.

In our paper , Andy Lundgren and I refactor existing expressions to provide a compact, accurate, intuitive expression for this precession, both as a function of time and a function of gravitational wave frequency. These analytic expressions enable previously-intractable analytic calculations like the Fisher matrix: a way of characterizing how similar neighboring signals are to one another and hence how well measurements can distinguish between them.

Our analysis provides an accessible foundation for the detection and interpretation of gravitational waves from generic compact binaries.

For experts By expressing the gravitational wave signal in radiation-frame coordinates, restricted to one line of sight, several authors following our work (e.g., Klein et al) have artificially introduced unnecessary coordinate-dependent complexity to the precessing gravitational wave signal. Our expressions are compact, correct, build on prior work, and enable new insight and calculations.

Brown, Lundgren, and O'Shaughnessy PRD 86 4020 (2012) : A previous work easily explained using our simple result.

Activity on: 2013-04

Precession during merger

The merger of two precessing black holes produces a complicated gravitational wave signal which in principle fully encodes its highly nonlinear dynamics. Intuition gained from analytic studies prior to merger provide a simple picture: the two black holes spiral inward, with their spin and orbital angular momenta precessing around one another. Analytic studies after merger show the isolated black hole loses its ``hair", radiating away energy and angular momentum in ``quasinormal modes," determined by eigenfunctions of the final black hole. How are these two epochs bridged for generic sources? How can observations probe those dynamics?
In 2011, I identifed a robust ``corotating frame" , a way of choosing time-dependent angular coordinates at large
distances using only the radiated signal. In this frame the binary's orbital plane is not precessing prior to merger. Prior to and during merger,
the corotating-frame waveform signal is easy to understand and similar to previously-simulated nonprecessing results. We suspect differences can be modeled with perturbation theory.
In our recent paper, we re-expressed the gravitational wave signal from simulated binary black hole mergers in this frame.

our preferred frame seems to be physical, and connected to the line of sight polarization.
Intuitively, the binary radiates cicularly polarized gravitational waves perpendicular to the instantaneous orbital plane. As the orbital plane precesses, radiation along the line of sight receives distinctive amplitude and phase modulations.

the corotating-frame signal does not (and cannot) be identical to the signal from nonprecessing
binaries. For example, corotating-frame modes generically have modulations on a precession timescale.

the merger of precessing binaries coherently excites quasinormal modes, which "precess" around
the total angular momentum direction. We speculate the details of this process provide a signature
of strong-field gravity.

I am often asked to explain how often compact binaries merge in the local universe; how often gravitational wave detectors will find the ripples in the fabric of the universe produced by these mergers; and what science these measurements enable.
Recent presentations of this kind include

The conservative answer involves only extrapolation from experience. We know pairs of neutron stars which will merge, in our galaxy; having lots of experience with finding neutron stars, we know how many exist in our galaxy, from what we've seen; and we know how galaxies similar to our own form stars in the nearby universe over the last few billion years. Combining these together, we find LIGO will almost certainly see the gravitational wave signal from merging NS-NS binaries.

The more aggressive answer involves substantial extrapolations away from known experience, using our best understanding of how compact binaries form. Compact binaries are known to form through binary evolution; "population synthesis" predictions involve using our best understanding of stellar evolution to generate synthetic binary populations. Compact binaries have also been observed in interacting stellar environments -- globular clusters. Both by extrapolating from experience and using our best knowledge, these interacting environments could contribute many mergers...but probably don't, based on our current expectations from the physics (e.g., Tsang et al 2013 review).

For more information, see

Abadie et al 2010, CQG 27 173001 Predictions for the rates of compact binary coalescences : A slightly dated review of the compact binary literature provided by my collaborators and I in LIGO. My work features prominently.

J. Aasi et al, arxiv:1304.0760 Prospects for localization of gravitational wave transients

The big dog: Can gravitational wave detectors identify a signal?

The LIGO and Virgo Collaborations quizzed ourselves: a group hid a realistic signal in our data. We wanted to confirm we could find a gravitational wave and identify its properties.

This was the first time the collaborations had tested the parameter estimation codes in realistic conditions. I was the parameter estimation review co-chair: my job was to make sure any claims we made about parameters we could measure were correct. I had a particularly active role, devising specific statements which were astrophysically interesting that our data could support (e.g., on spin; whether a NS was present); organizing efforts to track down possible sources of error; coordinating between people who understood the detector and its idiosyncracies (e.g., Andy Lundgren) and our review; et cetera.

This process established new directions for the parameter estimation group, culminating in a unified code library (lalinference); a unified signal model interface and library (lalsimulation); and other technical improvements and consistency checks.

The often-torturous process of code validation has continued for years (to 2013, as of this post), long after my active role in the review. With a well-understood codebase, signal model, and detector, gravitational wave scientists are now in a position to ask pointed questions about what information future gravitational wave measurements will provide.

For more information

GW20100916 : gravitational wave scientists quiz themselve. This is what first gravitational wave detection might look like. Descriptions are available for the public and other scientists