arXiv subjects

Daniel Wysocki

Publications and source records attributed to Daniel Wysocki.

At least 19 recordsLinked to original sources

arXiv2025

Geometric approaches to Lie bialgebras, their classification, and applications

This PhD Thesis consists of two parts. The first part focuses on novel algebraic and geometric approaches to the classification problem of coboundary Lie bialgebras up to Lie algebra automorphisms. More specifically, Grassmann, graded algebra and algebraic invariant techniques are discussed. Using these algebraic methods, equivalence classes of r-matrices for three-dimensional coboundary Lie bialgebras are studied. Moreover, particular higher-dimensional cases, e.g. $\mathfrak{so}(2,2)$ and $\mathfrak{so}(3,2)$, are partially analysed. From the geometric perspective, the main role is played by the newly introduced notion: the Darboux family. This powerful tool allows an efficient and thorough study of equivalence classes of r-matrices for four-dimensional indecomposable coboundary Lie bialgebras. In order to showcase its ability to tackle decomposable examples, $\mathfrak{gl}_2$ is additionally studied. The second part of the Thesis sketches interesting directions for applications of r-matrices. Firstly, it is illustrated how r-matrices might be useful to describe foliated Lie-Hamilton systems. Secondly, the role of r-matrices in deformations of certain cases of Lie systems is discussed. In particular, based on the general procedure for deformations of Lie-Hamilton systems, its extension to Jacobi-Lie systems is suggested and supported by the detailed computation of the deformed Schwarz equation.

math-ph↗

arXiv2025

Reconstructing the origin of black hole mergers using sparse astrophysical models

The astrophysical origin of binary black hole mergers discovered by LIGO and Virgo remains uncertain. Efforts to reconstruct the processes that lead to mergers typically rely on either astrophysical models with fixed parameters, or continuous analytical models that can be fit to observations. Given the complexity of astrophysical formation mechanisms, these methods typically cannot fully take into account model uncertainties, nor can they fully capture the underlying processes. Here, we present a merger population analysis that can take a discrete set of simulated model distributions as its input to interpret observations. The analysis can take into account multiple formation scenarios as fractional contributors to the total set of observations, and can naturally account for model uncertainties. We apply this technique to investigate the origin of black hole mergers observed by LIGO Virgo. Specifically, we consider a model of AGN assisted black hole merger distributions, exploring a range of AGN parameters along with several {{SEVN}} population synthesis models that vary in common envelope efficiency parameter ($\alpha$) and metallicity ($Z$). We estimate the posterior distributions for AGN+SEVN models using $87$ BBH detections from the $O1--O3$ observation runs. The inferred total merger rate is $46.2 {Gpc}^{-3} {yr}^{-1}$, with the AGN sub-population contributing $21.2{Gpc}^{-3}{yr}^{-1}$ and the SEVN sub-population contributing $25.0 {Gpc}^{-3} {yr}^{-1}$.

astro-ph.HE↗

arXiv2024

Effects of waveform systematics on inferences of neutron star population properties and the nuclear equation of state

Gravitational waves from inspiralling neutron stars carry information about matter at extreme gravity and density. The binary neutron star (BNS) event GW170817 provided, for the first time, insight into dense matter through this window. Since then, another BNS (GW190425) and several neutron star-black hole events have been detected, although the tidal measurements were not expected to be well-constrained from them. Collective information regarding the behavior of nuclear matter at extreme densities can be done by performing a joint population inference for the masses, spins, and equation-of-state [1] to enable better understanding. This population inference, in turn, relies on accurate estimates of intrinsic parameters of individual events. In this study, we investigate how the differences in parameter inference of BNS events using different waveform models can affect the eventual inference of the nuclear equation-of-state. We use the state-of-the-art model TEOBResumS with IMRPhenomD NRTidalv2 as a comparison model.

gr-qc↗

arXiv2023

Low-latency gravitational wave alert products and their performance at the time of the fourth LIGO-Virgo-KAGRA observing run

Multi-messenger searches for BNS and NSBH mergers are currently one of the most exciting areas of astronomy. The search for joint electromagnetic and neutrino counterparts to GWs has resumed with O4. To support this effort, public semi-automated data products are sent in near real-time and include localization and source properties to guide complementary observations. In preparation for O4, we have conducted a study using a simulated population of compact binaries and a MDC in the form of a real-time replay to optimize and profile the software infrastructure and scientific deliverables. End-to-end performance was tested, including data ingestion, running online search pipelines, performing annotations, and issuing alerts to the astrophysics community. We present an overview of the low-latency infrastructure and the performance of the data products that are now being released during O4 based on the MDC. We report the expected median latency for the preliminary alert of full bandwidth searches (29.5s) and show consistency and accuracy of released data products using the MDC. For the first time, we report the expected median latency for triggers from early warning searches (-3.1s), which are new in O4 and target neutron star mergers during inspiral phase. This paper provides a performance overview for LVK low-latency alert infrastructure and data products using the MDC and serves as a useful reference for the interpretation of O4 detections.

astro-ph.HE↗

arXiv2023

Iteratively Comparing Gravitational-Wave Observations to the Evolution of Massive Stellar Binaries

Gravitational-wave observations have the capability to strongly differentiate between different assumptions for how binary compact objects form. In this work, we show how to carefully interpolate a marginal likelihood between choices of binary evolution model parameters. Using the StarTrack binary evolution code, we compare one- and four-dimensional binary evolution models to the compact binary mergers reported in recent gravitational-wave observing runs. We first consider a one-dimensional model, studying the effect of supernova kick velocity (drawn from a Maxwellian with dispersion σ_eff) on the simulated population of compact binary mergers, and find support for substantial SN recoil kicks. We follow this up with a four-dimensional study of σ_eff, mass transfer efficiency (fa) and the efficiency of angular momentum depletion from ejected material (\b{eta}) during Roche-lobe accretion, and an observation-driven reduction in the mass-loss rate estimated from stellar wind models (fwind1). We find that three of them (σ_eff, fa, and fwind1) can be efficiently limited by these observational comparisons. After initially sampling from a uniform prior in the space of these parameters, we refined our sampling by iteratively estimating a Bayesian likelihood for each simulation and fitting that likelihood to a parametric model (a truncated Gaussian) in order to propose new. Our maximum likelihood simulation (K0559) has parameters: σ_eff = 108.3 km/s (indicating substantial SN recoil kicks), fa = 0.922 (indicating efficient mass transfer), and fwind1 = 0.328 (indicating support for reduced wind-driven mass loss). Note that our estimates are only valid within one particular model of compact binary formation through isolated binary evolution and do not yet take into account the impact of other uncertain pieces of stellar physics and binary evolution.

gr-qc↗

arXiv2023

Gravitational wave source populations: Disentangling an AGN component

The astrophysical origin of the over 90 compact binary mergers discovered by the LIGO and Virgo gravitational wave observatories is an open question. While the unusual mass and spin of some of the discovered objects constrain progenitor scenarios, the observed mergers are consistent with multiple interpretations. A promising approach to solve this question is to consider the observed distributions of binary properties and compare them to expectations from different origin scenarios. Here we describe a new hierarchical population analysis framework to assess the relative contribution of different formation channels simultaneously. For this study we considered binary formation in AGN disks along with phenomenological models, but the same framework can be extended to other models. We find that high-mass and high-mass-ratio binaries appear more likely to have an AGN origin compared to the same origin as lower-mass events. Future observations of high-mass black hole mergers could further disentangle the AGN component from other channels.

gr-qc↗

arXiv2022

Compressed Parametric and Non-Parametric Approximations to the Gravitational Wave Likelihood

Gravitational-wave observations of quasicircular compact binary mergers imply complicated posterior measurements of their parameters. Though Gaussian approximations to the pertinent likelihoods have decades of history in the field, the relative generality and practical utility of these approximations hasn't been appreciated, given focus on careful, comprehensive generic Bayesian parameter inference. Building on our previous work in three dimensions, we demonstrate by example that bounded multivariate normal likelihood approximations are a sufficiently accurate representation of the full likelihood of observed gravitational-wave sources. Fits for each event published in the Gravitatinoal-Wave Transient Catalogs at https://gitlab.com/xevra/nal-data, along with a code release at https://gitlab.com/xevra/gwalk. We argue our approximations are more than accurate enough for popultion inference and introduce much smaller errors than waveform model systematics. To demonstrate the utility of these approximations as parametric models for the likelihood of individual gravitational-wave sources, we show examples of their application to modeling the population of observed gravitational-wave sources as well as low-latency parameter inference.

astro-ph.IM↗

arXiv2022

Flexible and Fast Estimation of Binary Merger Population Distributions with Adaptive KDE

The LIGO Scientific, Virgo and KAGRA Collaborations recently released the third gravitational wave transient catalog or GWTC-3, significantly expanding the number of gravitational wave (GW) signals. To address the -- still uncertain -- formation channels of the source compact binaries, their population properties must be characterized. The computational cost of the Bayesian hierarchical methods employed thus far scales with the size of the event catalogs, and such methods have until recently assumed fixed functional forms for the source distribution. Here we propose a fast and flexible method to reconstruct the population of LIGO--Virgo merging black hole (BH) binaries without such assumptions. For sufficiently high event statistics and sufficiently low individual event measurement error (relative to the scale of population features) a kernel density estimator (KDE) reconstruction of the event distribution will be accurate. We improve the accuracy and flexibility of KDE for finite event statistics using an adaptive bandwidth KDE (awKDE). We apply awKDE to publicly released parameter estimates for 44 significant (69) BH binary mergers in GWTC-2 (GWTC-3), in combination with a fast polynomial fit of search sensitivity, to obtain a non-parametric estimate of the mass distribution, and compare to Bayesian hierarchical methods. We also demonstrate a robust peak detection algorithm based on awKDE and use it to calculate the significance of the apparent peak in the BH mass distribution around $35\, M_\odot$. We find such a peak is very unlikely to have occurred if the true distribution is a featureless power-law (significance of $3.6σ$ for confident GWTC-2 BBH events, $3.0σ$ for confident GWTC-3 BBH events).

gr-qc↗

arXiv2022

Normal Approximate Likelihoods to Gravitational Wave Events

Gravitational wave observations of quasicircular compact binary mergers in principle provide an arbitrarily complex likelihood over eight independent intrinsic parameters: the masses and spins of the two merging objects. In this work, we demonstrate by example that a simple normal approximation over fewer (usually, three) effective dimensions provides a very accurate representation of the likelihood, and allows us to replicate the eight-dimensional posterior over the mass and spin degrees of freedom. Alongside this paper, we provide the parameters for multivariate normal fits for each event published in GWTC-1 and GWTC-2, using the posterior samples from the catalog for each associated release. These normal approximations provide a highly efficient way to characterize gravitational wave observations when combining large numbers of events.

gr-qc↗

arXiv2021

A Common Origin for Low Mass Ratio Events Observed by LIGO and Virgo in the First Half of the Third Observing Run

In its third observing run, the LIGO/Virgo collaboration has announced a potential neutron star-black hole (NSBH) merger candidate, GW190426_152155. Together with GW190814, these two events belong to a class of binaries with a secondary mass less than $3 \, M_{\odot}$. While the secondary system in GW190426_152155 is consistent with being a neutron star with a mass of $1.5^{+0.8}_{-0.5} \, M_{\odot}$, that of GW190814 is a $2.59^{+0.08}_{-0.09} \, M_{\odot}$ object and counts as the first confirmed detection of a mass-gap object. Here we argue that these two events could have a common origin as follows: both are formed as NSBH systems; however, the larger escape velocity of a system with more massive primary BH increases the bound fraction of the ejecta material from the supernova explosion leading to the formation of a NS. This bound material forms a disk, which is preferentially accreted onto the NS. This scenario predicts the secondary component mass should correlate with the primary component mass, which is consistent with GW190426_152155 and GW190814. If this hypothesis is corroborated by upcoming observations, GW190814-like events can be excluded from the binary black hole population when inferring their global characteristics.

astro-ph.HE↗

arXiv2020

Impact of subdominant modes on the interpretation of gravitational-wave signals from heavy binary black hole systems

Over the past year, a handful of new gravitational wave models have been developed to include multiple harmonic modes thereby enabling for the first time fully Bayesian inference studies including higher modes to be performed. Using one recently-developed numerical relativity surrogate model, NRHybSur3dq8, we investigate the importance of higher modes on parameter inference of coalescing massive binary black holes. We focus on examples relevant to the current three-detector network of observatories, with a detector-frame mass set to $120 M_\odot$ and with signal amplitude values that are consistent with plausible candidates for the next few observing runs. We show that for such systems the higher mode content will be important for interpreting coalescing binary black holes, reducing systematic bias, and computing properties of the remnant object. Even for comparable-mass binaries and at low signal amplitude, the omission of higher modes can influence posterior probability distributions. We discuss the impact of our results on source population inference and self-consistency tests of general relativity. Our work can be used to better understand asymmetric binary black hole merger events, such as GW190412. Higher modes are critical for such systems, and their omission usually produces substantial parameter biases.

gr-qc↗

arXiv2020

Black Hole Coagulation: Modeling Hierarchical Mergers in Black Hole Populations

Data from the LIGO and Virgo detectors has confirmed that stellar-mass black holes can merge within a Hubble time, leaving behind massive remnant black holes. In some astrophysical environments such as globular clusters and AGN disks, it may be possible for these remnants to take part in further compact-object mergers, producing a population of hierarchically formed black holes. In this work, we present a parameterized framework for describing the population of binary black hole mergers, while self-consistently accounting for hierarchical mergers. The framework casts black holes as particles in a box which can collide based on an effective cross-section, but allows inputs from more detailed astrophysical simulations. Our approach is relevant to any population which is comprised of second or higher generation black holes, such as primordial black holes or dense cluster environments. We describe some possible inputs to this generic model and their effects on the black hole merger populations, and use the model to perform Bayesian inference on the catalog of black holes from LIGO and Virgo's first two observing runs. We find that models with a high rate of hierarchical mergers are disfavored, consistent with previous population analyses. Future gravitational-wave events will further constrain the inputs to this generic hierarchical merger model, enabling a deeper look into the formation environments of binary black holes.

astro-ph.HE↗

arXiv2020

Inferring the neutron star equation of state simultaneously with the population of merging neutron stars

Observations of the properties of multiple coalescing neutron stars will simultaneously provide insight into neutron star mass and spin distribution, the neutron star merger rate, and the nuclear equation of state. Not all merging binaries containing neutron stars are expected to be identical. Plausible sources of diversity in these coalescing binaries can arise from a broad or multi-peaked NS mass distribution; the effect of different and extreme NS natal spins; the possibility of NS-BH mergers; or even the possibility of phase transitions, allowing for NS with similar mass but strongly divergent radius. In this work, we provide a concrete algorithm to combine all information obtained from GW measurements into a joint constraint on the NS merger rate, the distribution of NS properties, and the nuclear equation of state. Using a concrete example, we show how biased mass distribution inferences can significantly impact the recovered equation of state, even in the small-$N$ limit. With the same concrete example, we show how small-$N$ observations could identify a bimodal mass and spin distribution for merging NS simultaneously with the EOS. Our concordance approach can be immediately generalized to incorporate other observational constraints.

gr-qc↗

arXiv2019

Reconstructing phenomenological distributions of compact binaries via gravitational wave observations

Gravitational wave measurements will provide insight into the population of coalescing compact binaries throughout the universe. We describe and demonstrate a flexible parametric method to infer the event rate as a function of compact binary parameters, accounting for Poisson error and selection biases. Using concrete synthetic data based on projections for LIGO and Virgo's O3 run, we discuss how well GW measurements could constrain the mass and spin distribution of coalescing neutron stars and black holes in the near future, within the context of several phenomenological models described in this work. We demonstrate that only a few tens of events can enable astrophysically significant constraints on the spin magnitude and orientation distribution of BHs in merging binaries. We discuss how astrophysical priors or other measurements can inform the interpretation of future measurements. Using publicly-available results, we estimate the event rate versus mass for binary black holes. To connect to previously-published work, we provide estimates including reported O2 BBH candidates, making several unwarranted but simplifying assumptions for the sensitivity of the network and compleness of the reported set of events. Consistent with prior work, we find BHs in binaries likely have low natal spin. With available results and a population favoring low spin, we can't presently constrain the typical misalignments of the binary black hole population. All of the tools described in this work are publicly available and ready-to-use to interpret real or synthetic LIGO data, and to synthesize projected data from future observing runs.

gr-qc↗

arXiv2019

A note on cohomology for multiplier Hopf algebras

In this note we discuss the possibility of constructing the cosimplicial complex for the multiplier Hopf algebras and extending the cyclicity operator to obtain the Hopf-cyclic cohomology for them. We show that the definition of modular pairs in involution for multiplier Hopf algebras and provide the definition of Hopf-cyclic cohomology for algebras of functions over discrete groups.

math.QA↗

arXiv2019

Anisotropies in the astrophysical gravitational-wave background: The impact of black hole distributions

We use population inference to explore the impact that uncertainties in the distribution of binary black holes (BBH) have on the astrophysical gravitational-wave background (AGWB). Our results show that the AGWB monopole is sensitive to the nature of the BBH population (particularly the local merger rate), while the anisotropic $C_\ell$ spectrum is only modified to within a few percent, at a level which is insignificant compared to other sources of uncertainty (such as cosmic variance). This is very promising news for future observational studies of the AGWB, as it shows that (i) the monopole can be used as a new probe of the population of compact objects throughout cosmic history, complementary to direct observations by LIGO and Virgo and (ii) we are able to make surprisingly robust predictions for the $C_\ell$ spectrum, even with only very approximate knowledge of the black hole population. As a result, the AGWB anisotropies have enormous potential as a new probe of the large-scale structure of the Universe, and of late-Universe cosmology in general.

astro-ph.CO↗

arXiv2019

Response to Cusin et al's comment on arXiv:1810.13435

We offer a brief response to the criticisms put forward by Cusin et al in arXiv:1811.03582 about our work arXiv:1810.13435 and arXiv:1806.01718, emphasising that none of these criticisms are relevant to our main results.

astro-ph.CO↗

arXiv2018

Spin orientations of merging black holes formed from the evolution of stellar binaries

We study the expected spin misalignments of merging binary black holes (BHs) formed in isolation by combining state-of-the-art population-synthesis models with efficient post-Newtonian evolutions, thus tracking sources from stellar formation to gravitational-wave detection. We present extensive predictions of the properties of sources detectable by both current and future interferometers. We account for the fact that detectors are more sensitive to spinning BH binaries with suitable spin orientations and find that this significantly impacts the population of sources detectable by LIGO, while this is not the case for 3rd-generation detectors. We find that three formation pathways, differentiated by the order of core collapse and common-envelope phases, dominate the observed population, and that their relative importance critically depends on the recoils imparted to BHs at birth. Our models suggest that measurements of the "effective-spin" parameter $χ_{\rm eff}$ will allow for powerful constraints. For instance, we find that the role of spin magnitudes and spin directions in $χ_{\rm eff}$ can be largely disentangled, and that the symmetry of the effective-spin distribution is a robust indicator of the binary's formation history. Our predictions for individual spin directions and their precessional morphologies confirm and extend early toy models, while exploring substantially more realistic and broader sets of initial conditions. Our main conclusion is that specific subpopulations of BH binaries will exhibit distinctive precessional dynamics: these classes include (but are not limited to) sources where stellar tidal interactions act on sufficiently short timescales, and massive binaries produced in pulsational pair-instability supernovae. Measurements of BH spin orientations have enormous potential to constrain specific evolutionary processes in the lives of massive binary stars.

astro-ph.HE↗