arXiv subjects

Will M. Farr

Publications and source records attributed to Will M. Farr.

At least 55 records · Page 3Linked to original sources

arXiv2022

A Standard Siren Cosmological Measurement from the Potential GW190521 Electromagnetic Counterpart ZTF19abanrhr

The identification of the electromagnetic counterpart candidate ZTF19abanrhr to the binary black hole merger GW190521 opens the possibility to infer cosmological parameters from this standard siren with a uniquely identified host galaxy. The distant merger allows for cosmological inference beyond the Hubble constant. Here we show that the three-dimensional spatial location of ZTF19abanrhr calculated from the electromagnetic data remains consistent with the updated sky localization of GW190521 provided by the LIGO-Virgo Collaboration. If ZTF19abanrhr is associated with the GW190521 merger and assuming a flat wCDM model we find that $H_0 =48^{+24}_{-10}$ km/s/Mpc, $Ω_m =0.39^{+0.38}_{-0.29}$, and $w_0 = -1.29^{+0.63}_{-0.50}$ (median and 68% credible interval). If we use the Hubble constant value inferred from another gravitational-wave event, GW170817, as a prior for our analysis, together with assumption of a flat $Λ$CDM and the model-independent constraint on the physical matter density $ω_m$ from Planck, we find $H_0 = 69.1^{8.7}_{-6.0}$ km/s/Mpc.

astro-ph.CO↗

arXiv2022

Evidence of large recoil velocity from a black hole merger signal

The final black hole left behind after a binary black hole merger can attain a recoil velocity, or a "kick", reaching values up to 5000 km/s. This phenomenon has important implications for gravitational wave astronomy, black hole formation scenarios, testing general relativity, and galaxy evolution. We consider the gravitational wave signal from the binary black hole merger GW200129_065458 (henceforth referred to as GW200129), which has been shown to exhibit strong evidence of orbital precession. Using numerical relativity surrogate models, we constrain the kick velocity of GW200129 to $v_f \sim 1542^{+747}_{-1098}$ km/s or $v_f \gtrsim 698$ km/s (one-sided limit), at 90\% credibility. This marks the first identification of a large kick velocity for an individual gravitational wave event. Given the kick velocity of GW200129, we estimate that there is a less than $0.48\%$ ($7.7\%$) probability that the remnant black hole after the merger would be retained by globular (nuclear star) clusters. Finally, we show that kick effects are not expected to cause biases in ringdown tests of general relativity for this event, although this may change in the future with improved detectors.

astro-ph.HE↗

arXiv2022

Comparing Bayes factors and hierarchical inference for testing general relativity with gravitational waves

In the context of testing general relativity with gravitational waves, constraints obtained with multiple events are typically combined either through a hierarchical formalism or though a combined multiplicative Bayes factor. We show that the well-known dependence of Bayes factors on the analysis priors in regions of the parameter space without likelihood support can lead to strong confidence in favor of incorrect conclusions when one employs the multiplicative Bayes factor. Bayes factors $\mathcal{O}(1)$ are ambivalent as they depend sensitively on the analysis priors, which are rarely set in a principled way; additionally, combined Bayes factors $>\mathcal{O}(10^3)$ can be obtained in favor of the incorrect conclusion depending on the analysis priors when many $\mathcal{O}(1)$ Bayes factors are multiplied, and specifically when the priors are much wider than the underlying population. The hierarchical analysis that instead infers the ensemble distribution of the individual beyond-general-relativity constraints does not suffer from this problem, and generically converges to favor the correct conclusion. Rather than a naive multiplication, a more reliable Bayes factor can be computed from the hierarchical analysis. We present a number of toy models showing that the practice of multiplying Bayes Factors can lead to incorrect conclusions.

gr-qc↗

arXiv2022

Inferring the properties of a population of compact binaries in presence of selection effects

Shortly after a new class of objects is discovered, the attention shifts from the properties of the individual sources to the question of their origin: do all sources come from the same underlying population, or several populations are required? What are the properties of these populations? As the detection of gravitational waves is becoming routine and the size of the event catalog increases, finer and finer details of the astrophysical distribution of compact binaries are now within our grasp. This Chapter presents a pedagogical introduction to the main statistical tool required for these analyses: hierarchical Bayesian inference in the presence of selection effects. All key equations are obtained from first principles, followed by two examples of increasing complexity. Although many remarks made in this Chapter refer to gravitational-wave astronomy, the write-up is generic enough to be useful to researchers and graduate students from other fields.

astro-ph.IM↗

arXiv2022

Revisiting the ringdown of GW150914

We examine recent claims that evidence for an overtone in the ringdown of the GW150914 binary black hole merger was a result of noise anomalies. We cannot reproduce these claims, finding that our previous analysis of this event is robust to data analysis choices and consistent with the expectation that strain after the peak is well described as a superposition of quasinormal modes of the remnant black hole. We discuss the meaning and implications of establishing that any specific ringdown mode was detected, and argue that it is misguided to expect actual LIGO-Virgo data to inform the discussion of whether or why the merger looks linear.

gr-qc↗

arXiv2022

Constraining Unmodeled Physics with Compact Binary Mergers from GWTC-1

We present a flexible model to describe the effects of generic deviations of observed gravitational wave signals from modeled waveforms in the LIGO and Virgo gravitational wave detectors. With the detection of 11 gravitational wave events from the GWTC-1 catalog, we are able to constrain possible deviations from our modeled waveforms. In this paper we present our coherent spline model that describes the deviations, then choose to validate our model on an example phenomenological and astrophysically motivated departure in waveforms based on extreme spontaneous scalarization. We find that the model is capable of recovering the simulated deviations. By performing model comparisons we observe that the spline model effectively describes the simulated departures better than a normal compact binary coalescence (CBC) model. We analyze the entire GWTC-1 catalog of events with our model and compare it to a normal CBC model, finding that there are no significant departures from the modeled template gravitational waveforms used.

gr-qc↗

arXiv2022

Measuring binary black hole orbital-plane spin orientations

Binary black hole spins are among the key observables for gravitational wave astronomy. Among the spin parameters, their orientations within the orbital plane, $ϕ_1$, $ϕ_2$ and $Δϕ=ϕ_1-ϕ_2$, are critical for understanding the prevalence of the spin-orbit resonances and merger recoils in binary black holes. Unfortunately, these angles are particularly hard to measure using current detectors, LIGO and Virgo. Because the spin directions are not constant for precessing binaries, the traditional approach is to measure the spin components at some reference stage in the waveform evolution, typically the point at which the frequency of the detected signal reaches 20 Hz. However, we find that this is a poor choice for the orbital-plane spin angle measurements. Instead, we propose measuring the spins at a fixed dimensionless time or frequency near the merger. This leads to significantly improved measurements for $ϕ_1$ and $ϕ_2$ for several gravitational wave events. Furthermore, using numerical relativity injections, we demonstrate that $Δϕ$ will also be better measured near the merger for louder signals expected in the future. Finally, we show that numerical relativity surrogate models are key for reliably measuring the orbital-plane spin orientations, even at moderate signal-to-noise ratios like $\sim 30-45$.

astro-ph.HE↗

arXiv2022

Hints of spin-orbit resonances in the binary black hole population

Binary black hole spin measurements from gravitational wave observations can reveal the binary's evolutionary history. In particular, the spin orientations of the component black holes within the orbital plane, $ϕ_1$ and $ϕ_2$, can be used to identify binaries caught in the so-called spin-orbit resonances. In a companion paper, we demonstrate that $ϕ_1$ and $ϕ_2$ are best measured near the merger of the two black holes. In this work, we use these spin measurements to provide the first constraints on the full six-dimensional spin distribution of merging binary black holes. In particular, we find that there is a preference for $Δϕ= ϕ_1 - ϕ_2 \sim \pm π$ in the population, which can be a signature of spin-orbit resonances. We also find a preference for $ϕ_1 \sim -π/4$ with respect to the line of separation near merger, which has not been predicted for any astrophysical formation channel. However, the strength of these preferences depends on our prior choices, and we are unable to constrain the widths of the $ϕ_1$ and $Δϕ$ distributions. Therefore, more observations are necessary to confirm the features we find. Finally, we derive constraints on the distribution of recoil kicks in the population, and use this to estimate the fraction of merger remnants retained by globular and nuclear star clusters. We make our spin and kick population constraints publicly available.

astro-ph.HE↗

arXiv2021

Who Ordered That? Unequal-Mass Binary Black Hole Mergers Have Larger Effective Spins

Hierarchical analysis of the binary black hole (BBH) detections by the Advanced LIGO and Virgo detectors has offered an increasingly clear picture of their mass, spin, and redshift distributions. Fully understanding the formation and evolution of BBH mergers will require not just the characterization of these marginal distributions, though, but the discovery of any correlations that exist between the properties of BBHs. Here, we hierarchically analyze the ensemble of BBHs discovered by the LIGO and Virgo with a model that allows for intrinsic correlations between their mass ratios $q$ and effective inspiral spins $χ_\mathrm{eff}$. At $98.7\%$ credibility, we find that the mean of the $χ_\mathrm{eff}$ distribution varies as a function of $q$, such that more unequal-mass BBHs exhibit systematically larger $χ_\mathrm{eff}$. We find Bayesian odds ratio of $10.5$ in favor of a model that allows for such a correlation over one that does not. Finally, we use simulated signals to verify that our results are robust against degeneracies in the measurements of $q$ and $χ_\mathrm{eff}$ for individual events. While many proposed astrophysical formation channels predict some degree correlation between spins and mass ratio, these predicted correlations typically act in an opposite sense to the trend we observationally identify in the data.

astro-ph.HE↗

arXiv2021

Analyzing black-hole ringdowns

A perturbed black hole rings down by emitting gravitational waves in tones with specific frequencies and durations. Such tones encode prized information about the geometry of the source spacetime and the fundamental nature of gravity, making the measurement of black hole ringdowns a key goal of gravitational wave astronomy. However, this task is plagued by technical challenges that invalidate the naive application of standard data analysis methods and complicate sensitivity projections. In this paper, we provide a comprehensive account of the formalism required to properly carry out ringdown analyses, examining in detail the foundations of recent observational results, and providing a framework for future measurements. We build on those insights to clarify the concepts of ringdown detectability and resolvability -- touching on the drawbacks of both Bayes factors and naive Fisher matrix approaches -- and find that overly pessimistic heuristics have led previous works to underestimate the role of ringdown overtones for black hole spectroscopy. We put our framework to work on the analysis of a variety of simulated signals in colored noise, including analytic injections and a numerical relativity simulation consistent with GW150914. We demonstrate that we can use tones of the quadrupolar angular harmonic to test the no-hair theorem at current sensitivity, with precision comparable to published constraints from real data. Finally, we assess the role of modeling systematics, and project measurements for future, louder signals. We release ringdown, a Python library for analyzing black hole ringdowns using the the methods discussed in this paper, under a permissive open-source license at https://github.com/maxisi/ringdown

gr-qc↗

arXiv2021

Probing multiple populations of compact binaries with third-generation gravitational-wave detectors

Third-generation (3G) gravitational-wave (GW) detectors will be able to observe binary-black-hole mergers (BBHs) up to redshift of $\sim 30$. This gives unprecedented access to the formation and evolution of BBHs throughout cosmic history. In this paper we consider three sub-populations of BBHs originating from the different evolutionary channels: isolated formation in galactic fields, dynamical formation in globular clusters and mergers of black holes formed from Population III (Pop III) stars at very high redshift. Using input from populations synthesis analyses, we created two months of simulated data of a network of 3G detectors made of two Cosmic Explorers and an Einstein Telescope, consisting of $\sim16000$ field and cluster BBHs as well as $\sim400$ Pop III BBHs. First, we show how one can use non-parametric models to infer the existence and characteristic of a primary and secondary peak in the merger rate distribution. In particular, the location and the height of the secondary peak around $z\approx 12$, arising from the merger of Pop III remnants, can be constrained at $\mathcal{O}(10\%)$ level. Then we perform a modeled analysis, using phenomenological templates for the merger rates of the three sub-population, and extract the branching ratios and the characteristic parameters of the merger rate densities of the individual formation channels. With this modeled method, the uncertainty on the measurement of the fraction of Pop III BBHs can be improved to $\lesssim 10\%$, while the ratio between field and cluster BBHs can be measured with an uncertainty of $\sim 50\%$.

astro-ph.CO↗

arXiv2021

Testing the black-hole area law with GW150914

We present observational confirmation of Hawking's black-hole area theorem based on data from GW150914, finding agreement with the prediction with 97% (95%) probability when we model the ringdown including (excluding) overtones of the quadrupolar mode. We obtain this result from a new time-domain analysis of the pre- and postmerger data. We also confirm that the inspiral and ringdown portions of the signal are consistent with the same remnant mass and spin, in agreement with general relativity.

gr-qc↗

arXiv2021

When are LIGO/Virgo's Big Black-Hole Mergers?

We study the evolution of the binary black hole (BBH) mass distribution across cosmic time. The second gravitational-wave transient catalog (GWTC-2) from LIGO/Virgo contains BBH events out to redshifts $z \sim 1$, with component masses in the range $\sim5$--$80\,M_\odot$. In this catalog, the biggest black holes, with $m_1 \gtrsim 45\,M_\odot$, are only found at the highest redshifts, $z \gtrsim 0.4$. We ask whether the absence of high-mass BBH observations at low redshift indicates that the astrophysical BBH mass distribution evolves: the biggest BBHs only merge at high redshift, and cease merging at low redshift. Alternatively, this feature might be explained by gravitational-wave selection effects. Modeling the BBH primary mass spectrum as a power law with a sharp maximum mass cutoff (Truncated model), we find that the cutoff increases with redshift ($> 99.9\%$ credibility). An abrupt cutoff in the mass spectrum is expected from (pulsational) pair instability supernova simulations; however, GWTC-2 is only consistent with a Truncated mass model if the location of the cutoff increases from $45^{+13}_{-5}\,M_\odot$ at $z < 0.4$ to $80^{+16}_{-13}\,M_\odot$ at $z > 0.4$. Alternatively, if the primary mass spectrum has a break in the power law (Broken power law) at ${38^{+15}_{-8}\,M_\odot}$, rather than a sharp cutoff, the data are consistent with a non-evolving mass distribution. In this case, the overall rate of mergers, at all masses, increases with increasing redshift. Future observations will confidently distinguish between a sharp maximum mass cutoff that evolves with redshift and a non-evolving mass distribution with a gradual taper, such as a Broken power law. After $\sim 100$ BBH merger observations, a continued absence of high-mass, low-redshift events would provide a clear signature that the mass distribution evolves with redshift.

astro-ph.HE↗

arXiv2021

Measuring the star formation rate with gravitational waves from binary black holes

A measurement of the history of cosmic star formation is central to understand the origin and evolution of galaxies. The measurement is extremely challenging using electromagnetic radiation: significant modeling is required to convert luminosity to mass, and to properly account for dust attenuation, for example. Here we show how detections of gravitational waves from inspiraling binary black holes made by proposed third-generation detectors can be used to measure the star formation rate (SFR) of massive stars with high precision up to redshifts of ~10. Depending on the time-delay model, the predicted detection rates ranges from ~2310 to ~56,740 per month with the current measurement of local merger rate density. With 30,000 detections, parameters describing the volumetric SFR can be constrained at the few percent level, and the volumetric merger rate can be directly measured to 3% at z ~ 2. Given a parameterized SFR, the characteristic delay time between binary formation and merger can be measured to ~60%.

astro-ph.HE↗

arXiv2020

Inferring the maximum and minimum mass of merging neutron stars with gravitational waves

We show that the maximum and the minimum mass of merging neutron stars can be estimated with upcoming gravitational wave observations. We simulate populations of binary neutron star signals and model their mass distribution including upper and lower cutoffs. The lower(upper) limit can be measured to $\sim 0.2(0.1)\text{M}_{\odot}$ with $50$ detections if the mass distribution supports neutron stars with masses close to the cutoffs. The upper mass limit informs about the high density properties of the neutron star equation of state, while the lower limit signals the divide between neutron stars and white dwarfs.

astro-ph.HE↗

arXiv2020

Cosmological Inference using Gravitational Wave Standard Sirens: A Mock Data Challenge

The observation of binary neutron star merger GW170817, along with its optical counterpart, provided the first constraint on the Hubble constant $H_0$ using gravitational wave standard sirens. When no counterpart is identified, a galaxy catalog can be used to provide the necessary redshift information. However, the true host might not be contained in a catalog which is not complete out to the limit of gravitational-wave detectability. These electromagnetic and gravitational-wave selection effects must be accounted for. We describe and implement a method to estimate $H_0$ using both the counterpart and the galaxy catalog standard siren methods. We perform a series of mock data analyses using binary neutron star mergers to confirm our ability to recover an unbiased estimate of $H_0$. Our simulations used a simplified universe with no redshift uncertainties or galaxy clustering, but with different magnitude-limited catalogs and assumed host galaxy properties, to test our treatment of both selection effects. We explore how the incompleteness of catalogs affects the final measurement of $H_0$, as well as the effect of weighting each galaxy's likelihood of being a host by its luminosity. In our most realistic simulation, where the simulated catalog is about three times denser than the density of galaxies in the local universe, we find that a 4.4\% measurement precision can be reached using galaxy catalogs with 50\% completeness and $\sim 250$ binary neutron star detections with sensitivity similar to that of Advanced LIGO's second observing run.

gr-qc↗

arXiv2020

A self-consistent method to estimate the rate of compact binary coalescences with a Poisson mixture model

The recently published GWTC-1 - a journal article summarizing the search for gravitational waves (GWs) from coalescing compact binaries in data produced by the LIGO-Virgo network of ground-based detectors during their first and second observing runs - quoted estimates for the rates of binary neutron star, neutron star black hole binary, and binary black hole mergers, as well as assigned probabilities of astrophysical origin for various significant and marginal GW candidate events. In this paper, we delineate the formalism used to compute these rates and probabilities, which assumes that triggers above a low ranking statistic threshold, whether of terrestrial or astrophysical origin, occur as independent Poisson processes. In particular, we include an arbitrary number of astrophysical categories by redistributing, via mass-based template weighting, the foreground probabilities of candidate events, across source classes. We evaluate this formalism on synthetic GW data, and demonstrate that this method works well for the kind of GW signals observed during the first and second observing runs.

astro-ph.HE↗

arXiv2020

A Population-Informed Mass Estimate for Pulsar J0740+6620

Galactic double neutron star systems have a tight mass distribution around $\sim 1.35 M_{\odot}$, but the mass distribution of all known pulsars is broader. Here we reconstruct the Alsing, et al. (2018) bimodal mass distribution of pulsars observed in binary systems, incorporating data from observations of J0740+6620 which were not available at the time of that work. Because J0740+6620 is an outlier in the mass distribution with non-negligible uncertainty in its mass measurement, its mass receives a large correction from the population, becoming $m_{J0740+6620} = 2.03^{+0.10}_{-0.08} \, M_\odot$ (median and 68\% CI). Stochastic samples from our population model, including population-informed pulsar mass estimates, are available at https://github.com/farr/AlsingNSMassReplication .

astro-ph.GA↗