arXiv subjects

John T. Whelan

Publications and source records attributed to John T. Whelan.

At least 19 recordsLinked to original sources

arXiv2025

Investigating Hardware Injections in LIGO O3 Data: Simulated Signals from a Neutron Star in a Low-Mass X-ray Binary

During LIGO-Virgo-KAGRA's third observing run (O3), simulated continuous gravitational wave (CW) signals were added to the LIGO detectors as hardware (HW) injections, which are physical injections into the interferometer control loop via auxiliary laser actuation on test-mass mirrors. These included two periodic signals mimicking a spinning neutron star in a binary system, similar to the low-mass X-ray binary Scorpius X-1 (Sco X-1). HW injections serve as an important validation of a search method, as they occur before data cleaning and preparation. We searched for these injections using the model-based cross-correlation pipeline, which was used to search for CWs from Sco X-1 in the first three LVK observing runs. To simulate a realistic search, we used a search region of orbital parameter space of similar size to the plausible parameter ranges for Sco X-1, but containing the parameters of each HW injection. Our self-blinded analysis confidently detected one of the injections. The other, which was generated with a lower amplitude and in a more expensive region of frequency space, was not detected. We verified the imprint of this second signal by performing a deeper targeted search at its true parameters. However, such a deep search across the full parameter range would have been computationally infeasible.

gr-qc↗

arXiv2023

Search for Gravitational Waves from Scorpius X-1 in LIGO O3 Data With Corrected Orbital Ephemeris

Improved observational constraints on the orbital parameters of the low-mass X-ray binary Scorpius~X-1 were recently published in Killestein et al (2023). In the process, errors were corrected in previous orbital ephemerides, which have been used in searches for continuous gravitational waves from Sco~X-1 using data from the Advanced LIGO detectors. We present the results of a re-analysis of LIGO detector data from the third observing run of Advanced LIGO and Advanced Virgo using a model-based cross-correlation search. The corrected region of parameter space, which was not covered by previous searches, was about 1/3 as large as the region searched in the original O3 analysis, reducing the required computing time. We have confirmed that no detectable signal is present over a range of gravitational-wave frequencies from $25\textrm{Hz}$ to $1600\textrm{Hz}$, analogous to the null result of Abbott et al (2022). Our search sensitivity is comparable to that of Abbott et al (2022), who set upper limits corresponding, between $100\textrm{Hz}$ and $200\textrm{Hz}$, to an amplitude $h_0$ of about $10^{-25}$ when marginalized isotropically over the unknown inclination angle of the neutron star's rotation axis, or less than $4\times 10^{-26}$ assuming the optimal orientation.

astro-ph.HE↗

arXiv2023

Prediction and Evaluation in College Hockey using the Bradley-Terry-Zermelo Model

We describe the application of the Bradley-Terry model to NCAA Division I Men's Ice Hockey. A Bayesian construction gives a joint posterior probability distribution for the log-strength parameters, given a set of game results and a choice of prior distribution. For several suitable choices of prior, it is straightforward to find the maximum a posteriori point (MAP) and a Hessian matrix, allowing a Gaussian approximation to be constructed. Posterior predictive probabilities can be estimated by 1) setting the log-strengths to their MAP values, 2) using the Gaussian approximation for analytical or Monte Carlo integration, or 3) applying importance sampling to re-weight the results of a Monte Carlo simulation. We define a method to evaluate any models which generate predicted probabilities for future outcomes, using the Bayes factor given the actual outcomes, and apply it to NCAA tournament results. Finally, we describe an on-line tool which currently estimates probabilities of future results using MAP evaluation and describe how it can be refined using the Gaussian approximation or importance sampling.

stat.AP↗

arXiv2021

Bradley-Terry Modeling with Multiple Game Outcomes with Applications to College Hockey

The Bradley-Terry model has previously been used in both Bayesian and frequentist interpretations to evaluate the strengths of sports teams based on win-loss game results. It has also been extended to handle additional possible results such as ties. We implement a generalization which includes multiple possible outcomes such as wins or losses in regulation, overtime, or shootouts. A natural application is to ice hockey competitions such as international matches, European professional leagues, and NCAA hockey, all of which use a zero-sum point system which values overtime and shootout wins as 1/3 of a win, and overtime and shootout losses as 1/3 of a win. We incorporate this into the probability model, and evaluate the posterior distributions for the associated strength parameters using techniques such as Gaussian expansion about maximum a posteriori estimates, and Hamiltonian Monte Carlo.

stat.AP↗

arXiv2021

Template Lattices for a Cross-Correlation Search for Gravitational Waves from Scorpius X-1

We describe the application of the lattice covering problem to the placement of templates in a search for continuous gravitational waves from the low-mass X-Ray binary Scorpius X-1. Efficient placement of templates to cover the parameter space at a given maximum mismatch is an application of the sphere covering problem, for which an implementation is available in the LatticeTiling software library. In the case of Sco X-1, potential correlations, in both the prior uncertainty and the mismatch metric, between the orbital period and orbital phase, lead to complications in the efficient construction of the lattice. We define a shearing coordinate transformation which simultaneously minimizes both of these sources of correlation, and allows us to take advantage of the small prior orbital period uncertainty. The resulting lattices have a factor of about 3 fewer templates than the corresponding parameter space grids constructed by the prior straightforward method, allowing a more sensitive search at the same computing cost and maximum mismatch.

gr-qc↗

arXiv2018

An Analytic Approximation to the Bayesian Detection Statistic for Continuous Gravitational Waves

We consider the Bayesian detection statistic for a targeted search for continuous gravitational waves, known as the $\mathcal{B}$-statistic. This is a Bayes factor between signal and noise hypotheses, produced by marginalizing over the four amplitude parameters of the signal. We show that by Taylor-expanding to first order in certain averaged combinations of antenna patterns (elements of the parameter space metric), the marginalization integral can be performed analytically, producing a closed-form approximation in terms of confluent hypergeometric functions. We demonstrate using Monte Carlo simulations that this approximation is as powerful as the full $\mathcal{B}$-statistic, and outperforms the traditional maximum-likelihood $\mathcal{F}$-statistic, for several observing scenarios which involve an average over sidereal times. We also show that the approximation does not perform well for a near-instantaneous observation, so the approximation is suited to long-time continuous wave observations rather than transient modelled signals such as compact binary inspiral.

gr-qc↗

arXiv2018

OctApps: a library of Octave functions for continuous gravitational-wave data analysis

Gravitational waves are minute ripples in spacetime, first predicted by Einstein's general theory of relativity in 1916. Gravitational waves from rapidly-rotating neutron stars, whose shape deviates from perfect axisymmetry, are a potential astrophysical source of gravitational waves, but which so far have not been detected. The search for this type of signals, also known as continuous waves, presents a significant data analysis challenge, as their weak signatures are expected to be buried deep within the instrumental noise of the LIGO and Virgo detectors. The OctApps library provides various functions, written in Octave, intended to aid research scientists who perform searches for continuous gravitational waves.

astro-ph.IM↗

arXiv2018

Resampling to accelerate cross-correlation searches for continuous gravitational waves from binary systems

Continuous-wave (CW) gravitational waves (GWs) call for computationally-intensive methods. Low signal-to-noise ratio signals need templated searches with long coherent integration times and thus fine parameter-space resolution. Longer integration increases sensitivity. Low-mass x-ray binaries (LMXBs) such as Scorpius X-1 (Sco X-1) may emit accretion-driven CWs at strains reachable by current ground-based observatories. Binary orbital parameters induce phase modulation. This paper describes how resampling corrects binary and detector motion, yielding source-frame time series used for cross-correlation. Compared to the previous, detector-frame, templated cross-correlation method, used for Sco X-1 on data from the first Advanced LIGO observing run (O1), resampling is about 20x faster in the costliest, most-sensitive frequency bands. Speed-up factors depend on integration time and search setup. The speed could be reinvested into longer integration with a forecast sensitivity gain, 20 to 125 Hz median, of approximately 51%, or from 20 to 250 Hz, 11%, given the same per-band cost and setup. This paper's timing model enables future setup optimization. Resampling scales well with longer integration, and at 10x unoptimized cost could reach respectively 2.83x and 2.75x median sensitivities, limited by spin-wandering. Then an O1 search could yield a marginalized-polarization upper limit reaching torque-balance at 100 Hz. Frequencies from 40 to 140 Hz might be probed in equal observing time with 2x improved detectors.

astro-ph.IM↗

arXiv2017

Hierarchical Bayesian Bradley-Terry for Applications in Major League Baseball

A common problem faced in statistical inference is drawing conclusions from paired comparisons, in which two objects compete and one is declared the victor. A probabilistic approach to such a problem is the Bradley-Terry model, first studied by Zermelo in 1929 and rediscovered by Bradley and Terry in 1952. One obvious area of application for such a model is sporting events, and in particular Major League Baseball. With this in mind, we describe a hierarchical Bayesian version of Bradley-Terry suitable for use in ranking and prediction problems, and compare results from these application domains to standard maximum likelihood approaches. Our Bayesian methods outperform the MLE-based analogues, while being simple to construct, implement, and interpret.

stat.AP↗

arXiv2017

Prior Distributions for the Bradley-Terry Model of Paired Comparisons

The Bradley-Terry model assigns probabilities for the outcome of paired comparison experiments based on strength parameters associated with the objects being compared. We consider different proposed choices of prior parameter distributions for Bayesian inference of the strength parameters based on the paired comparison results. We evaluate them according to four desiderata motivated by the use of inferred Bradley-Terry parameters to rate teams on the basis of outcomes of a set of games: invariance under interchange of teams, invariance under interchange of winning and losing, normalizability and invariance under elimination of teams. We consider various proposals which fail to satisfy one or more of these desiderata, and illustrate two proposals which satisfy them. Both are one-parameter independent distributions for the logarithms of the team strengths: 1) Gaussian and 2) Type III generalized logistic.

math.ST↗

arXiv2017

The challenging task of determining star formation rates: the case of a massive stellar burst in the brightest cluster galaxy of Phoenix galaxy cluster

Star formation in galaxies at the center of cooling-flow galaxy clusters is an important phenomenon in the context of formation and evolution of massive galaxies in the Universe. Yet, star formation rates (SFRs) in such systems continue to be elusive. We use our Bayesian-motivated spectral energy distribution (SED)-fitting code, BAYESCOOL, to estimate the plausible SFR values in the brightest cluster galaxy of a massive, X-ray luminous galaxy cluster, Phoenix. Previous studies of Phoenix have resulted in the highest measurement of SFR for any galaxy, with the estimates reaching up to 1000 solar masses/yr. However, a very small number of models have been considered in those studies. BAYESCOOL allows us to probe a large parameter space. We consider two models for star formation history, instantaneous bursts and continuous star formation, a wide range of ages for the old and the young stellar population, along with other discrete parameters, such as the initial mass function, metallicities, internal extinction and extinction law. We find that in the absence of any prior except that the maximum cooling rate < 3000 solar masses/yr, the SFR lies in the range (2230-2890) solar masses/yr. If we impose an observational prior on the internal extinction, E(B-V) < 0.6, the best-fit SFR lies in (454-494) solar masses/yr, and we consider this as the most probable range of SFR values for Phoenix. The SFR dependence on the extinction is a reflection of the standard age-extinction degeneracy, which can be overcome by using a prior on one of the two quantities in question.

astro-ph.GA↗

arXiv2015

Model-Based Cross-Correlation Search for Gravitational Waves from Scorpius X-1

We consider the cross-correlation search for periodic GWs and its potential application to the LMXB Sco X-1. This method coherently combines data from different detectors at the same time, as well as different times from the same or different detectors. By adjusting the maximum time offset between a pair of data segments to be coherently combined, one can tune the method to trade off sensitivity and computing costs. In particular, the detectable signal amplitude scales as the inverse fourth root of this coherence time. The improvement in amplitude sensitivity for a search with a coherence time of 1hr, compared with a directed stochastic background search with 0.25Hz wide bins is about a factor of 5.4. We show that a search of 1yr of data from Advanced LIGO and Advanced Virgo with a coherence time of 1hr would be able to detect GWs from Sco X-1 at the level predicted by torque balance over a range of signal frequencies from 30-300Hz; if the coherence time could be increased to 10hr, the range would be 20-500Hz. In addition, we consider several technical aspects of the cross-correlation method: We quantify the effects of spectral leakage and show that nearly rectangular windows still lead to the most sensitive search. We produce an explicit parameter-space metric for the cross-correlation search in general and as applied to a neutron star in a circular binary system. We consider the effects of using a signal template averaged over unknown amplitude parameters: the search is sensitive to a combination of the intrinsic signal amplitude and the inclination of the neutron star rotation axis, and the peak of the expected detection statistic is systematically offset from the true signal parameters. Finally, we describe the potential loss of SNR due to unmodelled effects such as signal phase acceleration within the Fourier transform timescale and gradual evolution of the spin frequency.

gr-qc↗

arXiv2015

Constraining star formation rates in cool-core brightest cluster galaxies

We used broad-band imaging data for 10 cool-core brightest cluster galaxies (BCGs) and conducted a Bayesian analysis using stellar population synthesis to determine the likely properties of the constituent stellar populations. Determination of ongoing star formation rates (SFRs), in particular, has a direct impact on our understanding of the cooling of the intracluster medium (ICM), star formation and AGN-regulated feedback. Our model consists of an old stellar population and a series of young stellar components. We calculated marginalized posterior probability distributions for various model parameters and obtained 68% plausible intervals from them. The 68% plausible interval on the SFRs is broad, owing to a wide range of models that are capable of fitting the data, which also explains the wide dispersion in the star formation rates available in the literature. The ranges of possible SFRs are robust and highlight the strength in such a Bayesian analysis. The SFRs are correlated with the X-ray mass deposition rates (the former are factors of 4 to 50 lower than the latter), implying a picture where the cooling of the ICM is a contributing factor to star formation in cool-core BCGs. We find that 9 out of 10 BCGs have been experiencing starbursts since 6 Gyr ago. While four out of 9 BCGs seem to require continuous SFRs, 5 out of 9 seem to require periodic star formation on intervals ranging from 20 Myr to 200 Myr. This time scale is similar to the cooling-time of the ICM in the central (< 5 kpc) regions.

astro-ph.CO↗

arXiv2014

New Coordinates for the Amplitude Parameter Space of Continuous Gravitational Waves

The parameter space for continuous gravitational waves (GWs) can be divided into amplitude parameters (signal amplitude, inclination and polarization angles describing the orientation of the source, and an initial phase) and phase-evolution parameters. The division is useful in part because the Jaranowski-Krolak-Schutz (JKS) coordinates on the four-dimensional amplitude parameter space allow the GW signal to be written as a linear combination of four template waveforms with the JKS coordinates as coefficients. We define a new set of coordinates on the amplitude parameter space, with the same properties, which is more closely connected to the physical amplitude parameters. These naturally divide into two pairs of Cartesian-like coordinates on two-dimensional subspaces, one corresponding to left- and the other to right-circular polarization. We thus refer to these as CPF (circular polarization factored) coordinates. The corresponding two sets of polar coordinates (known as CPF-polar) can be related in a simple way to the physical parameters. We illustrate some simplifying applications for these various coordinate systems, such as: a calculation of Jacobians between various coordinate systems; an illustration of the signal coordinate singularities associated with left- and right-circular polarization, which correspond to the origins of the two two-dimensional subspaces; and an elucidation of the form of the log-likelihood ratio between hypotheses of Gaussian noise with and without a continuous GW signal. These are used to illustrate some of the prospects for approximate evaluation of a Bayesian detection statistic defined by marginalization over the physical parameter space. Additionally, in the presence of simplifying assumptions about the observing geometry, we are able to explicitly evaluate the integral for the Bayesian detection statistic, and compare it to the approximate results.

gr-qc↗

arXiv2013

Improving the sensitivity of a search for coalescing binary black holes with non-precessing spins in gravitational wave data

We demonstrate the implementation of a sensitive search pipeline for gravitational waves from coalescing binary black holes whose components have spins aligned with the orbital angular momentum. We study the pipeline recovery of simulated gravitational wave signals from aligned-spin binary black holes added to real detector noise, comparing the pipeline performance with aligned-spin filter templates to the same pipeline with non-spinning filter templates. Our results exploit a three-parameter phenomenological waveform family that models the full inspiral-merger-ringdown coalescence and treats the effect of aligned spins with a single effective spin parameter χ. We construct template banks from these waveforms by a stochastic placement method and use these banks as filters in the recently-developed gstlal search pipeline. We measure the observable volume of the analysis pipeline for binary black hole signals with total mass in [15,25] solar masses and χin [0, 0.85]. We find an increase in observable volume of up to 45% for systems with 0.2 <= χ<= 0.85 with almost no loss of sensitivity to signals with 0 <= χ<= 0.2. We demonstrate this analysis on 25.9 days of data obtained from the Hanford and Livingston detectors in LIGO's fifth observation run.

gr-qc↗

arXiv2012

Herschel observations of extended atomic gas in the core of the Perseus cluster

We present Herschel observations of the core of the Perseus cluster of galaxies. The brightest cluster galaxy, NGC 1275, is surrounded by a network of filaments previously imaged extensively in Hα and CO. In this work, we report detections of FIR lines with Herschel. All but one of the lines are spatially extended, with the [CII] line emission extending up to 25 kpc from the core. There is spatial and kinematical correlation among [CII], Hα and CO, which gives us confidence to model the different components of the gas with a common heating model. With the help of FIR continuum Herschel measurements, together with a suite of coeval radio, submm and infrared data, we performed a SED fitting of NGC 1275 using a model that contains contributions from dust emission as well as synchrotron AGN emission. The data indicate a low dust emissivity index, beta ~ 1, a total dust mass close to 10^7 solar mass, a cold dust component with temperature 38 \pm 2 K and a warm dust component with temperature of 116 \pm 9 K. The FIR-derived star formation rate (SFR) is 24 \pm 1 solar mass per yr, in close agreement with the FUV-derived SFR. We investigated in detail the source of the Herschel FIR and Hα emissions emerging from a core region 4 kpc in radius. Based on simulations conducted using the radiative transfer code, CLOUDY, a heating model comprising old and young stellar populations is sufficient to explain these observations. We have also detected [CII] in three well-studied regions of the filaments. We find a [OI]/[CII] ratio about 1 dex smaller than predicted by the otherwise functional Ferland (2009) model. The line ratio suggests that the lines are optically thick, as is typical of galactic PDRs, and implies that there is a large reservoir of cold atomic gas. [abridged]

astro-ph.CO↗

arXiv2012

Treatment of Calibration Uncertainty in Multi-Baseline Cross-Correlation Searches for Gravitational Waves

Uncertainty in the calibration of gravitational-wave (GW) detector data leads to systematic errors which must be accounted for in setting limits on the strength of GW signals. When cross-correlation measurements are made using data from a pair of instruments, as in searches for a stochastic GW background, the calibration uncertainties of the individual instruments can be combined into an uncertainty associated with the pair. With the advent of multi-baseline GW observation (e.g., networks consisting of multiple detectors such as the LIGO observatories and Virgo), a more sophisticated treatment is called for. We describe how the correlations between calibration factors associated with different pairs can be taken into account by marginalizing over the uncertainty associated with each instrument.

gr-qc↗

arXiv2011

Designing a cross-correlation search for continuous-wave gravitational radiation from a neutron star in the supernova remnant SNR 1987A

A strategy is devised for a semi-coherent cross-correlation search for a young neutron star in the supernova remnant SNR 1987A, using science data from the Initial LIGO and/or Virgo detectors. An astrophysical model for the gravitational wave phase is introduced which describes the star's spin down in terms of its magnetic field strength $B$ and ellipticity $ε$, instead of its frequency derivatives. The model accurately tracks the gravitational wave phase from a rapidly decelerating neutron star under the restrictive but computationally unavoidable assumption of constant braking index, an issue which has hindered previous searches for such young objects. The theoretical sensitivity is calculated and compared to the indirect, age-based wave strain upper limit. The age-based limit lies above the detection threshold in the frequency band 75\,Hz $\lesssim ν\lesssim 450$\,Hz. The semi-coherent phase metric is also calculated and used to estimate the optimal search template spacing for the search. The range of search parameters that can be covered given our computational resources ($\sim 10^9$ templates) is also estimated. For Initial LIGO sensitivity, in the frequency band between 50\,Hz and 500\,Hz, in the absence of a detected signal, we should be able to set limits of $B \gtrsim 10^{11}$\,G and $ε\lesssim 10^{-4}$.

gr-qc↗