arXiv subjects

Neil J. Cornish

Publications and source records attributed to Neil J. Cornish.

At least 19 recordsLinked to original sources

arXiv2026

A compact time-frequency representation for gravitational-wave data analysis

Time-frequency (wavelet) domain analyses are seeing greater use for gravitational-wave data analysis due to the advantages they have in handling non-stationary noise. A popular choice is the Wilson-Daubechies-Meyer (WDM) wavelet transform, which uses a window function that is very compact in frequency, but more spread out in time. In this work, we consider an alternative window function that is built from a sum of phase-shifted Gaussians. This "Gaussian" window is more symmetric in time-frequency, and consequently more compact. We examine the properties of this window function and the implications it has for gravitational-wave analyses. We calculate the window's time-frequency variance product analytically and verify it numerically. For the symmetric case, where the window has the same form in time and frequency, the construction comes within $\sim2.4\%$ of saturating the Heisenberg-Gabor uncertainty limit. We conjecture that this Gaussian window achieves the minimum time-frequency area of any WD wavelet window.

gr-qc↗

arXiv2026

Pulsar Timing Array Sensitivity to Anisotropy: Empirical Sensitivity Curves, Scaling Relations, and the Multi-Resolution Pixel Basis

We quantify pulsar timing array (PTA) sensitivity to anisotropy in the gravitational wave background using the cross-correlation based Fisher information matrix in the pixel and spherical harmonic bases. We use a set of simulations to empirically determine scaling relations of a PTA's sensitivity to anisotropy with the number of pulsars $N_\mathrm{psr}$ in the array, the error $\delta t$ on the times of arrival, the frequency $f_\mathrm{GW}$ of the gravitational waves, and the angular scale $\Delta\Omega$ of the anisotropy. The sensitivity scales approximately as $N_\mathrm{psr}^{0.8}$, $\delta t^{-0.08}$, and $\Delta\Omega^{1.6}-\Delta\Omega^{2.1}$ (depending on the ranges of $\ell$ and $m$ under consideration). In addition, we use realistic simulations to project the NANOGrav PTA sensitivity to a 30-year baseline and quantify the growth in sensitivity at several timeslices. Except at the lowest frequencies, we find negligible effect on sensitivity through increasing the observation duration only. Finally, we introduce a multi-resolution pixel basis motivated by the large dependence of the sensitivity on sky location, and demonstrate the operation of the basis through a set of injections and recoveries.

astro-ph.IM↗

arXiv2026

GUEST: Gravitational Universe Exploration with Satellite Tracking. A passive satellite laser-ranging mission for the dark gravitational Universe

GUEST is a space mission concept whose central objective is the detection of gravitational waves (GWs) in the microhertz band -- a physics-rich frequency window that no other present or planned detector can reach at a significant level. The concept is simple: two dense, passive spheres, covered with cube-corner retroreflectors, deployed in {highly eccentric} Earth orbits ($e \gtrsim 0.7$, period $P \gtrsim 33$ h), tracked continuously by the global network of satellite laser-ranging stations over a minimum observation time of 10 years, with an expected total duration of 30 years. The orbits themselves act as resonant detectors of the oscillating gravitational perturbations, with the microhertz sensitivity emerging from the selected orbital parameters. From the same data stream, GUEST delivers a programme of fundamental and applied science that cuts across particle physics, gravitational-wave astronomy, cosmology, astrophysics, and geodesy: the first coherent search for GWs from supermassive black-hole binaries in the $\mu$Hz band, the exploration of primordial GW backgrounds in the unexplored energy-scale gap between pulsar-timing arrays and LISA, a dedicated probe of ultra-light dark matter in a parameter region untouched by any other experiment, a new way to search for ultra-light bosons, order-of-magnitude-improved tests of new gravitational interactions at astronomical ranges, and a step change in the absolute determination of $GM_\oplus$ that underpins the Global Geodetic Observing System and future navigation and Earth-observation missions. This white paper presents the motivation, scientific reach, and mission concept of GUEST.

astro-ph.CO↗

arXiv2026

Modeling non-stationary noise: applications in gravitational wave astronomy

In an ideal world, the measurement noise in gravitational wave data would be stationary and Gaussian. In reality, neither of these conditions holds. Here a general framework is introduced that can be used to model non-stationary noise in an easily interpretable way, using a dynamic power spectrum $S(f,t)$. The construction is a Gram-factor model for the noise covariance matrix that is positive semi-definite by construction. This construction generalizes the familiar stationary power spectrum $S(f)$. The dynamic spectrum encodes the properties of the noise covariance matrix in any basis, including the frequency domain, time domain, and time-frequency wavelet domain. Closed form expressions are given for discrete Fourier representations of the data, and for discrete Wilson-Daubechies wavelet representations of the data. Both take the form of Gramian matrices. Examples are provided, including the non-stationarity caused by window functions, the modulated response to galactic binary signals for space-based detectors, and other, more general types of non-stationarity.

gr-qc↗

arXiv2026

A new framework for lightning-fast gravitational wave analysis of pulsar timing data

Pulsar timing array data analysis is computationally expensive, limiting the complexity of models which can be studied. As pulsar timing datasets and their respective models grow in size and sophistication, faster and scalable inference methods are essential. In this paper, we accelerate pulsar timing analyses by sampling in the space of Fourier coefficients instead of analytically marginalizing over them. Previous studies have shown the Fourier space induces a complex, high-dimensional posterior geometry, from which it is generally difficult to sample. We show that under an appropriate coordinate transformation the Fourier coefficients approximately follow a standard normal distribution, and may be efficiently sampled using a Hamiltonian Monte Carlo scheme. Under this coordinate transformation, for datasets of size and complexity comparable to the NANOGrav 15-year release, the new method produces converged posterior distributions for a range of models which include inter-pulsar correlations, stochastic, and deterministic signals in approximately 15 minutes on an NVIDIA GeForce RTX 3090 GPU. By comparison, the legacy pulsar timing analysis software \texttt{ENTERPRISE} would require months of computation on a CPU cluster to analyze comparable datasets under the same joint stochastic and deterministic models.

gr-qc↗

arXiv2026

The NANOGrav 15 yr Data Set: Impacts of Customized Chromatic Noise Models on Gravitational Wave Analyses

We report updated nHz gravitational wave (GW) significance, characterization, and interpretations using the customized chromatic-noise models (CNMs) developed in Larsen, Baier et al. (2026). for the NANOGrav 15-year data set. We find increased evidence for the Hellings-Downs (HD) correlation signature of the stochastic gravitational wave background (GWB), with a Bayes factor of $1571\pm14$ for HD-correlations over a common uncorrelated red-noise process using a power-law model with $14$ Fourier modes. We find this $\sim8\times$ increase in Bayes factor from Agazie et al. (2023a) is a result of improved noise mitigation. Assuming an analytic null distribution for the frequentist interpulsar correlation statistic, this corresponds to a slightly more significant measurement from $3.16\sigma$ to $3.32\sigma$ against the no-correlation scenario. Spectral inference with CNMs brings the power-law GWB amplitude down to $A_{\rm GWB} = 2.1^{+0.6}_{-0.5}\times10^{-15}$ at fixed $\gamma_{\rm GWB} = 13/3$. In a varied-$\gamma$ analysis, the spectral index increases to $\gamma_{\rm GWB}=3.5^{+0.7}_{-0.6}$. We report updates on an all-sky continuous gravitational wave (CW) search as well as select targeted searches and calculate a $3.2\times$ larger detection volume for the NANOGrav detector. With CNMs, we find reduced evidence for a non-Einsteinian, scalar-transverse mode of gravity. Finally, we reinterpret the GWB first with the assumption of an astrophysical background sourced by SMBHBs and then assuming the more exotic origins of cosmic inflation, a first-order cosmological phase transition, and stable cosmic strings. Under both the SMBHB hypothesis and the cosmological hypotheses, we see only marginal shifts in model parameter posteriors which are consistent with the slightly quieter and steeper power-law GWB spectrum.

astro-ph.CO↗

arXiv2026

MaxWave Signal: Rapid, coherent maximum likelihood wavelet reconstruction of transient signals in gravitational wave data

Advances in gravitational-wave detector sensitivity have increased the rate of transient signal detections, demanding faster automated analysis. We extend MaxWave, a fast maximum likelihood wavelet reconstruction algorithm, to perform coherent multi-detector signal reconstruction and glitch rejection. We coherently search for a common set of wavelets modeling the signal in all detectors. Multi-detector data are aligned using z-statistic time and phase offsets and amplitude scalings relative to the dominant reconstruction, as well as adaptive noise weightings derived from a geometrically averaged noise spectrum. By aligning and weighting individual detectors, we form a synthetic detector that amplifies non-Gaussian features, down-weights noisy detectors, and preserves Gaussian noise statistics. We extract the coherent signal using this synthetic detector, improving sensitivity to weak events while rejecting coincident glitches that lack consistent phase and amplitude evolution. Our algorithm provides real-time, low-latency, model-independent signal reconstructions, safely denoises gravitational wave data without removing transient signals, and can complement existing burst search and reconstruction frameworks through a fundamentally distinct approach, strengthening detection confidence and improving sensitivity to diverse signal morphologies.

gr-qc↗

arXiv2026

Detecting classical nova-like explosions with LISA

Gravitational waves from close binary white dwarfs will form the bulk of measurements obtained by the Laser Interferometer Space Antenna (LISA). Previous studies have highlighted the importance of including the effects of steady-state mass transfer in waveform models as many individually resolvable white dwarf binaries will be interacting during the LISA observation window. However, few studies have considered the effect of novae on gravitational wave observations and parameter estimations. We fill in this gap by analyzing the detectability of novae in these systems and the biases in physical parameters when these bursts are not considered. We model a nova burst as a rapid loss of mass from the accretor that suddenly shifts the gravitational wave frequency. We analytically predict the signal-to-noise ratios for direct detection of the nova and where bias from mismodeling becomes greater than the statistical uncertainty. We also consider comparison of two halves of future LISA data to detect bursts in a model agnostic way. Our work has implications for identifying and classifying individual nova events as well as constraining the galactic nova rate throughout the entire galaxy, a challenging task for optical surveys.

astro-ph.HE↗

arXiv2026

Searching for a waveform-agnostic gravitational wave signal in pulsar timing arrays

Pulsar timing arrays have recently provided compelling evidence for a nanohertz stochastic gravitational wave background, motivating searches for gravitational waves from localized sources. Most existing searches assume specific waveform templates, which can be computationally demanding and potentially insensitive to unexpected signals. We introduce a waveform-agnostic framework that models signal-induced timing residuals via a Fourier expansion. A Lorentzian hyperprior is imposed on the variances of the Fourier coefficients, providing a flexible spectral envelope that captures the signal's dominant frequency and bandwidth while remaining agnostic to its exact shape. Analytical marginalization over the Fourier coefficients then yields a Bayesian hierarchical framework that concurrently infers the source sky location, its frequency content, and the stochastic background. To mitigate contamination from unmodeled pulsar noise, we further allow for additional flat-spectrum features for each pulsar. Tests on simulated datasets show that the method is robust and provides a flexible tool for future PTA searches, with sensitivity to both expected and unexpected gravitational wave phenomena.

gr-qc↗

arXiv2026

Gravitational Wave Measurement of the $M_\mathrm{BH}$-$M_\mathrm{bulge}$ Intrinsic Scatter at High Redshift

The observed GWB spectrum is higher in amplitude than model predictions by a factor of 2-3. Using a semi-analytic model, we evaluate the effect of a high-scatter supermassive black hole (SMBH) scaling relation ($M_\mathrm{BH}$-$M_\mathrm{bulge}$) on models of the nanohertz gravitational wave background (GWB). By implementing an intrinsic scatter of the $M_\mathrm{BH}$-$M_\mathrm{bulge}$ relation, which is larger at higher redshift, but matches local observations, we find that the amplitude of GWB models increases to be consistent with the low-frequency end of the GWB spectrum. This amplitude increase is not uniform across frequencies, a strongly evolving scatter preferentially increases the number density of the most massive SMBHs which, in the GWB spectrum, minimizes the strength of the low-frequency turnover. Our models with positively evolving intrinsic scatter can reproduce the electromagnetically observed overmassive SMBHs at $4 < z < 6$ without changing the $M_\mathrm{BH}$-$M_\mathrm{bulge}$ normalization though we find that including moderate normalization evolution marginally improves fits to the GWB data. We conclude that the $M_\mathrm{BH}$-$M_\mathrm{bulge}$ relation which best describes the available GWB and electromagnetic data sets has intrinsic scatter that evolves as $\varepsilon(z) = \varepsilon_0 + (0.56 \pm 0.4) \log_{10}(1 + z)$ and normalization that evolves as $\alpha(z) = \alpha_0 (1 + z)^{0.84 \pm 0.35}$. The results of this work imply that the $M_\mathrm{BH}$-$M_\mathrm{bulge}$ relation we see today is not universal throughout cosmic time and that a diversity of seeding models and growth mechanisms may be at play in the early stages of SMBH-galaxy evolution.

astro-ph.HE↗

arXiv2026

The NANOGrav 15 yr Data Set: Piecewise Power-Law Reconstruction of the Gravitational-Wave Background

The NANOGrav 15-year (NG15) data set provides evidence for a gravitational-wave background (GWB) signal at nanohertz frequencies, which is expected to originate either from a cosmic population of inspiraling supermassive black-hole binaries or new particle physics in the early Universe. A firm identification of the source of the NG15 signal requires an accurate reconstruction of its frequency spectrum. In this paper, we provide such a spectral characterization of the NG15 signal based on a piecewise power-law (PPL) ansatz that strikes a balance between existing alternatives in the literature. Our PPL reconstruction is more flexible than the standard constant-power-law model, which describes the GWB spectrum in terms of only two parameters: an amplitude A and a spectral index gamma. Concurrently, it better approximates physically realistic GWB spectra -- especially those of cosmological origin -- than the free spectral model, since the latter allows for arbitrary variations in the GWB amplitude from one frequency bin to the next. Our PPL reconstruction of the NG15 signal relies on individual PPL models with a fixed number of internal nodes (i.e., constant power law, broken power law, doubly broken power law, etc.) that are ultimately combined in a Bayesian model average. The data products resulting from our analysis provide the basis for fast refits of spectral GWB models.

astro-ph.HE↗

arXiv2025

Non-stationary noise in gravitational wave analyses: The wavelet domain noise covariance matrix

Gravitational wave detectors produce time series of the gravitational wave strain co-added with instrument noise. For evenly sampled data, such as from laser interferometers, it has been traditional to Fourier transform the data and perform analyses in the frequency domain. The motivation being that the Fourier domain noise covariance matrix will be diagonal if the noise properties are constant in time, which greatly simplifies and accelerates the analysis. However, if the noise is non-stationary this advantage is lost. It has been proposed that the time-frequency or wavelet domain is better suited for studying non-stationary noise, at least when the time variation is suitably slow, since then the wavelet domain noise covariance matrix is, to a good approximation, diagonal. Here we investigate the conditions under which the diagonal approximation is appropriate for the case of the Wilson-Daubechies-Meyer (WDM) wavelet packet basis, which is seeing increased use in gravitational wave data analysis. We show that so long as the noise varies slowly across a wavelet pixel, in both time {\em and} frequency, the WDM noise correlation matrix is well approximated as diagonal. The off-diagonal terms are proportional to the time and frequency derivatives of the dynamic spectral model. The same general picture should apply to other discrete wavelet transforms with wavelet filters that are suitably compact in time and frequency. Strategies for handling data with rapidly varying noise that violate these assumptions are discussed.

gr-qc↗

arXiv2025

Escaping Neal's Funnel: a multi-stage sampling method for hierarchical models

Neal's funnel refers to an exponential tapering in probability densities common to Bayesian hierarchical models. Usual sampling methods, such as Markov Chain Monte Carlo, struggle to efficiently sample the funnel. Reparameterizing the model or analytically marginalizing local parameters are common techniques to remedy sampling pathologies in distributions exhibiting Neal's funnel. In this paper, we show that the challenges of Neal's funnel can be avoided by performing the hierarchical analysis, well, hierarchically. That is, instead of sampling all parameters of the hierarchical model jointly, we break the sampling into multiple stages. The first stage samples a generalized (higher-dimensional) hierarchical model which is parameterized to lessen the sharpness of the funnel. The next stage samples from the estimated density of the first stage, but under a constraint which restricts the sampling to recover the marginal distributions on the hyper-parameters of the original (lower-dimensional) hierarchical model. A normalizing flow can be used to represent the distribution from the first stage, such that it can easily be sampled from for the second stage of the analysis. This technique is useful when effective reparameterizations are computationally expensive to calculate, or a generalized hierarchical model already exists from which it is easy to sample.

stat.ME↗

arXiv2025

Rapid inference for individual binaries and a stochastic background with pulsar timing array data

The analysis of pulsar timing array data has provided evidence for a gravitational wave background in the nanohertz band. This raises the question of what is the source of the signal, is it astrophysical or cosmological in origin? If the signal originates from a population of supermassive black hole binaries, as is generally assumed, we can expect to see evidence for both anisotropy and to be able to resolve signals from individual binaries as more data are collected. The anisotropy and resolvable systems are caused by a small number of loud signals that stand out from the crowd. Here we focus on the joint detection of individual signals and a stochastic background. While methods have previously been developed to perform such an analysis, they are currently held back by the cost of computing the joint likelihood function. Each individual source is described by $N=8+2N_p$ parameters, where $N_p$ are the number of pulsars in the array. With the latest combined datasets having over one hundred pulsars, the parameter space is very large, and consequently, it takes a large number of likelihood evaluations to explore these models. Here we present a new approach that extends the Fourier basis method, previously introduced to accelerate analyses for stochastic signals, to also include deterministic signals. Key elements of the method are that the likelihood evaluations are per-pulsar, avoiding expensive operations on large matrices, and the templates for individual binaries can be computed analytically or using fast Fourier methods on a sparsely sampled grid of time samples. This analysis method scales better than quadratically with the size of the dataset, while the approach currently being used in most analyses scales quartically or worse with the number of data points. As datasets grow with more observations, this analysis will be orders of magnitude faster than previous approaches.

gr-qc↗

arXiv2025

Handling Data Gaps for the Next Generation of Gravitational-Wave Observatories

In the coming decades, as the low frequency sensitivity of detectors improves, the time that gravitational-wave signals remain in the sensitive band will increase, leading to new challenges in analyzing data, namely non-stationary noise and data gaps. Time-frequency (wavelet) methods can efficiently handle non-stationary noise, but data gaps still lead to spectral leakage due to the finite length of the wavelet filters. It was previously shown that Bayesian data augmentation - "gap filling" - could mitigate spectral leakage in frequency domain analyses, but the computational cost associated with the matrix operations needed in that approach is prohibitive. Here we present a new, computationally efficient approach to Bayesian data augmentation in the time-frequency domain that avoids repeated, costly matrix operations. We show that our approach efficiently solves the problem of data gaps in simulated LISA data, and can be smoothly integrated into the LISA Global Fit. The same approach can also be used for future 3G ground-based interferometers.

gr-qc↗

arXiv2025

Uncertainty-aware waveform modeling for high signal-to-noise ratio gravitational-wave inference

Semi-analytical waveform models for black hole binaries require calibration against numerical relativity waveforms to accurately represent the late inspiral and merger, where analytical approximations fail. After the fitting coefficients contained in the model are optimized, they are typically held fixed when the model is used to infer astrophysical parameters from real gravitational-wave data. Though point estimates for the fitting parameters are adequate for most applications, they provide an incomplete description of the fit, as they do not account for either the quality of the fit or the intrinsic uncertainties in the numerical relativity data. Using the IMRPhenomD model, we illustrate how to propagate these uncertainties into the inference by sampling the fitting coefficients from a prior distribution and marginalizing over them. The prior distribution is constructed by ensuring that the model is compatible with a training set of numerical relativity surrogates, within a predefined mismatch threshold. This approach demonstrates a pathway to mitigate systematic bias in high signal-to-noise events, particularly when envisioned for the next generation of semi-analytical models.

gr-qc↗

arXiv2025

The NANOGrav 15 yr Data Set: Targeted Searches for Supermassive Black Hole Binaries

We present the first targeted searches for continuous gravitational waves (CWs) from 114 active galactic nuclei (AGN) that may host supermassive black hole binaries, using the NANOGrav 15 yr data set. By incorporating electromagnetic priors on sky location, distance, redshift, and CW frequency, our strain and chirp mass upper limits are typically improved by a factor of $\sim 2$ (median 2.2) relative to all-sky limits at the same frequency. Bayesian comparisons against a model including only a Hellings-Downs correlated background disfavors a CW signal for all targets, with a mean Bayes factor of $0.73 \pm 0.32$. Two targets have Bayes factors slightly above unity, but coherence tests, random targeting experiments, and a conservative accounting of the 114-target trials factor all indicate that they are consistent with noise. We use these two candidates as worked examples to illustrate an end-to-end targeted CW search analysis and a suite of follow up tests that future promising candidates would need to pass. We find that the electromagnetic interpretations of both candidates are ambiguous, and we update the constraints on a putative binary in 3C 66B, ruling out part of its previously allowed parameter space. Ultimately, our results demonstrate the current sensitivity of targeted pulsar timing array searches for CWs and define a roadmap for future multimessenger CW detections.

astro-ph.HE↗

arXiv2025

MaxWave: Rapid maximum likelihood wavelet reconstruction of non-Gaussian features in gravitational wave data

Advancements in the sensitivity of gravitational wave detectors have increased the detection rate of transient astrophysical signals. We improve the existing BayesWave initialization algorithm and present a rapid, low latency approximate maximum likelihood solution for reconstructing non-Gaussian features. We include three enhancements: (1) using a modified wavelet basis to eliminate redundant inner product calculations; (2) shifting from traditional time-frequency-quality factor wavelet transforms to time-frequency-time extent transforms to optimize wavelet subtractions; and (3) implementing a downsampled heterodyned wavelet transform to accelerate initial calculations. Our model can be used to denoise long-duration signals, which include the stochastic gravitational wave background from numerous unresolved sources and continuous wave signals from isolated sources such as rotating neutron stars. Through our model, we can also supplement machine learning applications that use spectrographic training data to classify and understand glitches by providing nonwhitened, time and frequency domain reconstructions of any glitch.

gr-qc↗