arXiv subjects

Stephen Taylor

Publications and source records attributed to Stephen Taylor.

14 recordsLinked to original sources

arXiv2025

Multi-messenger Analysis of Supermassive Black Hole Binaries: The Joint-likelihood Approach

Supermassive black hole binaries (SMBHBs) formed in galaxy mergers are promising multi-messenger sources. They can be identified as quasars with periodic variability in electromagnetic (EM) time-domain surveys. The most massive of those systems can be detected by Pulsar Timing Arrays (PTAs) in the nanohertz frequency gravitational-wave (GW) band. We present a method to simultaneously analyze EM lightcurves and PTA observations as a multi-messenger data stream. For this, we employ a joint likelihood analysis, in which the likelihood of the EM data and the PTA likelihood are multiplied. We test this approach by simulating 208 binary signals that can be detected both by the Rubin Observatory in the nominal ten-year survey and by a PTA dataset with a ~30-year baseline, which resembles our expectations for a dataset of the International Pulsar Timing Array (IPTA) collaboration in ~2035. We compare our multi-messenger analysis with analyses that take into account the EM and PTA data separately. We find that the joint likelihood approach results in improved parameter estimation with smaller percent errors compared to the distinct analyses that consider only EM or PTA data separately. Among the SMBHB parameters, the binary total mass and the orbital inclination show the greatest improvement. We also compare our multi-messenger pipeline with an analysis, in which the EM constraints are used as priors to the PTA analysis. We demonstrate that the joint likelihood approach delivers tighter constraints on all binary parameters, with systematically higher values of Kullback-Leibler divergence, which measures the deviation of the posterior distribution from the prior.

astro-ph.GA↗

arXiv2025

Inferring Mbh-Mbulge Evolution from the Gravitational Wave Background

We test the impact of an evolving supermassive black hole (SMBH) mass scaling relation (Mbh-Mbulge) on the predictions for the gravitational wave background (GWB). The observed GWB amplitude is 2-3 times higher than predicted by astrophysically informed models which suggests the need to revise the assumptions in those models. We compare a semi-analytic model's ability to reproduce the observed GWB spectrum with a static versus evolving-amplitude Mbh-Mbulge relation. We additionally consider the influence of the choice of galaxy stellar mass function on the modeled GWB spectra. Our models are able to reproduce the GWB amplitude with either a large number density of massive galaxies or a positively evolving Mbh-Mbulge amplitude (i.e., the Mbh / Mbulge ratio was higher in the past). If we assume that the Mbh-Mbulge amplitude does not evolve, our models require a galaxy stellar mass function that implies an undetected population of massive galaxies (Mstellar > 10^11 Msun at z > 1). When the Mbh-Mbulge amplitude is allowed to evolve, we can model the GWB spectrum with all fiducial values and an Mbh-Mbulge amplitude that evolves as alpha(z) = alpha_0 (1 + z)^(1.04 +/- 0.5).

astro-ph.HE↗

arXiv2025

Iterative Refinement of Arbitrary Micro-Optical Surfaces

We introduce an adaptive optical refinement method enabling ultra-precise micro-milling of arbitrary surfaces. Through repeated iteration, our method reduces surface error without requiring significant specific surface engineering. This remediates the long sample preparation times and lack of refinement capability that previously reported methods suffer from. The iterative refinement milling method was used to produce spherical mirrors with small radii of curvature and low surface roughness for use in micro Fabry-Perot cavities. We demonstrate the use of this adaptive process to produce a variety of arbitrary surface geometries on both optical fiber tips as well as optical flats. We additionally discuss our capability to apply iterative refinement milling adaptively to various materials, including to construct GRIN lenses.

physics.optics↗

arXiv2023

The NANOGrav 15-year Data Set: Bayesian Limits on Gravitational Waves from Individual Supermassive Black Hole Binaries

Evidence for a low-frequency stochastic gravitational wave background has recently been reported based on analyses of pulsar timing array data. The most likely source of such a background is a population of supermassive black hole binaries, the loudest of which may be individually detected in these datasets. Here we present the search for individual supermassive black hole binaries in the NANOGrav 15-year dataset. We introduce several new techniques, which enhance the efficiency and modeling accuracy of the analysis. The search uncovered weak evidence for two candidate signals, one with a gravitational-wave frequency of $\sim$4 nHz, and another at $\sim$170 nHz. The significance of the low-frequency candidate was greatly diminished when Hellings-Downs correlations were included in the background model. The high-frequency candidate was discounted due to the lack of a plausible host galaxy, the unlikely astrophysical prior odds of finding such a source, and since most of its support comes from a single pulsar with a commensurate binary period. Finding no compelling evidence for signals from individual binary systems, we place upper limits on the strain amplitude of gravitational waves emitted by such systems.

astro-ph.HE↗

arXiv2022

The Lick Observatory Supernova Search follow-up program: photometry data release of 70 stripped-envelope supernovae

We present BVRI and unfiltered Clear light curves of 70 stripped-envelope supernovae (SESNe), observed between 2003 and 2020, from the Lick Observatory Supernova Search (LOSS) follow-up program. Our SESN sample consists of 19 spectroscopically normal SNe~Ib, two peculiar SNe Ib, six SN Ibn, 14 normal SNe Ic, one peculiar SN Ic, ten SNe Ic-BL, 15 SNe IIb, one ambiguous SN IIb/Ib/c, and two superluminous SNe. Our follow-up photometry has (on a per-SN basis) a mean coverage of 81 photometric points (median of 58 points) and a mean cadence of 3.6d (median of 1.2d). From our full sample, a subset of 38 SNe have pre-maximum coverage in at least one passband, allowing for the peak brightness of each SN in this subset to be quantitatively determined. We describe our data collection and processing techniques, with emphasis toward our automated photometry pipeline, from which we derive publicly available data products to enable and encourage further study by the community. Using these data products, we derive host-galaxy extinction values through the empirical colour evolution relationship and, for the first time, produce accurate rise-time measurements for a large sample of SESNe in both optical and infrared passbands. By modeling multiband light curves, we find that SNe Ic tend to have lower ejecta masses and lower ejecta velocities than SNe~Ib and IIb, but higher $^{56}$Ni masses.

astro-ph.HE↗

arXiv2020

UWB @ DIACR-Ita: Lexical Semantic Change Detection with CCA and Orthogonal Transformation

In this paper, we describe our method for detection of lexical semantic change (i.e., word sense changes over time) for the DIACR-Ita shared task, where we ranked $1^{st}$. We examine semantic differences between specific words in two Italian corpora, chosen from different time periods. Our method is fully unsupervised and language independent. It consists of preparing a semantic vector space for each corpus, earlier and later. Then we compute a linear transformation between earlier and later spaces, using CCA and Orthogonal Transformation. Finally, we measure the cosines between the transformed vectors.

cs.CL↗

arXiv2020

UWB at SemEval-2020 Task 1: Lexical Semantic Change Detection

In this paper, we describe our method for the detection of lexical semantic change, i.e., word sense changes over time. We examine semantic differences between specific words in two corpora, chosen from different time periods, for English, German, Latin, and Swedish. Our method was created for the SemEval 2020 Task 1: \textit{Unsupervised Lexical Semantic Change Detection.} We ranked $1^{st}$ in Sub-task 1: binary change detection, and $4^{th}$ in Sub-task 2: ranked change detection. Our method is fully unsupervised and language independent. It consists of preparing a semantic vector space for each corpus, earlier and later; computing a linear transformation between earlier and later spaces, using Canonical Correlation Analysis and Orthogonal Transformation; and measuring the cosines between the transformed vector for the target word from the earlier corpus and the vector for the target word in the later corpus.

cs.CL↗

arXiv2015

The NANOGrav Nine-year Data Set: Limits on the Isotropic Stochastic Gravitational Wave Background

We compute upper limits on the nanohertz-frequency isotropic stochastic gravitational wave background (GWB) using the 9-year data release from the North American Nanohertz Observatory for Gravitational Waves (NANOGrav) collaboration. We set upper limits for a GWB from supermassive black hole binaries under power law, broken power law, and free spectral coefficient GW spectrum models. We place a 95\% upper limit on the strain amplitude (at a frequency of yr$^{-1}$) in the power law model of $A_{\rm gw} < 1.5\times 10^{-15}$. For a broken power law model, we place priors on the strain amplitude derived from simulations of Sesana (2013) and McWilliams et al. (2014). We find that the data favor a broken power law to a pure power law with odds ratios of 22 and 2.2 to one for the McWilliams and Sesana prior models, respectively. The McWilliams model is essentially ruled out by the data, and the Sesana model is in tension with the data under the assumption of a pure power law. Using the broken power-law analysis we construct posterior distributions on environmental factors that drive the binary to the GW-driven regime including the stellar mass density for stellar-scattering, mass accretion rate for circumbinary disk interaction, and orbital eccentricity for eccentric binaries, marking the first time that the shape of the GWB spectrum has been used to make astrophysical inferences. We then place the most stringent limits so far on the energy density of relic GWs, $\Omega_\mathrm{gw}(f)\,h^2 < 4.2 \times 10^{-10}$, yielding a limit on the Hubble parameter during inflation of $H_*=1.6\times10^{-2}~m_{Pl}$, where $m_{Pl}$ is the Planck mass. Our limit on the cosmic string GWB, $\Omega_\mathrm{gw}(f)\, h^2 < 2.2 \times 10^{-10}$, translates to a conservative limit of $G\mu<3.3\times 10^{-8}$ - a factor of 4 better than the joint Planck and high-$l$ CMB data from other experiments.

astro-ph.GA↗

arXiv2014

Accelerated Bayesian model-selection and parameter-estimation in continuous gravitational-wave searches with pulsar-timing arrays

We describe several new techniques which accelerate Bayesian searches for continuous gravitational-wave emission from supermassive black-hole binaries using pulsar timing arrays. These techniques mitigate the problematic increase of search-dimensionality with the size of the pulsar array which arises from having to include an extra parameter per pulsar as the array is expanded. This extra parameter corresponds to searching over the phase of the gravitational-wave as it propagates past each pulsar so that we can coherently include the pulsar-term in our search strategies. Our techniques make the analysis tractable with powerful evidence-evaluation packages like MultiNest. We find good agreement of our techniques with the parameter-estimation and Bayes factor evaluation performed with full signal templates, and conclude that these techniques make excellent first-cut tools for detection and characterisation of continuous gravitational-wave signals with pulsar timing arrays. Crucially, at low to moderate signal-to-noise ratios the factor by which the analysis is sped up can be > 100, permitting rigorous programs of systematic injection and recovery of signals to establish robust detection criteria within a Bayesian formalism.

gr-qc↗

arXiv2014

Mapping gravitational-wave backgrounds using methods from CMB analysis: Application to pulsar timing arrays

We describe an alternative approach to the analysis of gravitational-wave backgrounds, based on the formalism used to characterise the polarisation of the cosmic microwave background. In contrast to standard analyses, this approach makes no assumptions about the nature of the background and so has the potential to reveal much more about the physical processes that generated it. An arbitrary background can be decomposed into modes whose angular dependence on the sky is given by gradients and curls of spherical harmonics. We derive the pulsar timing overlap reduction functions for the individual modes, which are given by simple combinations of spherical harmonics evaluated at the pulsar locations. We show how these can be used to recover the components of an arbitrary background, giving explicit results for both isotropic and anisotropic uncorrelated backgrounds. We also find that the response of a pulsar timing array to curl modes is identically zero, so half of the gravitational-wave sky will never be observed using pulsar timing, no matter how many pulsars are included in the array. An isotropic, unpolarised and uncorrelated background can be accurately represented using only three modes, and so a search of this type will be only slightly more complicated than the standard cross-correlation search using the Hellings and Downs overlap reduction function. However, by measuring the components of individual modes of the background and checking for consistency with isotropy, this approach has the potential to reveal much more information. Each individual mode on its own describes a background that is correlated between different points on the sky. A measurement of the components that indicates the presence of correlations in the background on large angular scales would suggest startling new physics.

gr-qc↗

arXiv2013

Hyper-efficient model-independent Bayesian method for the analysis of pulsar timing data

A new model independent method is presented for the analysis of pulsar timing data and the estimation of the spectral properties of an isotropic gravitational wave background (GWB). We show that by rephrasing the likelihood we are able to eliminate the most costly aspects of computation normally associated with this type of data analysis. When applied to the International Pulsar Timing Array Mock Data Challenge data sets this results in speedups of approximately 2 to 3 orders of magnitude compared to established methods. We present three applications of the new likelihood. In the low signal to noise regime we sample directly from the power spectrum coefficients of the GWB signal realization. In the high signal to noise regime, where the data can support a large number of coefficients, we sample from the joint probability density of the power spectrum coefficients for the individual pulsars and the GWB signal realization. Critically in both these cases we need make no assumptions about the form of the power spectrum of the GWB, or the individual pulsars. Finally we present a method for characterizing the spatial correlation between pulsars on the sky, making no assumptions about the form of that correlation, and therefore providing the only truly general Bayesian method of confirming a GWB detection from pulsar timing data.

astro-ph.IM↗

arXiv2007

Locally Isometric Families of Minimal Surfaces

We consider a surface $M$ immersed in $\mathbb{R}^3$ with induced metric $g=ψδ_2$ where $δ_2$ is the two dimensional Euclidean metric. We then construct a system of partial differential equations that constrain $M$ to lift to a minimal surface via the Weierstrauss-Enneper representation demanding the metric is of the above form. It is concluded that the associated surfaces connecting the prescribed minimal surface and its conjugate surface satisfy the system. Moreover, we find a non-trivial symmetry of the PDE which generates a one parameter family of surfaces isometric to a specified minimal surface. We demonstrate an instance of the analysis for the helicoid and catenoid.

math.DG↗

arXiv2006

Minimal Surface Linear Combinatoin Theorem

Given two univalent harmonic mappings $f_1$ and $f_2$ on $\mathbb{D}$, which lift to minimal surfaces via the Weierstrass-Enneper representation theorem, we give necessary and sufficient conditions for $f_3=(1-s)f_1+sf_2$ to lift to a minimal surface for $s\in[0,1]$. We then construct such mappings from Enneper's surface to Scherk's singularly periodic surface, Sckerk's doubly periodic surface to the catenoid, and the 4-Enneper surface to the 4-noid.

math.DG↗

arXiv2005

High fidelity simulations of ion trajectories in miniature ion traps using the boundary-element method

In this paper we present numerical modeling results for endcap and linear ion traps, used for experiments at the National Physical Laboratory in the UK and Innsbruck University respectively. The secular frequencies for Strontium-88 and Calcium-40 ions were calculated from ion trajectories, simulated using boundary-element and finite-difference numerical methods. The results were compared against experimental measurements. Both numerical methods showed high accuracy with boundary-element method being more accurate. Such simulations can be useful tools for designing new traps and trap arrays. They can also be used for obtaining precise trapping parameters for desired ion control when no analytical approach is possible as well as for investigating the ion heating rates due to thermal electronic noise.

quant-ph↗