arXiv subjects

Emiko C. Gardiner

Publications and source records attributed to Emiko C. Gardiner.

15 recordsLinked to original sources

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 $δt$ on the times of arrival, the frequency $f_\mathrm{GW}$ of the gravitational waves, and the angular scale $ΔΩ$ of the anisotropy. The sensitivity scales approximately as $N_\mathrm{psr}^{0.8}$, $δt^{-0.08}$, and $ΔΩ^{1.6}-ΔΩ^{2.1}$ (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

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 $3.16σ$ to $3.32σ$ 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 $γ_{\rm GWB} = 13/3$. In a varied-$γ$ analysis, the spectral index increases to $γ_{\rm GWB}=3.5^{+0.7}_{-0.6}$. 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

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 $α(z) = α_0 (1 + z)^{0.84 \pm 0.35}$. 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

Inference on inner galaxy structure via gravitational waves from supermassive binaries

The detection of a stochastic gravitational wave background by pulsar-timing arrays indicates the presence of a population of supermassive black hole binaries. Although the observed spectrum generally matches predictions for orbital evolution driven by gravitational-wave emission in circular orbits, there is a preference for a spectral turnover at the lowest observed frequencies, which may point to substantial hardening during a transition from early environmental influences to later stages dominated by emission. In the vicinity of these binaries, the ejection of stars or dark matter particles through gravitational three-body slingshots efficiently extracts orbital energy, leading to a low-frequency turnover in the spectrum. Here we model how the gravitational-wave spectrum depends on the initial inner galactic profile before scouring by binary ejections while accounting for a range of initial binary eccentricities. By analysing the NANOGrav 15-year data, we find that a parsec-scale galactic-centre density of around $10^6 M_{\odot} \mathrm{pc}^{-3}$ is favoured across most of the parameter space, thus shedding light on the environmental effects that shape black hole evolution and the combined matter density near galaxy centres.

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↗

arXiv2026

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

Characterizing Continuous Gravitational Waves from Supermassive Black Hole Binaries in Realistic Pulsar Timing Array Data

Pulsar timing arrays recently found evidence for a gravitational wave background (GWB), likely the stochastic overlap of GWs from many supermassive black hole binaries. Anticipating a continuous gravitational wave (CW) detection from a single binary soon to follow, we examine how well current Bayesian methods can detect CWs and characterize their binary properties by modeling the response of the NANOGrav 15-year pulsar timing array to simulated binary populations. We run Markov Chain Monte Carlo searches for CWs in these datasets and compare them to quicker detection statistics including the optimal signal-to-noise ratio (S/N), matched filter detection statistic, and reduced log-likelihood ratio between the signal and noise models calculated at the injected parameters. The latter is the best proxy for Bayesian detection fractions, corresponding to a 50% detection fraction (by Bayes factors > 10 favoring a CW detection over noise-only model) at an S/N = 4.6. Source confusion between the GWB and a CW, or between multiple CWs, can cause false detections and unexpected dismissals. 53% of realistic binary populations consistent with the recently observed GWB have successful CW detections. 82% of these CWs are in the 4th or 5th frequency bin of the 16.03 yr dataset (6.9 and 10.8 nHz), with 95th percentile regions spanning 4-12nHz frequencies, 0.7-20$\times10^9 M_\odot$ chirp masses, 60Mpc-8Gpc luminosity distances, and 18-13,000 sq. deg 68% confidence localization areas. These successful detections often poorly recover the chirp mass, with only 29% identifying the chirp mass accurately to within 1 dex with a 68% posterior width also narrower than 1 dex.

astro-ph.CO↗

arXiv2025

The NANOGrav 15 Yr Data Set: Removing Pulsars One by One from the Pulsar Timing Array

Evidence has emerged for a stochastic signal correlated among 67 pulsars within the 15-year pulsar-timing data set compiled by the NANOGrav collaboration. Similar signals have been found in data from the European, Indian, Parkes, and Chinese PTAs. This signal has been interpreted as indicative of the presence of a nanohertz stochastic gravitational wave background. To explore the internal consistency of this result we investigate how the recovered signal strength changes as we remove the pulsars one by one from the data set. We calculate the signal strength using the (noise-marginalized) optimal statistic, a frequentist metric designed to measure correlated excess power in the residuals of the arrival times of the radio pulses. We identify several features emerging from this analysis that were initially unexpected. The significance of these features, however, can only be assessed by comparing the real data to synthetic data sets. After conducting identical analyses on simulated data sets, we do not find anything inconsistent with the presence of a stochastic gravitational wave background in the NANOGrav 15-year data. The methodologies developed here can offer additional tools for application to future, more sensitive data sets. While this analysis provides an internal consistency check of the NANOGrav results, it does not eliminate the necessity for additional investigations that could identify potential systematics or uncover unmodeled physical phenomena in the data.

astro-ph.HE↗

arXiv2025

The NANOGrav 15 yr data set: Posterior predictive checks for gravitational-wave detection with pulsar timing arrays

Pulsar-timing-array experiments have reported evidence for a stochastic background of nanohertz gravitational waves consistent with the signal expected from a population of supermassive--black-hole binaries. Their analyses assume power-law spectra for intrinsic pulsar noise and for the background, as well as a Hellings--Downs cross-correlation pattern among the gravitational-wave--induced residuals across pulsars. These assumptions may not be realized in actuality. We test them in the NANOGrav 15 yr data set using Bayesian posterior predictive checks. After fitting our fiducial model to real data, we generate a population of simulated data-set replications. We use the replications to assess whether the optimal-statistic significance, inter-pulsar correlations, and spectral coefficients are extreme. We recover Hellings--Downs correlations in simulated data sets at significance levels consistent with the correlations measured in the NANOGrav 15 yr data set. A similar test on spectral coefficients shows that their values in real data are not extreme compared to their distributions across replications. We also evaluate the evidence for the stochastic background using posterior-predictive versions of the frequentist optimal statistic and of Bayesian model comparison, and find comparable significance (3.2 $σ$ and 3 $σ$ respectively) to what was previously reported for the standard statistics. We conclude with novel visualizations of the reconstructed gravitational waveforms that enter the residuals for each pulsar. Our analysis strengthens confidence in the identification and characterization of the gravitational-wave background.

astro-ph.HE↗

arXiv2025

The NANOGrav 15-year Data Set: Search for Gravitational Wave Memory

We present the results of a search for nonlinear gravitational wave memory in the NANOGrav 15-year data set. We find no significant evidence for memory signals in the dataset, with a maximum Bayes factor of 3.1 in favor of a model including memory. We therefore place upper limits on the strain of potential gravitational wave memory events as a function of sky location and observing epoch. We find upper limits that are not always more constraining than previous NANOGrav results. We show that it is likely due to the increase in common red noise between the 12.5-year and 15-year NANOGrav datasets.

gr-qc↗

arXiv2025

The NANOGrav 15 yr Data Set: Running of the Spectral Index

The NANOGrav 15-year data provides compelling evidence for a stochastic gravitational-wave (GW) background at nanohertz frequencies. The simplest model-independent approach to characterizing the frequency spectrum of this signal consists in a simple power-law fit involving two parameters: an amplitude A and a spectral index γ. In this paper, we consider the next logical step beyond this minimal spectral model, allowing for a running (i.e., logarithmic frequency dependence) of the spectral index, γ_run(f) = γ+ β\ln(f/f_ref). We fit this running-power-law (RPL) model to the NANOGrav 15-year data and perform a Bayesian model comparison with the minimal constant-power-law (CPL) model, which results in a 95% credible interval for the parameter βconsistent with no running, β\in [-0.80,2.96], and an inconclusive Bayes factor, B(RPL vs. CPL) = 0.69 +- 0.01. We thus conclude that, at present, the minimal CPL model still suffices to adequately describe the NANOGrav signal; however, future data sets may well lead to a measurement of nonzero β. Finally, we interpret the RPL model as a description of primordial GWs generated during cosmic inflation, which allows us to combine our results with upper limits from big-bang nucleosynthesis, the cosmic microwave background, and LIGO-Virgo-KAGRA.

astro-ph.HE↗

arXiv2024

The NANOGrav 15 yr Data Set: Harmonic Analysis of the Pulsar Angular Correlations

Pulsar timing array observations have found evidence for an isotropic gravitational wave background with the Hellings-Downs angular correlations, expected from general relativity. This interpretation hinges on the measured shape of the angular correlations, which is predominately quadrupolar under general relativity. Here we explore a more flexible parameterization: we expand the angular correlations into a sum of Legendre polynomials and use a Bayesian analysis to constrain their coefficients with the 15-year pulsar timing data set collected by the North American Nanohertz Observatory for Gravitational Waves (NANOGrav). When including Legendre polynomials with multipoles $\ell \geq 2$, we only find a significant signal in the quadrupole with an amplitude consistent with general relativity and non-zero at the $\sim 95\%$ confidence level and a Bayes factor of 200. When we include multipoles $\ell \leq 1$, the Bayes factor evidence for quadrupole correlations decreases by more than an order of magnitude due to evidence for a monopolar signal at approximately 4 nHz which has also been noted in previous analyses of the NANOGrav 15-year data. Further work needs to be done in order to better characterize the properties of this monopolar signal and its effect on the evidence for quadrupolar angular correlations.

astro-ph.HE↗

arXiv2024

Deep Neural Emulation of the Supermassive Black-hole Binary Population

While supermassive black-hole (SMBH)-binaries are not the only viable source for the low-frequency gravitational wave background (GWB) signal evidenced by the most recent pulsar timing array (PTA) data sets, they are expected to be the most likely. Thus, connecting the measured PTA GWB spectrum and the underlying physics governing the demographics and dynamics of SMBH-binaries is extremely important. Previously, Gaussian processes (GPs) and dense neural networks have been used to make such a connection by being built as conditional emulators; their input is some selected evolution or environmental SMBH-binary parameters and their output is the emulated mean and standard deviation of the GWB strain ensemble distribution over many Universes. In this paper, we use a normalizing flow (NF) emulator that is trained on the entirety of the GWB strain ensemble distribution, rather than only mean and standard deviation. As a result, we can predict strain distributions that mirror underlying simulations very closely while also capturing frequency covariances in the strain distributions as well as statistical complexities such as tails, non-Gaussianities, and multimodalities that are otherwise not learnable by existing techniques. In particular, we feature various comparisons between the NF-based emulator and the GP approach used extensively in past efforts. Our analyses conclude that the NF-based emulator not only outperforms GPs in the ease and computational cost of training but also outperforms in the fidelity of the emulated GWB strain ensemble distributions.

astro-ph.IM↗

arXiv2024

Beyond the Background: Gravitational Wave Anisotropy and Continuous Waves from Supermassive Black Hole Binaries

Pulsar timing arrays have found evidence for a low-frequency gravitational wave background (GWB). Assuming the GWB is produced by supermassive black hole binaries (SMBHBs), the next gravitational wave (GW) signals astronomers anticipate are Continuous Waves (CWs) from single SMBHBs and their associated GWB anisotropy. The prospects for detecting CWs and anisotropy are highly dependent on the astrophysics of SMBHB populations. Thus, information from single sources can break degeneracies in astrophysical models and place much more stringent constraints than the GWB alone. We simulate and evolve SMBHB populations, model their GWs, and calculate their anisotropy and detectability. We investigate how varying components of our semi-analytic model, including the galaxy stellar mass function, the SMBH--host galaxy relation ($M_\mathrm{BH}$--$M_\mathrm{bulge}$), and the binary evolution prescription impact the expected detections. The CW occurrence rate is greatest for few total binaries, high SMBHB masses, large scatter in $M_\mathrm{BH}$--$M_\mathrm{bulge}$, and long hardening times. The occurrence rate depends most on the binary evolution parameters, implying that CWs offer a novel avenue to probe binary evolution. The most detectable CW sources are in the lowest frequency bin for a 16.03-year PTA, have masses from $\sim\!\!10^9-10^{10}\mathrm{M}_\odot$, and are $\sim\!\!1$ Gpc away. The level of anisotropy increases with frequency, with the angular power spectrum over multipole modes $\ell$ varying in low-frequency $C_{\ell>0}/C_0$ from $\sim\!\!5\times 10^{-3}$ to $\sim\!\!2\times10^{-1}$, depending on the model; typical values are near current upper limits. Observing this anisotropy would support SMBHB models for the GWB over cosmological models, which tend to be isotropic.

astro-ph.HE↗

arXiv2023

Disk Wind Feedback from High-mass Protostars. IV. Shock-Ionized Jets

Massive protostars launch accretion-powered, magnetically-collimated outflows, which play crucial roles in the dynamics and diagnostics of the star formation process. Here we calculate the shock heating and resulting free-free radio emission in numerical models of outflows of massive star formation within the framework of the Turbulent Core Accretion model. We post-process 3D magneto-hydrodynamic simulation snapshots of a protostellar disk wind interacts with an infalling core envelope, and calculate shock temperatures, ionization fractions, and radio free-free emission. We find heating up to ~10^7 K and near complete ionization in shocks at the interface between the outflow cavity and infalling envelope. However, line-of-sight averaged ionization fractions peak around ~10%, in agreement with values reported from observations of massive protostar G35.20-0.74N. By calculating radio continuum fluxes and spectra, we compare our models with observed samples of massive protostars. We find our fiducial models produce radio luminosities similar to those seen from low and intermediate-mass protostars that are thought to be powered by shock ionization. Comparing to more massive protostars, we find our model radio luminosities are ~10 to 100 times less luminous. We discuss how this apparent discrepancy either reflects aspects of our modeling related to the treatment of cooling of the post-shock gas or a dominant contribution in the observed systems from photoionization. Finally, our models exhibit 10-year radio flux variability of ~5%, especially in the inner 1000 au region, comparable to observed levels in some hyper-compact HII regions.

astro-ph.GA↗