arXiv subjects

Heling Deng

Publications and source records attributed to Heling Deng.

At least 19 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 $\delta t$ 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

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

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

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

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

Searching beyond the fiducial stochastic gravitational wave background in pulsar timing array data using likelihood reweighting

Since the recent announcements of evidence for a stochastic gravitational wave background from several pulsar timing array collaborations, much effort has been devoted to explore features beyond the fiducial Hellings-Downs background including those arising in modified gravity theories and deterministic gravitational wave signals. Inspired by previous studies, we propose a method to efficiently screen these models using likelihood reweighting based on the fiducial model. In order to alleviate the well-known unstable weight estimates in vanilla importance sampling, we implement reweighting for the second time making use of the kernel density estimation of the previously reweighted samples. We tested this method by analyzing three simulated datasets with an injected sinusoid signal applied to all pulsars. It is found that likelihood reweighting not only gives results compatible with those from full Bayesian analyses when the signal is subdominant, but is also able to recover the signal posterior to a reasonable accuracy in the presence of a rather strong signal. Given samples from the fiducial model, this method could bring an at least $\mathcal{O}(10)$-time speedup in analyzing new models.

gr-qc↗

arXiv2025

Sound waves from primordial black hole formations

We present a numerical investigation of primordial black hole (PBH) formation from super-horizon curvature perturbations and the subsequent generation and propagation of sound waves, which can serve as a new source of stochastic gravitational wave backgrounds (SGWBs) presented in a companion letter. Using the Misner-Sharp formalism with an excision technique, our simulations extend to significantly later times than previous work and indicate that the near-critical perturbations produce a distinct compression wave featuring both overdense and underdense shells, while significantly supercritical perturbations yield only an underdense shell. We also show that a softer equation of state suppresses the formation of compression waves. Furthermore, the comoving thickness of sound shells remains nearly constant during propagation and scales with the Hubble radius at horizon re-entry, thereby serving as a key link between the gravitational-wave peak frequency and PBH mass in the companion letter. These results offer new insights into the dynamics of PBH formation and suggest potential observational signatures of PBHs in the gravitational wave (GW) spectrum from associated sound waves.

gr-qc↗

arXiv2025

Relic gravitational waves from primordial gravitational collapses

A large primordial density perturbation of the Hubble scale will gravitationally collapse, generating an outgoing sound shell, whether or not a primordial black hole (PBH) is formed. In this Letter, we report a hybrid numerical analysis of the stochastic gravitational wave background induced by the collision of sound shells in the early Universe. The peak frequency and amplitude in the GW spectrum depend on the Hubble horizon and the abundance of sound shells. Abundant density perturbations would lead to GW backgrounds potentially detectable for future pulsar timing arrays and ground-based/space-borne detectors. For those perturbations that collapse into PBHs, future null detection of the corresponding high-frequency GW background could put new observational constraints on those PBHs that have already evaporated.

gr-qc↗

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↗

arXiv2024

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↗

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

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↗

arXiv2024

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 \gamma. 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, \gamma_run(f) = \gamma + \beta \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 \beta consistent with no running, \beta \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 \beta. 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: 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 $\sigma$ and 3 $\sigma$ 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↗

arXiv2024

The NANOGrav 15 yr Data Set: Looking for Signs of Discreteness in the Gravitational-wave Background

The cosmic merger history of supermassive black hole binaries (SMBHBs) is expected to produce a low-frequency gravitational wave background (GWB). Here we investigate how signs of the discrete nature of this GWB can manifest in pulsar timing arrays through excursions from, and breaks in, the expected $f_{\mathrm{GW}}^{-2/3}$ power-law of the GWB strain spectrum. To do this, we create a semi-analytic SMBHB population model, fit to NANOGrav's 15 yr GWB amplitude, and with 1,000 realizations we study the populations' characteristic strain and residual spectra. Comparing our models to the NANOGrav 15 yr spectrum, we find two interesting excursions from the power-law. The first, at $2 \; \mathrm{nHz}$, is below our GWB realizations with $p$-value significance $p = 0.05$ to $0.06$ ($\approx 1.8 \sigma - 1.9 \sigma$). The second, at $16 \; \mathrm{nHz}$, is above our GWB realizations with $p = 0.04$ to $0.15$ ($\approx 1.4 \sigma - 2.1 \sigma$). We explore the properties of a loud SMBHB which could cause such an excursion. Our simulations also show that the expected number of SMBHBs decreases by three orders of magnitude, from $\sim 10^6$ to $\sim 10^3$, between $2\; \mathrm{nHz}$ and $20 \; \mathrm{nHz}$. This causes a break in the strain spectrum as the stochasticity of the background breaks down at $26^{+28}_{-19} \; \mathrm{nHz}$, consistent with predictions pre-dating GWB measurements. The diminished GWB signal from SMBHBs at frequencies above the $26~\mathrm{nHz}$ break opens a window for PTAs to detect continuous GWs from individual SMBHBs or GWs from the early universe.

astro-ph.HE↗

arXiv2023

Searching for gravitational wave burst in PTA data with piecewise linear functions

Transient gravitational waves (aka gravitational wave bursts) within the nanohertz frequency band could be generated by a variety of astrophysical phenomena such as the encounter of supermassive black holes, the kinks or cusps in cosmic strings, or other as-yet-unknown physical processes. Radio-pulses emitted from millisecond pulsars could be perturbed by passing gravitational waves, hence the correlation of the perturbations in a pulsar timing array can be used to detect and characterize burst signals with a duration of $\mathcal{O}(1\text{-}10)$ years. We propose a fully Bayesian framework for the analysis of the pulsar timing array data, where the burst waveform is generically modeled by piecewise straight lines, and the waveform parameters in the likelihood can be integrated out analytically. As a result, with merely three parameters (in addition to those describing the pulsars' intrinsic and background noise), one is able to efficiently search for the existence and the sky location of {a burst signal}. If a signal is present, the posterior of the waveform can be found without further Bayesian inference. We demonstrate this model by analyzing simulated data sets containing a stochastic gravitational wave background {and a burst signal generated by the parabolic encounter of two supermassive black holes.

gr-qc↗