arXiv subjects

Qing-Hua Zhu

Publications and source records attributed to Qing-Hua Zhu.

At least 19 recordsLinked to original sources

arXiv2026

Finite velocity effect of ultralight vector dark matter in pulsar timing arrays

Pulsar timing array (PTA) collaborations have recently reported evidence of the stochastic gravitational waves. In addition to gravitational wave signals from cosmological or astrophysical origins, PTAs are also capable of detecting coherently oscillating ultralight dark matter. This study investigates the PTA response to ultralight vector dark matter, incorporating the realistic finite velocity effects ($v\sim 10^{-3}$) in our galaxy. Using a rigorous calculation framework, we demonstrate that both the timing residual amplitude (for deterministic signals) and the angular correlations (for stochastic backgrounds) depend sensitively on individual pulsar distances. Significantly, we find that the timing residuals are dominated by the Newtonian potential, contradicting prior studies which identified the curvature perturbation and tensor part of metric perturbation as the leading contributions. As expected, the PTA response to vector dark matter exhibits a characteristic anisotropic signature, making it distinguishable from the isotropic signal of scalar dark matter.

gr-qc↗

arXiv2026

Flux enhancement of corotating hot spots in accretion disks from the slow-light effect

With the Event Horizon Telescope and future Very Long Baseline Interferometry arrays poised to image supermassive black holes, there is a strong motivation to understand the dynamic aspects of the accretion flow near the black hole. Interestingly, in such highly relativistic regime, the finite light-travel time should be taken into account to correctly simulate the images, known as the slow-light effect. This paper investigates the impact of the slow-light effect on the observational signatures of hotspots corotating with the Keplerian disks. It is found that the magnification can be modulated by the hotspot's orbital velociy. Specifically, the corotating hotspots at the maxima of magnification are located at the image positions shifted relative to the positions behind the black hole. This subsequently causes the peak of the magnification profile to shift towards alignment with the peak of the redshift factor profile, ultimately leading to flux enhancement relative to the results of previous studies. This enhancement becomes particularly pronounced for corotating hotspots in the strong-field regime at large inclination angle, indicating that the slow-light effect is essential for accurately modeling high-energy emission in the vicinity of the black hole.

gr-qc↗

arXiv2026

Reassessing the SIGW Interpretation of PTA Signal: The Role of Third-Order Gravitational Waves and Implications for the PBH Overproduction

In light of recent interpretations attributing pulsar timing array (PTA) signal to second-order gravitational waves induced by linear cosmological curvature perturbations in the early universe, the overproduction of primordial black holes (PBHs) poses a theoretical tension. In this work, we address this issue through extending such a scalar-induced gravitational wave (SIGW) framework to include third-order gravitational waves, which allow for a substantial enhancement in the spectral amplitude of SIGWs. Analyzing a combined dataset from cosmic microwave background and baryon acoustic oscillations, we derive cosmological constraints on the physical energy-density fraction of cosmological gravitational waves. Further incorporating PTA data, we obtain constraints on the spectral amplitude and peak frequency of SIGWs. Our results indicate that the parameter region favored by the data combination can to some extent alleviate the PBH overproduction problem, thereby supporting the theoretical consistency of our model. Furthermore, we demonstrate the robustness of our SIGW interpretation for the PTA signal by extending the analysis to include a gravitational wave background from supermassive black hole binaries. These findings are poised for further scrutiny with future high-precision observations.

astro-ph.CO↗

arXiv2026

Detectability of secondary images from flares near Sgr A* with mock GRAVITY data

The orbital motion of near-infrared flares reported by the GRAVITY collaboration encodes information about both the dynamics of accretion matter and the underlying spacetime geometry. The centroid track of these flares, which corresponds to the flux-weighted center of light, incorporates contributions from primary, secondary and higher-order images. Thus, it potentially indicates distinctive signatures of the spacetime geometry, even when these individual multiple images remain unresolved. In this study, we explore the detectability of the secondary images from flares orbiting Sgr A* through mock data simulating future GRAVITY observations. Specifically, we compare the model in which the centroid coincides with the track of the primary images with another model in which the centroid incorporates flux-weighted contributions from both the primary and secondary images. Fitting these models to the mock data based on Bayesian framework, we quantify the conditions under which the signature of secondary images can be statistically distinguishable. We demonstrate that increasing the sample size by an order of magnitude alone could not yield strong evidence for distinguishing the secondary image. Robust detectability ($|Δ\text{BIC}| >7.9$) is achieved when both with the improved sample size and astrometric uncertainties reduced to 40\% of current uncertainties of GRAVITY astrometric data. Unlike the primary image, which is dominated by accretion flow physics, the secondary images originate from gravitational lensing in the strong-field regime. Their detection is an essential first step toward probing higher-order images and the photon rings.

astro-ph.HE↗

arXiv2026

Exploring the statistical anisotropy of primordial curvature perturbations with pulsar timing arrays

The recent detection of a stochastic gravitational wave background by pulsar timing arrays has opened a new window in understanding supermassive black hole binaries and in probing the universe at the early time. Recently, pulsar timing array (PTA) collaborations have been further paving the way to probe anisotropies in the stochastic gravitational wave background. This study investigates dipole-type statistical anisotropy in the primordial power spectrum within a phenomenological framework. We demonstrate that the primordial dipole induces both dipolar and quadrupolar anisotropies in the energy density spectrum of scalar-induced gravitational waves (SIGWs), without generating extra polarization modes. Based on this anisotropic spectrum, we derive the corresponding PTA overlap reduction functions (ORFs), which exhibit frequency dependence, with the anisotropies enhanced on small scales. Furthermore, owing to the non-uniform distribution of millisecond pulsars over the sky in current PTA dataset, the ORFs exhibit a morphology that explicitly depends on the preferred direction of the anisotropy. However, our bayesian analysis of the NANOGrav 15-year dataset still yields no significant evidence for a preferred direction and a weak upper limit on anisotropy amplitude $(g\lesssim0.5)$. This result arises because the observational frequency band lies below the spectral peak, where our models predict suppressed anisotropic contributions. This limitation highlights the potential of future PTA observations. Specifically, datasets with broader frequency coverage are expected to tighten constraints on dipole-type anisotropy.

gr-qc↗

arXiv2026

Investigating non-Keplerian motion in flare events with astrometric data

The GRAVITY interferometer has achieved microarcsecond precision in near-infrared interferometry, enabling the tracking of flare centroid motion in the strong gravitational field near the Sgr A*. It might be promising to serve as a unique laboratory for exploring the accretion matter near black holes or testing Einstein's gravity. Recent studies debated whether there is a non-Keplerian motion of the flares in the GRAVITY dataset. This motivates us to present a comprehensive analysis based on error estimation under the Bayesian framework. This study uses astrometric flare data to investigate the possibility that the flares exhibit deviations from the circular Keplerian motion. We analyze both averaged and individual flare data, modeling the hotspot with either circular orbits parameterized by a non-Keplerian correction or planar geodesic orbits. It is confirmed that the astrometric data favor the circular orbits over non-circular ones, with the orbital circularity parameter of $γ= 0.99_{-0.10}^{+0.07}$. Our results show that the joint posteriors for black hole mass and non-Keplerian parameter are negatively correlated. Fixing the mass to be its established value yields a non-Keplerian parameter of $ω/ω_k = 1.45^{+0.35}_{-0.38}$, at approximately the 1$σ$ level. The statistical significance is insufficiently high, and the conclusion is found to be sensitive to the presence of correlations in the astrometric data, which might originate from the non-uniform $u$-$v$ coverage in interferometer measurements. In this sense, the current data might be insufficient to draw a definitive conclusion regarding the presence of non-Keplerian motion. Future improvements in astrometry precision might enable stronger constraints on the kinematical behavior of the flares.

astro-ph.HE↗

arXiv2025

Ray tracing for the Terrell-Penrose effect in black hole spacetime

Motivated by recent images of black holes in M87 and our galaxy, efficient relativistic ray tracing was developed to simulate the snapshots of variable emissions around the black holes. Half a century ago, the appearance of a moving emission source was addressed by Terrell and Penrose, who independently found that the aberration effect induces a conformal transformation on the observer's celestial sphere. Consequently, a snapshot of a moving sphere should remain circular. In this study, we examine the Terrell-Penrose effect with our ray-tracing simulations for two contrasting cases: i) static emission sources in the view of a moving observer, ii) and moving emission sources in the view of a static observer. In flat spacetime, it was believed that the images of the emission sources in these two cases are equivalent due to the relativity of motion. Our simulation demonstrates that although both cases remain apparent shape of the sphere, the apparent distortions of the images are different, and case ii) violates conformality on the observer's celestial sphere. Furthermore, we extended similar situations to a black hole spacetime. For case i), it is found that the conformal transformation induced by the aberration effect also holds in black hole spacetime, and is not restricted to observers in geodesic motion. For case ii), we study the slow-light effect on the moving sources, and show that the gravity introduces additional influence on the snapshots of a moving source.

gr-qc↗

arXiv2025

Auto- and cross-correlations for multiple images of corotating hotspots in accretion disks

Due to the short gravitational timescale of Sgr A*, variable emissions near the galactic center are expected in the Very-long-baseline interferometry observations. Phenomenologically, the high-flux variable emissions could be interpreted as occasional events from hotspots within accretion disks. It provides a probe of black hole (BH) geometry and accretion matter in the strong-field regime of gravity. In this study, we find that light curve profile alone is not proper for distinguishing BH geometries, as our results show that the profiles, even including those from higher-order images, are dependent on hotspot shapes, which are known in practice as amorphous. To alleviate this situation, we examine the spatial-temporal correlations between multiple images of the corotating hotspots. Our results find that the correlations, particularly those from higher-order images, could serve as a robust observable to reflect the inclination angles and BH geometries, because i) the correlated band structure is independent of the hotspot shapes, and ii) the correlations from higher-order images could encode BH geometries and exhibit no overlap with observational signatures from the lower-order ones. We present a comprehensive study on correlations from primary the eighth-order images with various orbital configurations and inclination angles, and show its observational signatures. It is expected that BH geometries can be inferred via the spatial-temporal correlation analysis.

astro-ph.HE↗

arXiv2025

Flattened bispectrum of the scalar-induced gravitational waves

Recent pulsar timing array collaborations have reported evidence of the stochastic gravitational wave background. The gravitational waves induced by primordial curvature perturbations, referred to as scalar-induced gravitational waves (SIGWs), could potentially be the physical origins of the gravitational wave background. Due to nonlinearity of Einstein's gravity, there is non-Gaussianity of SIGWs even when the sourced primordial curvature perturbation is Gaussian. This paper investigates the intrinsic non-Gaussianity of SIGWs influenced by formation of primordial black holes. Specifically, we examine whether spectral width of Gaussian primordial curvature perturbations can affect non-Gaussianity of SIGWs. In order to ensure us to correctly quantify the degree of non-Gaussianity, we introduce an oscillation average scheme that can conserve the exact results of skewness of SIGWs. In this framework, the oscillation of SIGWs not only suppresses the bispectrum amplitude but also leads to a flattened-type bispectrum. Based on our results of skewness, it is found that the primordial curvature power spectrum with a narrower width can enhance the intrinsic non-Gaussianity.

gr-qc↗

arXiv2025

Ultralight scalar dark matter versus nonadiabatic perfect fluid dark matter in pulsar timing

Recent evidence for stochastic gravitational waves reported by pulsar timing array (PTA) collaborations might open a new window for studying cosmology and astrophysical phenomena. In addition to signals from gravitational waves, there is motivation to explore residual signals from oscillating dark matter, which might partially comprise the galactic halo. We investigate fluctuations in pulsar timing originating from the coherent oscillation of scalar dark matter up to the subleading-order correction of $\mathcal{O}(k/m)$, as well as from acoustic oscillations of non-adiabatic perfect fluid dark matter. Both types of dark matter can induce the Newtonian potential and curvature perturbations, thereby affecting pulsar timing. We show distinctive signatures in pulsar timing residuals and angular correlations in the PTA frequency band and considering the known distances of pulsars. For scalar dark matter, both the timing residuals and the angular correlation are sensitive to small variations in the distance, $δL$, due to the subleading-order correction of $\mathcal{O}(k/m)$. In contrast, for perfect fluid dark matter, it is insensitive to the $δL$. For deterministic sources from scalar dark matter, the distance of a pulsar has influence on the degree of directional dependence of timing residuals, significantly. For stochastic sources from perfect fluid dark matter, the angular correlation tends to a constant and enhances only when the pulsar pair is very close to each other. In this sense, perfect fluid dark matter is shown to be a more suitable physical origin for monopolar signals in angular correlations compared to the scalar dark matter.

gr-qc↗

arXiv2025

Observational signatures from higher-order images of moving hotspots in accretion disks

The efforts to probe the horizon-scale structure of black holes, such as Event Horizon Telescope and GRAVITY interferometer, might provide valuable insights into the strong-field regime of Einstein's theory of gravity. In the near field region of a black hole, the observational signatures of moving hotspots might potentially reveal the mechanism causing the flares, or reflect the spacetime geometries. This paper develops a ray tracing scenario to study higher-order images of moving hotspots in a thin disk around a spherical black hole. Our ray-tracing scenario establishes a one-to-one mapping between emission locations and observer's sky. It enables us to perform infinite-precision simulations for the images, because the emission sources are projected directly onto the image plane. Furthermore, we show that a source located anywhere outside the black hole can be repeatedly mapped onto the observer's sky, from primary to higher-order images. We investigate the observational signatures of hotspots, focusing on temporal fluxes and flux centroids from the primary to sixth-order images. The hotspots are considered to be moving in circular, escape, and plunging orbits. Our results find that the higher-order images can be categorized into two types. Within each type, the temporal fluxes exhibit a self-similar profile. Furthermore, as the hotspots approach the event horizon of a black hole, the fluxes from higher-order images alternately dominate the observed flux, which subsequently result in the flux decaying with time in an oscillatory manner.

gr-qc↗

arXiv2024

Primordial black holes and scalar induced density perturbations: the effects of probability density functions

We investigate the second order energy density perturbation $δ^{(2)}$ induced by small-scale Gaussian and local-type non-Gaussian primordial curvature perturbations. The relative abundance of primordial black hole is calculated in terms of the probability density function of total energy density perturbation $δ_r=δ^{(1)}+\frac{1}{2}δ^{(2)}$. The effects of second order density perturbation greatly reduce the upper bounds of small-scale power spectra of primordial curvature perturbations by one to two orders of magnitude. For log-normal primordial power spectrum, its amplitude $A_ζ$ is constrained to be about $A_ζ\sim 3\times10^{-3}$. And for local-type non-Gaussianity with $f_{\mathrm{NL}}=10$, the upper bound of $A_ζ$ is about $2.5\times10^{-4}$.

astro-ph.CO↗

arXiv2024

Unraveling the early universe's equation of state and primordial black hole production with PTA, BBN, and CMB observations

Pulsar timing array (PTA) data releases showed strong evidence for a stochastic gravitational-wave background in the nanohertz band. When the signal is interpreted by a scenario of scalar-induced gravitational waves (SIGWs), we encounter overproduction of primordial black holes (PBHs). We wonder if varying the equation of state (EoS) of the early Universe can resolve this issue and thereby lead to a consistent interpretation of the PTA data. Analyzing a data combination of PTA, big-bang nucleosynthesis, and cosmic microwave background, we find that an epoch with EoS $w\sim\mathcal{O}(10^{-2})$ between the end of inflation and the onset of radiation domination can significantly suppress the production of PBHs, leading to alleviation of the PBH-overproduction issue. With the inferred interval $w=0.44_{-0.40}^{+0.52}$ at 95\% confidence level, our scenario can interpret the PTA data just as well as the conventional scenario of SIGWs produced during the radiation domination.

astro-ph.CO↗

arXiv2024

Photon ring autocorrelations from gravitational fluctuations around a black hole

The images of supermassive black holes in M87 and our galaxy captured by the Event Horizon Telescope (EHT) might open up a new way for exploring black hole physics at the horizon scale. Theoretically, this could provide insights into studying the emission sources around a black hole or the geometries of the black hole itself. This paper investigates the two-point correlations of intensity fluctuations on the photon ring, resulting from the existence of shock waves or gravitational fluctuations around a black hole. Following approaches used in the field of gravitational wave detectors, we introduce response functions of very long baseline interferometry (VLBI) for detecting gravitational fluctuations and study the shape of the overlap reduction functions. It is found that the shape of the correlations here differs from that resulting from stochastic emission sources. By providing an order-of-magnitude estimate for the signal-to-noise ratio (SNR), we obtain sensitivity curves for the detection of gravitational fluctuations. This might reveal the potential for detecting gravitational fluctuations with future VLBI observations in the LIGO frequency band.

gr-qc↗

arXiv2024

Non-linear corrections of overlap reduction functions for pulsar timing arrays

The signals from international pulsar timing arrays have presented a hint of gravitational stochastic background in nHz band frequency. Further confirmation will be based on whether the signals follow the angular correlation curves formulated by the overlap reduction functions, known as Hellings-Downs curves. This paper investigates the non-linear corrections of overlap reduction functions in the present of non-Gaussianity, in which the self-interaction of gravity is first taken into considerations. Based on perturbed Einstein field equations for the second order metric perturbations, and perturbed geodesic equations to the second order, we obtain non-linear corrections for the timing residuals of pulsar timing, and theoretically study corresponding overlap reduction functions for pulsar timing arrays. There is order-one correction for the overlap reduction functions from the three-point correlations of gravitational waves, and thus the shapes of the overlap reduction functions with non-linear corrections can be distinguished from the Hellings-Downs curves.

gr-qc↗

arXiv2024

Constraints On Scalar-Induced Gravitational Waves Up To Third Order From Joint Analysis of BBN, CMB, And PTA Data

Recently, strong evidence for a gravitational wave background has been reported by collaborations of pulsar timing arrays (PTA). In the framework of scalar-induced gravitational waves (SIGWs), we concurrently investigate the second and third order gravitational waves by jointly analyzing PTA data, alongside big-bang nucleosynthesis (BBN), and cosmic microwave background (CMB) datasets. We determine the primordial curvature spectral amplitude as $0.021<A_ζ<0.085$ and the spectral peak frequency as $10^{-7.3}\ \mathrm{Hz}<f_\ast<10^{-6.3}\ \mathrm{Hz}$ at a 95\% confidence interval, pointing towards a mass range for primordial black holes of $10^{-4.5}M_\odot<m_{\mathrm{PBH}}<10^{-2.5}M_\odot$. Our findings suggest that third order gravitational waves contribute more significantly to the integrated energy density than the second order ones when $A_ζ\gtrsim0.06$. Furthermore, we expect future PTA projects to validate these findings and provide robust means to investigate the genesis and evolution of the universe, especially inflation.

astro-ph.CO↗

arXiv2023

Aberration effect on lower-order images of thin accretion disk in the astrometric approach

With recent advancements in observing supermassive black holes with the Event Horizon Telescope, there has been persistent exploration into what the images can reveal about fundamental physics, including space-time geometries and astrophysical emission sources. Inspired by Penrose's aberration formula for a rigid sphere, which clarified that increased speed does not flatten the appearance of the sphere, we extend the studies to the behavior of the images of accretion emissions. This paper examines the impact of aberration effects on the images of a thin accretion disk around Kerr-de Sitter black holes for finite distant observers, specifically focusing on the primary, secondary, and $n=2$ images. We employ the analytical ray-tracing scenario and extend the astrometric approach to investigate the images in the presence of aberration. This study is non-trivial because we do not assume a specific form of the aberration formula, instead, all aberration effects emerge from a coordinate-independent and tetrad-independent framework referred to as the astrometric approach. Our study finds that the shapes of the lower-order images get highly distorted for finite observers in motion, and the shapes and sizes of primary images are more sensitive to aberration than those of the $n=2$ images. This finding suggests that the primary images could theoretically be distinguished from the shadow based on their distinctive variations.

gr-qc↗

arXiv2023

New constraints on primordial non-Gaussianity from missing two-loop contributions of scalar induced gravitational waves

We analyze the energy density spectrum of \acp{SIGW} using the NANOGrav 15-year data set, thereby constraining the primordial non-Gaussian parameter $f_{\mathrm{NL}}$. For the first time, we calculate the seventeen missing two-loop diagrams proportional to $f_{\mathrm{NL}}A_ζ^3$ that correspond to the two-point correlation function $\langle h^{λ,(3)}_{\mathbf{k}} h^{λ',(2)}_{\mathbf{k}'} \rangle$ for local-type primordial non-Gaussianity. The total energy density spectrum of \acp{SIGW} can be significantly suppressed by these two-loop diagrams. If \acp{SIGW} dominate the \acp{SGWB} observed in \ac{PTA} experiments, the parameter interval $f_{\mathrm{NL}}\in [-5,-1]$ is notably excluded based on NANOGrav 15-year data set. After taking into account abundance of \acp{PBH} and the convergence of the cosmological perturbation expansion, we find that the only possible parameter range for $f_{\mathrm{NL}}$ might be $-1\le f_{\mathrm{NL}}< 0$.

astro-ph.CO↗