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.Comment: 33 pages in 11pt, 22 figure

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.Comment: v2: accepted version, 24 pages, 11 figures, 11p

Intrinsic 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 this gravitational wave background. In addition to the statistical properties of SIGWs derived from the primordial fluctuations, SIGWs also have intrinsic non-Gaussianity originating from the non-linear interactions of Einstein's gravity, which, however, is rarely explored. In this paper, we study the intrinsic non-Gaussianity of SIGWs with the bispectrum and the skewness under the assumption of the Gaussian primordial curvature perturbations, phenomenologically modeled as a lognormal spectrum. The bispectrum is shown to be vanishing in the collinear limit, which is independent of the initial conditions and the dynamics of SIGWs. For the SIGWs generated during the radiation-dominated era, the bispectrum is of flatten-type non-Gaussianity, with only four polarization components left to be non-vanishing. Additionally, in order to obtain the correct bispectrum, we also propose a time-oscillation average scheme and a regularization scheme. Utilizing the skewness for quantifying the degree of non-Gaussianity, it is found that the curvature power spectrum with a narrow width can result in an enhancement of the third-order non-Gaussianity. The conclusion holds for both the SIGWs generated in the radiation-dominated era and the matter-dominated era.Comment: 31 pages, 11 figure

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.Comment: 20 pages, 8 figures, 11p

Searching for Charged Higgs Boson in Polarized Top Quark

The charged Higgs boson is quite common in many new physics models. In this study we examine the potential of observing a heavy charged Higgs boson in its decay mode of top-quark and bottom-quark in the Type-II Two-Higgs-Doublet-Model. In this model, the chirality structure of the coupling of charged Higgs boson to the top- and bottom-quark is very sensitive to the value of $\tan\beta$. As the polarization of the top-quark can be measured experimentally from the top-quark decay products, one could make use of the top-quark polarization to determine the value of $\tan\beta$. We preform a detailed analysis of measuring top-quark polarization in the production channels $gb\to tH^-$ and $g\bar{b}\to \bar{t}H^+$. We calculate the helicity amplitudes of the charged Higgs boson production and decay.Our calculation shows that the top-quark from the charged Higgs boson decay provides a good probe for measuring $\tan\beta$, especially for the intermediate $\tan\beta$ region. On the contrary, the top-quark produced in association with the charged Higgs boson cannot be used to measure $\tan\beta$ because its polarization is highly contaminated by the $t$-channel kinematics.Comment: 21 pages, 12 figures, 2 table