Strong Deflection Research Articles

Solar Orbiter Observations of Proton and Alpha Particle Kinetic Signatures Related to the Presence of Switchbacks in the Inner Heliosphere: A Case Study

We investigate how ions, namely protons and alpha particles, kinetically react to the presence of strong deflections in the magnetic field, the so-called switchbacks, in the first stream of slow Alfvénic wind observed by Solar Orbiter at the heliocentric distance of 0.64 au. We focus on an isolated, large-scale switchback, and we study in detail ion kinetic properties. Beyond the expected correlation between the magnetic deflection and ion velocity related to the Alfvénic nature of the switchbacks, we find that, within the switchback, proton and alpha particle densities increase, suggesting ongoing wave activity. Very interestingly, we observe a clear correlation between the magnetic deflection and alpha particle temperature, while no correlation has been found with proton temperature. This is an indication of a possible role played by switchbacks in preferentially heating heavy ions. Our results suggest that the presence of switchbacks can induce a deformation of the proton velocity distribution function, while the preferential heating of alpha particles could be due to a denser secondary beam and a smaller relative drift speed between the beam and core.

Strong deflection limit analysis of black hole lensing in inhomogeneous plasma

Strong deflection limit analysis of black hole lensing in inhomogeneous plasma

Effects of non-commutative geometry on black hole properties

In this study, we investigate the signatures of a non-commutative black hole solution. Initially, we calculate the thermodynamic properties of the system, including entropy, heat capacity, and Hawking radiation. For the latter quantity, we employ two distinct methods: surface gravity and the topological approach. Additionally, we examine the emission rate and remnant mass within this context. Remarkably, the lifetime of the black hole, after reaching its final state due to the evaporation process, is expressed analytically up to a grey-body factor. We estimate the lifetime for specific initial and final mass configurations. Also, we analyze the tensorial quasinormal modes using the 6th-order WKB method. Finally, we study the deflection angle, i.e., gravitational lensing, in both the weak and strong deflection limits.

Observation of a Fully-formed Forward–Reverse Shock Pair due to the Interaction between Two Coronal Mass Ejections at 0.5 au

We report direct observations of a fast magnetosonic forward–reverse shock pair observed by Solar Orbiter on 2022 March 8 at the short heliocentric distance of 0.5 au. The structure, sharing some features with fully-formed stream interaction regions, is due to the interaction between two successive coronal mass ejections (CMEs), never previously observed to give rise to a forward–reverse shock pair. The scenario is supported by remote observations from extreme ultraviolet cameras and coronagraphs, where two candidate eruptions compatible with the in situ signatures have been found. In the interaction region, we find enhanced energetic particle activity, strong nonradial flow deflections, and evidence of magnetic reconnection. At 1 au, well radially aligned Wind observations reveal a complex event, with characteristic observational signatures of both stream interaction region and CME–CME interaction, thus demonstrating the importance of investigating the complex dynamics governing solar eruptive phenomena.

Analytical perturbations of relativistic images in Kerr space-time

Light rays passing very close to black holes may wind several times before escaping. For any given electromagnetic source around the black hole, a distant observer would thus observe two infinite sequences of images on either side of the black hole. These images are generated by light rays performing an increasing numbers of loops. The strong deflection limit provides a simple analytic formalism to describe such higher order images for spherically symmetric metrics, while for axially symmetric black holes one typically resorts to numerical approaches. Here we present the leading order perturbation to higher order images when the black hole spin is turned on. We show that the images slide around the black hole shadow as an effect of space-time dragging. We derive analytical formulae for their shifts and the perturbation of their time delays. We also discuss how such simple analytical formulae for images by Kerr black holes can be of great help in many applications.

Deflection of light by a Reissner–Nordström black hole and Painlevé VI equation

We consider the bending angle of the trajectory of a photon incident from and deflected to infinity around a Reissner–Nordström black hole. We treat the bending angle as a function of the squared reciprocal of the impact parameter and the squared electric charge of the background normalized by the mass of the black hole. It is shown that the bending angle satisfies a system of two inhomogeneous linear partial differential equations with polynomial coefficients. This system can be understood as an isomonodromic deformation of the inhomogeneous Picard–Fuchs equation satisfied by the bending angle in the Schwarzschild spacetime, where the deformation parameter is identified as the background electric charge. Furthermore, the integrability condition for these equations is found to be a specific type of the Painlevé VI equation that allows an algebraic solution. We solve the differential equations both at the weak and strong deflection limits. In the weak deflection limit, the bending angle is expressed as a power series expansion in terms of the squared reciprocal of the impact parameter and we obtain the explicit full-order expression for the coefficients. In the strong deflection limit, we obtain the asymptotic form of the bending angle that consists of the divergent logarithmic term and the finite O(1) term supplemented by linear recurrence relations which enable us to straightforwardly derive higher order coefficients. In deriving these results, the isomonodromic property of the differential equations plays an important role. Lastly, we briefly discuss the applicability of our method to other types of spacetimes such as a spinning black hole.

Strong gravitational lensing by SgrA∗\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$Sgr A^*$$\\end{document} and M87∗\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$M87^*$$\\end{document} black holes embedded in dark matter halo exhibiting string cloud and quintessential field

We investigate the strong gravitational lensing phenomena caused by a black hole with a dark matter halo in the presence of cloud string and quintessence. This study examines strong gravitational lensing with two significant dark matter models: the universal rotation curve model and the cold dark matter model. To do this, we first numerically estimate the strong lensing coefficients and strong deflection angles for both the universal rotation curve and cold dark matter models. It is observed that the deflection angle, denoted as αD\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\alpha _D$$\\end{document}, increases with the parameter α\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\alpha $$\\end{document} while holding the value of 2Mγ\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$2M \\gamma $$\\end{document} constant. Additionally, it increases with the parameter 2Mγ\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$2M \\gamma $$\\end{document} while keeping the value of α\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\alpha $$\\end{document} constant. The strong deflection angle αD\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\alpha _D$$\\end{document}, for the black hole with a dark matter halo, with parameters α\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\alpha $$\\end{document} and 2Mγ\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$2\\,M \\gamma $$\\end{document}, greatly enhances the gravitational bending effect and surpasses the corresponding case of the standard Schwarzschild black hole (A=B=0=α=2Mγ\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$A=B=0=\\alpha =2M\\gamma $$\\end{document}). Furthermore, we investigate the astrophysical consequences through strong gravitational lensing observations, using examples of two supermassive black holes, namely M87∗\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$M87^{*}$$\\end{document} and SgrA∗\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$Sgr A^{*}$$\\end{document}, located at the center of nearby galaxies. It is observed that black holes with dark matter halos in the presence of cloud string and quintessence can be quantitatively distinguished and characterized from the standard Schwarzschild black hole (A=B=0=α=2Mγ\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$A=B=0=\\alpha =2M\\gamma $$\\end{document}). The findings in our analysis suggest that observational tests for black holes influenced by dark matter halos, cloud string and quintessence are indeed feasible and viable.

The Bow Shock and Magnetosheath Responses to Density Depletion Structures

AbstractHot flow anomalies (HFAs) are typical and important foreshock transients characterized by large flow deflection and plasma heating. HFAs can deform the Earth's bow shock by dynamic pressure perturbation resulting in disturbance in the magnetosphere and ionosphere. Traditionally, HFAs are believed to be associated with discontinuities. But recently, HFA‐like structures were simulated by a magnetohydrodynamics (MHD) model without the discontinuity prerequisite. In this study, three HFA‐like structures are shown to present the MHD formation mechanism. Multi‐points observation by the Time History of Events and Macroscale Interactions during Substorms (THEMIS) mission tracks the formation of an HFA from a density depletion upstream. HFAs with high‐ or low‐ density cores are observed by the Magnetospheric Multiscale mission in the flank region. The comparisons of the observation and their simulation show general agreement, particularly in the presence of a core with strong heating and velocity deflection, and two compression regions (shocks) with clear maxima in the ram pressure with a strongly inclined normal boundary at the leading edge and moderately inclined at the trailing edge. Agreement is better when the MHD simulations used a transient change to quasi‐parallel solar wind magnetic field during the events.

Gravitational lensing by a stable rotating regular black hole

Recent observational data from the Event Horizon Telescope (EHT) collaboration provide convincing realistic evidence for the existence of black hole rotation. From a phenomenological perspective, a recently proposed stable rotating regular (SRR) black hole circumvents the theoretical flaws of the Kerr solution. For the purpose of obtaining observational signatures of this black hole, we study its gravitational lensing effect. In the strong deflection limit, we calculate the deflection angle of light on the equatorial plane, the radius of the photon sphere, and other observables. The observables include the relativistic image position, separation, magnification, and time delays between different images. Then, by modeling M87* and Sgr A* as the SRR black hole, we compute their observables and evaluate the deviation of the observables from the Kerr case. In the weak deflection limit, we calculate the light deflection angle on the equatorial plane of M87* and Sgr A* via the Gauss-Bonnet theorem (GBT). With the growth of deviation parameter e, the gravitational lensing effect in the weak deflection limit intensifies monotonically, and the gravitational lensing effect in the strong deflection limit changes dramatically only at high spins. Our research may contribute to distinguish between SRR black holes from Kerr black holes under higher-precision astronomical observations.

Gravitational lensing of Schwarzschild and charged black holes immersed in perfect fluid dark matter halo

Dark matter and dark energy dominate the behavior of our universe. The dark matter usually forms halo structures in large number of galaxies. Properties of dark matter halo can be revealed and understood from the gravitational lensing observations. In this work, a comprehensive study on the gravitational lensing of black holes immersed in dark matter halos is presented. To effectively model the supermassive black hole in a galaxy center (which is surrounded by dark matter halo) in a simple way, we investigate the Schwarzschild black hole and charged Reissner-Nordström black hole immersed in a perfect fluid dark matter halo. In the present work, several basic quantities in gravitational lensing (the gravitational deflection angle of light, photon sphere, black hole shadow radius, gravitational lens equation and Einstein ring) are calculated and analyzed analytically and numerically. A second order analytical expansion of gravitational deflection angle is obtained in the weak deflection limit, and the full gravitational deflection angle (including all order perturbation contributions applicable to both weak and strong deflection limits) is also calculated numerically as comparisons. It enables us to analyze the perfect fluid dark matter influences on gravitational deflection angle and gravitational lensing beyond the leading order, which were not sufficiently studied in previous works. Assuming M ∼ λDM ∼ Q, our results show that dark matter can greatly influence the gravitational lensing of central black holes.

Strong gravitational lensing by loop quantum gravity motivated rotating black holes and EHT observations

We investigate gravitational lensing in the strong deflection regime by loop quantum gravity (LQG)-motivated rotating black hole (LMRBH) metrics with an additional parameter l besides mass M and rotation a. The LMRBH spacetimes are regular everywhere, asymptotically encompassing the Kerr black hole as a particular case and, depending on the parameters, describe black holes with one horizon only (BH-I), black holes with an event horizon and a Cauchy horizon (BH-II), black holes with three horizons (BH-III), or black holes with no horizons (NH) spacetime. It turns out that as the LQG parameter l increases, the unstable photon orbit radius xps\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$x_{ps}$$\\end{document}, the critical impact parameter ups\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$u_{ps}$$\\end{document}, the deflection angle αD(θ)\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\alpha _D(\ heta )$$\\end{document} and angular position θ∞\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\ heta _{\\infty }$$\\end{document} also increases. Meanwhile, the angular separation s decreases, and relative magnitude rmag\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$r_{mag}$$\\end{document} increases with increasing l for prograde motion but they show opposite behaviour for the retrograde motion. Using supermassive black holes (SMBH) Sgr A* and M87* as lenses, we compare the observable signatures of LMRBH with those of Kerr black holes. For Sgr A*, the angular position θ∞\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\ heta _{\\infty }$$\\end{document}∈\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\in $$\\end{document} (16.4, 39.8) μ\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\upmu $$\\end{document}as, while for M87* ∈\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\in $$\\end{document} (12.33, 29.9) μ\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\upmu $$\\end{document}as. The angular separation s, for SMBHs Sgr A* and M87*, differs significantly, with values ranging ∈\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\in $$\\end{document} (0.008–0.376) μ\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\upmu $$\\end{document}as for Sgr A* and ∈\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\in $$\\end{document} (0.006–0.282) μ\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\upmu $$\\end{document}as for M87*. The deviations of the lensing observables Δθ∞\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\Delta \ heta _{\\infty }$$\\end{document} and Δs\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\Delta s$$\\end{document} for LMRBH (a=0.80,l=2.0\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$a=0.80,l=2.0$$\\end{document}) from Kerr black holes can reach up to 10.22μ\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$10.22\\,\\upmu $$\\end{document}as and 0.241μ\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$0.241~\\upmu $$\\end{document}as for Sgr A*, and 7.683μ\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$7.683~\\upmu $$\\end{document}as and 0.181μ\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$0.181~\\upmu $$\\end{document}as for M87*. The relative magnitude rmag\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$r_{mag}$$\\end{document}∈\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\in $$\\end{document} (0.047, 1.54). We estimate the time delay between the first and second relativistic images using twenty supermassive galactic centre black holes as lenses to find, for example, the time delay for Sgr A* and M87* can reach approximately 23.26 min and 33,261.8 min, respectively. Our analysis concludes that, within the 1σ\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$1 \\sigma $$\\end{document} region, a significant portion of the BH-I and BH-II parameter space agrees with the EHT results of M87* and Sgr A*. The possibility of LMRBH being a BH-III with three horizons has been almost ruled out, except for a small portion of parameter space, by θsh\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\ heta _{sh}$$\\end{document} bounds of Sgr A* and M87* measured by EHT. In contrast, NH without a horizon is completely ruled out. We discover that the EHT results of Sgr A* place more stringent limits on the parameter space of LMRBH black holes than those established by the EHT results of M87*.

Effect of electric interaction on the deflection and gravitational lensing in the strong field limit

The deflection angle Delta phi of charged signals in general charged spacetime in the strong deflection limit is analyzed in this work using a perturbative method generalized from the neutral signal case. The solved Delta phi naturally contains the finite distance effect and takes a quasi-power series form with a logarithmic divergence at the leading order. The coefficients of the series contain both the gravitational and electric contributions. Using the Reissner–Nordström spacetime as an example, we found that an electric repulsion (or attraction) tends to decrease (or increase) the critical impact parameter b_c. If the repulsion is strong enough, then b_c can shrink to zero and the critical particle sphere r_{0c} will disappear. These results are applied to the gravitational lensing of charge signal, from which we solved the image positions, their magnifications and time delays. It is found that in general, the electric repulsion (or attraction) will decrease (or increase) the image apparent angles, the black hole shadow sizes as well as their magnifications but increase (or decrease) the time delays.

Experimental and numerical investigation of transverse combustion instability in a rectangle multi-injector rocket combustor

Rocket engines are prone to suffer from transverse combustion instabilities, manifesting as periodic oscillations in pressure and heat release rate. Self-excited transverse instabilities in a rectangle multi-injector rocket combustor powered by n-C12H26 and O2, are investigated experimentally and numerically in this paper. Transverse combustion instabilities are captured during repeatable experiments, while dynamic characteristics in the combustion chamber and driving mechanisms of instabilities are analyzed via numerical simulation based on stress-blended eddy simulation. Dynamic mode decomposition analysis reveals coupling behaviors between the transverse mode in the combustion chamber and longitudinal mode in the oxidizer post, resulting in propellant mass flow rate oscillations. Substantial evidence demonstrates that the intensities of heat release rate near the end walls are higher than that detected around the chamber center due to its intense coupling to the local first transverse (1W) acoustic mode. Flow field animations indicate strong deflection of oxygen posts and liquid particles by a transverse moving gas mixture leading to flame interactions and collision between adjacent share injectors. The propellant injected into the chamber does not burn immediately and is transported to the combustor end wall. Propellant mixing performance is significantly enhanced during interactions between acoustic pressure and end wall, causing a sudden heat release near 1W pressure anti-node, thereby strengthening pressure oscillations. Finally, a combustion instability driving mechanism associated with propellant mass flow rate oscillations, and interactions between unsteady acoustic pressure and heat release rate is proposed. The insights obtained from this work can aid comprehension of transverse combustion instabilities encountered by rocket engines.

Research on AGV cart control system based on fuzzy PID control

Abstract As an important carrier of intelligent logistics, AGV can effectively reduce the labor cost of factories and warehouses. With the comprehensive promotion of “smart manufacturing”, the manufacturing industry has a stronger demand for automated AGV logistics systems. This paper firstly analyzes the principle of fuzzy PID controller and establishes its kinematic model to obtain the intrinsic relationship between the motion form and the speed of each driving wheel. Secondly, through the data measured and fed back by the fuzzy PID control system, the AGV driving angle deviation and position deviation are used as the input of the fuzzy controller; its fuzzy deviation correction technology is applied to realize the path correction of the AGV and ensure the stable operation of the AGV through the cooperative motion control technology. Finally, MATLAB software establishes the joint simulation model of the AGV fuzzy PID control system. The results show that through the two algorithms of PID control and fuzzy PID control correction test, the fuzzy PID controller system corrects the deflection efficiency by 47.41%; in the kinematic test, the path tracking efficiency is increased by 30.76%, the distance correction efficiency is increased by 69.56%, the angle correction efficiency is increased by 69.56%, and the average performance is increased by 53.44%. Through the two comparisons, it is concluded that the fuzzy controller designed in this paper has the advantages of fast response speed, good stability, and strong deflection correction performance, which substantially improves the speed and accuracy of intelligent search of intelligent vehicles.

Backsplash galaxies and their impact on galaxy evolution: a three-stage, four-type perspective

ABSTRACT We study the population of backsplash galaxies at z = 0 in the outskirts of massive, isolated clusters of galaxies taken from the mdpl2-sag semi-analytical catalogue. We consider four types of backsplash galaxies according to whether they are forming stars or passive at three stages in their lifetimes: before entering the cluster, during their first incursion through the cluster, and after they exit the cluster. We analyse several geometric, dynamic, and astrophysical aspects of the four types at the three stages. Galaxies that form stars at all stages account for the majority of the backsplash population (58 per cent) and have stellar masses typically below $M_\star \sim 3\times 10^{10} \ h^{-1}\, {\rm {M_\odot }}$ that avoid the innermost cluster’s regions and are only mildly affected by it. In a similar mass range, galaxies that become passive after exiting the cluster (26 per cent) follow orbits characterized by small pericentric distance and a strong deflection by the cluster potential well while suffering a strong loss of both dark matter and gas content. Only a small fraction of our sample (4 per cent) becomes passive while orbiting inside the cluster. These galaxies have experienced heavy pre-processing and the cluster’s tidal stripping and ram pressure provide the final blow to their star formation. Finally, galaxies that are passive before entering the cluster for the first time (12 per cent) are typically massive and are not affected significantly by the cluster. Using the bulge/total mass ratio as a proxy for morphology, we find that a single incursion through a cluster does not result in significant morphological changes in all four types.

Deflection and gravitational lensing with finite distance effect in the strong deflection limit in stationary and axisymmetric spacetimes

We study the deflection and gravitational lensing (GL) of both timelike and null signals in the equatorial plane of arbitrary stationary and axisymmetric spacetimes in the strong deflection limit. Our approach employs a perturbative method to show that both the deflection angle and the total travel time take quasi-series forms ∑ n=0 [Cn ln (1-bc/b) + Dn ] (1-bc/b) n , with the coefficients Cn and Dn incorporating the signal velocity and finite distance effect of the source and detector. This new deflection angle allows us to establish an accurate GL equation from which the apparent angles of the relativistic images and their time delays are found. These results are applied to the Kerr and the rotating Kalb-Ramond (KR) spacetimes to investigate the effect of the spacetime spin in both spacetimes, and the effective charge parameter and a transition parameter in the rotating KR spacetime on various observables. Moreover, using our approach, the effect of the signal velocity and the source angular position on these variables is also studied.

Perturbation on atomic alignment of Ag L3-subshell by multiple ionization for heavy ions impact

Alignment of silver ion after electron in L3-subshell ionized by 1H+, 4He2+, 40Ar12+ and 129Xe30+ ions impact respectively are reported. Low incident energy range is investigated to explore collision-induced alignment in case of strong Coulomb deflection effect. Characteristic L X-ray spectra are measured in emission angle range of 115∘-155∘. For Lα and Lβ2 lines, anisotropy parameter β is determined respectively and then converted to degree of alignment A20 by taking anisotropy coefficient α and Coster-Kronig (CK) correction coefficient κ into account. The measured atomic alignment is compared to theoretical prediction basing on semiclassical model and satisfactory agreement is observed only for light ions impact. While the dealignment coefficient is determined to be 0.98, 0.71 and 0.30 for 4He2+, 40Ar12+ and 129Xe30+ ions impact at (vp/vL3)2=0.011, respectively. This work demonstrates the strong dealignment due to multiple ionization for heavy ions impact even in ultra low incident energy regime.

Synthesis of Nano-Structured Ge as Transmissive or Reflective Saturable Absorber for Mode-Locked Fiber Laser.

Amorphous-Ge (α-Ge) or free-standing nanoparticles (NPs) synthesized via hydrogen-free plasma-enhanced chemical vapor deposition (PECVD) were applied as transmissive or reflective saturable absorbers, respectively, for starting up passively mode-locked erbium-doped fiber lasers (EDFLs). Under a threshold pumping power of 41 mW for mode-locking the EDFL, the transmissive α-Ge film could serve as a saturable absorber with a modulation depth of 52-58%, self-starting EDFL pulsation with a pulsewidth of approximately 700 fs. Under a high power of 155 mW, the pulsewidth of the EDFL mode-locked by the 15 s-grown α-Ge was suppressed to 290 fs, with a corresponding spectral linewidth of 8.95 nm due to the soliton compression induced by intra-cavity self-phase modulation. The Ge-NP-on-Au (Ge-NP/Au) films could also serve as a reflective-type saturable absorber to passively mode-lock the EDFL with a broadened pulsewidth of 3.7-3.9 ps under a high-gain operation with 250 mW pumping power. The reflection-type Ge-NP/Au film was an imperfect mode-locker, owing to their strong surface-scattered deflection in the near-infrared wavelength region. From the abovementioned results, both ultra-thin α-Ge film and free-standing Ge NP exhibit potential as transmissive and reflective saturable absorbers, respectively, for ultrafast fiber lasers.

Gravitational lensing by using the 0th order of affine perturbation series of the deflection angle of a ray near a photon sphere

The 0th order of affine perturbation series of the deflection angle of a ray near a photon sphere is more accurate than a deflection angle in a strong deflection limit, which is used often, because the later has hidden error terms. We investigate gravitational lensing by using 0th order affine perturbation series of the deflection angle in a general asymptotically-flat, static, and spherical symmetric spacetime with the photon sphere. We apply our formula to Schwarzschild black hole, Reissner–Nordström black hole, and Ellis–Bronnikov wormhole spacetimes as examples. By comparing observables by using the deflection angles, we show that we can ignore the effect of the hidden error terms in the the deflection angle in the strong deflection limit on the observables in a usual lens configuration with the photon sphere since the hidden error terms are tiny. On the other hand, in a retro lensing configuration, the deflection angle in the strong-deflection-limit analysis have error of several percent and the 0th order of affine perturbation series of the deflection angle has almost half of the error. Thus, in the retro lensing configuration, we should use the 0th order of affine perturbation series of the deflection angle rather than the deflection angle in the strong-deflection-limit analysis. The 0th order of affine perturbation series of the deflection angle can give a brighter magnification by a dozen percent than the one by using the deflection angle in the strong-deflection-limit analysis.

Gravitational Lensing of Acoustic Charged Black Holes

We study the gravitational lensing of acoustic charged black holes in strong and weak field limit approximations. For this purpose, we first numerically obtain the deflection limit coefficients and deflection angle in the strong field limit. We observe that the strong deflection angle α D increases with increasing magnitude of the charged parameter Q and that the strong deflection angle α D of an acoustic charged black hole with tuning parameter ξ = 4 is greater than that of a standard Reissner–Nordström black hole (ξ = 0). We also study the astrophysical consequences via strong gravitational lensing by taking the example of various supermassive black holes in the center of several galaxies and observe that the acoustic charged black hole could be quantitatively distinguished from standard Reissner–Nordström (ξ = 0) and standard Schwarzschild (ξ = 0, Q = 0) black holes. Furthermore, by using the Gauss–Bonnet theorem, we derive the weak deflection angle in the background of an acoustic charged black hole in the curved spacetime. We find that, for fixed values of the charged parameter Q and the tuning parameter (ξ = 0 or 4), the weak deflection angle σ D decreases with the impact parameter b. We also observe that the weak deflection angle σ D decreases with increasing magnitude of the charged parameter Q for a fixed value of the tuning parameter (ξ = 0 or 4). Our results suggest that the observational test for an acoustic charged black hole is indeed feasible, and it is generalized to the cases of acoustic Schwarzschild (Q = 0), standard Reissner–Nordström (ξ = 0), and standard Schwarzschild (ξ = 0, Q = 0) black holes.