Evaluating the Effects of Graviton Redshift upon Spiral Galaxy Rotation Curves, Surface Brightness Magnitudes and Gravitational Lensing

The effects of the gravitational redshift of gravitons upon spiral galaxy rotation energy are compared to the standard mass to light analyses in obtaining rotation curves. The derivation of the total baryonic matter compares well with the standard theory and the rotation velocity is matched to a high precision. The stellar mass distributions obtained from the fit with graviton energy loss are used to derive the surface brightness magnitudes for the galaxies, which agree well with the observed measurements. In a new field of investigation, the graviton theory is applied to the observations of gravitational lenses. The results of these applications of the theory suggest that it can augment the standard methods and may eliminate the need for dark matter.

Theoretical Analysis of Random Scattering Induced by Microlensing

Theoretical investigations into the deflection angle caused by microlenses offer a direct path to uncovering principles of the cosmological microlensing effect.This work specifically concentrates on the the probability density function(PDF)of the light deflection angle induced by microlenses.We have made several significant improvements to the widely used formula from Katz et al.First,we update the coefficient from 3.05 to 1.454,resulting in a better fit between the theoretical PDF and our simulation results.Second,we developed an elegant fitting formula for the PDF that can replace its integral representation within a certain accuracy,which is numerically divergent unless arbitrary upper limits are chosen.Third,to facilitate further theoretical work in this area,we have identified a more suitable Gaussian approximation for the fitting formula.

Understanding the Predication Mechanism of Deep Learning through Error Propagation among Parameters in Strong Lensing Case

The error propagation among estimated parameters reflects the correlation among the parameters.We study the capability of machine learning of"learning"the correlation of estimated parameters.We show that machine learning can recover the relation between the uncertainties of different parameters,especially,as predicted by the error propagation formula.Gravitational lensing can be used to probe both astrophysics and cosmology.As a practical application,we show that the machine learning is able to intelligently find the error propagation among the gravitational lens parameters(effective lens mass ML and Einstein radiusθ_(E))in accordance with the theoretical formula for the singular isothermal ellipse(SIE)lens model.The relation of errors of lens mass and Einstein radius,(e.g.,the ratio of standard deviations F=σ_(ML)/σ_(θ_(E)))predicted by the deep convolution neural network are consistent with the error propagation formula of the SIE lens model.As a proof-of-principle test,a toy model of linear relation with Gaussian noise is presented.We found that the predictions obtained by machine learning indeed indicate the information about the law of error propagation and the distribution of noise.Error propagation plays a crucial role in identifying the physical relation among parameters,rather than a coincidence relation,therefore we anticipate our case study on the error propagation of machine learning predictions could extend to other physical systems on searching the correlation among parameters.

The Chromatic Point-spread Function of Weak Lensing Measurement in the Chinese Space Station Survey Telescope

Weak gravitational lensing is a powerful tool in modern cosmology.To accurately measure the weak lensing signal,one has to control the systematic bias on a small level.One of the most difficult problems is how to correct the smearing effect of the Point-Spread Function(PSF)on the shape of the galaxies.The chromaticity of PSF for a broad-band observation can lead to new subtle effects.Since the PSF is wavelength-dependent and the spectrum energy distributions between stars and galaxies are different,the effective PSF measured from the star images will be different from those that smear the galaxies.Such a bias is called color bias.We estimate it in the optical bands of the Chinese Space Station Survey Telescope from simulated PSFs,and show the dependence on the color and redshift of the galaxies.Moreover,due to the spatial variation of spectra over the galaxy image,another higher-order bias exists:color gradient bias.Our results show that both color bias and color gradient bias are generally below 0.1%in CSST.Only for small-size galaxies,one needs to be careful about the color gradient bias in the weak lensing analysis using CSST data.

On the Physical Nature of Einstein’s Gravitational Lensing Effect

Gravitational lensing has become a powerful research tool for exploring the distribution of matter and energy in the universe nowadays, as glare phenomena around the Sun and massive galaxies are indeed observed on the Earth. What is the physical nature of gravitational lensing effect? Both Newton’s law of gravitation and Einstein’s theory of relativity are difficult to physically explain these glare phenomena. This study points out that the observed glare around the Sun and large galaxies is a result or product of the orthogonal interaction of high-energy particles emitted from different star light sources. It shows a new physical state associated with abnormal high mass-energy density.

Simultaneous Gravitational and Refractive Lensing

The principal testing ground for general relativity is the observable Universe. Gravitational lensing is the leading observational technique that gives insight into the distribution of baryonic matter in the stellar, galactic and cosmological scale, as well as the distribution of dark matter and dark energy, due to their gravitational interaction. Interpretation of ever more precise observational data requires increasingly subtle analytical techniques. In this paper, I discuss a formalism that can handle a nonlinear superposition of gravitational and refractive lensing by a grouping of baryonic matter, dark matter and dark energy for a given distribution of those entities (i.e. for a given spacetime metric) and their refractive properties. The role of refraction in gravitational lensing is exemplified in the case of a microlensing event and a signature of such an effect is discussed.

Discovery of four gravitational lensing systems by clusters in the SDSS DR6

We report the discovery of 4 strong gravitational lensing systems by visual inspections of the Sloan Digital Sky Survey images of galaxy clusters in Data Release 6 （SDSS DR6）. Two of the four systems show Einstein rings while the others show tangen- tial giant arcs. These arcs or rings have large angular separations （〉 8″） from the bright central galaxies and show bluer color compared with the red cluster galaxies. In addition, we found 5 probable and 4 possible lenses by galaxy clusters.

Lensing clusters of galaxies in the SDSS-Ⅲ

We identify new strong lensing clusters of galaxies from the Sloan Digital Sky Survey Ⅲ （SDSS DR8） by visually inspecting color images of a large sample of clusters of galaxies. We find 68 new clusters showing giant arcs in addition to 30 known lensing systems. Among 68 cases, 13 clusters are ＂almost certain＂ lensing systems with tangential giant arcs, 22 clusters are ＂probable＂ and 31 clusters are ＂pos- sible＂ lensing systems. We also find two exotic systems with blue rings. The giant arcs have angular separations of 2.0jj - 25.7j~ from the bright central galaxies. We note that the rich clusters are more likely to be lensing systems and the separations between the arcs and the central galaxies increase with cluster richness.

Search for strong galaxy-galaxy lensing in SDSS-Ⅲ BOSS

Strong lensing is one of the most spectacular views in the universe.Many cosmological applications have been proposed,but the number of such lensing systems is still limited.In this work,we applied an improved version of a previously developed spectroscopic lensing search method to the SDSS-Ⅲ BOSS and proposed a list of highly possible candidates.Follow-up CFHT Megacam imaging observations were performed for five systems,and two out of five are probably strong lensing systems with at least one image close to the central galaxy,although no counter images are detected.

Intra-Atomic Gravitational Shielding (Lensing), Nuclear Forces and Radioactivity

The discovery by the author of real magnetic charges and true anti-electrons in the atomic structures allowed him to establish that the gravitational field (GF) in reality is the vortex electromagnetic field. Depending on the vector conditions the gravitational fields can be either paragravitational (PGF) or ferrogravitational (FGF). Masses (atoms, nucleons, etc.) emitting PGF manifest so-called attraction to each other. In fact, this process is the pressing of atoms or nucleons to each other by the forces of gravitational “Dark energy”. Namely the gravitational “Dark energy” which is formed between the masses emitting PGF and compressing of nucleons in atomic nuclei is the main force factor determining the formation of nuclear forces. Masses that emit FGF are repelled from PGF sources, for example, from the Earth. The last gravitational manifestation, discovered by the author, this is of the effect of the gravitational levitation. The atomic shell and atomic nucleus are autonomous sources of gravitational field in atomic compositions. The gravitational fields emitted these sources, by its physical parameters, are different gravitational fields, what associated with differences in the magnitudes charges of magnetic and electric particles in their compositions. The noted differences in the parameters of the GF are of reason that in atoms the process of extrusion of foreign gravitational field from the region of given gravitational source is realized. This effect should be called the effect of intra-atomic gravitational shielding (IAGS). Within the framework of this effect the shell of the atom is a kind of gravitational “insulator” that prevents the PGF of the nucleons from leaving beyond of the atom. As result of the IAGS effect, the concentration PGF of nucleons is realized only in the region of the nucleus, which leads to an increase in nuclear forces. However, the resistance of the marked “insulator” is finite and if the critical voltage PGF on the nucleus is exceeded, the complete shielding of the nucleon fields by the atomic shell is broken. As result of the leakage of a part of the PGF of nucleons beyond the atom, the density of this field in the region of the nucleus decreases significantly, which leads to a weakening of the nuclear forces and often leads to radioactivity. The effect of gravitational shielding is directly related to such a well-known concept as the mass defect of the nucleus. It is the exclusion of the gravitational field formed by the nucleons in the composition of the atomic nucleus as a result of the full IAGS effect that creates the illusion of atomic mass defect.

Astrophysical applications of gravitational microlensing

Since the first discovery of microlensing events nearly two decades ago, gravitational microlensing has accumulated tens of TBytes of data and developed into a powerful astrophysical technique with diverse applications. The review starts with a theoretical overview of the field and then proceeds to discuss the scientific highlights. （1） Microlensing observations toward the Magellanic Clouds rule out the Milky Way halo being dominated by MAssive Compact Halo Objects （MACHOs）. This confirms most dark matter is non-baryonic, consistent with other observations. （2） Microlensing has discovered about 20 extrasolar planets （16 published）, including the first two Jupiter-Saturn like systems and the only five ＂cold Neptunes＂ yet de- tected. They probe a different part of the parameter space and will likely provide the most stringent test of core accretion theory of planet formation. （3） Microlensing pro- vides a unique way to measure the mass of isolated stars, including brown dwarfs and normal stars. Half a dozen or so stellar mass black hole candidates have also been pro- posed. （4） High-resolution, target-of-opportunity spectra of highly-magnified dwarf stars provide intriguing ＂age＂ determinations which may either hint at enhanced he- lium enrichment or unusual bulge formation theories. （5） Microlensing also measured limb-darkening profiles for close to ten giant stars, which challenges stellar atmo- sphere models. （6） Data from surveys also provide strong constraints on the geometry and kinematics of the Milky Way bar （through proper motions）; the latter indicates predictions from current models appear to be too anisotropic compared with observa- tions. The future of microlensing is bright given the new capabilities of current surveys and forthcoming new telescope networks from the ground and from space. Some open issues in the field are identified and briefly discussed.

Cosmic Constraints to the wCDM Model from Strong Gravitational Lensing

We study the cosmic constraint to the wCDM （cold dark matter with a constant equation of state w） model via 118 strong gravitational lensing systems which are compiled from SLA CS, BELLS, LSD and SL2S surveys, where the ratio between two angular diameter distances Dobs =DA（Zl, Zs ） / D A （ O, Zs ） is taken as a cosmic observable. To obtain this ratio, we adopt two strong tensing models： one is the singular isothermal sphere model （SIS） and the other one is the power-law density profile （PLP） model. Via the Markov chain Monte Carlo method, the posterior distribution of the cosmological model parameters space is obtained. The results show that the cosmological model parameters are not sensitive to the parameterized forms of the power-law index γ. Furthermore, the PLP model gives a relatively tighter constraint to the cosmological parameters than that of the SIS model. The predicted value of Ωm = 0.31＋0.44 -0.24 by the SIS model is compatible with that obtained by P1anck2015： Ωm = 0.313 ± 0.013. However, the value of Ωm =0.15＋0.13 -0.11 based on the PLP model is smaller and has 1.25σ tension with that obtained by Planck2015.

The Multiple Images of the Plasma Lensing FRB

We investigate the formation of multiple images as the radio signals from fast radio bursts(FRBs)pass through the plane of a plasma clump.The exponential model for the plasma clump is adopted to analyze the properties of the multiple images.By comparing with the classical dispersion relations,we find that one image has exhibited specific inverse properties to others,such as their delay times at high frequency is higher than that at low frequency,owing to the lensing effects of the plasma clump.We demonstrate that these inverse effects should be observable in some repeating FRBs.Our results predict deviation in the estimated dispersion measure(DM)across multiple images,consistent with the observations of FRB 121102 and FRB 180916.J0158+65.If other plasma lenses have effects similar to an exponential lens,we find that they should also give rise to a similar dispersion relation in the multiple images.For some repeating FRBs,analysis of the differences in time delay and in DM between multiple images at different frequencies can serve as a method to reveal the plasma distribution.

Cusp-core problem and strong gravitational lensing

Cosmological numerical simulations of galaxy formation have led to the cuspy density profile of a pure cold dark matter halo toward the center, which is in sharp contradiction with the observations of the rotation curves of cold dark matter-dominated dwarf and low surface brightness disk galaxies, with the latter tending to favor mass profiles with a flat central core. Many efforts have been devoted to resolving this cusp-core problem in recent years, among them, baryon-cold dark matter interactions are considered to be the main physical mechanisms erasing the cold dark matter （CDM） cusp into a flat core in the centers of all CDM halos. Clearly, baryon-cold dark matter interactions are not customized only for CDM-dominated disk galaxies, but for all types, including giant ellipticals. We first fit the most recent high resolution observations of rotation curves with the Burkert profile, then use the constrained core size-halo mass relation to calculate the lensing frequency, and compare the predicted results with strong lensing observations. Unfortunately, it turns out that the core size constrained from rotation curves of disk galaxies cannot be extrapolated to giant ellipticals. We conclude that, in the standard cosmological paradigm, baryon-cold dark matter interactions are not universal mechanisms for galaxy formation, and therefore, they cannot be true solutions to the cusp-core problem.

Dependence of curvature type of thermal lensing on number of bounces in a zigzag slab laser:numerical modeling

The curvature type of the thermal lens generated in a zigzag slab laser is numerically analysed. It is found that the curvature type of the thermal lens varies alternatively between the convex and the concave lenses with the number of bounces of light within the slab, which can be well explained by the trace of the zigzag propagation. In addition, we conclude that the beamlet with a larger number of bounces experiences weaker thermal lensing but more serious wavefront deformation due to the large side lobe portion in the curve of optical path difference.

Statistical Cluster-QSO Weak Lensing in the Sloan Digital Sky Survey

We investigate the cross-correlation between galaxy clusters and QSOs using Sloan Digital Sky Survey （SDSS） DR4 - 5000 deg^2 data. With photometric redshifts of galaxies, we select galaxy clusters based on the local projected densities of LRGs brighter than Mr′ = -22. The QSOs are from the main sample of SDSS QSO spectroscopic survey to i′ = 19. A significant positive correlation is found between the clusters and QSOs. Under the assumption that the signal is caused by gravitational lensing, we fit the signal with singular isothermal sphere （SIS） model and NFW profile halo model. The velocity dispersion σv = 766 km s^-1 is derived for the best-fit of SIS model. Best-fit for the NFW model requires the dark matter halo mass within 1.5 h^-1 Mpc to be 4.6 × 10^14 h^-1 M⊙. The mass parameter Ωcl of the cluster sample is deduced as 0.077 with the SIS model and 0.083 with the NFW model. Our results of Ωcl are smaller than those given by Croom ＆ Shanks and by Myers et al.

Weak lensing magnification reconstruction with the modified internal linear combination method

Measuring weak lensing cosmic magnification signal is very challenging due to the overwhelming intrinsic clustering in the observed galaxy distribution.In this paper,we modify the Internal Linear Combination(ILC)method to reconstruct the lensing signal with an extra constraint to suppress the intrinsic clustering.To quantify the performance,we construct a realistic galaxy catalogue for the LSST-like photometric survey,covering 20000 deg^(2) with mean source redshift at z_(s)~1.We find that the reconstruction performance depends on the width of the photo-z bin we choose.Due to the correlation between the lensing signal and the source galaxy distribution,the derived signal has smaller systematic bias but larger statistical uncertainty for a narrower photo-z bin.We conclude that the lensing signal reconstruction with the Modified ILC method is unbiased with a statistical uncertainty <5% for bin width Δz^(P)=0.2.

Characterizing microlensing planetary system OGLE-2014-BLG-0676Lb with adaptive optics imaging

We constrain the host-star flux of the microlensing planet OGLE-2014-BLG-0676 Lb using adaptive optics(AO)images taken by the Magellan and Keck telescopes.We measure the flux of the light blended with the microlensed source to be K=16.79±0.04 mag and J=17.76±0.03 mag.Assuming that the blend is the lens star,we find that the host is a 0.73_(-0.29)^(+0.14)M_(⊙)star at a distance of2.67_(-1.41)^(+0.77)kpc,where the relatively large uncertainty in angular Einstein radius measurement is the major source of uncertainty.With mass of M_(p)=3.68_(-1.44)^(+0.69)M_J,the planet is likely a"super Jupiter"at a projected separation of r_(⊥)=4.53_(-2.50)^(+1.49)AU,and a degenerate model yields a similar M_p=3.73_(-1.47)^(+0.73)M_(J)at a closer separation of r_(⊥)=2.56_(-1.41)^(+0.84)AU.Our estimates are consistent with the previous Bayesian analysis based on a Galactic model.OGLE-2014-BLG-0676 Lb belongs to a sample of planets discovered in a"secondgeneration"planetary microlensing survey and we attempt to systematically constrain host properties of this sample with high-resolution imaging to study the distribution of planets.

Measuring Microlensing Parallax via Simultaneous Observations from Chinese Space Station Telescope and Roman Telescope

Simultaneous observations from two spatially well-separated telescopes can lead to measurements of the microlensing parallax parameter,an important quantity toward the determinations of the lens mass.The separation between Earth and Sun–Earth L2 point,~0.01 au,is ideal for parallax measurements of short and ultra-short(~1 hr to 10 days) microlensing events,which are candidates of free-floating planet (FFP) events.In this work,we study the potential of doing so in the context of two proposed space-based missions,the Chinese Space Station Telescope (CSST) in a low-Earth orbit (LEO) and the Nancy Grace Roman Space Telescope (Roman) at L2.We show that joint observations of the two can directly measure the microlensing parallax of nearly all FFP events with timescales t_(E)■10 days as well as planetary (and stellar binary) events that show caustic crossing features.The potential of using CSST alone in measuring microlensing parallax is also discussed.

Constraining Equation of State of Dark Matter:Including Weak Gravitational Lensing

Usually the equation of state （EoS） of dark matter is zero when it is cold, however there exists the possibility of a （effective） nonzero EoS of dark matter due to its decay and interaction with dark energy. In this work, we try to constrain the EoS of dark matter/JAdm using the currently available cosmic observations which include the geometrical and dynamical measurements. For the geometrical measurements, the luminosity distance of type Ia supernovae, the angular diameter distance and comoving sound horizon from baryon acoustic oscillations and the cosmic microwave background radiation will be employed. The data points from the redshift-space distortion and weak gravitational lensing will be taken as dynamical measurements. Using the Markov chain Monte Carlomethod, we obtain a very tight constraint on the-EoS of dark matter：wdm=0.0000532 ＋0.000692＋0.00136＋0.00183 -0.000686-0.00136-0.00177.