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.

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.

Weak gravitational lensing of quantum perturbed lukewarm black holes and cosmological constant effect

The aim of the paper is to study weak gravitational lensing of quantum （perturbed） and classical lukewarm black holes （QLBHs and CLBHs respectively） in the presence of cosmological parameter A. We apply a numerical method to evaluate the deflection angle of bending light rays, image locations θ of sample sourceβ = π- 4, and corresponding magnifications μ. There are no obtained real values for Einstein ring locations θE（β = 0） for CLBHs but we calculate them for QLBHs. As an experimental test of our calculations, we choose mass M of 60 types of the most massive observed galactic black holes acting as a gravitational lens and study quantum matter field effects on the angle of bending light rays in the presence of cosmological constant effects. We calculate locations of non-relativistic images and corresponding magnifications. Numerical diagrams show that the quantum matter effects cause absolute values of the quantum deflection angle to be reduced with respect to the classical ones. The sign of the quantum deflection angle is changed with respect to the classical values in the presence of the cosmological constant. This means dominance of the anti-gravity counterpart of the cosmological horizon on the angle of bending light rays with respect to absorbing effects of 60 local types of the most massive observed black holes. Variations of the image positions and magnifications are negligible when increasing dimensionless cosmological constant ∈ = 16AM2 /2The deflection angle takes positive （negative） values for CLBHs （QLBHs） and they decrease very fast （slowly） by increasing the closest distance x0 of bending light ray and/or dimensionless cosmological parameter for sample giant black holes with 0.001 〈 ∈ 〈 0.01.

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.

Probing the dark side of the Universe with weak gravitational lensing effects

Arising from gravitational deflections of light rays by large-scale struc- tures in the Universe, weak-lensing effects have been recognized as one of the most important probes in cosmological studies. In this paper, we review the main progress in weak-lensing analyses, and discuss the challenges in future investigations aiming to understand the dark side of the Universe with unprecedented precisions.

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.

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.

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.

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.

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.

Statistical improvement in detection level of gravitational microlensing events from their light curves

In astronomy,the brightness of a source is typically expressed in terms of magnitude.Conventionally,the magnitude is defined by the logarithm of received flux.This relationship is known as the Pogson formula.For received flux with a small signal to noise ratio（S/N）,however,the formula gives a large magnitude error.We investigate whether the use of Inverse Hyperbolic Sine function（hereafter referred to as the Asinh magnitude）in the modified formulae could allow for an alternative calculation of magnitudes for small S/N flux,and whether the new approach is better for representing the brightness of that region.We study the possibility of increasing the detection level of gravitational microlensing using 40 selected microlensing light curves from the 2013 and 2014 seasons and by using the Asinh magnitude.Photometric data of the selected events are obtained from the Optical Gravitational Lensing Experiment（OGLE）.We found that utilization of the Asinh magnitude makes the events brighter compared to using the logarithmic magnitude,with an average of about 3.42×10^（-2）magnitude and an average in the difference of error between the logarithmic and the Asinh magnitude of about 2.21×10（-2）magnitude.The microlensing events OB140847 and OB140885 are found to have the largest difference values among the selected events.Using a Gaussian fit to find the peak for OB140847 and OB140885,we conclude statistically that the Asinh magnitude gives better mean squared values of the regression and narrower residual histograms than the Pogson magnitude.Based on these results,we also attempt to propose a limit in magnitude value for which use of the Asinh magnitude is optimal with small S/N data.

Gravitational Lensing Described by Its Electromagnetic Processes

In the present paper, gravitational lensing is described as the electromagnetic influence from gravity waves on light waves. Previous reports have described the dynamic electromagnetic processes of the atom, the photon and gravity. Results from these reports have been compiled into a theoretical model. The theoretical model describes the mechanism which results in gravitational lensing. The study also displays how the electromagnetic characteristics of gravity waves and light waves and the mechanism creating gravitational lensing are measured.

Mass to light ratio of galaxies and gravitational lensing

We investigate the potential of constraining the mass to light ratio of field galaxies using weak lensing shear and flexions. A suite of Monte Carlo simulations are used to generate weak lensing observations with different noise models. Using mock data, we find that the inclusion of flexions can improve the estimate of foreground halo parameters, but the details are strongly dependent on noise in the model. In the intrinsic noise limit, both shear and flexions are promising tools to study the mass to light ratio of galaxies. However, if the noise model of flexions follows the form described by Rowe et al., there is only - 5% improvement in the constraints even with next generation lensing observations.

Gravitational lensing properties of an isothermal universal halo profile

N-body simulations predict that dark matter halos with different mass scales are described by a universal model, the Navarro-Frenk-White （NFW） den- sity profiles. As a consequence of baryonic cooling effects, these halos will become more concentrated, and similar to an isothermal sphere over a large range in radii （～ 300 h-1 kpc）. The singular isothermal sphere （SIS） model however has to be trun- cated artificially at large radii since it extends to infinity. We model a massive galaxy halo as a combination of an isothermal sphere and an NFW density profile. We give an approximation for the mass concentration at different baryon fractions and present exact expressions for the weak lensing shear and flexion for such a halo. We compare the lensing properties with the SIS and NFW profiles. We find that the combined pro- file can generate higher order lensing signals at small radii and is more efficient in generating strong lensing events. In order to distinguish such a halo profile from the SIS or NFW profiles, one needs to combine strong and weak lensing constraints for small and large radii.

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.

The Amplitude of Mass Fluctuations and Mass Density of the Universe Constrained by Strong Gravitational Lensing

We investigate the linear amplitude of mass fluctuations in the universe, σ8, and the present mass density parameter of the Universe, Ωm, from statistical strong gravitational lensing. We use the two population model of lens halos with fixed cooling mass scale Mc = 3×1013h-1M⊙ to match the observed lensing probabilities, and leave σ8 orΩm as a free parameter to be constrained by the data. Another varying parameter, the equation of state of dark energy ω, and its typical values of -1, -2/3, -1/2 and -1/3 are investigated. We find that σ8 is degenerate with Ωm in a way similar to that suggested by present day cluster abundance as well as cosmic shear lensing measurements: σ8Ω0.6m≈0.33. However, both σ8≤0.7 and Ωm≤0.2 can be safely ruled out, the best fit is when σ8 = 1.0, Ωm = 0.3 and ω= - 1. This result is different from that obtained by Bahcall & Bode, who gave σ8 = 0.98±0.1 and Ωm = 0.17 ±0.05. For σ8 = 1.0, the higher value ofΩm = 0.35 requires ω = -2/3 and Ωm = 0.40 requires ω= -1/2.

Is the Variable X-ray Source in M82 due to Gravitational Lensing?

We explore the possibility of attributing the recent discovery of the variable hard X-ray source CXO M82 J095550.2+694047 in M82 to the gravitational magnification by an intervening stellar object along the line of sight acting as a microlens. The duration of the event (> 84 days) allows us to set robust constraints on the mass and location of the microlensing object when combined with the dynamical properties of the Galactic halo, M82 and typical globular clusters. Except for the extremely low probability, the microlensing magnification by MACHO in either the Galactic halo or M82 halo is able to explain the X-ray variability of CXO M82 J095550.2+694047. It is hoped that the lensing hypothesis can be tested soon by measurement of the light curve.

A Remark on Using Gravitational Lensing Probability as a Probe of the Central Regions of CDM Halos

We calculate the gravitational lensing probabilities by cold dark matter (CDM) halos with different density profiles, and compare them with current observations from the Cosmic Lens All-Sky Survey (CLASS) and the Jodrell-Bank VLA Astrometric Survey (JVAS). We find that the lensing probability is dramatically sensitive to the clumping of the dark matter, or quantitatively, the concentration parameter. We also find that our predicted lensing probabilities in most cases show inconsistency with the observations. It is argued that high lensing probability may not be an effective tool for probing the statistical properties of inner structures of dark matter halos.

Regular Magnetic Black Hole Gravitational Lensing

The Bronnikov regular magnetic black hole as a gravitational lens is studied. In nonlinear electrodynamics, photons do not follow null geodesics of background geometry, but move along null geodesics of a corresponding effective geometry. To study the Bronnikov regular magnetic black hole gravitational lensing in the strong deflection limit, the corresponding effective geometry should be obtained firstly. This is the most important and key step. We obtain the deflection angle in the strong deflection limit, and further calculate the angular positions and magnifications of relativistic images as well as the time delay between different relativistic images. The influence of the magnetic charge on the black hole gravitational tensing is also discussed.