The gravitational bending of light by stars: a continuing story of curiosity,scepticism, surprise,and fascination

Driven entirely by human curiosity, the effect of the gravitational bending of light has evolved on unforeseen paths, in an interplay between shifts in prevailing paradigms and advance of technology, into the most unusual way to study planet populations. The confirmation of the bending angle predicted by Einstein with the Solar Eclipse measurements from 1919 marked the breakthrough of the theory of General Relativity, but it was not before the detection of the double image of the quasar 0957+561 that ‘gravitational lensing’ really entered the observational era. The observation of a characteristic transient brightening of a star caused by the gravitational deflection of its light by an intervening foreground star, constituting a ‘microlensing event’, required even further advance in technology before it could first emerge in 1993. While it required more patience in waiting before ‘Einstein’s blip’ for the first time revealed the presence of a planet orbiting a star other than the Sun, such detections can now be monitored live, and gravitational microlensing is not only sensitive to masses as low as that of the Moon, but can even reveal planets around stars in galaxies other than the Milky Way.     

Quasar microlensing

Quasar microlensing deals with the effect of compact objects along the line of sight on the apparent brightness of the background quasars. Due to the relative motion between quasar, lenses and observer, the microlensing magnification changes with time which results in uncorrelated brightness variations in the various images of multiple quasar systems. The amplitudes of the signal can be more than a magnitude with time scales of weeks to months to years. The effect is due to the “granular” nature of the gravitational microlenses—stars or other compact objects in the stellar mass range. Quasar microlensing allows to study the quasar accretion disk with a resolution of tens of microarcseconds, hence quasar microlensing can be used to explore an astrophysical field that is hardly accessible by any other means. Quasar microlensing can also be used to study the lensing objects in a statistical sense, their nature (compact or smoothly distributed, normal stars or dark matter) as well as transverse velocities. Quasar microlensing light curves are now being obtained from monitoring programs across the electromagnetic spectrum from the radio through the infrared and optical range to the X-ray regime. Recently, spectroscopic microlensing was successfully applied, it provides quantitative comparisons with quasar/accretion disk models. There are now more than a handful of systems with several-year long light curves and significant microlensing signal, lending to detailed analysis. This review summarizes the current state of the art of quasar microlensing and shows that at this point in time, observational monitoring programs and complementary intense simulations provide a scenario where some of the early promises of quasar microlensing can be quantitatively applied. It has been shown, e.g., that smaller sources display more violent microlensing variability, first quantitative comparison with accretion disk models has been achieved, and quasar microlensing has been used to determine the fraction of dark matter in a lensing galaxy for the first time. This is the quantitative beginning. The future of quasar microlensing is bright.     

Microlensing of Kepler stars as a method of detecting primordial black hole dark matter

If the dark matter consists of primordial black holes (PBHs), we show that gravitational lensing of stars being monitored by NASA's Kepler search for extrasolar planets can cause significant numbers of detectable microlensing events. A search through the roughly 150,000 light curves would result in large numbers of detectable events for PBHs in the mass range 5×10(-10) M(⊙) to 10(-4) M(⊙). Nondetection of these events would close almost 2 orders of magnitude of the mass window for PBH dark matter. The microlensing rate is higher than previously noticed due to a combination of the exceptional photometric precision of the Kepler mission and the increase in cross section due to the large angular sizes of the relatively nearby Kepler field stars. We also present a new formalism for calculating optical depth and microlensing rates in the presence of large finite-source effects.     

Pixel lensing

Pixel lensing is gravitational microlensing of unresolved stars. The main target explored up to now has been the nearby galaxy of Andromeda, M31. The scientific issues of interest are the search for dark matter in form of compact halo objects, the study of the characteristics of the luminous lens and source populations and the possibility of detecting extra-solar (and extra-galactic) planets. In the present work we intend to give an updated overview of the observational status in this field.     

Possible evidence for the observation of noncompact (nonbaryonic) gravitational microlenses (“neutralino stars”)

The microlensing of distant stars by noncompact objects such as neutralino stars is considered. Recently, Gurevich and Zybin considered the objects as microlenses. Using a nonsingular density distribution, we analyze microlensing by noncompact objects. We obtain analytic solutions to the gravitational-lens equation and an analytic expression for the amplification factor of the gravitational lens. We show that, on the basis of a model of microlensing by noncompact objects, it is possible to interpret microlensing-event candidates having two typical maxima of light curves which are usually interpreted as binary microlenses.     

Microlensing as a probe of the Galactic structure: 20 years of microlensing optical depth studies

Microlensing is now a very popular observational astronomical technique. The investigations accessible through this effect range from the dark matter problem to the search for extra-solar planets. In this review, the techniques to search for microlensing effects and to determine optical depths through the monitoring of large samples of stars will be described. The consequences of the published results on the knowledge of the Milky-Way structure and its dark matter component will be discussed. The difficulties and limitations of the ongoing programs and the perspectives of the microlensing optical depth technique as a probe of the Galaxy structure will also be detailed.     

Dark matter bodies in star and planet structures

The lowest frequency of the dipole f mode (surface gravity wave) of the Sun and some other stars is shown to be close to the orbital frequency of a trial body near the star surface, as well as the wave amplitude is shown to be resonantly increased to the values large enough to be observed. Therefore the Sun is considered to be a sensitive detector for hypothetical compact cosmic bodies made of dark matter particles. In this connection some possible characteristics of the dark matter bodies (DMB) are discussed, and DMB orbits in the Sun are calculated within a standard solar model in order to compare the wave amplitudes with data for the solar surface oscillations, and to estimate the masses and radii of the DMB. As well, some possible phenomena in star and planet structures are discussed with special attention on generation of flares of high X-ray classes, specific behavior of the Moon dust, formation of short-time vertical flows in deserts, oceans, and atmospheres on the Earth and other planets.     

Gravitational Microlensing by Ellis Wormhole: Second Order Effects

Gravitational lensing is the effect of light bending in a gravitational field. It can be used as a possible observational method to detect or exclude the existence of wormholes. In this work, we extend the work by Abe on gravitational microlensing by Ellis wormhole by including the second order deflection term. Using the lens equation and definition of Einstein radius, we find the angular locations of the physical image inside and outside Einstein ring. The work contains a comparative analysis of light curves between the Schwarzschild black hole and the Ellis wormhole that can be used to distinguish such objects though such distinctions are too minute to be observable even in the near future. We also tabulate the optical depth and event rate for lensing by bulge and Large Magellanic Cloud (LMC) stars.     

Infrared detection of a planet next to a bright star

Humans have always dreamt about the possibility of existence of planets in solar systems other than our own. After flying by, dropping probes, and even landing devices on most planets within our own solar system, the search for extra-solar planet is included in every proposal to either build a larger and better earth-, space-, or moon-based telescope, or observatory facility. The preliminary analysis seems to indicate that wavelength band from 25 μm to 30 μm is most promising in solving this problem. A number of IR technological challenges are to be overcome before the actual detection system can even be considered in a detailed design. The significant technical challenges of finding a planet will be described. Then details are given on the feasibility of detecting a planet with an instrument concept designed specifically for this purpose, a space-based, rotating rotationally shearing interferometer.     

Simulations for terrestrial planets formation

In this paper, the formation of terrestrial planets in the late stage of planetary formation is investigated using the two-planet model. At that time, the protostar formed for about 3 Ma and the gas disk dissipated. In the model, the perturbations from Jupiter and Saturn are considered. Variations of the mass of outer planet, and the initial eccentricities and inclinations of embryos and planetesimals are also considered. Our results show that, terrestrial planets are formed in 50 Ma, and the accretion rate is about 60%–80%. In each simulation, 3–4 terrestrial planets are formed inside “Jupiter” with masses of 0.15–3.6 M _⊕. In the 0.5–4 AU, when the eccentricities of planetesimals are excited, planetesimals are able to accrete material from wide radial direction. The plenty of water material of the terrestrial planet in the Habitable Zone may be transferred from the farther places by this mechanism. Accretion could also happen a few times between two major planets only if the outer planet has a moderate mass and the small terrestrial planet could survive at some resonances over time scale of 10⁸ a. In one of our simulations, commensurability of the orbital periods of planets is very common. Moreover, a librating-circulating 3:2 configuration of mean motion resonance is found. Supported by the National Natural Science Foundation of China (Grant Nos. 10573040, 10673006, 10833001, and 10233020) and the Foundation of Minor Planets of Purple Mountain Observatory     

A variety of radars designed to explore the hidden structures and properties of the Solar System's planets and bodies

Since the very first observations of the Moon from the Earth with radar in 1946, radars are more and more frequently selected to be part of the payload of exploration missions in the Solar System. They are, in fact, able to collect information on the surface structure of bodies or planets hidden by opaque atmospheres, to probe the planet subsurface or even to reveal the internal structure of a small body comet nucleus.A brief review of radars designed for the Solar System planets and bodies' exploration is presented in the paper. This review does not aim at being exhaustive but will focus on the major results obtained. The variety of radars that have been or are currently designed in terms of frequency or operational modes will be highlighted.     

Super-Earths: a new class of planetary bodies

Super-Earths, a class of planetary bodies with masses ranging from a few Earth-masses to slightly smaller than Uranus, have recently found a special place in exoplanetary science. Being slightly larger than a typical terrestrial planet, super-Earths may have physical and dynamical characteristics similar to those of Earth whereas unlike terrestrial planets, they are relatively easier to detect. Because of their sizes, super-Earths can maintain moderate atmospheres and possibly dynamic interiors with plate tectonics. They also seem to be more common around low-mass stars where the habitable zone is in closer distances. This article presents a review of the current state of research on super-Earths, and discusses the models of the formation, dynamical evolution, and possible habitability of these objects. Given the recent advances in detection techniques, the detectability of super-Earths is also discussed, and a review of the prospects of their detection in the habitable zones of low-mass stars is presented.     

The magnetospheres of Mercury,Earth, and the giant planets Jupiter and Saturn

Brief information is given on the magnetospheres of the planets in the solar system that have intrinsic magnetic fields: Mercury, Earth, Jupiter, and Saturn. A universal model is constructed for the magnetosphere of a planet. Modifications of this model that are applied to individual planets are considered. The proposed models describe the basic physical processes that are responsible for the structure and dynamics of the magnetosphere. The numerical results of the simulations are compared with the direct measurements of magnetic fields and charged particle fluxes in the vicinity of the planets obtained in spacecraft (SC) missions.     

The atmospheres of the Earth and the terrestrial planets: Their origin and evolution

The stability of the Earth's atmosphere is reviewed, and the importance of the hydrosphere and biosphere in the development of the atmosphere is emphasized. Although the Earth's atmosphere has naturally been investigated in the greatest detail, the atmospheres of other terrestrial planets may have had a simpler developmental history. The atmospheres of the Earth, Venus and Mars are compared, and it is shown that a consistent model of their evolution can be obtained on the basis of degassing from the solid planet.     

对原行星盘中易挥发物质缺失问题的简要综述

年轻恒星周围存在盘状的气体和尘埃分布,称为原行星盘,行星在其中形成. 为了认识恒星和行星的形成和演化以及构成行星的原材料,对这些盘的观测是必须的. 数值模型有助于从观测数据提取出重要的物理参数,包括盘的尘埃和气体的质量. 这些参数可以作为进一步模拟的输入参数,预期热化学模拟能复现各种分子的观测数据. 但是,对于许多原行星盘,模型算出的多种分子的发射强度高于观测值. 真实的盘中这些分子的丰度比理论预期低,这是易挥发物质的缺失问题. 本文指出在这个问题上理论与观测的差异意味着尘埃的演化对气体化学有重要影响,提示在这些盘中行星形成的早期阶段已经开始了.     

On the gravitational angular momentum of rotating sources

The gravitational energy–momentum and angular momentum satisfy the algebra of the Poincaré group in the full phase space of the teleparallel equivalent of general relativity. The expression for the gravitational energy–momentum may be written as a surface integral in the three-dimensional spacelike hypersurface, whereas the definition for the angular momentum is given by a volume integral. It turns out that in practical calculations of the angular momentum of the gravitational field generated by localized sources like rotating neutron stars, the volume integral reduces to a surface integral, and the calculations can be easily carried out. Similar to previous investigations in the literature, we show that the total angular momentum is finite provided a certain asymptotic behaviour is verified. We discuss the dependence of the gravitational angular momentum on the frame, and argue that it is a measure of the dragging of inertial frames.     

Gravitational microlensing: Results and perspectives in brief

Basics of the standard theory of microlensing are introduced. The results of microlensing observations toward Magellanic Clouds and relations with the dark matter (DM) problem in our Galaxy are described. Pixel microlensing observations and recent discoveries of planets with microlensing observations are listed. The text was submitted by the author in English.     

Relativistic perihelion precession of orbits of Venus and the Earth

Among all the theories proposed to explain the “anomalous” perihelion precession of Mercury’s orbit first announced in 1859 by Le Verrier, the general theory of relativity proposed by Einstein in November 1915 alone could calculate Mercury’s “anomalous” precession with the precision demanded by observational accuracy. Since Mercury’s precession was a directly derived result of the full general theory, it was viewed by Einstein as the most critical test of general relativity from amongst the three tests he proposed. With the advent of the space age, the level of observational accuracy has improved further and it is now possible to detect this precession for other planetary orbits of the solar system — viz., Venus and the Earth. This conclusively proved that the phenomenon of “anomalous” perihelion precession of planetary orbits is a relativistic effect. Our previous papers presented the mathematical model and the computed value of the relativistic perihelion precession of Mercury’s orbit using an alternate relativistic gravitational model, which is a remodeled form of Einstein’s relativity theories, and which retained only experimentally proven principles. In addition this model has the benefit of data from almost a century of relativity experimentation, including those that have become possible with the advent of the space age. Using this model, we present in this paper the computed values of the relativistic precession of Venus and the Earth, which compare well with the predictions of general relativity and are also in agreement with the observed values within the range of uncertainty.      

Gravitation with a modified Weber force

With a modified Weber force for gravitation we show how the values of both the advance of the perihelion of the planets and the gravitational deflection of fast particles of general relativity can be reproduced.