by Vladimir ZHAROV, Dr. Sc. (Phys. & Math.), Head of Celestial Mechanics, Astrometry and Gravity Measurements Lab, Physics Department of Lomonosov Moscow State University, Winner of the Rene Descartes Prize (EU);

Mikhail SAZHIN, Dr. Sc. (Phys. & Math.), Leading research fellow of the P. K. Shternberg State Astronomy Institute of Lomonosov Moscow State University

The science of Physics regards the subject matter that environs the man in his everyday life as consisting of baryons, leptons and photons, that is of three kinds of stable particles. As to the Astronomy standpoint, it is a single type of matter called visible matter. However, in the 1930s the scientists discovered a new type of substance, the so-called "dark" matter which was invisible to telescopes. The existence of such matter has been established by measuring the velocities of stars in our Galaxy, as well as by considering the rotation characteristics of other stellar systems.

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If the angular separation between star S and body L is smaller than the so-called Einstein Cone (indicated by a dotted line), the image of distant star S turns into two flipped "crescents".

The astronomers discovered yet another type of matter now called "quintessence" at the end of the 20th century. The "dark" matter and "quintessense" are two different kinds of matter in principle. While the first type of matter might be subjected to laboratory testing in the future, the second kind will be accessible only by way of astronomical research.

There are a few methods that can be used to estimate the amount of "dark" matter within a galaxy. One such technique is a gravitational lensing, that is using the effect of light bending in the neighborhood of massive objects.

What is such a process? The nature is known to have four basic interactions: electromagnetic, weak, strong and gravitational. The first one is in charge of bonding nucleus and electrons within atoms, ensures the elastic force in solids, as well as the frictional force. A transporting vehicle for this interaction is the electromagnetic field, or, more precisely, the photons which provide for us the most of information on the Universe. The second interaction comes into operation only at extremely short distances. The third influences nucleus stability by linking its protons and neutrons. The fourth interaction stands apart for its universality: all particles irrespective of their composition are equally accelerated by the field of gravity which is in accord with the fundamental principle of the Theory of Relativity. Its effective radius is infinite: from a laboratory to the Solar system and farther to the Universe.

Just a reminder: a man-made satellite, electrons and photons all experience the same gravitational attraction of the Earth and have the same accelerated velocity of 9.8 m/s". However, they move along different trajectories. The curve path of any object's movement shall be defined by the magnitude and vector of its commencing speed.

This means that a satellite can orbit the Earth along either an elliptical or hyperbolic path. To get the second result the satellite will have to be accelerated to a velocity above 11 km/s. The higher is the velocity of an object traveling past the Earth, the closer the hyperbolic curve will be to a straight line. The light velocity is the fastest we know in the world. That's why the photons move along almost a straight line, though certain deflections can be observed anyway. This can be explained as follows: if we draw two tangents to a photon trajectory, so that one of them is before and the other one is after the attracting object, they will cross at some angle. It is a very tiny angle. This phenomenon was predicted by the great German scientist, foreign honorary member of the USSR Academy of Sciences Albert Einstein (1879 - 1955) and was later discovered by the US astronomer, foreign honorary member of the USSR Academy of Sciences Sir Arthur Eddington (1882 - 1944) at the time of a complete solar eclipse. The effect by itself was not a great deal: a ray of light from a distant star when passing near the solar limb deflected just by 1.75".

This phenomenon with significantly less deviation magnitudes can be also observed when a ray from a remote source travels in the neighborhood of a more closely located star. Two rays of light going on different sides of the star and deflected from the straight path can get crossed. Thus, an observer will see two images of the same space object, which as a matter of fact is exactly the effect of gravitational lensing.

Let's consider some stellar body with a spherical symmetry (same property as that of the gravitational field) to be a lens. An observer using a high resolution telescope will see a distant star image as two flipped crescents. Their dimensions and brightness will be different, but their cumulative brilliance is always higher.

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As a result of gravitational tensing two light beams from star S passing on both sides of object L cross at point O (the location of an observer). The latter will see two images l₁ and l₂ of the same star S.

The angular separation between two main images (crescents) is roughly equal to the angular dimension of the so-called Einstein Cone*. However, when the distance between the lens and the background star exceeds significantly the indicated value, the second image is either absorbed by the lens substance, or its flux is so faint that its crescent cannot be detected at all. This is called weak microlensing which allows only detecting nonlinear motion of the star's first image.

Just a reminder: gravitational fields of most space objects have no spherical symmetry. That is why the lensing process may result in several images of the same object with different brightness characteristics. If some galaxy functions as a lens, the angular separation between different images makes roughly a second of arc while the microlensing by a star gives us only a millisecond. It is quite difficult, though possible, to see two or more images in the first case and totally impossible to distinguish them from the Earth in the second case. In this situation, however, there is a helping variability factor of the lensing effect. Below are a few explanatory comments.

All space objects, including lenses, are in motion. Of course, the extragalactic objects are very slow in traveling across the celestial sphere: it will take hundreds of thousands of years for an object to make a distance of a second of arc. But when lensing stars with one of them used as a lens, this movement is much faster since those objects are much closer to us and their rate of angular motion is much higher. Now, let's imagine a similar situation: a transient car against the background of a distantly flying aircraft. The car is closer and it has a higher rate of angular motion for the same period of time. The plane is farther away, and it looks as if it moves more slowly.

Since the angular separation between the lens and the star is changing, so is the cumulative brightness of the images-crescents. The variability time during the microlensing is from one to several months.

It has to be noted as well that according to the equivalence principle various mass objects gravitate with the same accelerated velocity. This means that two photons with different frequencies (i. e. with different energies and thus different masses) experience the same accelerated velocity. In other words, photons of different electromagnetic spectral regions deviate to the same angle within the gravitational field of the object - lens.

For the first time the effect of a gravity lens on extra-galactic objects was revealed some 20 years ago. One of the best investigated such objects is quasar QSO 0957 + 561 A, B. Nowadays, there are more than fifty objects of the kind, and their number is ever-growing. Angular separations between the images in different lenses are varying from 0.77 to 6", but some objects provide separations measuring tens of seconds of angle. This happens when the lens effect is formed by a cluster of galaxies.

As for QSO 0957 + 561 A, B, the object's structure has been mapped in detail and its radiating power has been studied within the full range of radio to optical emissions. Long-duration measurements of this quasar's luminosity allowed for a new method of defining the Hubble* optical path constant. Since the optical paths producing two images are different, it takes light beams different time to

* Einstein Cone is an imaginary ring overhead the center of which coincides with the lens center and the dimensions of which are proportional to a square root of the lens mass and inversely proportional to a square root of the lens distance to the Earth. - Auth.

* Edwin Hubble (1889 - 1953) - a US astronomer who established the star nature of anagalactic nebulae and estimated distances to some of them, developed the basics for their structural classification and determined (1929) the regular pattern of despersion of galaxies. The Hubble Constant is a multiplying factor in the Hubble law which denominates linear relationship of the velocity of galactic clusters depending on their distance to the Earth. - Ed.

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travel along them. If there is a burst on the quasar, the observer will see the light coming via the shortest path first and the light taking the longer path second, that is the observer will see the repeated image of the burst (in the angular measure closer to the galaxy-lens). By measuring the subtracted time of arriving signals we may determine the difference between optical paths, which in combination with the known angular separation between the images will help us calculate the distance to the quasar and the galaxy-lens. By comparing it with the red shift* of objects we may also calculate the Hubble Constant.

Groups of scientists, including experts from the Special Astrophysical Observatory (Zelenchukskaya station in Karachaevo-Cherkessia), have been involved in measuring the brightness of two components of quasar QSO 0957 + 561 А, В for some 10 years. Their observations made it possible to lower the Hubble Constant upper value to 70 km/s/megaparsec. Such accuracy is quite comparable to the results obtained by other methods of extragalactic astronomy.

Another object QSO 2237 + 030 is named the "Einstein Cross". It is a quasar with red shift z = 1.7. The nucleus of the galactic-lens has a quadrupole** density distribution, which results in four quasar images in a cruciform configuration. Working with such object, besides measuring the Hubble Constant one can try to find the microlensing effect as well. It happens when the quasar-to-Earth ray meets on its way a star of the galaxy-lens. As a result it produces additional breaking of the ray, which leads to additional images and changes of their total luminosity. The value of this breaking equals a few tens of microseconds of arc, which cannot be measured by optical instruments. However, the brightness changes can be tenths of the stellar magnitude, which the modern instrumentation can resolve.

The microlensing in our Galaxy was discovered in the early 1990s, when two groups of scientists reported their results of searching for massive invisible objects in the Galaxy using the effect of microlensing. In particular, the US-Australian group of scientists MACHO (Massive Compact Halo Objects) conducted a year long observations of about 2 million stars within the Large Magellanic Cloud (LMC). In February-March 1993 the scientists discovered that one of the stars became 7 times brighter and 34 days later the brightness returned to its normal level. This discovery was made on the 1.27-m telescope at Mount Stromlo Observatory (Australia).

In turn, French astronomers of the EROS group (Experience de Recherches d'Objects Sombres) were monitoring some 3 million stars within the LMC. They also reported the effect of microlensing. One of the objects grew in brightness by 2.5 times in 54 days and the other by 3.3 times in 60 days. At present we know about more than 100 such events that took place against the background stars of the LMC.

The issue of the day of modern astronomy is also the task of defining principal limitations in accuracy for experiments associated with non-stationarity of our space-and-time. Apart from the practical requirements relative to space and navigation, the issue of extreme accuracy for positional measurements involves one of the fundamental physical concepts-a possibility of constructing an inertial reference system with quasars used today as fixed datum points*.

The axis system non-stationarity is caused by changing directions of light (or radio) beams arriving to telescopes from distant, i. e. reference point sources. There are two reasons for this event. First, the radiating areas are non-stationary. Say, the movement of radiating plasma clouds within an extragalactic source results in notable displacements of the brightness center and consequently in fluctuations of the corresponding reference point. Second, photon's movement is generally not so straight-line. Its path can be altered by the environment with a refraction index other than 1, which can be attributed to the occurrence of matter in the line of sight.

There is also another reason for the light to deviate from a straight line path. What we are talking about here is the non-stationarity of our space-and-time. Now, let's try to

* Red shift is proportional to the difference of spectral line wavelength from a space source and the wavelength of the same line as measured in fixed (laboratory) system. - Auth.

** Quadrupole is an electrically neutral in general system of charged particles which can be viewed as a combination of two dipoles with equal in size, but opposite in sign, dipole moments located closely to each other. - Ed.

* Fixed datum point (or reference point) is a check point with known coordinates and velocity, -Ed.

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explain some basic principles for considering influence of a gravity field of material objects on the architecture of an inertial reference system. In astronomy such a system is formed by a number of objects serving as reference points and by freezing physical moments of observations in a selected time measurement system. At present, the quasars are exactly such reference points. Their angular velocities are very slow and thus the axis system rotation in the space is equally small. The light from quasars goes to the Earth along a twisted locus defined by gravitational fields of stars and other objects of our Galaxy. The stars, however, are in motion and so the picture of gravitational fields is not stationary. Accordingly variable is the path of light rays from any quasar to an observer on the Earth. All this leads to a changed position of the object overhead. The mean-root-square value of these fluctuations imposes a certain limit on determining a quasar's position and on fundamental cataloguing of distant stars. In so doing, according to calculations, the angular deflection of the reference point from its undisturbed position is about 4 microseconds of arc. And this is a minimal estimation. Real values by computer modeling might be tens of times as higher.

Furthermore, at the end of the 20th century while studying the effect of microlensing the scientists from MACHO and EROS groups discovered a new population of objects in our Galaxy - dark bodies with masses of some ~0.1 of the Sun mass. They are so numerous that they define the Galaxy's rotation curve and constitute at least half of its total mass. These objects are distributed unevenly, so the astrometric observations will allow determining in the future their density in the neighborhood of our day-star.

We shall now discuss the problem of gauging the parallaxes (distances) of stellar bodies from the Solar system using the effect of weak microlensing. If defined by a direct trigonometric calculation for the most of sources, it may change the existing scale, which in its turn will require a cardinal revision of certain astronomical challenges.

It has to be mentioned that phenomena associated with the space-and-time non-stationarity in our Galaxy will affect the measurements of parallaxes. Since the masses and velocities of stars causing this non-stationarity are mostly unknown, it will be impossible to reconstruct the correct distance values. And their distortions can be so big that the parallaxes can become negative. So far this was attributed to measurement errors. Now we have to admit that this is the issue of a real physical phenomenon.

In conclusion we shall note the following: non-stationary gravitational fields of our Galaxy affect the propagation of light in such manner that light beams adopt curved paths. Consequently, a light source direction will not coincide with the straight line of sight. Moreover, since fields in the Galaxy are non-stationary, the direction of light eventually changes as well. In other words, the source's visible position on the celestial sphere will experience incidental "jumping." This effect is similar to the "jumping" of a star when its light runs through the turbulent* atmosphere of the Earth. Just in this latter case the non-stationary air currents alter the path of star photons within the atmosphere. The difference is in distinctive jumping amplitudes and the timing. The swing amplitude of coordinate variations caused by microlensing is 1 to 50 microseconds of arc and the timing is tens or even hundreds of years. Occasional "overswings" may reach magnitudes of hundreds of microseconds of arc; however, these are non-stationary events with a distinctive timing of a few months to a year. They cannot be of any significance for fundamental astrometric cataloguing. Nevertheless, within a timeframe of several decades almost all reference sources find their positions changed. Thus, the high accuracy catalogues need to be revised every 30 years in order to establish a renewed reference grid for celestial coordinates.

In such a manner the microlensing establishes a limit for determining distances in the Universe by precise astrometric methods.

* "Turbulent" means "disordered," "stormy." The word is often used to describe the current of fluids or gases, which is characterized by violent agitation, intensive mass and heat exchange processes. - Ed.