Recently Holz & Wheeler considered a very attracting possibility to detect retro-MACHOs, i.e. he most effective method of discovering exoplanets is based on radial velocity measurements using the HARPS (High Accuracy Radial velocity Planet Searcher) spectrograph. The gravitational microlensing of a star by another star produces a symmetric and achromatic light curve, which is the main signature of the phenomenon. The searches for microlensing events are closely related to the question of dark matter (DM). The corresponding characteristic time of microlensing is usually determined as the half-time it takes for the lens to cross the Einstein +- Chwolson cone. At cosmological distances between objects and the typical mass of the lensing galaxy, the angular distance between images is on the order of a few arcseconds. In the simplest case of a point-like gravitational lens, the angular distances between images are on the order of the Einstein +- Chwolson diameter, which is proportional to the square root of the lens mass.

It can be visualized as if a gravitating body attracts photons. Gravitational lensing is based on the gravitational light bending effect. Gravitational microlensing (including pixel-lensing) is among the most promising techniques if we are interested to find Earth-like planets at distances about a few astronomical units from the host star. There are different methods for finding exoplanets such as radial spectral shifts, astrometrical measurements, transits, pulsar timing etc. So, one can name searches for planets with gravitational lens method a gravitational nanolensing. Thus, generally speaking, one can call a regime with a planet mass lens a nanolensing (independently on lens and source locations). An angular distance depends on a lens mass as a square root and therefore, if a lens has a typical Earth-like planet mass of 10-6M⊙, such a regime is called nanolensing. If a gravitational lens has a typical stellar mass, this regime is named a microlensing because a typical angular distance between images is about microarcseconds in the case when sources and lenses are located at cosmological distances. Therefore, the launch of the space interferometer Radioastron will enable the investigation of microlensing in the radio band, giving rise 1055 Int.ĭifferent regimes of gravitational lensing depend on lens masses and roughly correspond to angular distance between images. Astro-metric microlensing due Galactic MACHOs is not very important because of low optical depths and long typical time scales. In the case of a confirmation (or a negation) of claims about microlensing in gravitational lens systems, one can speculate about the microlens contribution to the gravitational lens mass. Alternatively, they may be observed by increasing an integration time, assuming that a radio source has a typical core–jet structure and microlensing phenomena are caused by the superluminal apparent motions of knots. However, to directly resolve these images and to directly detect the apparent motion of the knots, the Radioastron sensitivity would have to be improved, since the estimated flux density is below the sensitivity threshold. Therefore, for example, gravitationally lensed objects, like the CLASS gravitational lens B1600+434, appear to be most suitable to detect astrometric microlensing, since features of photo-metric microlensing have been detected in these objects. It is known that in gravitationally lensed systems the probability (the optical depth) of observing microlensing is relatively high. Moreover, one could not exclude the pos-sibility that non-baryonic dark matter could also form microlenses if the corresponding optical depth were high enough. In this case, an analysis of their variability and a solid determination of microlensing could lead to an estimation of their cosmological mass density. The basic targets for microlensing searches should be bright point-like radio sources at cosmological distances. Such an angular resolution will be reached with the space–ground VLBI interferometer, Radioastron.

For the case of microlensing, angular distances between images or typical astrometric shifts are about 10 −5 − 10 −6 arcsec. Typical angular dis-tances between images and typical time scales depend on the gravitational lens masses. It is well-known that gravitational lensing is a powerful tool in the investigation of the distribution of matter, including that of dark matter (DM).

Astrometry for astrophysics pdf