An Etymological Dictionary of Astronomy and Astrophysics
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In gravitational lens phenomenon, the critical distance from the → lensing object for which the light ray from the source is deflected to the observer, provided that the source, the lens, and the observer are exactly aligned. Consider a massive object (the lens) situated exactly on the line of sight from Earth to a background source. The light rays from the source passing the lens at different distances are bent toward the lens. Since the bending angle for a light ray increases with decreasing distance from the lens, there is a critical distance such that the ray will be deflected just enough to hit the Earth. This distance is called the Einstein radius. By rotational symmetry about the Earth-source axis, an observer on Earth with perfect resolution would see the source lensed into an annulus, called Einstein ring, centered on its position. The size of an Einstein ring is given by the Einstein radius: θ_E = (4GM/c²)^0.5 (d_LS/(d_L.d_S)^0.5, where G is the → gravitational constant, M is the mass of the lens, c is the → speed of light, d_L is the angular diameter distance to the lens, d_S is the angular diameter distance to the source, and d_LS is the angular diameter distance between the lens and the source. The equation can be simplified to: θ_E = (0''.9) (M/10¹¹Msun)^0.5 (D/Gpc)^-0.5. Hence, for a dense cluster with mass M ~ 10 × 10¹⁵ Msun at a distance of 1 Gigaparsec (1 Gpc) this radius is about 100 arcsec. For a gravitational → microlensing event (with masses of order 1 Msun) at galactic distances (say D ~ 3 kpc), the typical Einstein radius would be of order milli-arcseconds.

→ Einstein; → radius.