MODERN COSMOLOGY
Lens equation 387 usingξ=Ddθ. In this case the lens equation (14.13) is linear, which means that βis proportional toθ: β=θ−β=θ− ...
388 Gravitational lensing Iνdoes not change, since the total number of photons stays constant as well as their frequency. The am ...
Lens equation 389 and the position anglesφ±for the axes are tanφ±= γ 1 γ 2 ∓ √( γ 1 γ 2 ) 2 +1or tan2φ±=− γ 2 γ 1 . (14.48) The ...
390 Gravitational lensing (a) nI≥ 1 (b) ntot<∞ (c) nI+nIII= 1 +nII (d) for|β|sufficiently large ntot=nI= 1. It thus follows f ...
Simple lens models 391 forθ ≥0. Due to the axial symmetry it is enough to considerβ≥0. Since m(θ)≥0 it follows thatθ≥β(forθ≥0). ...
392 Gravitational lensing to the critical curve (which must be a circle). We see readily that the first case occurs for a tangen ...
Simple lens models 393 In several lens models the Einstein radius delimits the region within which multiple images occur, wherea ...
394 Gravitational lensing For the Schwarzschild lens, which is a limiting case of an axial symmetric one, we can substituteβusin ...
Simple lens models 395 14.3.3 Singular isothermal sphere A simple model for describing the matter distribution in a galaxy is to ...
396 Gravitational lensing whereξis the distance (in the lens plane) from the the centre of mass. For the light deflection angle ...
Simple lens models 397 radius of a galaxy.p=0 corresponds to the Plummer distribution, whereas for p= 1 /2 we get the isothermal ...
398 Gravitational lensing profileI(r/R),whereris the distance of a source point from the centre of the source. Adopting polar co ...
Galactic microlensing 399 astrophysical compact halo objects (MACHOs), and to study the content of low- mass stars in the galact ...
400 Gravitational lensing with the satellite Infrared Space Observatory (ISO) also seem to exclude M- dwarfs as significantly co ...
Galactic microlensing 401 Figure 14.3. The set-up of a gravitational lens situation: The lens L located between source S and obs ...
402 Gravitational lensing Figure 14.5.Light curves for the different cases of figure 4.2. The maximal magnification ism= 0 .32 ...
Galactic microlensing 403 Table 14.1.The expected number of eventsNevis obtained for a halo made entirely of MACHOs of a given m ...
404 Gravitational lensing Figure 14.6.Microlensing event observed by the MACHO collaboration in their first year of data towards ...
Galactic microlensing 405 Figure 14.7.Binary microlensing event towards the LMC by the MACHO collaboration (taken from the web p ...
406 Gravitational lensing the alert events, which are constantly updated†. During their first season, the MACHO team found 45 ev ...
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