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Gravitational lenses in .NET Generator barcode code 128 in .NET Gravitational lenses

23. Gravitational lenses using .net vs 2010 toadd code 128 code set c in asp.net web,windows application ISO Standards by black holes is a fascina ANSI/AIM Code 128 for .NET ting subject, since the light that passes near the horizon can circle the hole more than once before emerging. Images in such circumstances become very distorted!.

In this section: by using l ensing one can measure the sizes of quasars, and they are astoundingly small.. The astronomer Zwicky, whom Code 128A for .NET we rst met in 14, was the rst to suggest, in 1937, that lensing by galaxies could be observable. As with his other work on neutron stars and dark matter, he was well ahead of his time.

. Lensing shows us the true s ize of quasars Gravitational lensing has its main application in astronomy today in the eld of cosmology. This is partly because of the numbers: if we take the equation for the Einstein radius, Equation 23.1 on page 337, and put in numbers that are appropriate for cosmological distances, then the angles look rather different.

For example, suppose the lensing mass is a dense cluster of galaxies with M = 1014 M , at a distance of 100 Mpc, and suppose the lensed object is a quasar twice as far away. (This is nearer than typical lensing systems, but it will serve to illustrate the point.) Then the Einstein radius works out to be about 30 kpc, about three times the radius of our Galaxy.

The angular size of this ring in an astronomer s telescope is about 1 minute of arc. This is much bigger than the microlensing rings, and it is an angle that modern telescopes can easily resolve, even from the ground. For this kind of lensing, nding images will be as important as nding brightening.

A picture of lensing, such as the image on the right-hand side in Figure 23.1 on page 332, can therefore yield quantitative information about the system. From the size of the Einstein radius, it is possible to estimate the mass of the lens.

By comparing this mass to the mass that one would deduce from the brightness of the galaxies, one can estimate the amount of dark matter in galaxies and clusters. The amount found in this way is consistent with our other estimates, as described in 14. The positions of the images are not the only information that astronomers can gather about the lens.

If the lensed object is a quasar, it can be expected to vary in brightness by signi cant amounts on time-scales of days or weeks. These changes will not be seen at the same time in the different images, because the light rays of these images follow different paths. The paths have different lengths and, importantly, they experience different propagation time-delays due to the different gravitational redshifts they experience in the gravitational eld of the lens.

If one can guess the mass of the lens, say from photographs of the galaxies, then one can calculate the time-delay if one knows how far away the galaxies are. Since the timedelay is measured, one can use it to infer the distance to the lens. By measuring the redshift of the lensing galaxies, one can nally infer the value of the Hubble constant ( 14).

This is one of the key methods astronomers use today to measure the expansion rate of the Universe. Alternatively, if one assumes a value for the Hubble constant, then one can use the measured time-delays to constrain models of the lens and pin down the overall mass and size of the lensing cluster. This is being done to determine the amount of dark matter in lenses, or indeed to discover regions in which there are condensations of dark matter with no visible galaxies at all.

One of the important side-effects of looking for correlated changes in brightness in the Einstein Cross lens system was the discovery that some brightness changes occur only in one image and not in the others. This does not mean that the images come from different sources, i.e.

that the lensing model is wrong; the spectra of the four images are too similar for them to come from different objects. Rather, it indicates that another, short-lived lensing phenomenon may be acting. In particular, individual stars in the lensing galaxy will occasionally pass across the image and produce microlensing, just as we have described above.

Scientists have shown that the number of observed events is consistent with what one would expect if the lensing galaxy has a population of stars similar to that of our Galaxy. More importantly,.
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