Gravitational Lensing by Scott Dodelson

Author:Scott Dodelson [Dodelson, Scott]
Language: eng
Format: azw3
Publisher: Cambridge University Press
Published: 2017-05-31T04:00:00+00:00

(6.18)

The ellipticities of the galaxies can then be expressed as a ratio of the moments and T. Explicitly,

(6.19)

6.4

Ellipticity and Shear with Weighting and Intrinsic Ellipticity1

We are now in a position to move beyond the ideal ellipticity–shear relation of Eq. (6.16) and include two necessary complications: (i) the weighting of moments and (ii) the fact that the unlensed galaxies are not always circular. This second effect, called intrinsic ellipticity, is obvious: most galaxies we see in the sky, even the ones close to us, that are by and large unlensed, do not appear circular. Intrinsic ellipticity means that a measurement of does not immediately translate into a measurement of shear. Indeed, one might wonder how shear can be inferred at all if every observed ellipticity could have nothing to do with the shear field, i.e., could be intrinsic. The short, qualitative answer is that the intrinsic ellipticities of galaxies are (more or less) random, so if we average the ellipticities of many galaxies in the same region on the sky, the mean intrinsic ellipticity will be zero, while the ellipticity due to shear will be the same for each galaxy. This is a classic case of the signal (ellipticity due to shear) emerging from the noise (intrinsic ellipticity) since the noise averages to zero over many measurements while the signal persists. Clearly, then, surveys will be most powerful in measuring the shear if they image many background galaxies.

The goal of this section, then, is to relate the observed ellipticities as defined in Eq. (6.19) to the two components of shear defined in Eq. (6.1) in the presence of weighting and intrinsic ellipticity. The starting point is the relation between the observed intensity, in the image plane, and the unlensed intensity in the source plane:

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