Question

s A point source directly behind a galaxy, at double the observer-gala tationally lensed by the galaxy's potential into an Einstein ring. The symmetic, and has a fiat rotation curve, vi) -e. The bending angle ing through a spherical mass distribution with imact parameter r from the distib distance d, is gra Answer 2.4 x 10 a light center is 4GMicr) where M(cr) is the mass enclosed within r a Find the angular radius y of the Einstein ring, in terms ofve assuming small anges Calculate &t, in arcseconds, for v 300 km s. At d- 0.5 Gpc, to what physical radius, Ri, will this y correspond? Answers 2v/c RE 1 kpc. b. Distant light sources (e.g., quasars; see also chapter 10), are distributed at random on the sky. It turns out that those of them that are projected behind a galaxy within de of that galaxy will be noticeably lensed. Assume a Euclidean space with a constant number density of galaxies, n 1o2 Mpe, Re from item (a), and a typical distance to the sources of 2d -1Gpc. Write an expr sou ession for the fraction ofthe distant that is lensed by intervrening galaxies, and evaluate it numeriall. Actual su measure the fraction of distant sources that are lensed can probe the p the lensing galaxy population, even when those galaxies are not directiy means of their light Hint: Find the number of "targets" with density n, and with cros that are "hit" by a random line of sight going out to the source consider the fraction of the sky that is covered by the total so galaxies' Einstein rings Answer: 3.1 x1 observed by

Answer 1

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