12: Gravitational Lenses
- Page ID
- 48010
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\(\newcommand{\avec}{\mathbf a}\) \(\newcommand{\bvec}{\mathbf b}\) \(\newcommand{\cvec}{\mathbf c}\) \(\newcommand{\dvec}{\mathbf d}\) \(\newcommand{\dtil}{\widetilde{\mathbf d}}\) \(\newcommand{\evec}{\mathbf e}\) \(\newcommand{\fvec}{\mathbf f}\) \(\newcommand{\nvec}{\mathbf n}\) \(\newcommand{\pvec}{\mathbf p}\) \(\newcommand{\qvec}{\mathbf q}\) \(\newcommand{\svec}{\mathbf s}\) \(\newcommand{\tvec}{\mathbf t}\) \(\newcommand{\uvec}{\mathbf u}\) \(\newcommand{\vvec}{\mathbf v}\) \(\newcommand{\wvec}{\mathbf w}\) \(\newcommand{\xvec}{\mathbf x}\) \(\newcommand{\yvec}{\mathbf y}\) \(\newcommand{\zvec}{\mathbf z}\) \(\newcommand{\rvec}{\mathbf r}\) \(\newcommand{\mvec}{\mathbf m}\) \(\newcommand{\zerovec}{\mathbf 0}\) \(\newcommand{\onevec}{\mathbf 1}\) \(\newcommand{\real}{\mathbb R}\) \(\newcommand{\twovec}[2]{\left[\begin{array}{r}#1 \\ #2 \end{array}\right]}\) \(\newcommand{\ctwovec}[2]{\left[\begin{array}{c}#1 \\ #2 \end{array}\right]}\) \(\newcommand{\threevec}[3]{\left[\begin{array}{r}#1 \\ #2 \\ #3 \end{array}\right]}\) \(\newcommand{\cthreevec}[3]{\left[\begin{array}{c}#1 \\ #2 \\ #3 \end{array}\right]}\) \(\newcommand{\fourvec}[4]{\left[\begin{array}{r}#1 \\ #2 \\ #3 \\ #4 \end{array}\right]}\) \(\newcommand{\cfourvec}[4]{\left[\begin{array}{c}#1 \\ #2 \\ #3 \\ #4 \end{array}\right]}\) \(\newcommand{\fivevec}[5]{\left[\begin{array}{r}#1 \\ #2 \\ #3 \\ #4 \\ #5 \\ \end{array}\right]}\) \(\newcommand{\cfivevec}[5]{\left[\begin{array}{c}#1 \\ #2 \\ #3 \\ #4 \\ #5 \\ \end{array}\right]}\) \(\newcommand{\mattwo}[4]{\left[\begin{array}{rr}#1 \amp #2 \\ #3 \amp #4 \\ \end{array}\right]}\) \(\newcommand{\laspan}[1]{\text{Span}\{#1\}}\) \(\newcommand{\bcal}{\cal B}\) \(\newcommand{\ccal}{\cal C}\) \(\newcommand{\scal}{\cal S}\) \(\newcommand{\wcal}{\cal W}\) \(\newcommand{\ecal}{\cal E}\) \(\newcommand{\coords}[2]{\left\{#1\right\}_{#2}}\) \(\newcommand{\gray}[1]{\color{gray}{#1}}\) \(\newcommand{\lgray}[1]{\color{lightgray}{#1}}\) \(\newcommand{\rank}{\operatorname{rank}}\) \(\newcommand{\row}{\text{Row}}\) \(\newcommand{\col}{\text{Col}}\) \(\renewcommand{\row}{\text{Row}}\) \(\newcommand{\nul}{\text{Nul}}\) \(\newcommand{\var}{\text{Var}}\) \(\newcommand{\corr}{\text{corr}}\) \(\newcommand{\len}[1]{\left|#1\right|}\) \(\newcommand{\bbar}{\overline{\bvec}}\) \(\newcommand{\bhat}{\widehat{\bvec}}\) \(\newcommand{\bperp}{\bvec^\perp}\) \(\newcommand{\xhat}{\widehat{\xvec}}\) \(\newcommand{\vhat}{\widehat{\vvec}}\) \(\newcommand{\uhat}{\widehat{\uvec}}\) \(\newcommand{\what}{\widehat{\wvec}}\) \(\newcommand{\Sighat}{\widehat{\Sigma}}\) \(\newcommand{\lt}{<}\) \(\newcommand{\gt}{>}\) \(\newcommand{\amp}{&}\) \(\definecolor{fillinmathshade}{gray}{0.9}\)Chapter 12 delves into the phenomenon of gravitational lensing. Light from distant sources is deflected by the curved spacetime around massive objects, providing astrophysicists with the ability to map out mass, both seen and unseen. In the first part of the chapter you will examine the geometric properties of simple gravitational lenses. In the second part, you will use astrophysical gravitational lenses as instruments for studying dark matter, weighing galaxy clusters, and finding extra-solar planets.
- 12.0: Gravitational Lensing Introduction
- In this chapter we will consider several more instances of gravitational lensing, some from point-like masses such as stars and some from extended mass distributions such as galaxy clusters. We will discover that the lensing phenomenon is an important tool for astrophysics. Beyond being an interesting consequence of general relativity in its own right, lensing can provide information about mass that is otherwise unseen, but that still affects the path of light through space.
- 12.1: What Are Gravitational Lenses?
- You will understand that gravity can bend the path of light. You will understand that this bending of light depends on the mass of the source of the gravity. You will understand that objects other than the Sun can act as lenses and that many instances of gravitational lensing have been seen.
- 12.2: Lensing by Point Masses
- You will understand how the lensing effect depends on the relative positions of the source, lens and observer and understand that the mass of the lens can be determined using gravitational lensing. You will understand that objects such as dim stars, brown dwarfs, and stellar remnants (white dwarfs, neutron stars, black holes) can act as gravitational lenses - collectively called MACHOs.
- 12.3: Lensing by Extended Mass Distributions
- You will understand that galaxies and clusters of galaxies can act as gravitational lenses. You will understand that many astrophysical lenses are complex in nature. You will understand that lensing suggests that most of the mass of galaxies and galaxy clusters is dark. You will understand that lensing provides an independent and distinct prediction of dark matter than does star , gas or galaxy motions based upon Newtonian dynamics.
- 12.4: Weak Lensing
- You will understand the difference between strong and weak lensing. You will understand that weak lensing reveals the presence of dark matter throughout the Universe.
- 12.5: Wrapping It Up 12 - Measuring Gravitational Lenses
- You will be able to put the above concepts together to determine the mass and the level of complexity of the geometry of the lens for various systems.
Thumbnail: Einstein cross: four images of the same astronomical object, produced by a gravitational lens. Image used wtih permission (Public Domain; NASA and ESA).