8: Dark Matter
- Page ID
- 30485
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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 8 focuses on applying the law of gravity to the motions of astronomical systems to determine how much matter is present and how it is distributed. In the first half of the chapter, you will develop models of rotating systems for various velocity and mass distributions. Next you will explore the evidence for dark matter in galaxies and galaxy clusters by comparing the luminous mass and total gravitational mass. You will also explore models for what dark matter might be and why its nature remains so elusive.
- 8.0: Dark Matter Introduction
- In this chapter we step up in scale, applying the law of gravity to the motions of stars and gas in galaxies and galaxy clusters. These larger-scale gravitational studies began early in the 20th century and continue to the present. They have resulted in surprising revelations about our Universe and its composition. Here we begin to explore some of these revelations.
- 8.1: Making Models for Rotation
- In this chapter, we will talk a lot about models. Not the kind of models you might have made as a child, of planes or boats or cars. The models we will talk about will be conceptual models. They will involve mathematics and physics. In the dialogue above, models of galaxies are mentioned. What other models can you think of that we use in everyday life? Try to think of several common examples of conceptual and physical models that are commonly used.
- 8.2: Velocities, Mass, and Gravity - The Solar System
- The systems we have talked about so far in this chapter may not seem like they have anything to do with astronomy. But as you will see, these everyday examples will help us understand the motions of planets in the Solar System, the motions of stars and gas in galaxies, and the motions of galaxies in galaxy clusters. Here, we will look at our first astronomical example of rotation, but we will start locally, astronomically speaking— we will look at how the Solar System rotates.
- 8.3: Gravity and Models for Different Mass Distributions
- Unlike the terrestrial examples discussed at the outset, gravity plays a major role on the motions of astronomical objects, including planets orbiting stars, stars and gas moving within galaxies, and galaxies moving inside clusters. The everyday examples we discussed at the outset are familiar and serve as a good introduction to thinking about rotation and revolution.
- 8.4: Velocity and Mass Distributions in Galaxies
- In this section, the connection to dark matter will start to become clear. Here, we will discuss how objects orbit within galaxies and what that tells us about galaxy masses.
- 8.5: Velocity and Mass Distributions in Galaxy Clusters
- The motions of stars and gas in galaxies were not the first evidence that galaxies contain enormous amounts of unseen material, or dark matter. They merely confirmed a mostly forgotten result from decades earlier.
- 8.6: Possible Explanations for the Missing Mass in Galaxies and Clusters
- If we take the observations of the motions of stars and gas in galaxies, and the motions of galaxies in galaxy clusters, at face value, then they imply the existence of additional mass that is unseen: dark matter. The unseen mass could take several forms. Some are fairly simple, others quite exotic. We will consider several possibilities and explore what evidence exists for and against them.
- 8.7: Wrapping It Up 8 - What Is the Matter With NGC 3198?
- You will be able to put the above concepts together to demonstrate your understanding of the rotation curve for NGC 3198. You will calculate both the total and luminous mass distributions of a galaxy, determine the percentage of luminous matter at different radii within the galaxy, and learn about how much of the galaxy is made up of dark matter.
Thumbnail: A NASA/ESA Hubble Space Telescope images of the MACS J0717.5+3745 galaxy cluster, which was observed in a study of how dark matter in clusters of galaxies behaves when the clusters collide. 72 large cluster collisions were studied in total. Using visible-light images from Hubble, the team was able to map the post-collision distribution of stars and also of the dark matter (colored in blue). (CC BY-4.0 Unported; NASA, ESA, D. Harvey (École Polytechnique Fédérale de Lausanne, Switzerland), R. Massey (Durham University, UK), the Hubble SM4 ERO Team, ST-ECF, ESO, D. Coe (STScI), J. Merten (Heidelberg/Bologna), HST Frontier Fields, Harald Ebeling (University of Hawaii at Manoa), Jean-Paul Kneib (LAM) and Johan Richard (Caltech, USA) via Wikipedia)