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Extended Mass Distributions: Spiral Galaxies

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Part of the book series: Undergraduate Lecture Notes in Physics ((ULNP))

Abstract

There is much to say about galaxies, but with our current theme we focus on motion and mass. The stars in a galaxy are always moving, but the sheer number of them means the galaxy’s overall mass distribution hardly changes with time. To a good approximation we can take the mass distribution to be static, which makes the gravitational force static and effectively puts us back in the realm of the one-body problem. The difference now is that the mass distribution is spatially extended, which affects the gravitational force and therefore the motion.

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Notes

  1. 1.

    See the book by Sparke and Gallagher [1] for a more thorough discussion of galaxies.

  2. 2.

    Unless the galaxy is undergoing some dramatic event such as a collision. We will examine interactions between galaxies in Sect. 8.3.

  3. 3.

    We can write this as an indefinite integral because Φ is only defined up to an arbitrary constant.

  4. 4.

    Evidence for “missing mass” appeared as early as the 1930s, from an analysis of motions in the Coma cluster of galaxies by Fritz Zwicky [6] and an analysis of vertical motions of stars in the Milky Way by Jan Oort [7]. Those analyses were hindered, especially by poor knowledge of mass-to-light ratios, but notice that they too were based on the motion → mass principle.

  5. 5.

    We will study gas in a gravitational potential in Sect. 12.2.

  6. 6.

    “Cold” refers to the fact that the particles are slow compared with the speed of light. As we will see in Chap. 12, the temperature of a gas is related to the typical speed of its constituent particles.

  7. 7.

    With one important modification: dark energy.

  8. 8.

    This question is inspired in part by a problem in the book by Carroll and Ostlie [27].

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Keeton, C. (2014). Extended Mass Distributions: Spiral Galaxies. In: Principles of Astrophysics. Undergraduate Lecture Notes in Physics. Springer, New York, NY. https://doi.org/10.1007/978-1-4614-9236-8_7

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  • DOI: https://doi.org/10.1007/978-1-4614-9236-8_7

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