Galaxies Lecture 11

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Rotation Curves

Today we’ll talk about the measurement of rotation curves. This will cover Chapter 8 of Binney & Merrifield. Rotation curves are usually measured using the 21 cm line. As before, we note that we have approximately linear growth in as a function of radius, until we hit a regime where . For linearly growing , we derived that .\

It is important to not that when we measure rotational curves of galaxies, we are almost always measuring the velocity of gas. This gas comes in 3 forms:

  • Atomic Gas
    • Characterized by electronic transitions in optical/UV wavebands. To excite these transitions, gas must be hot.
    • We also see 21 cm radiation. We can estimate the inherent width of the 21 cm line by saying . Using , and . Plugging this in, we find that , so we can ignore the inherent line width of the 21 cm line. However, we cannot ignore the effects of temperature on linewidth. For high-end temperatures , we get . The lowest we expect to see is , which gives us . This sets a lower bound on the resolution needed for 21 cm spectrometers.
  • Molecular Gas
    • The most common molecule in the ISM is (99.98%). has no dipole transition (), so the strongest rotational transition in is at , and this is a weak (forbidden) transition.
    • Since is hard to detect, we look more to other abundant molecules: , , , . These molecules have dipole transitions, and are much easier to see. Most molecules form in high-density regions. The critical density for populating the first rotational transition of is . However, we typically observe the transition of to be thermalized around . This is caused by collisions with . We use as a tracer for , because it forms at comparable densities, and is dissociated at comparable temperatures.
  • Ionized Gas
    • One region of pressure equilibrium in the ISM are HII regions, typically around O stars. Around O7 stars, there are stable regions of gas. We’ll talk more about these regions later.

In the region of a galaxy, we can typically measure , and . We’ve discussed isophotes (relating to ), but now we’d like to know what lines of constant velocity look like (isovelocity contours). If a galaxy is tilted with respect to our vantage point, we’ll see circles as ellipses:

and we define . If is the actual radius of the galaxy, and is the actual rotational velocity, we’d like to determine the velocity that we would measure. As discussed previously, . Then:

where is the angle around the galaxy. If is constant (isovelocity contours), then must be constant. Thus, isovelocity contours are lines through the center of the galaxy.

For next class, we should answer the question for (solid-body rotation).