Measuring the Properties of Stars (ch. 17) [Material in smaller font on this page will not be present on the exam] Although we can be certain that other stars are as complex as the Sun, we will try to reduce their description to a fairly small number of properties, since these are the only attributes of stars that can be determined by observations. We will attempt to use relations between these properties to answer questions like: Why do there appear to be different “types” of stars? How are stars born, evolve, and die? You will find it useful to keep in mind these general and important “big picture” questions. ⇒ First we discuss how the properties of stars are measured and how they can be interpreted (ch. 17). That is the content of this set of notes. ⇒ Then we do the same for the gas between the stars (the “interstellar medium,” ch. 18) and try to put them together to understand how stars form (ch. 19), especially as a function of mass. [For the next exam, however, we will probably have to omit ch. 19.] ⇒ Finally, in the next section of the course we will consider in detail how stars of different mass evolve from birth to death. [Not on the exam: Discover 17-1, p. 441; More Precisely 17-1, p. 445; you should just have a basic idea of what the “magnitude system” means when referring to stellar brightnesses; More precisely 17-3. I won’t test you on the different types of binary stars (pp. 469-470) or specifically how masses are determined for each type, but you should be comfortable with the general idea; recall that we have been talking about this, off and on, since we discussed how to get the mass of the Sun from the Earth’s semimajor axis and period, using Kepler’s 2nd law. ]Basic properties of stars 1. Distances. The most basic method is to measure a star’s parallax angle, a subject we discussed early in the course. (See Fig. 17.1 for a useful illustration.) This method gives rise to the unit of distance we will use throughout the remainder of the course, the parsec, which is the distance of a star with a parallax of one second of arc. (The nearest stars are a few parsecs distant from us, while our Galaxy is about 30,000 parsecs across.) A parsec is about 3 x 1018 cm, or over a hundred thousand times larger than the distance from the Earth to the Sun (1AU). Distance (in parsecs) is equal to the inverse of the parallax angle (expressed in seconds of arc). For example, a star 10 pc distant has a parallax angle of 0.1 seconds of arc. Distant stars have such small parallax angles that they cannot be measured (recall our discussion of the diffraction and seeing limits for telescopes). So there is a distance limit for this method, and it is only about 100-500 pc.(Think: size of our Galaxy ~ 30,000 pc, nearest other galaxies millions of pc away, most distant galaxies we can see are billions of pc away.) The Hipparcos space mission revolutionized our knowledge of parallaxes (p. 452). Planned future space missions (around 2010; SIM and GAIA) aim to enormously extend the distances to which parallaxes can be measured, covering our entire Galaxy. Important to note: Most objects we’ll encounter in astronomy are too far away to get distances by parallax, so we have to use other, less direct measurements (the idea of “standard candles” is the most important). But parallax is crucial because it serves as the calibration of all these other methods; it is the “yardstick” upon which other distance measurements are based.2. Motions We already know how to measure the component of star’s motion along our line of sight, called the radial velocity: obtain a spectrum and measure the Doppler shift using spectral lines. But the star also has a component across our line of sight; this is called the transverse velocity. All we can directly measure is the angular speed across our line of sight (“proper motion”); in order to get the transverse velocity, we also need the distance. (Think about mosquito/UFO used in class.) ⇒ What kind of star do you expect to exhibit the largest proper motion? When you combine the two components of velocity, you get the total space velocity of the star. We won’t use this information much until we get to topics like the origin of our galaxy and the evidence for “dark matter.” But you should still know that most stars in the disk of our Galaxy are moving relative to each other at around 5 to 50 km/sec. Our sun and solar system are moving about 15 km/sec relative to the average of nearby stars. But we orbit our Galaxy about 250 km/s. These numbers are important because they allow us to obtain the mass of our galaxy, just as we obtained the mass of the Sun from Kepler’s third law.3. Luminosities. This is how much energy a star is emitting per unit time, i.e. the rate at which photon energy is being emitted. It is exactly the same as the power of a light bulb in Watts. You can think of it as the absolute brightness of the star, to distinguish it from how much energy an observer is receiving from the star, its apparent brightness, which obviously depends on the star’s distance. The three quantities are related by the inverse square law of light: apparent brightness ∝ luminosity/(distance)2 Since apparent brightness is EASY to measure (if you can see something, you can measure how bright it appears), and we can get distance, at least for some stars, from parallax, we can solve this for L. Examples given in class should make this clear if it’s not already. [You do NOT have to know anything about “magnitude scales” except the basic idea, if that. I won’t use this idea on the exam, but if you encounter it in the book, just remember that it’s just a handy way to assign numbers to apparent brightness and luminosity that have a smaller range, like the Richter scale for earthquakes.]4. Temperature. We are talking about the photospheric temperature, which is all we can directly observe. There are 2 ways to get T: a. Color—remember Wien’s law? Even though stars aren’t perfect blackbodies, we can get fairly accurate temperatures (especially in a relative sense) by colors. See p. 456-8, esp. Fig. 17.9, so that you understand “color” as a measure of how much energy is being radiated in two different wavelength bands. b. Spectra and spectral classification—We’ve already discussed how the strengths of spectral
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