Measuring the Properties of Stars (ch. 17) Stars (and everything) are undoubtedly much more complex than our descriptions of them. Nevertheless, we will try to reduce the nature of stars to a fairly small number of properties that can be used in an attempt to answer questions like: Why do there appear to be different “types” of stars? How are stars born, evolve, and die? ⇒ First we discuss how the properties of stars are measured and how they can be interpreted (ch. 17). ⇒ 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. ⇒ 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.]Basic properties of stars 1. Distances. The most basic method is to measure a star’s parallax angle, a subject we already covered early in the course. (See Fig. 17.1 for review.) Recall that 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 arcs). 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)The Hipparcos space mission revolutionized our knowledge of parallaxes. Read “Discovery 17-2” on p. 454 on this topic. 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.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. 446-7, 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 lines of different elements are extremely sensitive to the temperature of the gas. E.g. if helium lines, star’s photosphere must be really hot, since it takes so much energy to excite its electron levels. Look carefully at Fig. 17.10 to see how different absorption lines appear for stars of different temperatures. Astronomers have classified stars into spectral types that turn out to be a temperature sequence in the order” O B A F G K M ⇒ memorize this 50,000K ………………..6,000K…….3,000K ← temperature HeII HeI H various metals molecules ← strongest lines5. Sizes. Since stars only appear as points of light to even the largest telescopes (with a very few exceptions, using interferometry for the largest nearby stars: see Fig. 17.11 for the best example), we can’t get their diameters directly. Instead we use a method that is based on Stefan’s law
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