Sept 4 class In this class, we reviewed and added to some of the ideas from Sept 2, and we began a discussion of stellar structure and evolution. The latter will be our focus, along with the relevant physics, for a couple of upcoming lectures. I. RADIATION We pointed out that RADIATION is another work that has a special meaning in science, but that has acquired unfortunate, and often simply wrong, connotations in ordinary speech. RADIATION is simply the transfer of energy from one place to another. Usually this transfer is done with photons, but there are other ways to transfer energy. So, a normal radiative process is broling a steak. The cooking is done with photons, and can be done in a vacuum! But in everyday speech, RADIATION has somehow been linked to RADIOACTIVITY. Indeed, radioactivity transfers energy using small particles, and of course radioactivity can be used to make a bomb (or to make electricity, as in the Palo Verde Nuclear Power Plant west of Phoenix). But if you shine photons at an object, then turn off the light source, there is no residual radioactivity (there was never any radioactivity in the first place!). So, the process of irradiating meat with UV light is to kill bacteria and viruses on the surface. If the bacteria and viruses are dead, the meat can't spoil quickly. And of course, SOME bacteria, introduced into your gut, cause "stomach flu." But people are so freaked out over the radiation/radioactivity link that they just say no, immediately. Now of course, we used to be told about how safe various things radioactive are. So it's wise to be cautious, but to me this irradiating meat stuff seems to be safe. It's just using photons to kill bacteria on the surface of meat, and has nothing to do with radioactivity. Unfortunately, radioactivity has gotten a bad name (partly justified and partly unjustified), and the mixup of "radioactivity" with "radiation" ends up with an unjustified response. II. Wien's Law and the Stefan-Boltzman Law and Kirchoff's laws a) Wien's law Jane discussed Wien's law, which says that the wavelength at which the dominant light is emitted from a solid (or dense gas) is inversely proportional to temperature. lambda_max is proportional to 1/T. So something at room temperature emits in the infrared, at a wavelength of about 10 microns (1 micron is 10**-6 meters). An object at 5000 degrees, like the Sun, emits most strongly at .58 microns, or 5800 Angstroms (there are 10,000 Angstroms in a micron), or YELLOW-ish. An object at 20,000 degrees emits most strongly at 1400 Angstroms, or the ultraviolet. Just some sociology: Visible light is .3 to .7 (or so) microns 3000 7000 Angstroms So, Wien's law tells you that you can look at a horseshoe, and tell its temperature by its color. Stars, being dense gases, work the same way. b) An important digression on "temperature" Most Americans feel comfortable discussing temperatures in Fahrenheit degrees. Most Europeans, South Americans, and Canadians (and mostly the whole rest of the world) discuss weather temperatures in degrees Celcius. Scientists use Kelvins, which are Celcius degrees with a proper zeropoint. Fahrenheit- in 1717 Gabriel Fahrenheit wanted to improve on Galileo's termoscope (which you can buy in the Sharper Image catalog, for instance). His zeropoint was the coldest winter day in Amsterdam, and 100 degrees was the 'temperature of a man's body". So water freezes at 32F and boils at 212F, at least at sea level. Celcius, also in the early 1700s, set the freezing point of water to be 100C, and the boiling point 0C. After his death it was switched around to freezing=0C and boiling = 100C. The Kelvin scale was introduced in 1848, and sets the zeropoint to ABSOLUTE ZERO, the COLDEST POSSIBLE TEMPERATURE. [This parenthetical comment is for fun only, you don't have to know what's in the link here, but someone asked how close we'd gotten to absolute zero... http://www.sun.rhbnc.ac.uk/~uhap057/LTWeb/Absolute.html http://www-tech.mit.edu/V120/N65/book_review.65a.html So if the quest for supercold temperatures intersts you, you have some starting points] Kelvins degrees C degrees F absolute zero 0 -273.15 -459.67 water freezes 273.15 0 32 water boils 373.15 100 212 The important point is that since Kelvins start out at absolute zero, 200K is twice as hot as 100K. 100F IS NOT twice as hot as 50F, it's 9% different! So F and C scales, as much as we love them, are not useful for connecting energy to temperature without converting to a more sensible scale, which happens to be Kelvins! c) Stefan-Boltzman law We've already learned how to tell the temperature of a star from its color, and we'll learn another way when we discuss spectra. Well, when you pull a horseshoe out of a fire, you note several things, two of which are important for astronomy. The first is the color, as already discussed. The second is that light and heat are being given off. So, a solid object at any temperature gives off light of all colors (and so does a dense gas). Using your hand as a detector, you note that a hot horseshoe gives off more light than a cold horseshoe [and you might also note that a big horseshoe gives off more light than a small horseshoe]. If you measured the total amount of energy coming off of a glowing horseshoe, say, by dumping it in a bucket of water and noting by how much the water temperature rose, you'd discover that a hot horseshoe gives off a LOT MORE light than a cold horseshoe. In fact, the total energy of a glowing horseshoe is proportional to T**4, temperature to the 4th power. So doubling the temperature makes a 16-fold increase in the amount of light given off. Graphs of this effect are found in the figures area of the website. [This also means that it takes a lot of energy to change the temperature of a horseshoe.] So E proportional to T**4 So, if we know the temperature [and size] of a star, we know how much energy it's giving off. And, if we know how much enrgy it's giving off AND how much fuel it has, we can calculate its lifetime. This of course is the reason we discuss this effect in an astronomy class. d) Kirchoff's Laws Some of this is review from last class, some of it is new. 40+ years before quantum mechanics came along to give us an understanding of the behavior of atoms, Kirchoff was able to describe the behavior of light-emitting substances. His first law, we've already discussed... FIRST LAW: Solids and dense gases (so dense that you can't see from one side to the other) give of LIGHT OF ALL COLORS, a CONTINUOUS SPECTRUM. [But we've seen above that the distribution of colors depends on the temperature.] SECOND LAW: A thin gas heated up to some temperature gives off a completely different distribution of light, namely, light at a distinct set of wavelengths [it's dark in between]. So, thin gases give off an emission spectrum. [This behavior was unexplained till about the year 1900 or 1910.] THIRD LAW: If a thin gas is placed in between you and a source of a continuous spectrum, that thin gas absorbs some of the light at a distinct set of wavelengths. So the light that reaches your eye is a continuous spectrum MINUS the missing light, giving what we call an absorption spectrum. We showed you a spectrum of the Sun, and the thin Solar atmosphere indeed absorbs light from the hotter interior. One of our chores in the next two weeks is to learn the physical mechanism behind Kirchoff's second and third laws. Before we leave this topic, remember that the absorption lines in the Solar spectrum were labelled. Some said "Calcium", some said "Iron", et cetera. So we need to learn how to figure out what elements are present in a spectrum. This ability will give us great power. We'll then know what stars [and planetary atmosphere and burning flames] are made of. III. On our way to understanding the structure and evolution of stars What we're going to do the next few classes is to review what makes ordinary stars work, then we'll review how they're born, and how they behave for most of their lives, and what happens at the end of their lives. To do this we need to learn: 1) How we know the chemical compositions of stars Answer: Spectroscopy, atomic physics 2) How we know the lifetimes of stars Answers: age of Earth, radioactive dating, stellar models 3) How do we know that all stars have the same structure [Well, this statement is only true at the 90% level, 90% of stars have the same structure] Answers: H-R diagram, computer models, stellar seismicity and pulsation, neutrinos 4) How do we know WHERE stars are born Answer: if we can identify stars that have short lifetimes, they must still be in their birth places 5) How do we know nuclear fusion is occurring in the centers of stars- Answer: this is the only energy source that can provide enormous amounts of energy over enormous lifetimes; plus, the centers of stars are perfect places for fusion 6) How do we know the inside of a star is hotter than the outside Answer: properties of gases and radition laws 7) How do we know that the surface of the Sun is gaseous Answer: spectroscopy