Introduction
Your eyes are stellar thermometers. Every time you look into the night sky and notice the color of a star, you have taken the temperature of that distant, massive ball of cosmic gas! This is only possible through the power of blackbody radiation.
You can't take an astronomy course without learning about blackbody radiation. It's one of those ideas that form the cornerstone for what astronomers know, and how they know it. But what, really, is a blackbody? How did astronomers (actually physicists) come up with that slightly misleading name? How do blackbodies end up being so important? The point of this Interactive is to let you learn about blackbody radiation for yourself but first, here is a summary of the fundamentals.
A short definition of a blackbody might go like this: An object is a "blackbody" if the radiation it emits into space originates completely from its temperature. This means the radiation produced by the object comes from light waves mixing it up with the jiggling motions of all the zillions of atoms that make up the object. Inside a blackbody, radiation cannot travel very far before it is absorbed by a jiggling atom. It is then quickly re-emitted, travels a short distance and then gets absorbed again by another atom. This happens over and over again, so there is a constant interplay between the matter and the radiation bouncing around in a blackbody. The one-to-one relationship between the amount of jiggling heat motion of atoms, and the spectral signature they produce, makes blackbodies unique, distinctive and of primary importance. Blackbody spectra do not depend on an object's chemical composition, its size or its age.
Don't let the name confuse you, blackbodies do not have to be black. They can be blue or red or yellow. So where does the name come from? Anything colored black absorbs all the wavelengths (colors) of light that fall onto it. Blackbodies do this as well, and that is why physicists came up with the name "blackbody". How can blackbody appear blue or red? You'll get a better sense of how this works when you play with the Interactive. For now, the important idea is that a blackbody pumps radiation into space in a very special way. Anything which has heat and is dense enough will emit as a blackbody. That means you, the chair you're sitting on and the Earth on which the chair rests are all blackbodies.
Every blackbody emits light with an easily identified pattern, its "spectral" signature (also called a spectral energy distribution or, more specifically, the blackbody curve). The blackbody curve is the particular way the total light emitted by a blackbody varies with its frequency. The number of red photons, the number of green photons, the number of infrared and ultraviolet photons are all exactly specified by the blackbody curve. Now here is the killer point - the exact form of the curve depends only on the object's temperature. Every blackbody at 2000 degrees emits light with exactly the same curve. The spectral signature of a 2000 degree iron bar in a blast furnace is identical to a 2000 degree star a trillion, trillion miles away in deep space. That is what makes blackbodies so useful, and that is why the color of a star is also a measure of its temperature.
How To
Stars are vast collections of hot gas. A star like the Sun is more than ten billion, billion, billion tons of matter crammed together under the force of its own gravity. The conditions in a star (dense and hot) make it a pretty nice example of a blackbody. The stellar atoms jiggle around, absorbing and re-radiating radiation in just the right way, so that light pouring out at the surface has just the mix of colors (wavelengths) predicted by the blackbody curve. This is good news for astronomers. By measuring the energy emitted by the star in different colors, they can work backwards to figure out its temperature.
If you change the temperature slider on the Interactive (below the graph), you will see how the highest point, or peak, of the curve shifts left or right to different wavelengths. (Notice the visual part of the spectrum is indicated by the rainbow of colors). Since the peak of the blackbody curve is where most of the radiation is emitted, you can see how changing the star's temperature changes its color.
The peak wavelength doesn't tell the whole story, since your eye will pick up a mix of colors in the visible band. After you set the temperature, the actual color of the star appears in the upper right corner of the Interactive, so you can see directly how changing the temperature changes the color.
The relationship of temperature to color is captured in Wien's law, which gives the wavelength where the blackbody peaks as a function of temperature. It's written like this:
lambda max = (2.9 * 10^6) / T in units of nm-K
The Greek letter lambda represents wavelength.
The brightness or luminosity of a star is very sensitive to both its temperature and its size (area). The luminosity relation for blackbodies says that if two stars have the same radius but different temperatures, the hotter (bluer) star is a whole lot brighter than the cooler (redder) star. By changing the radius and the temperature of the star in the Interactive, you can see how the brightness of the star changes.
You can use the interactive to plot two blackbody curves of different temperature. The interactive uses the first plot you created to set the scale of yaxis (which is the radiation's intensity). When you plot the second curve you can then see how its intensity compares to the first. Try plotting a high temperature blackbody curve and then, using the "new graph" button, try plotting one with a slightly lower temperature.Exercises
Solutions