Astronomy 105G Lecture Notes, 09 Feb. 2004

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Temperature Scales

In astronomy, temperatures are measured in Kelvins, which is another scale like Fahrenheight or Celsius. We use this scale because at absolute zero (0 K), all motion ceases. The universe's background temperature is 3 K. Recent physics experiments have cooled something down to 10-9K. To give you a feeling for how Kelvins relate to more familiar temperatures, consider the following:





Radiation Laws

We spoke last time about the electromagnetic spectrum, which is defined as the entire range of electromagentic radiation. This includes visible light, as well as those forms of radiation much more and much less energetic than visible light.






Note the size of a wavelength of visible light. Light waves of visible light have a wavelength of ~ 400 - 750 nm, where 1 nm is 10-9 m (0.000000001 m).




Not all forms of electromagnetic radiation can pass through the Earth's atmosphere. The good news is that we are protected from the most harmful forms of radiation by our atmosphere, which absorbs the radiation before it reaches the ground.






We use the radiation received from an object to be a diagnostic for temperature. Every object emits radiation over a range of wavelengths, so when we study the radiation from a given object (e.g. the Sun), we see light from a range of energies, or wavelengths. We call this radiation blackbody radiation, which is the radiation that is intrinsically emitted by an object, assuming it is a perfect radiator. The distribution of energies (or wavelengths) coming from an object peaks at its average value, or the object's blackbody temperature.






Objects at higher temperatures emit more power (or radiation) at all wavelengths. Hotter objects give off more energy overall than cooler objects.




The higher the temperature of an object, the shorter the wavelength at which the maximum power is emitted. Blue stars are HOTTER than red stars (contrary to the meaning of the color-coding on water faucets, where red is hot and blue is cold). An example of this is the color of electric stove burners (infrared only, dull red, orange red....). Thus, we can use this fact to infer temperature information about an object.




The exact relation between peak wavelength and temperature is known as Wien's Law, which states that peak wavelength = 3 x 106 / Temp.
Here the peak wavelength is in units of nm, and the temperature is in units of Kelvins.




Example 1: Earth's effective temperature is ~ 255 K. At what wavelength will its blackbody curve peak?
peak wavelength = 3 x 106 / 255 = 11,765 nm (infrared)



Example 2: Sun emits most of its light at 520 nm (yellow). What is its average temperature?
T = 3 x 106 / 520 = 5770 K



Does this mean that a blue shirt is hotter than a red shirt? NO! The colors of shirts, lemons, grass, and planetary surfaces are all due to reflected sunlight, not blackbody radiation. The molecules in the dye of the blue shirt absorb red and yellow light, but reflect blue light, so the shirt appears blue. The iron on Mars' surface absorbs blue and yellow light but reflects red light, so the surface of Mars appears reddish. It is important that you are able to distinguish the difference between something seen due to reflected sunlight (or room light) versus something emitting blackbody radiation.





Spectroscopy

The most important tool that astronomer use to study objects is spectroscopy, or the study of a spectrum. The spectrum of an object can be used to determine its temperature, by determining what color the spectrum peaks at. More importantly, though, a spectrum can be used to determine the chemical composition of an object.

This is because all chemical elements (atoms and molecules) have very specific wavelengths (or colors) at which they absorb or emit light. Thus, if the spectrum of the Sun reveals that light at 396 nm is absorbed and we know that calcium absorbs at that wavelengths, then we can conclude that there is calcium in the Sun. See this page for a good illustration of a spectrum and how it works.