The diagram is what is known as a blackbody diagram. It is a graph showing how much of each wavelength of light an object produces. In a blackbody diagram, it is assumed that the object does not reflect any light, and that all of the light is emanating from it. Blackbodies do not necessarily look black. Stars are pretty good blackbodies, since they are not very reflective.
In short, a blackbody is an object that does not reflect light. All of the light coming from a blackbody is glowing out from within.
blackbody spectrum image source
This is a blackbody diagram. It shows a strip of colors representing wavelengths of visible light. It is a graph of intensithy vs. wavelength of light.
There are several curves in the diagram, shaped like skewed Gaussian curves, for different kinds of stars. The peaks of the curves mark the peak wavelengths of the stars, or the wavelength where they emit the most light.
The curves are also each marked with a temperature in Kelvins, the surface temperatures of the stars. Note that the hotter the star, the shorter the peak wavelength.
You can think of a blackbody spectrum as being analogous to a collection of bins of colored light bulbs. Each bin holds a different color, and some bins have more bulbs than others. In the above bins, the green bulbs outnumber the other colors. A blackbody spectrum similarly shows the relative abundance of different colors of photons, or different wavelengths of light. The peak wavelength gives a measure of the surface temperature of a star. The shorter the wavelength of the peak wavelength, the higher the average surface temperature of the star.
This PHet interactive simulation regarding blackbody radiation that allows you to see how the peak wavelength varies with the surface temperature. Move the slider on the right to see blackbody curves for stars of various surface temperatures.
This equation is known as Wien's law, and gives the relationship between the surface temperature (T in Kelvin) of a star and its peak wavelength. The inverse nature of the equation reflects the fact that the bigger the temperature, the smaller the peak wavelength.
real blackbody spectrum image source
This graph shows what a real blackbody spectrum of a star looks like. Notice that the edge is very jagged, not a smooth curve. We will learn about the reasons for this when we study our next topic, spectroscopy.
Orion image source
Even with the naked eye, you can tell the color of stars, red or blue. The blue ones are hotter. This is the constellation Orion with the red supergiant star Betelgeuse in the upper left. The red object in Orion's belt is not a star at all, it is the Orion Nebula.
Inverse square image source
Light propagates out from its source in all directions. The light passing through a unit square that is one unit from the source will pass through a square that is four times as large when it is two units from the source. This means that the light gets 1/4 dimmer per unit area. We say that light "goes as" 1/r2 or that it goes as the inverse square.
This plot shows the 1/r2 function. Notice that the light falls off very rapidly at first, but then at long distances, the signal tapers off much more gradually. In between those extremes, the function exhibits a "shoulder."
streetlights in the fog image source
This image of light propagating out through fog illustrates the 1/r2 function. The "shoulder" of the function gives something like a soft boundary to the light as it changes from very bright to falling off gradually.
Luminosity is how much light a star produces; it can be thought of as how much energy a star generates. Brightness is how bright the star looks to us. The brightness equals the luminosity divided by the surface area of the sphere with a radius at distance d.
Think of the luminosity of the "wattage" of the star, just like the watts of a light bulb. Imagine you are outside at night and your friend is off in the distance with a light bulb. If you know the light bulb is say, a 100 Watt bulb as opposed to a 25 Watt bulb, you can tell how far away it is.
The brightness is how bright the bulb looks to you. The brightness goes down as your friend walks away. The luminosity does not change.
brightness and luminosity equations
You can use the relationship between brightness, luminosity and distance to solve problems involving two stars. Here, Star A has brightness BA, luminosity LA and distance dA, with similarly defined quantities for Star B.
For example, two identical stars would have the same luminosity L. If they were different distances away, you could measure the brightness of each star and use this function to figure out how far away Star B was, compared to the distance to Star A.
link to Stefan's law equation
© Kathryn Hadley PhD 2020