A Star’s Color, Temperature, and Brightness are Related!

The Beginnings Late 1800’s, early 1900’s – how light is produced by atoms is being intensely studied by… Gustav Kirchoff (remember Mr. Spectroscopy?) Max Planck…Josef Stefan... Ludwig Boltzmann…Albert Einstein All these guys don’t sound familiar? (Take more chemistry and they will!)

Black Bodies During the same time as our Civil War, in 1862, Gustav Kirchoff coins the phrase “black body” to describe an imaginary object that would perfectly absorb any light (of any wavelength) that hit it. No light transmitted through, no light reflected off, just totally absorbed.

More Kirchoff Kirchoff realized that any object that would be a perfect absorber of light would also be a perfect emitter…but the amount of light energy it would give off each second (its brightness or luminosity) and the color of the light would be related to the object’s temperature.

Examples Molten lava and hot iron are two good examples of black bodies, but… a star is an excellent black body emitter.

Moving Right Along Max Planck, a German physicist, was able to make theoretical predictions of how much light of each color or wavelength would be given off by a perfect black body at any given temperature. These predictions or models are today called Planck Curves.

What do you notice? What 2 characteristics of the curves change as the temperature increases? The size of the curve increases. (2) The peak of the curves shift to the left, to shorter wavelengths & higher energies.

Can we draw some conclusions? Hotter stars should be brighter than cooler stars. Hotter stars should emit more of their light at shorter wavelengths (bluer light) while cooler stars should emit more of their light at longer wavelengths (redder light). Notice however that all stars emit some energy at all wavelengths!

Stick with me! In 1879, Josef Stefan discovered that the luminosity of a star was proportional to the temperature raised to the 4th power. In 1884, Stefan’s observations were confirmed when Ludwig Boltzmann derived Stefan’s equation from simpler thermodynamic equations.

Stefan-Boltzmann Law Today, we honor both scientists by naming the equation after them…the Stefan-Boltzmann Law: At the surface of the star, the energy that’s given off per square meter (Watts / m2) called the luminous flux is... W / m2 = 5.67 x 10-8 T4

An Example At 100 K (cold enough to freeze you solid in just seconds), a black body would emit only 5.67 W/m2. At 10x hotter, 1000 K, the same black body would emit 104 times as much light energy, or 56,700 W/m2.

You Try… If the temperature of a star were to suddenly double, how much brighter would the star become? If the temperature of a star somehow fell to 1/3 of what it was, how much fainter would the star become? 24 = 16 times brighter (1/3)4 = 1/81, or 81 times dimmer

The Other Half of the Puzzle In 1893, Wilhelm Wien (pronounce “vine”) discovered by experiment the relationship between the “main” color of light given off by a hot object and its temperature. By “main” color, I mean the peak wavelength, called λmax , at the top of the Planck Curve.

For each curve, the top of the curve is the peak wavelength.

Wien’s Law Wien’s Law says that the peak wavelength is proportional to the inverse of the temperature: λmax = 2.9 x 106 T = 2.9 x 106 T λmax T must be in Kelvin, and λmax in nanometers.

Examples What is the peak wavelength of our sun, with a T = 5750 K? What is the peak wavelength of a star with a surface temperature of 3500 K? 2.9 x 106 = 504 nm (yellowish-green) 5750 K 2.9 x 106 = 829 nm (this star emits the 3500 K majority of its light as infrared, IR).

Examples A reddish star has a peak wavelength of 650 nm. What is the star’s temperature? A star has a peak wavelength in the ultra-violet of 300 nm. What is the star’s temperature? 2.9 x 106 = 4462 K (cooler than the sun) 650 nm 2.9 x 106 = 9667 K 300 nm

Uses We now have a “color thermometer” that we can use to determine the temperature of any astronomical object, just by examining the light the object gives off. Astronomers have found that different classes of objects are at different temperatures and give off different peak wavelengths.

What kinds of objects? Clouds of cold hydrogen gas (nebulae) emit radio waves http://www.narrowbandimaging.com/images/vdb142_small.jpg

Warmer clouds of molecules where stars form emit microwaves and IR.

Protostars emit IR. http://www.antonine-education.co.uk/Physics_GCSE/Unit_3/Topic_10/protostar.jpg

Sun-like stars emit mostly visible light, while hotter stars peak in the UV. http://www.nasa.gov/images/content/138952main_whywe16full.jpg

Neutron stars and black holes peak in the X-ray.

Star cores emit gamma rays. http://aspire.cosmic-ray.org/labs/star_life/images/star_pic.jpg

How about these? Where would the peak wavelength be for your body a lightning bolt the coals from a campfire