1. Black Body Radiation Physics 113 Goderya Chapter(s): 7 Learning Outcomes:

2. The Amazing Power of Starlight Just by analyzing the light received from a star, astronomers can retrieve information about a star’s 1.Total energy output 2.Mass 3.Surface temperature 4.Radius 5.Chemical composition 6.Velocity relative to Earth 7.Rotation period

3. Temperature Scales o F = 9/5( o K) - 459.4 o F = 9/5( o C) + 32 o K = 273 + o C oCoC oKoK oFoF 0 32 273 100212373 -100173 -148

4. Brightness and Luminosity Luminosity (L): The total amount of energy a star radiates in 1 second per square meter. Brightness (B): Energy received from the source at different distances. Inverse square Law: B ≈ 1/(distance) 2 B = L / 4πR 2 Sun 5 x 10 26 watts 4 /1 2 = 4 4 / 2 2 = 1 Light rays

5. Star as a Black Body Black Body Radiator. A hypothetical object that emits Electromagnetic radiation and whose spectrum is continuous with a peak in the wavelength that corresponds to the temperature of the object. Wavelength Energy Peak wavelength

6. Black Body Radiation (1) The light from a star is usually concentrated in a rather narrow range of wavelengths. The spectrum of a star’s light is approximately a thermal spectrum called a black body spectrum. A perfect black body emitter would not reflect any radiation. Thus the name “black body”.

7. Two Laws of Black Body Radiation 2. The peak of the black body spectrum shifts towards shorter wavelengths when the temperature increases.  Wien’s displacement law :  max ≈ 3,000,000 nm / T K (where T K is the temperature in Kelvin). 1. The hotter an object is, the more luminous it is: L = A*  *T 4 where  = Stefan-Boltzmann constant A = surface area;

8. Sun’s Temperature The sun =500 nm T = 3 x 10 6 /500 = 6000 K 10,000 F Wein’s Law gives the surface temperature

9. Sun’s Luminosity The sun: T= 6000 K, R=7 x 10 8 meters. What is its Luminosity? L = 4x 3.14 x (7 x 10 8 ) 2 x 6 x 10 - 8 (6000) 4 = 5 x 10 26 Watts Compare with 40 watts light bulb

10. Color and Temperature Orion Betelgeuse Rigel Stars appear in different colors, from blue (like Rigel) via green / yellow (like our sun) to red (like Betelgeuse). These colors tell us about the star’s temperature.

11. The Color Index (1) B band V band The color of a star is measured by comparing its brightness in two different wavelength bands: The blue (B) band and the visual (V) band. We define B-band and V-band magnitudes just as we did before for total magnitudes (remember: a larger number indicates a fainter star).

12. The Color Index (2) We define the Color Index B – V (i.e., B magnitude – V magnitude). The bluer a star appears, the smaller the color index B – V. The hotter a star is, the smaller its color index B – V.