Download The Milky Way

Black Body Radiation
Physics 113 Goderya
Chapter(s): 7
Learning Outcomes:
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
Temperature Scales
•
o
•
o
F = 9/5(o C) + 32
•
o
K = 273 + o C
F = 9/5(o K) 459.4
373
o
o
o
K
C
F
100
273
173
212
0
-100
32
-148
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
Light rays
• B = L / 4πR2
• Sun 5 x 1026 watts
4 /12 = 4
4 / 22 = 1
Star as a Black Body
Peak wavelength
Energy
• 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
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”.
Two Laws of Black Body Radiation
1. The hotter an object is, the more luminous it is:
L = A*s*T4
where A = surface area;
s = Stefan-Boltzmann constant
2. The peak of the black body spectrum shifts
towards shorter wavelengths when the
temperature increases.
 Wien’s displacement law:
lmax ≈ 3,000,000 nm / TK
(where TK is the temperature in Kelvin).
Sun’s Temperature
• The sun l=500
nm
• T = 3 x 10 6/500 =
6000 K
• 10,000 F
• Wein’s Law gives
the surface
temperature
Sun’s Luminosity
• The sun: T=
6000 K , R=7 x
108 meters.
What is its
Luminosity?
• L = 4x 3.14 x (7
x 10 8)2 x 6 x 108 (6000)4 = 5 x
1026 Watts
• Compare with
40 watts light
bulb
Color and Temperature
Stars appear in
different colors,
from blue (like Rigel)
Orion
Betelgeuse
via green / yellow (like
our sun)
to red (like Betelgeuse).
These colors tell us
about the star’s
temperature.
Rigel
The Color Index (1)
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).
B band
V band
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.