Stars as Blackbodies

3RF Sciences, LLC
Blackbody defined…
 A blackbody is an
object that absorbs all
light that hits it
 Also emits light
provided that its
temperature is above
absolute zero
 http://www.handprint.
A Blackbody…
 Perfect “black body” – something which absorbs
all the radiation that falls on it
 Good absorber of radiant heat is also a good emitter
 Main scientist - 1859, G. Kirchhoff
 Foundation of blackbody radiation lies in the
idea that radiation is released from blackbodies
in the form of "quanta" or discrete packets of
light called photons
 Main scientist – 1900, Max Planck
More about a Blackbody…
 Is the best possible emitter of radiant energy
 Must both radiate and absorb energy at the
same rate in order to maintain a constant
 Total radiation from a black body depends only
on temperature of the body, not on chemical or
physical characteristics
Plotting Curves
 A curve can be
generated plotting the
temperature, intensity,
or brightness of the
black body versus the
wavelength coming
from it.
 These curves are
sometimes called
Planck curves.
Blackbody curves, 4 objects
a) Cool, invisible galactic
gas cloud called Rho
 Temperature of 60 K
 Emits mostly lowfrequency radio
Blackbody curves, 4 objects
b) A dim, young star
(shown here in red)
near the center of the
Orion Nebula.
 Temperature of star's
atmosphere ~ 600 K
 Radiates primarily in
infrared (IR)
Blackbody curves, 4 objects
c) The Sun
 Surface ~ 6000 K
 Brightest in the
visible (v) region of
the electromagnetic
Blackbody curves, 4 objects
d) A cluster of very bright
stars, called Omega
Centauri, as observed
by a telescope aboard
the space shuttle
 Temperature ~
60,000 K
 Radiate strongly in
ultraviolet (UV)
How is a star a blackbody?
 Because blackbody radiation is solely dependent
on temperature (simple)
 And to maintain a constant temperature, a
blackbody must emit radiation in the same
amount as it absorbs
Wein’s Law
 The hotter a blackbody becomes, the shorter its
wavelength of peak emission becomes
 The wavelength of peak emission is simply the
wavelength at which a blackbody emits most of
its radiation
Wein’s Law
 1893, German physicist Wilhelm Wien
 Quantified relationship between blackbody
temperature and wavelength of spectral peak
 λmax = 2.9 x 10-3 (microns)/T
 λmax (lambda max) = wavelength of Peak emission
 2898 microns
 T = temperature of Blackbody in Kelvin (K)
Wein’s Law in action…
Plank Curves - 1
 1900 , Max Planck
 Electromagnetic radiation absorbed or emitted
only in “chunks” of energy, quanta, E
 Quanta are proportional to the frequency of the
radiation E = h. (Constant of proportionality “h” is
Planck's constant.)
 Wanted to understand the shape of Wien's radiative
energy distribution as a function of frequency.
Plank Curves - 2
 Postulated that radiators or oscillators can only emit
electromagnetic radiation in finite amounts of
energy of size.
 At a given temperature T, there is not enough
thermal energy available to create and emit many
large radiation quanta.
 More large energy quanta can be emitted when
temperature is raised.
Plank’s Law
 The amount of blackbody radiative flux emitted
by a blackbody for a given wavelength is given
by Planck's Law:
 Where T is object temperature (in degrees
Kelvin); l is wavelength in microns; units are
(W/m2) per micron
 The wavelength of peak emission is:
Stefan–Boltzmann Law
 Independently formulated by Josef Stefan (1879)
and Ludwig Boltzmann (1884, 1889)
 Relationship between radiant energy and
temperature for a black body radiator
 Relates total radiant flux (F) (in W/m2), from
surface of black body to its temperature (T)
 F= σ T4
 σ = 5.6703 x 10-8 watt / m2 K4
Stefan–Boltzmann Law 2
 How much power a
blackbody radiates per
unit area of its surface
 For a blackbody of
temperature T, the
power radiated per unit
area is:
 P = constant x T4
Stefan–Boltzmann Law
Why use Stefan-Boltzmann(S-B) Law?
 Using the Stefan-Boltzmann law in conjunction
with other known quantities, it can be used to
infer properties of a star
 For example, if a star radiates like a blackbody,
then the luminosity of the star can be written as
 L = (Surface Area of the Star) x (power per unit area
produced by the star)
= 12.6 x R2 x constant x T4 So, if we know certain
information (obtained through independent means)
about a star, we can infer other properties. For
What can we learn from S-B law?
 If we know the luminosity and temperature, we
can infer the radius of the star;
 If we know the luminosity and radius of a star,
we can infer its temperature;
 If we know the radius and temperature of a star,
we can infer its luminosity
Blackbody Review
 Stefan-Boltzmann Law -
Area under the curve
increases as the
temperature is increased
 Wien's Law – Peak of the
curve in emitted energy
changes wavelength
 Planck’s Law – Peak of the
curve or the peak emission
wavelength of a blackbody
is related to the
temperature of the object
– hotter objects emit in
higher wavelengths.

similar documents