2. What if a source has a temperature of about 10,000 Kelvin, and a
luminosity of about 10^{3}. Explain what type of source this
could be, and the part of its life cycle the source is enduring.
3. Make a line plot superimposed on the HR diagram that would trace
the entire life cycle of our star, the Sun. Remember all of the stages of
this mainsequence, low mass star.
4. What will be the final stage of evolution (black dwarf, neutron
star, or black hole) for each of the following: (Hint: reread the text in
Sections I, II, and III)
(a) Type O main sequence star
(b) Type A main sequence star
(c) Type G main sequence star
Suggested Extension:
Examine the difference between absolute magnitude and apparent
magnitude. Why is an understanding of this crucial to an astronomer’s
ability to describe the evolution of any given star?
Blackbody Radiation & Wien's Law
A star is considered to be an example of a "perfect
radiator and perfect absorber" called a black body. This is an
idealized body that absorbs all electromagnetic energy incident on it. A
black body is black only in the sense that it is absolutely opaque at all
wavelengths; it need not look black. Its temperature depends only on the
total amount of radiant energy striking it each second. Stars are good
approximations to a black body because their hot gases are very opaque,
that is, the stellar material is a very good absorber of radiation.
The energy emitted by black bodies was studied by the German physicist
Max Planck. He derived an equation that gives the radiant energy emitted
per second from 1 cm^{2} of a black body's surface. This equation
is called Planck’s Radiation Law and can be written as
.
In this equation, T is the temperature in Kelvins, the wavelength in centimeters,
c the speed of light, k is Boltzmann’s constant (1.37 x
10^{18} erg/K), and h is Planck’s constant (6.626 x
10^{27} erg sec). Calculus students can prove to themselves that
for such a function there will be a single wavelength, , at which maximum light is emitted.
In fact, we can determine that for wavelength in cm and temperature in
Kelvins,
.
This is known as Wien's Law. This Law is very important to
astronomers. It tells us that the wavelength at which a star emits its
maximum light indicates the star's temperature.
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