Transcript star_temperatures

Deducing Temperatures and
Luminosities of Stars
(and other objects…)
Review: Electromagnetic Radiation
Increasing energy
10-15 m
10-9 m
10-6 m
10-4 m
10-2 m
103 m
Increasing wavelength
• EM radiation consists of regularly varying electric magnetic
fields which can transport energy over vast distances.
• Physicists often speak of the “particle-wave duality” of EM
radiation.
– Light can be considered as either particles (photons) or as waves,
depending on how it is measured
• Includes all of the above varieties -- the only distinction
between (for example) X-rays and radio waves is the
wavelength.
Wavelength

 Wavelength is the distance between two identical
points on a wave. (It is referred to by the Greek
letter  [lambda])
Frequency
time
unit of time
 Frequency is the number of wave cycles per unit
of time that are registered at a given point in
space. (referred to by Greek letter  [nu])
 It is inversely proportional to wavelength.
Wavelength and
Frequency Relation
 = v/
 Wavelength is proportional to the wave velocity, v.
 Wavelength is inversely proportional to frequency.
 eg. AM radio wave has a long wavelength (~200 m), therefore it has a low
frequency (~KHz range).
 In the case of EM radiation in a vacuum, the equation becomes
 = c/
Where c is the speed of light (3 x 108 m/s)
Light as a Particle: Photons
 Photons are little “packets” of energy.
 Each photon’s energy is proportional to its
frequency.
 Specifically, each photon’s energy is
E = h
Energy = (Planck’s constant) x (frequency of photon)
The Planck function
• Every opaque object (a human, a planet, a star) radiates a
characteristic spectrum of EM radiation
– spectrum (intensity of radiation as a function of wavelength)
depends only on the object’s temperature
• This type of spectrum is called blackbody radiation
ultraviolet
visible
infrared
radio
Intensity
(W/m2)
0.1
1.0
10
100
1000
10000
Temperature dependence
of blackbody radiation
• As temperature of an object increases:
– Peak of black body spectrum (Planck function) moves
to shorter wavelengths (higher energies)
– Each unit area of object emits more energy (more
photons) at all wavelengths
Wien’s Displacement Law
• Can calculate where the peak of the
blackbody spectrum will lie for a given
temperature from Wien’s Law:
 = 5000/T
Where  is in microns (10-6 m) and T is in degrees Kelvin
(recall that human vision ranges from 400 to 700 nm, or
0.4 to 0.7 microns)
Colors of Stars
• The color of a star provides a strong
indication of its temperature
– If a star is much cooler than 5,000 K, its
spectrum peaks in the IR and it looks reddish
• It gives off more red light than blue light
– If a star is much hotter than 15,000 K, its
spectrum peaks in the UV, and it looks blueish
• It gives off more blue light than red light
Betelguese and Rigel in Orion
Betelgeuse: 3,000 K
(a red supergiant)
Rigel: 30,000 K
(a blue supergiant)
Blackbody curves for stars at
temperatures of Betelgeuse and Rigel
Luminosities of stars
• The sum of all the light emitted over all
wavelengths is called a star’s luminosity
– luminosity can be measured in watts
– measure of star’s intrinsic brightness, as
opposed to what we happen to see from Earth
• The hotter the star, the more light it gives
off at all wavelengths, through each unit
area of its surface
– luminosity is proportional to T4 so even a small
increase in temperature makes a big increase in
luminosity
Consider 2 stars of different T’s
but with the same diameter
What about large & small stars of
the same temperature?
• Luminosity goes like R2 where R is the
radius of the star
• If two stars are at the same temperature but
have different luminosities, then the more
luminous star must be larger
How do we know that Betelgeuse
is much, much bigger than Rigel?
• Rigel is about 10 times hotter than
Betelgeuse
– Rigel gives off 104 (=10,000) times more
energy per unit surface area than Betelgeuse
• But the two stars have about the same total
luminosity
– therefore Betelguese must be about 102 (=100)
times larger in radius than Rigel
So far we haven’t considered
stellar distances...
• Two otherwise identical stars (same radius,
same temperature => same luminosity) will
still appear vastly different in brightness if
their distances from Earth are different
• Reason: intensity of light inversely
proportional to the square of the distance
the light has to travel
– Light wave fronts from point sources are like
the surfaces of expanding spheres
Stellar brightness differences as a tool
rather than as a liability
• If one can somehow determine that 2 stars are
identical, then their relative brightnesses translate
to relative distances
• Example: the Sun and alpha Centauri
– spectra look very similar => temperatures, radii almost
identical (T follows from Planck function, radius can be
deduced by other means) => luminosities about the
same
– difference in apparent magnitudes translates to relative
distances
– Can check using the parallax distance to alpha Cen
The Hertsprung-Russell Diagram