Transcript lecture11

Assigned Reading
• Today’s assigned reading is:
– Finish Chapter 7
Reminder: e.m. Radiation generally
contains bundles of waves of different
wavelengths (colors)
The strength of each color in a given bundle of e.m.
radiation, i.e. the intensity of the light at each
wavelength, is called the spectrum
Here is an example of optical (visible) light:
Blackbody Radiation (a.k.a.
Thermal Radiation)
–Every object with a temperature
greater than absolute zero emits
blackbody radiation.
–Hotter objects emit more total
radiation per unit surface area.
–Hotter objects emit photons with a
higher average energy.
Reminder: Blackbody Radiation, i.e. a
continuum of wavelengths with a characteristic
distribution of strengths
Hotter B.B. emitters “emit” more total radiation per unit area.
However, a big cold object can emit the same or more energy
(depending on how big it is) than a small, hotter one
Cold
Hot
Stefan-Boltzmann Law:
Emitted power per square meter = σ T4
σ = 5.7 x 10-8 W/(m2K4)
Total emitted power: E = 4 p R2 σ T4
An Object’s Spectrum
Encoded in an object’s spectrum
is information about the emitter/absorber.
This is how we learn what the Universe
is made of!
Stars come in different
colors
Color and Temperature
Stars appear in
different colors,
from blue (like Rigel)
Orion
Betelgeuse
via green / yellow (like
our sun)
to red (like Betelgeuse).
If the spectra of stars
are black bodies, then
these colors tell us
about the star’s
temperature.
Rigel
The spectrum of a star: nearly a Black
Body
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 black body
spectrum.
In fact, the spectrum of a star
at the photosphere, before the
light passes through the
atmosphere of the star, is a
nearly PERFECT black body
one
The Spectra of Stars
The inner, dense layers of a
star do produce a continuous
(blackbody) spectrum.
Cooler surface layers absorb light at specific frequencies.
The atmosphere also absorbes light at other specific
frequencies
=> Spectra of stars are B.B.absorption spectra.
The Spectrum of a star (the Sun)
There are similar absorption lines in the other regions of
the electromagnetic spectrum. Each line exactly
corresponds to chemical elements in the stars.
Again, remember the two Laws of Black
Body Radiation. I
1. The hotter an object is, the more energy it emits:
L = 4p R2s*T4
More area, more
energy
where
L = Energy =
= Energy given off in the form of radiation, per
unit time [J/s];
s = Stefan-Boltzmann constant
Again, remember the two Laws of
Black Body Radiation. II
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)
Stellar Spectra
The spectra of stars also
contain characteristic
absorption lines.
With what we
have learned
about atomic
structure, we can
now understand
how those lines
are formed.
Analyzing Absorption Spectra
• Each element produces a specific set of absorption
(and emission) lines.
• Comparing the relative strengths of these sets of
lines, we can study the composition of gases.
By far the
most
abundant
elements
in the
Universe
Lines of Hydrogen
Most prominent lines
in many astronomical
objects: Balmer
lines of hydrogen
The Balmer Lines
n=1
Transitions
from 2nd to
higher levels
of hydrogen
Ha
Hb
Hg
The only hydrogen
lines in the visible
wavelength range
2nd to 3rd level = Ha (Balmer alpha line)
2nd to 4th level = Hb (Balmer beta line)
…
Observations of the H-Alpha Line
Emission nebula, dominated
by the red Ha line
Absorption Spectrum Dominated
by Balmer Lines
Modern spectra are usually
recorded digitally and
represented as plots of intensity
vs. wavelength
The Balmer Thermometer
Balmer line strength is sensitive to temperature:
Most hydrogen
atoms are ionized
=> weak Balmer
lines
Almost all hydrogen atoms in
the ground state (electrons in
the n = 1 orbit) => few
transitions from n = 2 => weak
Balmer lines
Measuring the Temperatures of Stars
Comparing line strengths, we can
measure a star’s surface temperature!
Spectral Classification of Stars (1)
Temperature
Different types of stars show different
characteristic sets of absorption lines.
Spectral Classification of Stars (2)
Mnemonics to
remember the
spectral
sequence:
Oh
Oh
Only
Be
Boy,
Bad
A
An
Astronomers
Fine
F
Forget
Girl/Guy
Grade
Generally
Kiss
Kills
Known
Me
Me
Mnemonics
Stellar Spectra
F
G
K
M
Surface temperature
O
B
A
The Composition of Stars
From the relative strength of absorption lines (carefully
accounting for their temperature dependence), one can
derive the chemical composition of stars.
The Doppler Effect:
another key information contained in
spectrum
• The frequency of light (or of sound) of a
source in motion relative to an observer
has frequency altered by an amount that
depends on its speed relative to the
observer.
• In other words, speed changes the
perceived wavelength of a source (color
for light; pitch for sound)
• Listen to a moving fire truck…
• … or take a look at the police car to see
how this works.
The Doppler Effect (1)
Sound waves always travel at the
speed of sound – just like light
always travels at the speed of light,
independent of the speed of the
source of sound or light.
Blue Shift (to higher
frequencies)
vr
Red Shift (to lower
frequencies)
The light of a
moving source is
blue/red shifted by
Dl/l0 = vr/c
l0 = actual
wavelength
emitted by the
source
Dl = Wavelength
change due to
Doppler effect
vr = radial
velocity
The Doppler Effect (2)
The Doppler effect allows us to measure the component
of the source’s velocity along our line of sight.
This
component is
called radial
velocity, vr.
Doppler Effect
The first crest travels out in
circle from the original position
of the plane
Shorter wavelength
(more blue)
At a later time, a second
crest is emitted from the
planes new position,
but the old crest keeps
moving out in a circle
from the planes original
position
The same thing happens again at
a later time
Longer
wavelength
(more red)
In general …
• The “native” frequency at which an object is
emitting is called the rest frequency.
•
•
You will see/hear frequencies higher than the
rest frequency from objects moving towards you.
You will see/hear frequencies lower than the
rest frequency from objects moving away from
you.
• This is true with sound waves, as well as with
light waves and any other type of waves
Spectra tell us about the motion
of sources
The Doppler Effect (2)
Example:
The Doppler Effect
Take l0 of the Ha (Balmer alpha) line:
l0 = 656 nm
Assume, we observe a star’s spectrum
with the Ha line at l = 658 nm. Then,
Dl = 2 nm.
We find Dl/l0 = 0.003 = 3*10-3
Thus,
vr/c = 0.003,
or
vr = 0.003*300,000 km/s = 900 km/s.
The line is red shifted, so the star is receding from
us with a radial velocity of 900 km/s.
Two identical stars are moving towards the Earth.
Star A’s emission lines are observed to be at
visible wavelengths. The same emission lines
for Star B are observed to be at ultraviolet
wavelengths. From these observations you
conclude that:




Both stars are moving away from the Earth
Star A is moving towards the Earth faster than
Star B
Star B is moving towards the Earth faster than
Star A
Star B is moving away from the Earth while
Star A is moving towards the Earth.
The Doppler shift
• An object shining red light with l=656.3
nm is moving at V=5,000,000 m/s
toward you. What is the color of the light
that you see?
• V/c = (l- l0)/l0
• 5x106/3x108 = 1.67x10-2 = (l- l0)/l0
l0 = l x (1+1.67x10-2) = 667.3 nm
Two otherwise identical stars are rotating at
different rates. Star A is rotating slower
than Star B. How do Star A’s spectral
lines appear with respect to Star B’s
lines?
Star A’s lines are narrower than Star B’s
lines.
Star B’s lines are narrower than Star A’s
lines.
There is no difference in the lines of the
two stars.
Star A’s lines are stronger than Star B’s
lines.