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Temperature, Blackbodies
& Basic Spectral Characteristics.
Things that have one primary temperature but also exhibit a
range of temperatures are known in physics as “blackbodies.”
They radiate energy thermally.
Humans are blackbodies,
primarily glowing in the infrared.
Candles (fire!) and Incandescent
lightbulbs are blackbodies.
Stars are blackbodies. The sun glows
primarily in the visible light.
Basic spectral form of a blackbody.
energy output
peaks at a given wavelength
dives to near nothing at shorter
wavelengths (higher energies, higher
temperatures):
Wien’s approximation.
that wavelength indicates the overall
temperature of the blackbody
trails off at long wavelengths
this is called the “Rayleigh-Jeans tail”
(i.e. cooler temperatures, lower
energies than the peak)
wavelength
Property of a blackbody: If it’s the same size but
hotter then it’s giving off more energy at all
wavelengths…
energy output
Hotter
Cooler
wavelength
energy output
While blackbodies seem to be the most fundamental
form of “thermal” emission, or building block, and
stars are all blackbodies, astronomical objects are not
all blackbodies!
wavelength
Energy output can be flat, spiked, sloped, etc. and there is a
WEALTH of information in an object’s spectrum.
Spectrum of the Sun
The plot below shows three different blackbodies (A, B, & C).
2. Which one appears
the most blue?
3. Which one outputs
the most red light?
energy output
1. Which one outputs
the most blue light?
A
4. Which one appears
the most red?
B
C
wavelength
The plot below shows three different blackbodies (A, B, & C).
2. Which one appears
the most blue?
A
3. Which one outputs
the most red light?
energy output
1. Which one outputs
the most blue light? A
A
B
4. Which one appears
the most red?
C
B
C
wavelength
How gas interacts with light.
Take a specific gas, like
hydrogen. In chemistry class
you learn that it requires a
specific energy to move
electrons from different orbitals.
Those are very specific energies.
Shining a white light through a gas cloud that is cold results in
absorption of light of that specific energy.
ABSORPTION LINES
How gas interacts with light.
Shining a white light through a gas cloud that is cold results in
absorption of light of that specific energy.
wavelength
EMISSION LINES
energy output
energy output
ABSORPTION LINES
wavelength
energy leaves the
gas (cooling!)
energy goes into
the gas (heating!)
wavelength
EMISSION LINES
energy output
energy output
ABSORPTION LINES
wavelength
Spectrum of the Sun
What we have learned
Wien’s Displacement Law
Planck Function
2h⌫ 3
1
B⌫ (⌫, T ) = 2
h⌫
c e kT
1
energy output
T /⌫/
1
Hotter
Blackbodies!
Cooler
wavelength
What we have learned
Wien’s Displacement Law
Hotter
energy output
e
1
s
e
h !
T /⌫/
t
y
e
l
c
p
a
p
p
a
s
Planck Function
o
t
n
i
2h⌫
1nt
s
t
B (⌫, T ) =
a
c w
e
1 jec
e
b
w oo
w
t
o
N
Blackbodies!
Cooler
3
⌫
2
wavelength
h⌫
kT
s
l
o
to
STARS
1.
Magnitude System
2. Luminosity vs. Flux vs. Temperature
3. Stellar Classification & Composition
Stars’ Brightness ~ it’s energy output. How can we measure this?
2
2
1
3
1
1
2
1
3
3
3
3
2
2
2
1
3
2
3
Ancient methods of measuring stellar brightness:
classifying them into different “classes” or magnitudes
Stars’ Brightness ~ it’s energy output. How can we measure this?
2
2
1
3
1
?
1
2
1
3
3
3
3
Using our new numbering2system,
2
what number would you assign
the
2 star in the green circle here?
1
3
2
3
Ancient methods of measuring stellar brightness:
classifying them into different “classes” or magnitudes
The magnitude system.
m= −2.5log(Flux) + Const
WHAT?!
Why would this EVER
make sense?
But it’s actually how our
eyes see the world!
Our eyes are LOGARITHMIC light detectors!
Objects that we
perceive to be ~5
times brighter than a
reference object (e.g.
glowing screen vs sky)
are ACTUALLY 100
times brighter.
The magnitude system.
m= −2.5log(Flux) + Const
In astronomy, magnitudes computed
relative to a reference star, for
example: Vega.
We assert that Vega has a magnitude of 0, all other
magnitudes of objects in the sky are compared to Vega:
m= −2.5log(Flux) − 2.5log(FluxVega )
or
Flux
m= −2.5log(
)
FluxVega
We assert that Vega has a magnitude of 0,
all other magnitudes of objects in the sky
are compared to Vega:
m= −2.5log(Flux) − 2.5log(FluxVega )
or
Flux
m= −2.5log(
)
FluxVega
For example, if there is a faint star next to Vega
that is ~10 times fainter (10 times less flux) what
is its magnitude?
Comparing magnitudes and fluxes for two different stars:
m1
m2 =
F1
2.5 log( )
F2
How much fainter is a 4th magnitude star than a 0th
magnitude star? Discuss.
The Hubble Space
Telescope can see
stars/distant objects
down to 28th
magnitude. How
much fainter is that
than our naked eye
limit at ~6th
magnitude?
~6e8 times =
600,000,000 times
fainter
What we have learned.
remember!!
L
F =
4⇡r2
Flux follows an inverse
square law with distance.
Magnitudes…
F1
−2.5log(Flux)
− 2.5log(Fl
m1m= m
2.5 log(
)
2 =
F2
or
Flux
m= −2.5log(
)
FluxVega
How much does the luminosity of stars vary?
Knowing their distance with parallax, and measuring
flux, we can infer their luminosities.
sol
ar
L
lum
ino
sity
=
33
1
3.8 ⇥ 10 erg s
= 3.8 ⇥ 1026 J s
= 3.8 ⇥ 1026 W
1
The least to most luminous stars:
10
4
(1/10,000)
6
10 L
(1,000,000)
Absolute magnitudes
Much more analogous to luminosity than apparent
magnitude: does not vary with distance to the star.
It’s a way of stating a star’s luminosity in terms of a
magnitude… the magnitude that star would be on
the sky if put at a distance of 10pc.
10pc
Absolute magnitudes
Much more analogous to luminosity than apparent
magnitude: does not vary with distance to the star.
It’s a way of stating a star’s luminosity in terms of a
magnitude… the magnitude that star would be on
the sky if put at a distance of 10pc.
apparent mag.
M =m
5(log10 (DL )
absolute mag.
distance to star in parsecs
10pc
1)
STARS PART 2: Stellar Classification & How stars work
How would you start to classify these stars?
brightness ~ flux/luminosity
color ~ temperature
Brightest
Dimmest
Hottest
Coldest
The Hertzsprung-Russell Diagram: comparing stellar
luminosity with color/temperature
most stars sit on the
“main sequence”
stars that are at
some other point in
HR diagram: almost
always ‘dying’ or
‘dead’
The Hertzsprung-Russell (HR) Diagram: comparing stellar
luminosity with color/temperature
Brightest
supergiants
m
ain
s
t
n
se
qu
en
Sm
wh
alle
ite
st
dw
arf
s
a
i
g
ce
Lar
ges
t
by next
class period
you’ll be
able to
explain all
parts of
this!
Dimmest
Hottest
Coldest
Temperature of the Surface of the Sun
Temperature hard to measure this way
unless you have a very precise
(modern) camera!
From the overall shape of the spectrum.
The “Computers” of 1800s Harvard Observatory
actual astronomers
Annie Jump Cannon
(1863-1941)
classified most stars in the entire sky down to 9th magnitude.
Set classifications: O B A F G K M
Lines in a star's spectrum correspond to a
spectral type.
O B A F G K M
Strong evidence of elements like carbon,
nitrogen, sodium, calcium in the spectrum of
the sun & other stars:
It was largely
thought at the end
of the 19th century
that the stars were
mostly made of the
same elements
that make up the
Earth.
Cecilia Payne-Gaposchkin:
asked, what are stars made of using Cannon’s extensive catalog.
Cecilia Payne-Gaposchkin:
asked, what are stars made of using Cannon’s extensive catalog.
The most important PhD thesis in modern astrophysics:
the stars are MOSTLY hydrogen (and helium) with trace levels of other
elements. We only see those strong lines from the trace elements when
there are variations in stellar temperature.
Lines in a star's spectrum correspond to a
spectral type that reveals its temperature.
(Hottest)
O B A F G K M (Coldest)
The ionization states of different elements in the sun give
a very accurate temperature constraint! And was easy to
measure by eye…
Meghnad Saha developed the Saha equation to explain the
ionization of different elements as a function of temperature. Put together
with the work of Annie Jump Cannon & Cecelia Payne, describes our
understanding of stellar classification.
Saha Eq. (you don’t
need to know!)
So we can basically thank these three lovely people for figuring out the
difference between different types of stars for us by the 1920s
(i.e. stellar classification)
Annie Jump Cannon
Cecelia Payne
Meghnad Saha
Lines in a star's spectrum correspond to a
spectral type that reveals its temperature.
(Hottest)
O B A F G K M (Coldest)
Chemical Composition
From detailed spectral line structure (which
also gives pressure/density of the gas.)
Luminosity ~ Energy Output
Temperature has a relationship with
Luminosity… but this takes a particular form
for blackbodies: Stefan-Boltzmann Law…
F /T
4
F = T
4
= 5.67 ⇥ 10
Peak wavelength
temperature
8
Wm
2
K
4