Download Lecture 11: Stars, HR diagram.

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Chapter 15: Stars
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Stars
We can gather a lot of information about stars
(mostly using what we already know from the 1st half of the class)
1. Distance?
2. Temperature?
3. Composition?
4. Mass?
5. Size?
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1. Distance to stars
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Summary: How to measure the distance to a star?
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When the parallactic angle (P) is in arcseconds, the distance will be in
parsecs
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distance(parsec) =
p(arcsec)
1parsec = 206264 × AU
size
distance
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Quizz #9
What is the distance to a star with a parallax of 0.5 arcsec?
a) 1 parsec
b) 2 parsec
c) 0.5 parsec
d) 5 parsec
e) N.A.
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distance =
= 2parsec
0.5arcsec
size
distance
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Stars
We can gather a lot of information about stars
(mostly using what we already know from the 1st half of the class)
1. Distance ✓
1.1.Luminosity
2. Temperature?
3. Composition?
4. Mass?
5. Size?
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1.1 Luminosity
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We can measure the Flux (= energy/sec/meter2)
by collecting it here on Earth. We also call it “apparent brightness”.
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If we have both the flux and the distance...
Luminosity = 4π(distance)2 × Flux
we can get the luminosity of the star, which is an intrinsic property of it.
Surface area of a sphere:
4π(radius)2
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1.1 Luminosity
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We can measure the Flux and Distance at any location, like, from Earth.
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In the special case that the distance corresponds to the actual size of the
star, then
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“distance” becomes the radius of the star
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Flux (or the apparent brightness) is related to the temperature by
Flux = σT4
Luminosity = 4π(distance)2 × Flux
Luminosity = 4π(radius)2 × σT4
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1.1 Luminosity
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Stars exhibit a range in luminosities
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Most luminous stars: 106 LSun
(that’s a million times the Sun!)
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Least luminous stars: 10-4 LSun
(or 1/10000 times the Sun)
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Stars
We can gather a lot of information about stars
(mostly using what we already know from the 1st half of the class)
1. Distance ✓
1.1.Luminosity✓
2. Temperature?
3. Composition?
4. Mass?
5. Size?
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2. Temperature
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How can we measure the temperature of a star?
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We can see the colors of stars (or at which wavelength do we see it
emitting the most?)
λpeak T = 2.9mmK
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But just the color alone is not that much information...
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What else can we do?
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2. Temperature
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How can we measure the temperature of a star?
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We can see the colors of stars (or at which wavelength do we see it
emitting the most?)
λpeak T = 2.9mmK
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But just the color alone is not that much information...
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What else can we do? We can take a spectrum!
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What do you think?
A hotter star, would show more
or less absorption lines than the
sun? Think about what makes the lines.
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2. Temperature: Stellar classification
A hotter star, would show more or less absorption lines than the sun?
Less! Because the electrons would stop ‘belonging’ to a particular atom, so
no absorption lines (from going to higher energy levels).
Sun
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2. Temperature: Stellar classification
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A hotter star, would show more or less absorption lines than the sun?
Less! Because the electrons would stop ‘belonging’ to a particular atom
(ionized atoms), so no absorption lines (from going to higher energy levels).
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It wasn’t until 1925 that Cecilia Payne
related the temperature of stars to
the spectral classes.
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Sun
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2. Temperature: Stellar classification
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A hotter star, would show more or less absorption lines than the sun?
Less! Because the electrons would stop ‘belonging’ to a particular atom, so
no absorption lines (from going to higher energy levels).
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When ordered from hottest to coolest,
the order reads OBAFGKM
(Why? because first they were ordered
by the strength of the hydrogen lines
and they went ABCD...)
Sun
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2. Temperature: Stellar classification
•
A hotter star, would show more or less absorption lines than the sun?
Less! Because the electrons would stop ‘belonging’ to a particular atom
(ionized atoms), so no absorption lines (from going to higher energy levels).
•
When ordered from hottest to coolest,
the order reads OBAFGKM
Valentine’s Day mnemonic:
Oh Be A Fine Girl/Guy Kiss Me
Sun
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Stars
We can gather a lot of information about stars
(mostly using what we already know from the 1st half of the class)
1. Distance✓
1.1.Luminosity✓
2. Temperature✓
3. Composition?
4. Mass?
5. Size?
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3. Composition
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We already took a spectrum, and got the temperature of our star.
But a spectrum has a lot more information than that.
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We can measure individual lines (and quantum mechanics) to obtain the
relative amounts of different elements.
Sun
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Stars
We can gather a lot of information about stars
(mostly using what we already know from the 1st half of the class)
1. Distance✓
1.1.Luminosity✓
2. Temperature✓
3. Composition✓
4. Mass?
5. Size?
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4. Mass
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How can we measure the mass of a star?
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We can use Newton’s version of Kepler’s third law!
When we used it for a planet orbiting a star, we neglected the mass of the
planet.
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a
G(M + m)
=
2
P
4π 2
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0
a3
GM
=
2
P
4π 2
But if now we would like to measure the mass of a star instead... it is hard to
directly see planets outside our solar system
Binary stars!
Albireo
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4. Mass
If the system now has two stars, we cannot neglect either of the masses
because they are comparable
a3
G(M1 + M2 )
=
2
P
4π 2
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a: semi-major axis
P: period
G: gravitational constant
M1: mass of star 1
M2: mass of star 2
Albireo
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4. Mass
Binary systems:
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Visual binaries: In this case we can directly measure the orbital
motions of the stars
Sirius A and B
separation: 7.6 arcsec
Caveat: inclination angle.
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•
4. Mass
Binary systems:
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Visual binaries: In this case we can directly measure the orbital
motions of the stars
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Eclipsing binaries: if the system is close to edge on, the stars will
block each other’s light from us
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4. Mass
Binary systems:
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Visual binaries: In this case we can directly measure the orbital
motions of the stars
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Eclipsing binaries: if the system is close to edge on, the stars will
block each other’s light from us
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Spectroscopy binaries: use the doppler shifts in the spectral lines of
both objects.
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Stars
We can gather a lot of information about stars
(mostly using what we already know from the 1st half of the class)
1. Distance✓
1.1.Luminosity✓
2. Temperature✓
3. Composition✓
4. Mass✓
5. Size?
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5. Size
Stefan-Boltzmann law:
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If we know the flux and distance, then we can get the luminosity
Luminosity = Flux × 4π(dist)2
•
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We can use the temperature (from the spectra) and the luminosity
to get the radius of the star
Luminosity = σT4 × 4π(radius)2
Luminosity
(radius) =
σT4 × 4π
2
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Stars: summary of properties
Luminosity (from apparent brightness (flux) and distance)
10−4 L⊙ − 106 L⊙
Temperature (from color and spectral lines)
3,000 K - 50,000 K
Mass (from binary systems)
0.08M⊙ − 100M⊙
Size (from S-B law, measured distance and temperature)
0.001R ⊙ −1000R⊙ ??
⊙ :values for the Sun
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The Herzsprung-Russel Diagram
We are able to determine the characteristics of stars: temperature, mass,
size, distance, etc. But we would like to gain insight to how they work and
evolve.
Let’s begin with something more familiar: Humans.
Description? Height, weight, hair color/length, eye color, age, address, etc.
Are these characteristics related?
Not related,
just a scatter plot
Hair color
Height
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The Herzsprung-Russel Diagram
We are able to determine the characteristics of stars: temperature, mass,
size, distance, etc. But we would like to gain insight to how they work and
evolve.
Let’s begin with something more familiar: Humans.
Description? Height, weight, hair color/length, eye color, age, address, etc.
Are these characteristics related?
Not related,
just a scatter plot
Address
Height
38
The Herzsprung-Russel Diagram
We are able to determine the characteristics of stars: temperature, mass,
size, distance, etc. But we would like to gain insight to how they work and
evolve.
Let’s begin with something more familiar: Humans.
Description? Height, weight, hair color/length, eye color, age, address, etc.
Are these characteristics related?
Related!
not SIMPLE, but we can
learn something from this
Age
Height
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The Herzsprung-Russel Diagram
Stars now....
Description? temperature, luminosity, size, mass, radius, etc.
Are these characteristics related?
This is what the Herzsprung-Russel (or HR from now on) is all about.
Luminosity
Notice that the temperature axis is flipped!
Temperature
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The Herzsprung-Russel Diagram
Stars now....
Description? temperature, luminosity, size, mass, radius, etc.
Are these characteristics related?
This is what the Herzsprung-Russel (or HR from now on) is all about.
Example:
HR diagrams for two clusters
M67 (young) and M4 (old)
What can we learn from this?
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HR Diagram
Relations between luminosity, mass, size and temperature of stars.
Which star is hottest?
Star A : Wien’s law
C
Which star is most luminous?
Star C
B
Which star is the biggest?
Star C
D
A
E
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HR Diagram
Relations between luminosity, mass, size and temperature of stars.
Where are most of the stars?
In the “Main sequence”
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The Main Sequence
There is a very tight relationship between luminosity and temperature
We see that the Sun is in this
sequence...
Then there is something in
common between the Sun
and the rest of the stars in the
main sequence....
They are all burning H into
He in their cores
More luminous = hotter
= more massive!
Less luminous = cooler
= less massive!
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The Main Sequence
If we have a higher mass star, how can we keep it from collapsing under its
own weight?
The pressure needs to balance
the gravitational force.
Higher mass =
higher core pressure and
higher core temperature
fusion rate increases until it
supports the star’s mass
Lower mass =
lower core pressure and
lower core temperature
fusion rate matches the
weight of the outer layers
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The Main Sequence
If we have a higher mass star, how can we keep it from collapsing under its
own weight?
The pressure needs to balance
the gravitational force.
L∝M
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Luminosity is proportional to
the mass to the fourth power.
M
as
ss
eq
u
en
c
e
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The Main Sequence: summary
The main sequence is where the stars that are burning H into He are
(most of them).
More luminous stars are hotter.
More luminous stars are more massive.
Also, more luminous stars are bigger.
M
as
ss
eq
u
en
c
e
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The Main Sequence
If we have a higher mass star, how can we keep it from collapsing under its
own weight?
The pressure needs to balance
the gravitational force.
L∝M
4
Luminosity is proportional to
the mass to the fourth power.
More massive stars give out
more energy (more mass)...
They will run out of fuel sooner!
M
as
ss
eq
u
en
c
e
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Stellar evolution
How is the lifespan of a star related to its mass?
Lifespan is just how long will the hydrogen supply last.
Lifetime = energy supply / rate of energy consumption
Lifetime = energy supply / (energy/sec)
Since E=mc2
Lifetime = constant * Mass/ luminosity
Lifetime ∝ Mass/ Luminosity
But L is proportional to M4
Lifetime ∝ Mass/ Mass4
Lifetime∝1/M3
M
as
ss
eq
u
en
ce
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Stellar evolution
How is the lifespan of a star related to its mass?
Lifetime ∝ M−3
The Sun will last about 10 billion years
How about a star with M = 10 Msun?
Lifetime10M⊙ ∝ (10M⊙ )−3
Lifetime10M⊙
(10M⊙ )−3
=
Lifetime⊙
M−3
⊙
Lifetime10M⊙
10−3 M−3
⊙
=
Lifetime⊙
M−3
⊙
Lifetime10M⊙
Lifetime⊙
=
103
M
as
ss
eq
u
en
ce
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Stellar evolution
How is the lifespan of a star related to its mass?
Lifetime ∝ M−3
The Sun will last about 10 billion years
How about a star with M = 10 Msun?
Lifetime10M⊙
Lifetime⊙
=
103
It would last only 1/1000 times the
lifespan of the Sun!
M
as
ss
eq
u
en
ce
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Stellar evolution
High mass stars:
Are more luminous
Have large radius
Are bluer (hotter)
Live shorter lives
Low mass stars:
Are dimmer
Are smaller
Are redder (cooler)
Live longer lives