Physics - 13 - Astrophysics€¦ · 1 parsec (pc) = 3.26 ly distance at which the mean radius of...
Transcript of Physics - 13 - Astrophysics€¦ · 1 parsec (pc) = 3.26 ly distance at which the mean radius of...
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ASTROPHYSICSIB PHYSICS | UNIT 13 | ASTROPHYSICS
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The Scale of AstrophysicsIB PHYSICS | UNIT 13 | ASTROPHYSICS
13.1
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IB Physics Data Booklet
Anything look familiar?
𝑃 = 𝑒𝜎𝐴𝑇4 λmax(metres) =2.90 × 10−3
T (kelvin)
𝐼 =𝑃
𝐴=
𝑃
4𝜋𝑟2
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The Solar System
Mercury Venus Earth Mars Jupiter Saturn Uranus Neptune
Diameter[km]
4,880 12,104 12,756 6,787 142,800 120,000 51,800 49,500
Distance to Sun
[× 108 m]58 107.5 149.6 228 778 1,427 2,870 4,497
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Poor Pluto… :’(
A celestial body that (a) is in orbit around the Sun, (b) has sufficient mass for its self-gravity to overcome rigid body forces so that it assumes a hydrostatic equilibrium (nearly round) shape, and (c) has cleared the neighbourhood around its orbit.
Definition of a Planet (as of 2006)
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Measuring Distances
Speed of Light: c = 3.00 × 108 m s-1
How far is one light year (ly)
3.00×108 𝑚
1 𝑠×
60 𝑠
1𝑚𝑖𝑛×
60𝑚𝑖𝑛
1 ℎ𝑟×
24 ℎ𝑟
1 𝑑𝑎𝑦×
365 𝑑𝑎𝑦𝑠
1 𝑦𝑟
= 9.46 × 1015 𝑚 𝑦𝑟−1
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Measuring Distances
1.5 × 1011 m
Average Distance between the Earth and the Sun
Astronomical
Unit
[AU]
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Measuring Distances
1 light year (ly) = 9.46 × 1015 m The distance that light travels in an earth year
1 astronomical unit (AU) = 1.50 × 1011 m The average distance between the earth and the sun
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Measuring Angles
60 minutes in 1°
60 seconds in 1 minute
1° = 3600 arcseconds
1° = 3600 as
‘
“
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Parsecs
1 parsec (pc) = 3.26 lydistance at which the mean radius of the earth's orbit subtends an angle of one second of arc.
parsec stands for parallax angle of one second
1 second
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Parsecs
“It's the ship that made the Kessel run in less than 12 Parsecs.”
Why is this claim a little odd?
distance
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IB Physics Data Booklet
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The Black Hole – by the numbers
55 million light years from Earth
6.5 billion times the mass of the Sun
Just bigger than our solar system
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The Science Behind the Picture
Remember: 1° = 3600 arcseconds
1 arcsecond = 1,000,000 μas
*60 μas is about the same as resolving a picture of an orange sitting on the surface of the moon
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The Science Behind the Picture
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Stellar QuantitiesIB PHYSICS | UNIT 13 | ASTROPHYSICS
13.2
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Measuring Distances
1 light year (ly) = 9.46 × 1015 m The distance that light travels in an earth year
1 astronomical unit (AU) = 1.50 × 1011 m The average distance between the earth and the sun
1 parsec (pc) = 3.26 lydistance at which the mean radius of the earth's orbit subtends an angle of one second of arc.
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IB Physics Data Booklet
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Stellar Parallax
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Stellar Parallax
𝑑 𝑝𝑎𝑟𝑠𝑒𝑐 =1
𝑝 (𝑎𝑟𝑐 𝑠𝑒𝑐𝑜𝑛𝑑)
p (arc second)
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Stellar Parallax
The angle must be measured to a very distant field of other stars
*The parallax method only works for stars that are relatively close to earth
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Try This… | #1
The star Betelgeuse has a parallax angle of 7.7 × 10-3 arc seconds. Calculate its distance.
arc-seconds→ parsecs→ light years →meters
𝑑 =1
𝑝=
1
7.7 × 10−3 𝑎𝑟𝑐 𝑠𝑒𝑐𝑜𝑛𝑑𝑠= 129.9 𝑝𝑎𝑟𝑠𝑒𝑐𝑠
129.9 pc ×3.26 ly
1 pc×9.46 × 1015 m
1 ly= 4.0 × 1018 m
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Luminosity vs Brightness
Luminosity L Brightness b
Intensity
W/m2 or W m-2
*Depends on the observer distance
Power Emitted
Watts [W]
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Brightness
𝑏 =𝐿
4𝜋𝑑2Distance Brightness
x b
2x b/4
3x b/9
4x b/16
Distance
from star
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Same Brightness, Different Stars
It is possible for stars to have the same brightness but have different distances and luminosities
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Try This… | #2
The star Betelgeuse has an apparent brightness of 2.0 × 10-7 W m-2. Calculate its luminosity.
d = 4.0 × 1018 m𝑏 =
𝐿
4𝜋𝑑2
𝐿 = b 4𝜋𝑑2
= 2.0 × 10−7 4𝜋(4.0 × 1018)2
= 4.0 × 1031 W
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Wien’s Displacement Law
*Note: This assumes perfect blackbody radiation
𝜆max𝑇 = 2.90 × 10−3 mK
λmax(metres) =2.90 × 10−3
T (kelvin)
This equation shows up in
subtopic 8.2 as
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Try This… | #3
The star Betelgeuse has a max wavelength of 828.6 nm. What is its surface temperature?
𝜆max𝑇 = 2.90 × 10−3 mK
T =2.90 × 10−3 mK
λmax=2.90 × 10−3 mK
828.6 × 10−9= 3500 K
828.6 × 10−9 m
Solve for T
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Luminosity
𝐿 = 𝜎𝐴𝑇4 Stefan-BoltzmannConstant σ 5.67 × 10-8 W m-2 K-4
Luminosity[W]
Temperature[K]
Surface Area (sphere)A=4πr2
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Try This… | #4
Knowing everything else that we know about Betelgeuse, calculate the average radius of the star.
L = 4.0 × 1031 W
T = 3,500 K
𝐿 = 𝜎𝐴𝑇4
4.0 × 1031 = (5.67 × 10−8)(4𝜋𝑟2)(3500)4
𝑟 = 6.12 × 1011
Solve for r
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IB Physics Data Booklet
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All together now!
The brightest star in the sky is known as Sirius and has a parallax angle of 0.379 arc seconds, apparent brightness of 1.2 × 10-7
W m-2, and a max wavelength of 292 nm. Complete this table of stellar properties.
Brightness (W m-2) 1.2 × 10-7 W m-2
Max Wavelength (m) 292 × 10-9 m
Distance (m) 8.14 × 1016 m
Luminosity (W) 9.98 × 1027 W
Temperature (K) 9930 K
Radius (m) 1.2 × 109 m
𝑑 =1
𝑝=
1
0.379 𝑎𝑟𝑐 𝑠𝑒𝑐𝑜𝑛𝑑𝑠= 2.64 𝑝𝑎𝑟𝑠𝑒𝑐𝑠
2.64 pc ×3.26 ly
1 pc×9.46 × 1015 m
1 ly= 𝟖. 𝟏𝟒 × 𝟏𝟎𝟏𝟔 𝐦
𝐿 = b 4𝜋𝑑2 = 1.2 × 10−7 4𝜋(8.14 × 1016)2 = 𝟗. 𝟗𝟖 × 𝟏𝟎𝟐𝟕𝐖
T =2.90 × 10−3 mK
λmax=2.90 × 10−3 mK
292 × 10−9= 𝟗𝟗𝟑𝟎 𝐊
𝐿 = 𝜎𝐴𝑇4 9.98 × 1027 = (5.67 × 10−8)(4𝜋𝑟2)(9300)4
𝒓 = 𝟏. 𝟐 × 𝟏𝟎𝟗𝐦
𝟐𝟗𝟐× 𝟏𝟎−𝟗𝐦
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Atomic SpectraIB PHYSICS | UNIT 13 | ASTROPHYSICS
13.3
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Continuous Spectrum
When white light from the sun passes through a prism, the light is dispersed into its component colors in a continuous spectrum
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Emission Spectrum
If an electric current is passed through an element in the form of a low-pressure gas, it will produce its own unique emission spectrum
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Emission Spectrum
These spectra can be used to identify elements like a fingerprint
These are known as Line Spectra
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Absorption Spectrum
If white light is passed through a sample of gaseous atoms or molecules, it is found that the light of certain wavelengths is missing
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Absorption Spectrum
The emission and absorption spectra
are negative images of each other
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What is Light?
Energy
Wave
Particle(photon)
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Light is Quantized
Photons of light can only have certain ______________ values of energy
discrete
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Energy of a Photon
𝐸 = ℎ𝑓
Planck’s Constant h 6.63 × 10-34 J s
Energy[J]
Frequency[Hz]
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Energy of a Photon
𝐸 = ℎ𝑓 𝑐 = 𝑓𝜆
𝑓 =𝑐
𝜆
𝑐 = 3.00 × 108 𝑚 𝑠−1
𝐸 = ℎ𝑐
𝜆
𝜆 =ℎ𝑐
𝐸
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Quick Recap of eV
𝑒𝑉 → 𝑒𝑙𝑒𝑐𝑡𝑟𝑜𝑛 − 𝑣𝑜𝑙𝑡𝑠
Unit of Energy
𝐸𝑛𝑒𝑟𝑔𝑦 𝑖𝑛 𝑒𝑉 =𝐸𝑛𝑒𝑟𝑔𝑦 𝑖𝑛 𝐽
1.60 × 10−19
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IB Physics Data Booklet
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Try This…
Calculate the energy carried by one photon of microwaves of wavelength 10 cm (as might be used in a mobile phone) in J and eV
𝐸 =ℎ𝑐
𝜆=(6.63 × 10−34)(3 × 108)
(0.1)= 1.99 × 10−24 J
1.99 × 10−24
1.60 × 10−19= 1.24 × 10−5 eV
0.1 m
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Shortcut time ☺
Since h and c are both constants, hc acts as a constant as well
𝐸 =ℎ𝑐
𝜆
1.99 × 10−24 J m
0.1 m= 1.99 × 10−24 J
1.24 × 10−6 eV m
0.1 m= 1.24 × 10−5 eV
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Energy Levels
1
234567
Electrons in an atom exist at discrete energy levels
Absorbed
Emitted
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Energy Levels
E4
E3
E2
E1
A photon is emitted whenever an electron transitions from one energy level down to a lower energy level
How many different transitions are possible between these four energy levels?
6
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Energy Levels
n = 1 -13.6 eV
n = 2 -3.40 eV
n = 3 -1.51 eV
n = 4 -0.85 eVn = 5 -0.54 eV
n = 0.00 eV
Excited States
Ground State
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Energy Transitions
n = 1 -13.6 eV
n = 2 -3.40 eV
n = 3 -1.51 eV
n = 4 -0.85 eVn = 5 -0.54 eV
n = 0.00 eV
Lyman Series (UV)
Balmer Series (Visible)
Paschen Series (IR)
Different Energy transitions result in different energies (wavelengths) of light that are absorbed or emitted
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Calculating Wavelength Emitted
n = 1 -13.6 eV
n = 2 -3.40 eV
n = 3 -1.51 eV
n = 4 -0.85 eVn = 5 -0.54 eV
n = 0.00 eV What is the wavelength emitted?
𝜆 =ℎ𝑐
𝐸hc 1.99 × 10-25 J m 1.24 × 10-6 eV m
𝐸 = 13.6 − 1.51 = 12.09 eV
𝜆 =1.24 × 10−6 eV m
12.09 eV= 1.03 × 10−7 m
103 nm
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Try This…
n = 1 -13.6 eV
n = 2 -3.40 eV
n = 3 -1.51 eV
n = 4 -0.85 eVn = 5 -0.54 eV
n = 0.00 eV What is the wavelength emitted?
𝜆 =ℎ𝑐
𝐸hc 1.99 × 10-25 J m 1.24 × 10-6 eV m
𝐸 = 3.40 − 0.85 = 2.55 eV
4.86 × 10−7 m
486 nm
𝜆 =1.24 × 10−6 eV m
2.55 eV=
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Working Backwards…
What is the energy in eV for a 434 nm blue emission line?
𝜆 =ℎ𝑐
𝐸
hc 1.99 × 10-25 J m 1.24 × 10-6 eV m
2.86 eV𝐸 =ℎ𝑐
𝜆=1.24 × 10−6 eV m
434 × 10−9 m=
434 × 10-9 m
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Working Backwards…
n = 1 -13.6 eV
n = 2 -3.40 eV
n = 3 -1.51 eV
n = 4 -0.85 eVn = 5 -0.54 eV
n = 0.00 eV Draw in the Energy Transition for a 434 nm blue emission line?
What transition has an energy difference of 2.86 eV?
𝐸 = 3.40 − 0.54 = 2.86 eV
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Doppler Effect
As objects move away,
their wavelength is
stretched to be closer to
the red part of the
electromagnetic spectrum
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Red Shift, Blue Shift
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H-R Diagrams and Stellar SpectraIB PHYSICS | UNIT 13 | ASTROPHYSICS
13.4
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Organizing the Stars
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H-R Diagrams
Lsun
Lⵙ
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H-R Diagrams
Our Sun
Large
Hot
Small
Hot
Large
Cool
Small
Cool
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H-R Diagrams
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IB Physics Data Booklet
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H-R Diagram for Calculating Distance
The maximum wavelength of a distant star is measured to be 600 nm, suggesting that it has a temperature of ~4800 K. If this star has a brightness of 1.0 × 10-12 W m-2, what is its distance from Earth?
Lsun = 3.84 × 1024 W
𝑏 =𝐿
4𝜋𝑑2𝑑 =
𝐿
4𝜋𝑏
𝑑 =1.92 × 1024
4𝜋(1.0 × 10−12)= 3.9 × 1017 m
4800 K
~0.5 Lsun
Lstar = 0.5 × (3.84 × 1024)
= 3.84 × 1024 W
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Try This
The maximum wavelength of a distant star is measured to be 400 nm. If this star has a brightness of 0.5 × 10-12 W m-2, what is its distance from Earth?
Lsun = 3.84 × 1024 W
𝑏 =𝐿
4𝜋𝑑2𝑑 =
𝐿
4𝜋𝑏
𝑑 =3.84 × 1025
4𝜋(0.5 × 10−12)= 2.47 × 1018 m
𝑇 =2.90 × 10−3
400 × 10−9
𝑇 = 7250 K
7250 K
~10 Lsun
Lstar = 10 × (3.84 × 1024)
= 3.84 × 1025 W
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Mass-Luminosity Relationship
𝐿 ∝ 𝑀3.5
For stars on the main sequence, there is a relationship between luminosity and mass
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IB Physics Data Booklet
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Stellar Spectra
Studying the Spectra of Stars can help determine what the stars are made of
Are these Emission Spectra or Absorption Spectra?
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Stellar Spectra | Try it out
1 2 3 4 5 6 7 8 9 10
N N N N N N
N I N
I N N N N
N
N I N N I
N N I
Compare the spectra of the stars with the known absorption spectra of different elements to determine the composition of the stars
Redshifted
N → Neutral Spectra I → Ionic Spectra
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Evolution of StarsIB PHYSICS | UNIT 13 | ASTROPHYSICS
13.5
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Measuring the Age of the Stars
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Life Span of the Stars
Which stars have the longest life span?
Red Dwarfs
**Hotter stars
burn fuel faster
and die quicker
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Stellar Equilibrium
Increasing temperature increases pressure and causes expansion
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What happens as Stars Age??
H → He
• Heats up
• Hydrogen expands
• He → C
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What happens as Stars Age??
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Life Cycle of our Sun
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White Dwarf Stars
HOT but
SMALL
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White Dwarf Stars
Chandrasekhar Limit = 1.4 Mʘ
There is a maximum mass of a core that can become a white dwarf
The core only makes up about 1/3 of the stars mass so a star with a total mass greater than about 4 Mʘ will not form white dwarfs
Sun’s
Mass
It will become
a White Dwarf
Star’s
Total
Mass< 4MʘIf
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Life Cycle of Massive Star
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Life Cycle of Massive Star
Oppenheimer-Volkhoff Limit = 3 Mʘ
The mass of neutron stars are limited as well…
A Neutron star above the Oppenheimer-VolkhoffLimit will collapse and form a Black Hole.
Neutron Star< 3Mʘ→
Black Hole> 3Mʘ→
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Black Holes?
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Life Cycle of a Star
> 3Mʘ
< 1.4Mʘ
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The Expanding UniverseIB PHYSICS | UNIT 13 | ASTROPHYSICS
13.6
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IB Physics Data Booklet
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“Standard Candle”
Cephid Variables are with longer
brightness periods are more luminous
With this table, the luminosity of this
“standard candle” can be determined
as long as the period is known
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Cephid Variables
What is the distance of the Cephid Variable with the period shown in the graph above? The brightness of this star is 8 × 10-10 W m-2.
1 Lsun = 3.84 × 1024 W
𝑏 =𝐿
4𝜋𝑑2𝑑 =
𝐿
4𝜋𝑏𝑑 =
5.76 × 1027
4𝜋(8 × 10−10)= 7.57 × 1017 m
Lstar = 1500 × (3.84 × 1024)
= 5.76 × 1027 W
5.4 days
~1500 Lsun
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Type Ia Supernova
A type Ia Supernova forms when a white dwarf accretes matter from a companion star until it exceeds the Chandrasekhar limit and explodes
These supernovae have a constant luminosity so their brightness can be analyzed as a standard candle much like the Cephid Variables
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Red Shift, Blue Shift
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Calculating Redshift
𝑧 =∆𝜆
𝜆𝑜≈𝑣
𝑐
Redshift
Change in
Wavelength
Wavelength
Emitted
Velocity of
the Source
Speed
of Light
(3.00×108 ms-1)
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IB Physics Data Booklet
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Calculating Redshift
A characteristic absorption line often seen in stars is due to ionized helium. It occurs at 468.6 nm. If the spectrum of a star has this line at a measured wavelength of 499.3 nm what is the recession speed of the star?
∆𝜆
𝜆𝑜≈𝑣
𝑐499.3 − 468.6
468.6≈
𝑣
3.00 × 108
𝑣 = 1.97 × 107 m s−1
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Hubble’s Big Discovery
Edwin Hubble discovered that the amount of redshift changed by the distance
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The Universe is Expanding
𝑣 = 𝐻0𝑑
Slope = H0 H0 ≈ 70 km s-1 Mpc-1
*current value is not necessarily constant
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IB Physics Data Booklet
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Using the Hubble “Constant”
Estimate the distance from the Earth to a galaxy with a recessional velocity of 150 km s-1
If a galaxy is 20 Mpc from Earth, how fast will it be receding?
𝑣 = 𝐻0𝑑 𝑑 =𝑣
𝐻0=
150 km s−1
70 km s−1 Mpc−1= 2.14 Mpc
𝑣 = 𝐻0𝑑 = 70 km s−1 Mpc−1 20 Mpc = 1400 km s−1
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Calculating Redshift
Nothing can go faster than the speed of light so the Doppler effect can’t really hold up…
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Calculating Redshift
Think of the wavelength change due to the stretching of space-time
𝑧 =𝑅
𝑅𝑜− 1
Cosmological
Redshift
Current
Universe Size
Cosmic Scale Factor
[𝑅 = 1]
Size of the universe at the time the light
was emitted (relative to the current size)
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Calculating Redshift
If the redshift z = 3, what was the scale factor at the time that the light was emitted?
𝑧 =𝑅
𝑅𝑜− 1
3 =1
𝑅𝑜− 1
𝑅𝑜 =1
4= 0.25Note: This means that to result in this
cosmological redshift, the light had to have been emitted when the universe was a quarter of the size it is now
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The Universe is Expanding
4 cm6 cm
2 cm
Think of a rubber band with marks when it is stretched out… Relative to the first dot, which dot moves the fastest?
8 cm
12 cm
4 cm
The farthest dot moves away the fastest
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The Universe is Expanding
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What comes before and after?
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Pulling it all TogetherIB PHYSICS | UNIT 13 | ASTROPHYSICS
13.7
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IB Physics Data Booklet
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IB Physics Data Booklet
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Distance | Parallax
𝑑 𝑝𝑎𝑟𝑠𝑒𝑐 =1
𝑝 (𝑎𝑟𝑐 𝑠𝑒𝑐𝑜𝑛𝑑)1 parsec (pc) = 3.26 ly
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Distance | Cepheid Variables
𝑏 =𝐿
4𝜋𝑑2
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Distance | H-R Diagram
𝜆max𝑇 = 2.90 × 10−3 mK
𝑏 =𝐿
4𝜋𝑑2
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Distance | Redshift & Hubble’s Law
𝑣 = 𝐻0𝑑
𝑧 =∆𝜆
𝜆𝑜≈𝑣
𝑐
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How Old is the Universe?
𝑣 = 𝐻0𝑑
𝐻0 ≈ 70 km s−1 Mpc−1
𝑣 =𝑑
𝑡𝐻0𝑑 =
𝑑
𝑡𝑡 =
1
𝐻0
𝑡 =1
70 km s−1 Mpc−1= 0.0142 s Mpc km−1
0.0142 s Mpc
km×106 pc
1 Mpc×3.26 ly
1 pc×9.46 × 1015 m
1 ly×
1 km
1000 m= 𝟒. 𝟒 × 𝟏𝟎𝟏𝟕 𝐬
≈ 13.8 𝑏𝑖𝑙𝑙𝑖𝑜𝑛 𝑦𝑒𝑎𝑟𝑠
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The “Big Bang”
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Where’s the Evidence??
CMBCosmic Microwave Background
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Cosmic Microwave Background
λmax = 1 mm
0.001 m
𝑇 =2.9 × 10−3
0.001= 𝟐. 𝟗 𝐊
Temperature of the Universe
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What’s Next?
1. Static and Infinite2. Expanding and slowing to a stop3. Expanding, slowing, and
contracting in a “big crunch”4. Expanding and accelerating
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There’s more out there
Age of the Universe Critical Density Neutron Degeneracy Satellite
Andromeda Galaxy Dark Energy Neutron Star Schwarzschild Radius
Binary Star Dark Matter Nucleosynthesis Stellar Cluster
Black Hole Galaxy OBAFGKM Supernova
Comet Meteor Planet White Dwarf Star
Constellation Milkyway Galaxy Pulsar
Cosmological Principle
Nebula Red Giant Star
Click Here for the Quizlet