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This is a physics course on the options topic of Astrophysics based on the International Baccalaureate Program. It provides resources, guidelines, practices problems, external links and videos aimed at helping students master the topic of Astrophysics at the high school level. This course follow the International Baccalaureate program at the Standard Level.
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INTRODUCTION TO THE UNIVERSE
n Outline the general structure of the solar system
n Distinguish between a stellar cluster and a constellation
n Define the light year
n Compare the relative distances between stars within a galaxy and between galaxies, in terms of order of magnitude
n Describe the apparent motion of stars/constellations over a period of a night and over a period of a year, and explain these observations in terms of the rotation and revolution of the Earth
Objectives
+The Solar System
2
+The Solar System
1 AU = 1 Astronomical Unit = Earth-Sun distance
3
+Planets Data
Planet Distance to the Sun (x109 m)
Diameter( x106m)
Rplanet/Rearth
Orbital period around its axis
Orbital period
Surface day temp
(ºC)
Density (g/cm3)
Satellites
Mercury 58 4.878 0.4 59 days 88 days 167 5,43 0
Venus 108
12.104 0.95 -243 days 225 days 464 5,24 0
Earth 149,6
12.756 1 23, 93 h 365,2 days
15 5,52 1
Mars 228 6.794 0.5 24h 37min 687 days -65 3,04 2
Jupiter 778
142.800 11 9h 50min 30s 12 years -110 1,32 +63
Saturn 1 427
120.000 9.5 10h 14min 29,5 years
-140 0,69 +56
Uranus 2 870
51.800 4 16h 18min 84 years -195 1,27 27
Neptune 4 497
49.500 4 15h 48min 164 years
-200 1,77 13
4
+Asteroid Belt
Ceres (480km): it was the first asteroid to be
seen. Now it’s a dwarf planet.
Mathilde (52km)
Eros (13x13x33km)
5
+Constellations & Stellar Clusters
n Constellation: n A group of stars in a
recognizable pattern that appear to be near each other in space.
n Example ORION. The stars make a pattern in the sky without being next to each other.
As opposed to:
n Stellar cluster: n A group of star that are
physically near each other.
Orion
6
+Motion of the stars over a day
n Pattern of stars remains the same from one night to the next
n They appear to rotate about the Northern star over the period of one night
7
+Motion of the star over a year
n The constellations have the same relative positions to each other.
n Each night, over a period of a year, we don’t see the same portion of the night sky at the same time.
n The location of the Northern star changes slightly night after night.
n After a whole year, we see again the same sky at the same time of the night.
n The sun rises in the East, and set in the West. What changes over the period of a year is the size of the arc the Sun draws throughout the day.
8
+The light year
n One light year (ly) = distance traveled by light in one year
Show that a light-year is approximately equal to 9.5 x 1015 m.
n One parsec (pc) = 3.26 ly
n Average distance between stars is 1 pc.
n Average distance between galaxies from a hundred kpc to a few Mpc
9
+Order of magnitude for light-year distances
10
Earth – Moon 3.8 x 108 m 1.28 light-seconds
Earth – Sun 1.5 x 1011 m 8.3 light-minutes
Earth – Pluto 6 x 1012 m 4.3 light-days
Closest Star: Alpha Centauri
4.3 light-years
Our Galaxy’s diameter 100,000 ly
Our Galaxy’s thickness 2,000 ly
+Galaxies
n A galaxy is a collection of a very large number of stars mutually attracting each other through the gravitational force and staying together. The number of stars varies between a few million and hundreds of billions. There approximately 100 billion galaxies in the observable universe.
n There are three types of galaxies: n Spiral (Milky Way)
n Elliptical (M49)
n Irregular (Magellanic Clouds)
11
+The Universe n Stars are grouped in clusters. And clusters of stars in
Galaxies – About 100 Billions stars in a Galaxy.
n There are more than 100 Billions Galaxies, some are grouped in clusters of galaxies or super clusters of galaxies.
n The space between galaxies and stars appears to be empty
n Everything together is known as the UNIVERSE.
1.5x1026m (15 billion ly) The Visible Universe
5x1022m (5 million ly) Local group of Galaxies
1021 m (100 000 ly) Our Galaxy
1013 m (0.001 ly) Our Solar System
12
+Examples
1. Take the density of interstellar space to be one atom of H per cm3 of space.
a) How much mass is there in a volume of interstellar space equal to the volume of the Earth?
b) Give an order of magnitude.
2. The Local Group is a cluster of some 20 galaxies including our own Milky Way and the Andromeda galaxy. It extends over a distance of about 1 Mpc.
n Estimate the average distance between the galaxies of the Local Group.
3. The Milky Way galaxy has about 2 x 1011 stars. n Assuming an average mass equal to that of the sun estimate the mass of
the Milky Way.
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+
1. The observable universe contains some 100 billion galaxies.
n Assuming an average mass comparable to that of the Milky Way, estimate the mass of the observable universe.
2. Our own galaxy contains approximately 2 x 1011 stars and its diameter is approximately 105 light-years in diameter.
n Compare, in terms of order of magnitude, the relative distances between stars within galaxies and between galaxies
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?
+
3. Describe, using your own words and diagrams, the apparent motion of the stars over a period of a night and over a period of a year.
4. Explain the apparent motion of the stars over a period of a night and over a period of a year in terms of the rotation and revolution of the Earth.
? 15
+
Stellar Radiation & Stellar Types
Energy Source
n State that fusion is the main energy source of stars
n Explain that, in a stable star (such as the sun), there is an equilibrium between radiation, pressure and gravitational pressure.
Luminosity
n Define the luminosity of a star
n Define apparent brightness and state how it is measured.
Objectives
+But what exactly is a star?
n A star is a ball of matter at high enough temperature and pressure to be able to have on-going fusion reactions.
n In one sentence: Stars are gigantic manufactures of elements.
n And how are stars born? n Stars come from interstellar matter coming together due to the force
of gravity n As matter gets closer together, the loss of potential energy from
interstellar matter coming together transforms into kinetic energy. n This in turn attracts more matter, and generates more kinetic energy
and therefore more temperature and pressure. n This happens until a point where there is enough temperature and
pressure for the fusion process to start – H to He, then to C, O, Ca…and eventually Fe – depending on the star.
n The fusion process releases so much energy that the pressure created prevents the star from collapsing due to gravitational pressure.
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+Energy Source of Stars & Stability
Very high temperatures are needed in order to begin the fusion process: usually 107 K
Nuclear Fusion of Hydrogen to Helium
The source of energy is nuclear fusion H è He + release of energy
The sequence of fusion is called: “proton-proton cycle”
18
Gravity
Pressure
n The mass of a star determines the pressure in its core
n Gravity pulls outer layers in
n Gas Pressure pushes them out
n The more mass the star has, the higher the central pressure!
n The core supports the weight of the whole star!
+A star is a big ball of gas, with fusion at its center, held together by gravity!
There are some small variations between stars, but overall they are all based on the same principle
Massive Star
Sun-like Star
Low-mass Star
19
+The most important thing about a star?
Mass
• The mass of a normal star almost completely determines its LUMINOSITY and TEMPERATURE!
Note: “normal” star means a star that’s fusing Hydrogen into Helium in its center (we say “hydrogen burning”).
Mass Pressure & Temperature
Rate of Fusion LUMINOSITY
20
+LUMINOSITY of a star
n is an intrinsic property… it doesn’t depend on distance!
How much ENERGY it gives off per second
The energy the Sun emits is generated by the fusion in its core…
For Example: if this light bulb’s luminosity is 60W, no matter where it is, or where we view it from, it will always be a 60W light bulb! J
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+Luminosity (L)
n The Luminosity of a star is the energy that it releases per second. Unit: WATTS
n Sun has a luminosity of 3.90x1026 W n often written as L¤ n it emits 3.90x1026 joules per second in all directions
n The energy that arrives at the Earth is only a very small amount when compared will the total energy released by the Sun.
n Luminosity depends on n Surface temperature of the star n Surface area of the star
22
+Apparent Brightness (b)
n When the light from the Sun reaches the Earth it will be spread out over a sphere of radius d. The energy received per unit time per unit area is b, where:
n b is called the apparent brightness of the star, the Unit is Wm-2
d
24 dLbπ
=
23
+Example 1
1. The Sun is a distance d=1.5 x 1011 m from the Earth. Estimate how much energy falls on a surface of 1m2 in a year. L¤= 3.90x1026 W.
2. The apparent brightness of a star is 6.4x10-8 Wm-2. If the distance is 15 ly, what is its absolute luminosity?
24
+Example 2
1. The radius of a star A is 3 times that of star B and its temperature is double that of B. They have the same apparent brightness when viewed from Earth.
a) Find the ratio of the luminosity of A to that of B.
b) Calculate the ratio of their distances.
2. A star has half the sun’s surface temperature and 400 times its luminosity. How many times bigger is it?
25
+
n Briefly describe the nature of a star
n Distinguish between a constellation and a galaxy.
? 26
+
Stellar Radiation & Stellar Types
Wien’s Law and the Stefan-Boltzmann Law
n Apply the Stefan-Boltzmann Law to compare the luminosity of different stars
n State Wien’s Law and apply it to explain the connection between the color and temperature of stars.
Stellar Spectra
n Explain how atomic spectra maybe used to deduce chemical and physical data for stars.
n Describe the overall classification system of spectral classes.
Objectives
+Black-Body Radiation
n When heated, a low-pressure gas will emit a discrete spectrum
n When heated, a solid will emit a continuous spectrum
n Black-body radiation: radiation emitted by a “perfect” emitter n This means that an object that acts as a black body will perfectly
absorb all incoming radiation and not reflect any then perfectly radiate it.
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+Black-Body Radiation
n Not all wavelengths of light will be emitted with equal intensity.
n Wavelength with highest intensity is related to temperature.
n As body heats up, wavelength at which most power is radiated decreases.
Wien’s Displacement Law
€
λoT = 2.90 ×10−3mK
29
+Black-Body Radiation
n Stefan-Boltzmann Law: relates intensity of radiation and power to temperature of body
n Why is this important for stars? n The spectrum of stars is similar to the spectrum emitted by a black body.
n We can therefore use Wien Law to find the temperature of a star from its spectrum.
n If we know its temperature and its luminosity then its radius can be found from Stephan-Boltzmann law.
Stephan Boltzmann Law
€
I =σT 4
P =σAT 4
€
where σ = Stephan − Boltzmann constant
σ = 5.67 ×10−8 Wm−2K −4[ ]
30
+Stellar Spectra
n The radiation from stars is not a perfect continuous spectrum
n There are particular wavelengths that are missing
n The missing wavelength correspond to the absorption spectrum of a number of elements
n The surface temperature of the star is found by measuring the wavelength at which most of the radiation is emitted
wavelength
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+Stellar Spectra
n Radial velocity: If a star moves away or towards us, its spectral line will show a Doppler shift. n Red shift: the star moves away
n Blue shift: the star comes towards us
n Rotation: if a star rotates, than part of the star is moving toward the observer and part away from the observer.
n Light from different parts of the star will again show Doppler shift => speed can be calculated.
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+Stellar Spectra
Spectral Class Color Temperature
O Blue 25000 - 50000 K
B Blue-white 12000 - 25000 K
A White 7500 - 12000 K
F Yellow-white 6000 - 7500 K
G Yellow 4500 - 6000 K
K Yellow-red 3000 - 4500 K
M Red 2000 - 3000 K
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Oh Be A Fun Guy Kiss Me! Oh Be A Fun Girl Kiss Me!
+Examples
1. The sun has an approximate black body spectrum with most of the energy radiated at a wavelength of 5.0 x 10-7 m. Find the surface temperature of the sun.
2. The sun (radius r=7.0 x 108 m) radiates a total power of 3.9 x 1026 W. Find its surface temperature.
34
+
Stellar Radiation & Stellar Types
Types of Star n Describe different types of stars
n Discuss the characteristics of spectroscopic and eclipsing binary stars
The Hertzprung-Russel diagram
n Identify the general regions of star types on a Hertzsprung-Russel (HR) diagram.
Objectives
+Types of Stars
n Very large, cool stars with a reddish appearance. All main sequence stars evolve into a red giant. In red giants there are nuclear reactions involving the fusion of helium into heavier elements.
Red Giants
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+Types of Stars
n A red giant at the end stage of its evolution will throw off mass and leave behind a very small size (the size of the Earth), very dense star in which no nuclear reactions take place. It is very hot but its small size gives it a very small luminosity.
n As white dwarfs have mass comparable to the Sun's and their volume is comparable to the Earth's, they are very dense.
White dwarfs
A comparison between the white dwarf IK Pegasi B (center), its A-class companion IK Pegasi A (left) and the Sun (right). This white dwarf has a surface temperature of 35,500 K.
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+Types of Stars
n A neutron star is formed from the collapsed remnant of a massive star (usually supergiant stars – very big red stars).
n Models predict that neutron stars consist mostly of neutrons, hence the name. Such stars are very hot.
n A neutron star is one of the few possible conclusions of stellar evolution.
Neutron Stars
The first direct observation of a neutron star in visible light. The neutron star being RX J185635-3754.
38
+Types of Stars
n A supernova is a stellar explosion that creates an extremely luminous object.
n The explosion expels much or all of a star's material at a velocity of up to a tenth the speed of light, driving a shock wave into the surrounding interstellar medium.
n This shock wave sweeps up an expanding shell of gas and dust called a supernova remnant
n A supernova causes a burst of radiation that may briefly outshine its entire host galaxy before fading from view over several weeks or months. During this short interval, a supernova can radiate as much energy as the Sun would emit over 10 billion years.
Supernovae
Supernova remnant N 63A lies within a clumpy region of gas and
dust in the Large Magellanic Cloud. NASA image.
39
+Types of Stars
n A black hole is a region of space in which the gravitational field is so powerful that nothing can escape after having fallen past the event horizon.
n The name comes from the fact that even electromagnetic radiation is unable to escape, rendering the interior invisible.
n However, black holes can be detected if they interact with matter outside the event horizon, for example by drawing in gas from an orbiting star.
n The gas spirals inward, heating up to very high temperatures and emitting large amounts of radiation in the process.
Black Holes
40
+Types of Stars
n Cepheid variables: n Stars of variable luminosity. The luminosity increases sharply
and falls of gently with a well-defined period. n The period is related to the absolute luminosity of the star
and so can be used to estimate the distance to the star.
n A Cepheid is usually a giant yellow star, pulsing regularly by expanding and contracting, resulting in a regular oscillation of its luminosity. The luminosity of Cepheid stars range from 103 to 104 times that of the Sun.
n Binary Stars n Stellar system consisting of two stars orbiting around their
centre of mass. For each star, the other is its companion star. A large percentage of stars are part of systems with at least two stars.
n Binary star systems are very important in astrophysics, because observing their mutual orbits allows their mass to be determined. The masses of many single stars can then be determined by extrapolations made from the observation of binaries.
Hubble image of the Sirius binary system, in which Sirius B can be
clearly distinguished (lower left).
41
+Three classes of binary stars
n 1 – Visual binaries n They appear as two separate stars when viewed through a
telescope.
n They are in orbit around the center of mass of the 2 stars
n Common period of rotation and distance between the stars can be used to find their masses.
n 2 – Eclipsing binaries: n When the plane of the orbit of the stars is such that the light from
one of the stars in the binary may be blocked by the other => ECLIPSE of the star
42
+Eclipsing Binaries
A B C D E
App
. brig
htne
ss
A B C D E
Orbital period
Time/days 4 6 8
Light curve of AR Cassiopeia
43
+3 - Spectroscopic binaries
n Detected by analyzing the light from one or both stars of the binary.
n Observing if there is a Doppler effect: n Blue shift as the star approaches Earth
n Red shift as the star moves away from Earth
n Doppler effect: n λo the wavelength of a spectral line
n λ the wavelength received by Earth
n If the speed of the source << speed of light, the shift is defined as:
λ − λo
λ≅ cv
44
+Hertzsprung-Russel diagram
n Astronomers realized early that there is a correlation between Luminosity and Star Temperature.
n HR Diagram: n luminosity/temperature graph
n Vertical: luminosity relative to the sun’s luminosity (Sun = 1)
n Horizontal: temperature from high to low
n The stars are not randomly distributed
45
+ The Hertzsprung-Russel diagram 46
+
Stellar Distances
Parallax Method n Define the parsec n Describe the stellar parallax method
of determining the distance to a star n Explain why the method of stellar
parallax is limited to measuring stellar distances less than several hundred parsecs.
n Solve problems involving stellar parallax
Absolute & apparent magnitudes n Describe the apparent magnitude
scale n Define absolute magnitude n Solve problems involving apparent
magnitude, absolute magnitude and distance
n Solve problems involving apparent brightness and apparent magnitude
Objectives
+Parallax Method n If an object is viewed from 2 different positions, it appears different, relative
to a fixed background.
n If we measure the position of a star and repeat the measure some times later, the two positions will be different, relative to a background of stars.
n This method is accurate for angles > 1” (1” = 1/3600° = 1 arc second)
Earth July
January
Sun Star
Background of distant stars
p
d
R = 1 AU
€
p = parallax angle
p is small angle ⇒ tan p = p⇒ d =Rp
48
+Definition of a PARSEC
n Definition of a parsec (parallel angle of 1 second)
n 1 parsec = distance to a star whose parallax is 1 arc second
n Ex: Calculate the value of 1 parsec in meters (1 parsec = 3.09 x 1016m)
n If the parallax of the star is known to be “p” arc seconds then the distance “d” is in parsecs and:
R = 1 AU 1”
1 parsec
€
d in parsecs( ) =1
p in arc seconds( )
49
+Parallax Method
1. The Star Proxima Centauri’s has a parallax p=0.762”, calculate its distance in parsec, in light years and in meters.
2. The star Alpha Eridani (Achemar) is 1.32 x 1018 m away. Calculate its parallax angle.
Examples
50
+Classifying stars
n Usually, what we know is how bright the star looks to us here on Earth…
n A magnitude scale was defined by Hypparchus and Ptolemy about 2000 years ago. n 6 categories of stars
n The brightest are of magnitude m=1
n The faintest are of magnitude m=6
n The 6th magnitude was 100 times fainter than the 1st magnitude
n So 1 magnitude difference corresponds to 1001/5=2.512 factor
n The magnitude scale has been extended to numbers bigger than 6 to include faint stars and negative numbers to include very bright stars.
51
+ The apparent magnitude
n Given a star of apparent brightness b, we assign to the star an apparent magnitude m defined by:
n The reference value bo = 2.52 x 10-8 Wm-2
Human eye (m < 6), Simple binoculars (m < 9), Largest telescope (m < 27)
Close star (small luminosity) distant star
(high luminosity)
bb o
= 2.51 - m
€
m = −2.5logbbo
52
+Some Magnitudes
n Magnitudes can even be negative for really bright stuff!
n Apparent magnitude is useful for comparing apparent brightness of two stars b1/b2.
n However, knowing how bright a star looks doesn’t really tell us anything about the star itself!
Object Apparent Magnitude
The Sun -26.8
Full Moon -12.6
Venus (at brightest) -4.4
Sirius (brightest star) -1.5
Faintest naked eye stars 6 to 7
Faintest star visible from Earth telescopes
~25
53
+Apparent Magnitude
1. A star has a brightness of 6.43 x 10-9 Wm-2, find its apparent magnitude.
2. Compare the apparent brightness of Sirius and Proxima Centauri. Sirius has an apparent magnitude m=-1.5, and Proxima Centauri has an apparent magnitude m=0.3.
Examples
54
+Absolute magnitude n 2 stars of equal apparent magnitudes are not necessarily equally
bright!
n Absolute magnitude M:
n Measure of the magnitude of the star when placed at 10 pc from Earth
n Apparent and absolute magnitudes are related by:
1
2
Earth
True distance of star, d Apparent magnitude m
10 pc Absolute magnitude M
b 1
b 2= 2.51 M - m m −M = 5 log d
10pc⎛⎝⎜
⎞⎠⎟
55
+Absolute Magnitude
1. Calculate the absolute magnitude of a star whose distance is 25.0 ly and whose apparent magnitude is m=3.45.
2. Calculate the distance to Sirius and to Alpha Centauri in ly and pc.
Examples
Star m M
Sirius -1.43 1.4
Alpha Centauri -0.27 4.7
56
+Exercise #1
n The star α-Orionis (Betelgeuse) has an apparent magnitude of m=0.45 and an absolute magnitude of M=-5.14.
n Betelgeuse is the red star at the left shoulder of Orion (seen from Earth) and is a red supergiant. When viewed with the naked eye, it has a clear orange-red hue.
n Find the distance to Betelgeuse.
57
Apparent and Absolute Magnitude
+Exercise #2
n Α-Lyrae (Vega), with an absolute magnitude of 0.58, is at a distance of 7.76 parsec.
n Vega is the brightest star in the constellation of Lyra (the Lyre) and the upper right star in the Summer Triangle.
n Calculate Vega’s apparent magnitude.
58
Apparent and Absolute Magnitude
+Exercise #3
n Α-Cygni (Deneb) is the upper left star in the Summer Triangle and the main star in the Swan. Its apparent magnitude is 1.25 and the distance is 993 pc.
n Calculate the absolute magnitude. What does this tell you about the nature of Deneb?
59
Apparent and Absolute Magnitude
+Exercise #4
n The star α-Canis Majoris (Sirius) is the brightest star in the sky. It is at a distance of 2.64 pc and its apparent magnitude is -1.44.
n Calculate the absolute magnitude of Sirius. If you compare with the absolute magnitude of the three other stars what is your judgment of Sirius’ physical or intrinsic brightness?
60
Apparent and Absolute Magnitude
+Exercise #5
1. If the stars Vega, Sirius, Betelgeuse and Deneb where located 10 pc from the Earth (in the same region of the sky), what would we see?
2. The absolute magnitude, M, is defined as the apparent magnitude a star would have if it were placed 10 pc from the Sun. But wouldn’t it be more correct to measure this distance from the Earth? Why doesn’t it make a difference whether we measure this distance from the Sun or from the Earth?
61
Apparent and Absolute Magnitude
+
Stellar Distances
Spectroscopic Parallax n State that the luminosity of a star may
be estimated from its spectrum. n Explain how stellar distance may be
determined using apparent brightness and luminosity
n State that the method of spectroscopic parallax is limited to measuring stellar distances less than about 100 Mpc
Cepheid Variables n Outline the nature of a Cepheid
variable. n State the relationship between period
and absolute magnitude for Cepheid variables
n Explain how Cepheid variables may be used as “standard candles”
n Determine the distance to a Cepheid variable using the luminosity-period relationship.
Objectives
+Spectroscopic parallax
n The Luminosity of a star can be found using an absorption spectrum.
n Using its spectrum a star can be placed in a spectral class.
n Also the star’s surface temperature can determined from its spectrum (Wien’s law)
n Using the H-R diagram and knowing both temperature and spectral class of the star, its luminosity can be found.
€
b =L4πr2
d = L4πb
63
+Exercise #1
1. State an alternative unit for the axes x and y.
2. Using the HR diagram, complete this table:
3. Explain using the HR diagram how astronomers can deduce that star B is larger than star A.
64
This question is about the nature of certain stars on the HR diagram and determining stellar distances.
Star Type of star
A
B
C
D
+Exercise #1
n Using the following data and information from the HR diagram, show that star B is at a distance of about 700 pc from Earth. n Apparent brightness of the sun: 1.4 x 103 Wm-2
n Apparent brightness od star B: 7.0 x 10-8 Wm-2
n Mean distance of the Sun from Earth: 1 AU
n 1 pc = 2.1 x 105 AU
n Explain why the distance of star B from Earth cannot be determined by the method of stellar parallax.
65
Stellar distances
+Cepheid Variables
n Cepheid are stars whose luminosity varies between 2 values periodically (days or months)
n At the beginning of the 20th century, Henrietta Leavitt made the discovery of a relationship between Absolute luminosity and Periods of Cepheid.
66
+Exercise #2
1. Define a) Luminosity
b) Apparent brightness
2. State the mechanism for the variation in the luminosity of the Cepheid Variable
The variation with time t, of the apparent brightness b, of a Cepheid Variable is shown here:
67
Cepheid Variables
+Exercise #1
3. Assuming that the surface temperature of the star stays constant, deduce whether the star has a larger radius after two days or after six days.
4. Explain the importance of Cepheid Variables estimating distances of galaxies.
5. The maximum luminosity of this Cepheid Variable is 7.2 x 1029W. Us data from the graph to determine the distance of the Cepheid Variable.
6. Cepheids are sometimes referred to as “standard candles”. Explain what is meant by that.
68
Cepheid Variables
+Stellar distances
Parallax Spectroscopic parallax Cepheid variables
100 pc 10,000 pc 15 Mpc
69
+Spectroscopic & Cepheid Variables
1. A main sequence star emits most of its energy at a wavelength of 2.4x10-7m. Its apparent brightness is measured to be 4.3x10-9 Wm-2. How far is the star?
2. Use the Cepheid variables graph to calculate the distance to a Cepheid variable star whose period is 10 days and whose peak apparent brightness is 3.45 x 10-15 Wm-2.
Examples
70
+
Cosmology
Olber’s Paradox
n Describe Newton’s model of the universe
n Explain Olber’s Paradox
The Big Bang Model
n Suggest that the red-shift of light from galaxies indicates that the universe is expanding
n Describe both space and time as originating with the Big Bang
n Describe the discovery of cosmic microwave background (CMB) radiation by Penzias and Wilson
n Explain how cosmic radiation in the microwave region is consistent with the Big Bang model
n Suggest how the Big Bang model provides a resolution to Olber’s paradox.
Objectives
+Newton’s Universe vs. Olber’s Paradox
n Newton’s Universe: n The universe is infinite, uniform, static, and therefore has no
beginning
n Olber’s Paradox n If the Universe is eternal and infinite and if it has an infinite
number of stars, then the night sky should be bright.
n Very distant stars contribute with very little light to an observer on Earth; but there are many of them. So if there is an infinite number of stars, each one emitting a certain amount of light, the total energy received must be infinite, making the night sky infinitely bright, which is not.
Why is the night sky dark?
72
+Why is the night sky dark?
n n: the density of stars
n The number of stars in a shell of thickness d at a distance r from an observer is:
n At a distance r from a star the apparent brightness is defined as:
n Total energy / second / area from all stars is:
€
4πr2nd
€
b =L4πr2
€
L4πr2
4πr2nd = Lnd
73
+The Big Bang Model
n Why is Doppler effect so important?
n In 1920’s Edwin Hubble and Milton Humans on realised that the spectra of distant galaxies showed a red shift (Radiation is red shifted when its wavelength increases, and is blue shifted when its wavelength decreases), which means that they are moving away from Earth. So, if galaxies are moving away from each other then it they may have been much closer together in the past
n Matter was concentrated in one point and some “explosion” may have thrown the matter apart.
Part 1 – The Doppler Effect
74
+The Big Bang Model
n In 1960 two physicists, Dicke and Peebles, realising that there was more He than could be produced by stars, proposed that in the beginning of the Universe it was at a sufficiently high temperature to produce He by fusion.
n In this process a great amount of highly energetic radiation was produced. However, as the Universe expanded and cooled, the energy of that radiation decreased as well. It was predicted that the actual photons would have an maximum λ corresponding to a black body spectrum of 3K.
n So, we would be looking for microwave radiation.
n Shortly after this prediction, Penzias and Wilson were working with a microwave aerial and found that no matter in what direction they pointed the aerial it picked up a steady, continuous background radiation in the microwave region (T=3K).
Part 2 – Cosmic Microwave Background Radiation
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+The Big Bang Model
n The Big Bang Model is the accepted theory for the origin and evolution of our universe.
n It postulates that 12 to 14 billion years ago, the portion of the universe we can see today was only a few millimetres across.
n It has expanded from this hot dense state into the vast and much cooler cosmos we currently inhabit.
n We can see remnants of this hot dense matter as the now very cold CMB radiation.
n How does this Model resolve Olber’s paradox? n In a finite, expanding universe, the radiation received by an observer is small and
finite:
n There is a finite number of stars and each has a finite lifetime
n Because of the finite age of the universe, light of far away stars have not yet had time to reach us.
n The radiation energy is red shifted => contains less energy.
Part 3 – Explanation
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+Exercise
n Describe what is meant by Cosmic Background Radiation.
n Explain how cosmic background radiation is evidence in support of the Big Bang model of the universe.
n State one piece of evidence in support of the Big Bang model.
n A student makes the statement that “as a result of the Big Bang, the universe is expanding into a vacuum”. Discuss whether the student’s statement is correct.
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The Big Bang model
+
Cosmology
The development of the universe
n Distinguish between the terms open, flat, and closed when used to describe the development of the universe.
n Define the term critical density by reference to a flat model of the development of the universe.
n Discuss problems associated with determining the density of the universe.
n State that the current scientific evidence suggests that the universe is open.
n Discuss an example of the international nature of recent astrophysics research
n Evaluate arguments related to investing significant resources into researching the nature of the universe.
Objectives
+Future of the universe
n The universe is expanding at the moment, however…
n What is it going to do in the future?
n How is the rate of expansion of the universe changing?
n Open Universe: continues to expand forever. Low density of the universe.
n Closed Universe: Stops expanding and collapses back on itself. Very high density of the universe.
n Flat Universe: Between open and closed. The universe expands and a slowing down rate but would take an infinite time to stop.
n Critical Density: the density that would create a flat universe.
Closed
Flat
Open
Size
of o
bse
rvab
le u
nive
rse
Now
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+Future of the universe
n Density of the universe not easy to measure or evaluate
n The estimate of the mass of galaxies based on the number of stars that make it does not give a big enough number compared to numbers needed according to the motion a heavenly objects.
n We think that we can see a maximum of 10% of the matter that exist.
n Much of the mass of the universe must be Dark Matter (matter not radiating sufficiently for us to detect it)
Currently the scientific evidence suggests that the universe is open.
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+Exercise
n The sketch bellow shows three possible ways in which the size of the universe might change with time.
n Depending on which way the size of the universe changes with time, the universe is referred to either being open or flat or closed n Identify each type of universe on
the graph
n Complete the table to show how the mean density ρof each type of universe is related to the critical density ρo .
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About the possible evolution of the universe
Size
of o
bse
rvab
le u
nive
rse
Type of universe Relation between ρ and ρo
Open
Flat
Closed
+Bibliography
n Bertrand, Yann Arthus. «Photos» 22 01 2010 http://www.yannarthusbertrand.org/index_new.php.
n Kirk, Tim. Physics for the IB diploma. Oxford: Oxford University Press, 2007.
n Tim Kirk, Neil Hodgson. Physics Course Companion. Oxford: Oxford University Press, 2007.
n Tsokos, K.A. Physics for the IB diploma. Cambridge: Cambridge University Press, 2008.
n ESA. «The ESA/ESO Astronomy Exercise Series, Astronomical Toolkit.» ESA Portal. 2009 http://www.esa.int/esaCP/index.html
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