E.6.4 to E.6.7

E.6.4 State Hubble's law.
The recession velocity is proportional to distance.

E.6.5 Discuss the limitations of Hubble's law.

If the galaxy is at the distance x then Hubble's law predicts that the recessional velocity of the galaxy will be H.x. If it has been travelling at this constant speed since the beginning of the Universe, then the time that has elapsed can be calculated from the method shown in E.6.7. But this is the UPPER LIMIT OF THE AGE OF THE UNIVERSE. However, the gravitational attraction between galaxies means that the speed of recession decreases all the time. The fact that we assume that the recession velocity is constant, is therefore a limitation of Hubble's law. Also, the data points in the graph below are scattered around the trend line thus showing that there are quite big random errors in the measurements. Furthermore, there a few data points near the origin because it is difficult to measure the red shift (as it is really small) of galaxies that are close to us and moving away. This is therefore another limitation of Hubble's law.

The more data points you can get, the greater the accuracy of Hubble's law.


E.6.6 Explain how the Hubble constant may be determined.




As the images above show, the Hubble constant is the gradient of a graph that plots the recession velocity in km/s and distance in Mpc.


E.6.7 Explain how the Hubble constant may be used to determine the age of the universe.


The Big Bang started with a point of singularity - all parts of the universe were in the same place. So if we know how fast any two parts are moving apart and how far apart they are now, we can calculate the age of the universe.

To calculate the age of the universe in seconds, we first need to convert the distance into km.

This calculation assumes that the velocity is constant. However, gravitational attraction will slow galaxies down; the recessional velocity measured is therefore smaller than it was. This makes our value too large so according to these measurements, the maximum age of the the universe can't be more than 1.3 x 10^10 years.

E.6.8 Solve problems involving Hubble's law.


Resources: IB Heinemenn HL Physics by Chris Hamper (http://www.rcnuwc.org/ibphysics/) and IB Physics  Study Guide by Tim Kirk.

E.6.1 to E.6.3

E.6.1 Describe the distribution of galaxies in the universe.


Define the term galactic cluster- give an example
A cluster of roughly a few hundred young stars in a loose distribution. Also called an open cluster.
www.encyclopedia.com/doc/1G2-2830101489.html





Example: Seyfert Sextet
Source: http://upload.wikimedia.org/wikipedia/commons/2/20/Seyfert_Sextet_full.jpg

Define the term galactic supercluster- give an example
Superclusters are large groups of smaller galaxy groups and clusters and are among the largest structures of the cosmos.
en.wikipedia.org/wiki/Galactic_supercluster





Example: Virgo Supercluster
Source: http://www.fas.org/irp/imint/docs/rst/Sect20/A2a.html


E.6.2 Explain the red-shift of light from distant galaxies.

http://www.youtube.com/watch?v=BIW7EzHmndY&feature=related

http://www.youtube.com/watch?v=e6G2Z6iD-9M&feature=related

Why are the galaxies the furthest away red shifted the most?

Because the universe is expanding (the finding that the galaxies furthest away are red shifted the most implied the expansion of the universe).
"It is as if there was a big explosion, the outer parts flew off fastest and are still travelling outwards with the greatest speed and we are somewhere in the middle" Heinemenn HL Physics Course Companion


Video notes related to question:

• Relationship between the distance of the galaxy and how fast it appears to be moving is known as Hubble's Law.
• As the universe expands it "drags" the galaxies along with it.
• Overall motion of galaxies away from us is due to the expansion of the universe.
• As the universe expands, the galaxies within it do not.
• Small scale --> gravity can hold things together. Large scale--> expansion takes over, causing everything to move apart.
• Astronomers are finding that the universe is expanding at an accelerating rate.
• Where is the centre of the universe? Either nowhere is the centre of our universe or everywhere is the centre of the universe.

Why is it the expansion of space itself rather than the motion of the galaxy that results in the relative velocities of galaxies?
Because on the large scale, expansion is causing everything to move apart.We know that its the expansion of space and not just the motion of the galaxy because every galaxy in every direction that we can observe is moving away from us. This does not mean that we're the centre of the universe however, observed from any point in the universe, one would observe that all galaxies are moving away. Space itself is expanding.


Below is an imagine from Tim Kirk's IB Physics Study Guide showing how, in this model, the redshift of light can be thought of as the expansion of wavelength due to the 'stretching' of space.

E.6.3 Solve problems involving red-shift and the recession speed of galaxies.

E 5.5 to 5.8

Click to see spreadsheet.

5.1 to 5.5 Stellar Processes and Stellar Evolution

5.1 Describe the conditions that initiate fusion in a star.

• Stars are formed when huge clouds of gas and dust are compressed. 
• Something needs to cause the clouds to be compressed such as an exploding supernova or a collision between two dust clouds.
• Because of this the particles become closer and the gravitational force becomes sufficient to start pulling the particles together.
• Gas atoms pulled together by gravitational force --> gain KE --> temperature increases. Increase in temperature causes an outward pressure that pushes against the gravitational attraction.
• However, as atoms get closer, the gravitational force increases so the gas continues to collapse and get hot at an ever-increasing rate.
• PROTOSTAR: Gives out light due to it's high temperature but isn't visible because of the dust clouds (like a motorcycle bike's head lamp in the fog). Formed because as the could collapses, the centre of the dense core rapidly contracts resulting in HIGH TEMPERATURE AND HIGH PRESSURE.
• PRE-MAIN SEQUENCE STAR: After around 10^5 years of mass increase, the radiation from the protostar blows the dust cloud away and the star stabilises.
• The core continues to contract and heat up until the atoms are moving fast enough for FUSION to take place. Since hydrogen is so abundant in the universe, it follows that this gas is mainly hydrogen so the fusion that takes place is the fusion of hydrogren nuclei:
• Once fusion starts, the increase in temperature causes greater pressure, balancing the inward force of gravity. THE STAR STOPS CONTRACTING AND BECOMES A MAIN SEQUENCE STAR.

5.2 State the effect of a star's mass on the end product of a nuclear fusion.

Low mass star ==> HELIUM SYNTHESIS

High mass star ==> IRON (FE- greatest binding energy per nucleon) SYNTHESIS

• As star is fusing hydrogen into helium, at some point the hydrogren will become rare
• Fusion reactions will happen less often
• Star will be no longer in equilibrium and the gravitational force will cause the core to collapse
• Collapse increases the temperature of the core
• Helium fusion now possible
• Net result is for star to increase massively in size
• Expansion = outer layers become cooler= RED GIANT
• If it has a sufficient mass, a red giant can continue to fuse higher and higher elements and the process of nucelosynthesis will continue
• This process of nucleosynthesis comes to an end with THE FUSION OF IRON, iron has the highest binding energy per nucleon so the fusion of iron will need to TAKE IN energy, not release energy, therefore star will no longer shine.

5.3 Outline the changes that take place in nucleosynthesis when a star leaves the main sequence and becomes a red giant 

Students need to know the outline of the process of helium fusion and silicon fusion to form iron

5.4 Apply the mass-luminosity relation.

The luminosity of massive main sequence stars is greater than stars of small mass; this enables us to know where the different stars join the main sequence line. The equation relating mass, m and luminosity, L is:

E 4.8 to E 4.14

E.4.8 Distinguish between the terms open, flat and closed universe when used to describe the development of the universe.

Open universe: One that continues to expand. Gravity slows the rate of expansion but is not strong enough to stop it.

Closed universe: One that will eventually collapse back on itself. This would result in a BIG CRUNCH which is the reverse of the Big Bang.

Flat universe: The force of gravity keeps slowing down the expansion but theoretically, it'll take an infinite amount of time for it to come to rest.

E.4.9 Define the term critical density by reference to the flat model of the development of the universe.

Critical density: The theoretical value of density that would create a flat universe. The value of critical density is estimated to be 4.5 x 10^-27kgm^-3 but is not certain.

15) a) Actual density < Critical density: Open universe

Actual density > Critical density: Close universe

Actual density = Critical density: Flat universe

b) i) 

= 3 x ((2.7 x 10^-18)^2)/ (8 xπx 6.67x10^-11)

=1.3 x 10^-26

ii) Determining equivalent no. of nucleons per unit volume:

Density = mass / volume

1.3 x 10^-26= 


E.4.10 Discuss how the density of the universe determines the development of the universe
As stated above

Actual density < Critical density: Open universe

Actual density > Critical density: Close universe

Actual density = Critical density: Flat universe

E.4.11 Discuss the problems associated with determining the density of the universe.

• Remember that research in this area is ongoing and complex
• In common with many other aspects of the universe, much about this phenomenon is not well understood.

DARK MATTER: Matter that we cannot observe because it is not radiating sufficiently for us to observe it. Much of the mass of the universe itself is dark matter, in fact, we can only see a maximum of 10% of the matter which exists in the galaxy.

Why is there so much dark matter?

MACHOs: Matter can be found in MACHOs, stands for Massive Astronomical Compact Halo Objects. There is some evidence that lots of ordinary matter does exist in these groupings. These can be thought of as low-mass 'failed' stars or high mass planets. They could even be black holes which means that they would produce little or no light.

WIMPs: There could be new particles we do not know about, WIMPs, stands for Weakly Interacting Massive Particles. Many experimenters around the world are searching for WIMPs.

So why is the density of the universe so difficult to determine?

• We can only see 10% of the universe
• Most of universe is made up of dark matter - too cool to be detected 
• Dark matter may be in the form of MACHOs or perhaps yet to be discovered WIMPs

E.4.12 State that current scientific evidence suggests that the universe is open.

In 1997, cosmologists discovered that supernova explosions in distant galaxies showed that instead of the expected deceleration in the rate of the expansion of the universe, it appeared that the expansion was in fact accelerating. So the universe appears to be more open  than expected. There must be some other previously unknown force, acting in opposition to gravity, which is pushing the universe apart. THIS NEW PHENOMENON IS CALLED 'DARK ENERGY'.

E.4.13 Discuss an example of the international nature of recent astrophysics research.


Useful web links:

• http://physics-astronomy.jhu.edu/groups/astro/ 

•  http://www.astronomynow.com/news/n1005/24seti7a/ 

E.4.13 Evaluate arguments related to investing significant sources into researching the nature of the universe.


Summarise the arguments for and against astrophysics research:


FOR:

Understanding the nature of the universe helps shed light on philosophical questions such as Why are we here? and Is there other intelligent life in the universe?
 Fundamental interesting area of mankind as a whole
 Has the potential of improving quality of life for human beings because of subsequent technological developments
 Our planet may become inhabitable in the future


AGAINST:
 Opportunity cost- money could be better spent on providing food, shelter and medical care to the millions of people suffering from hunger, homelessness and disease
 If money is to be allocated to research, we might be able to get better returns from medical research
 Better to fund a great deal of small diverse research than putting lots of funding into one field
 Is the information gained really worth the cost?

Sources: Heinemenn HL Physics Book by Chris Hamper and IB Physics Study Guide by Tim Kirk

E4 Cosmology

E.4.1 Describe Newton's model of the universe.

Newton assumed that the universe was INFINITE IN SPACE AND TIME, UNIFORM and STATIC.
This implied that the universe was unchanging, and contained an infinite number of stars spreading out to infinity.

E.4.2 Explain Oblers' paradox.

1823- Heinrich Oblers described an apparent paradox, in that if the Netwonian model of the universe were right, it would imply that there were an infinite number of stationary stars, no matter which direction you look in the night sky, you should see a star. This meant that the sky at night should be bright, whereas it is dark = paradox.

There is also a quantitative explanation for this paradox:
Assume: Stars are evenly distributed in an infinite number of thin shells. Each star has the same luminosity L related it its apparent brightness b and the distance d by the inverse square law:

The image above shows a thin shell of stars with thickness T and distance d. The volume of this thin shell will be the thickness x surface area = 4πd^2T

If there are n stars per unit volume then the total number of stars in the shell N will be given by:

• This means that the total number of stars is directly proportional to d^2.
• If the shell is moved out to a greater distance then the shell will be dimmer according to the inverse square law: 
• Since the number of stars is DIRECTLY proportional to distance squared and the brightness is INVERSELY proportional to distance squared, the amount of light we receive from a shell does not depend on distance.
• If there were a billion stars therefore, total energy = energy received from one shell x BILLION = if the universe was infinite, then the NIGHT sky would be INFINITELY bright! 

E.4.3 Suggest that the red-shift of light from galaxies indicates that the universe is expanding.


1929 Edwin Hubble suggests that universe is expanding (not static) after making detailed observations of many observed galaxies and finding that the absorption lines in their spectra were usually shifted towards the red end of the spectrum. This, as explained by the Doppler effect, meant that these galaxies were moving away from us.


E.4.4. Describe both space and time as originating with the Big Bang.


If galaxies are moving away from eachother, then they must have been much closer in the past. Therefore, at some point of time, everything in the universe must have been located at a single point, called SINGULARITY. This is the basis for the idea that the universe began at certain time in the past - 13.7 billion years ago -with an explosion known as THE BIG BANG. 


E.4.5. Describe the discovery of cosmic microwave background (CMB) radiation by Penzias and Wilson.


CMB first observed inadvertently by Penzias and Wilson in 1965. Radiation was acting as a source of excess noise in a radio receiver they were building. Initially, the radiation was thought to be some sort of contamination and they tried to remove it by cleaning the receiver. The cosmic microwave background radiation is a kind of echo of the Big Bang still resonating around the universe. 


E.4.6 Explain how cosmic radiation in the microwave region is consistent with the Big Bang model.

Pensizas and Wilson found that the intensity of the radiation that they received, from all directions, had a wavelength in the microwave region. When they plugged this wavelength into Wien's displacement law they found that it gave a temperature of 2.7 K, and we know that 2.7K is the temperature of the ambient universe so CMB radiation provides excellent support for the Big Bang model. The universe has cooled down to this temperature from its extremely hot origin.


E.4.7. Suggest how the Big Bang model provides a resolution to Oblers' paradox.

If the galaxies are moving away from us in all directions then the radiation reaching us from them will be red shifted owing to the Doppler Effect. This explains why the sky appears dark at night - the light from receding stars has been shifted into the infrared region of the electromagnetic spectrum, therefore is no longer visible to us.

Some Images and diagrams from: Heinemenn HL Physics Course Companion

Stellar Distances

3.1. Define parsec.
The distance from Earth of a star that has a parallax angle of one second. The word parsec comes from one parallax angle per second and it is usually abbreviated to pc. 

3.2 Describe the stellar parallax method of determining a distance to a star.


The parallax angle can be measured by observing changes in the star's position over a period of a year. We can use trigonometry  to work out the distance of the star from the Earth (as we know the distance between the Earth and the Sun).

The parallax angle and distance from the Earth to star are always inversely proportional.

Units:

1. The distance from the Earth to the Sun can be described as 1 Au (Astronomical Unit) = 1.5 x 10^11m.
2. Calculations show that a star with an parallax angle of 1 second of arc must be 3.08 x 10^16m away (3.26 light years or ly).
3. This distance is defined as parsec (see above) 

3.3 Explain why the method of stellar parallax is limited to measuring stellar distances less than several hundred parsecs.
The parallax angles for stars are greater distances are too small to measure accurately. The smallest -parallax angle that can currently be measured is 0.01 arc-second. The limitation on ability to measure the angle accurately therefore, limits the method in that it can only be used to measure the distances of close stars.
.
3.4 Solve problems involving stellar parallax

3.5 Describe the apparent magnitude scale.

• Apparent magnitude: Its apparent brightness viewed by an observer on Earth.
• Each magnitude is 2.51 times brighter than the next.
• The Ancient Greeks: classified stars according to brightness, 1 = the brightest, 6= the dimmest magnitude, m=1. A magnitude 1 star was first considered to be twice as bright as a magnitude 2 star, which was in turn as bright as a magnitude 3 star and so on (simple logarithmic scale). 
• A magnitude 1 star = 2.51^5 = 100 times brighter than a magnitude 6 star.
• Modern magnitude scale: Star of brightness 2.52 x 10^-8 Wm^-2 is given an apparent magnitude of 0.
• Note: Apparent brightness has unit whereas apparent magnitude is a ratio.
• Apparent magnitude of star depends on LUMINOSITY and its DISTANCE FROM EARTH.
• The brightest objects have MORE NEGATIVE values whereas the dimmest objects are MORE POSITIVE.

3.6 Define absolute magnitude

Absolute magnitude (M) the apparent magnitude of a star if it were 10 parsecs (pc) from Earth.

Most stars are further away than only 10 pc from Earth therefore they would appear brighter if they were only 10pc away. Therefore for most stars their absolute magnitudes are more negative than their apparent magnitudes (more brightness in absolute).

3.7 Solve problems involving apparent magnitude, absolute magnitude and distance.
(below)
3.8 Solve problems involving apparent magnitude and apparent brightness.

Some Images and diagrams from: Heinemenn HL Physics Course Companion, IB Physics study guide by Tim Kirk

E.2.7 to E.2.11: Astrophysics

E.2.7 Explain how atomic spectra may be used to deduce chemical and physical data for stars.


The radiation from stars is not a perfectly continuous spectrum-- some wavelengths are missing. The missing wavelengths correspond to a number of elements. The absorption takes place in the outer layers of the star therefore this means that we have a way of telling which elements are in the star (or at least in its outer layers).

A star that is moving relative to Earth will show a Doppler shift in spectrum.

Red shift: light from stars that are receding
Blue shift: light from stars which are approaching.



E.2.8 Describe the overall classification system of spectral classes.


Different stars give out different spectra of light which allows us to classify stars by their spectral class. Stars that emit the same type of spectrum are allocated to the same spectral class.

There are several main spectral classes in order of decreasing surface temperature.

O: Oh

B: Be

A: A

F: Fine

G: Guy

K: Kiss

M: Me

E.2.9 Describe the different types of star.


BINARY STARS:

• Some stars like our Sun exist by themselves, but many have a partner
• Binary stars rotate around their own common centre of mass
• By analysing the orbital period and separation, the mass of each star in the binary system can be found

RED GIANT STARS: 

• Large in size
• Red in colour
• Comparatively cool
• Later possible stages for a star
• Source of energy: Fusion of some elements other than hydrogen
• Red supergiants are even larger

WHITE DWARF STARS:

• Small in size
• White in colour
• White therefore comparatively hot
• One of the final stages for some stars
• Fusion is no longer taking place - white dwarf is just a hot remnant that is cooling down
• Eventually it will cease to give out light when it becomes cold enough
• After ceasing to give out light (cold) it is called a brown dwarf 

CEPHEID VARIABLES:

• They are stars that are a little unstable.
• Observed to have a regular variation in brightness and (therefore) luminosity
• Aforementioned variation due to oscillation in the size of the star
• Rare but useful because there is a link between period of brightness variation and average luminosity
• Astronomers can therefore use them to help calculate the distances to some galaxies

E.2.10 Discuss the characteristics of spectroscopic and eclipsing binary stars.


VISUAL BINARIES
Binary stars (e.g. Sirius A) that can be seen with the naked eye of with a telescope are called visual binaries, when they are further away from us or closer together, resolution become difficult.

SPECTROSCOPIC BINARY STARS
In some cases, stellar spectra can be used to deduce the presence of two stars - these are called spectroscopic binary stars. As stars move around their common centre of mass, one star will be approaching whilst the other is receding.

The diagram above shows a spectroscopic binary system. In the right hand diagram, Star A approaches and Star B recedes from our line of sight. Therefore the absorption lines of A are blue shifted  and the absorption lines of B are red shifted (moving away so longer wavelength, therefore red). In the left hand diagram, because the motion of the stars relative to our line of sight is opposite, the shift is reversed.

ECLIPSING BINARY STARS
Show a periodic variation in the brightness of light emitted from the star system. This occurs because during their rotation, one star periodically obscures, or eclipses, the other.

The diagram above shows an eclipsing binary system.
Position-
1 and 3: light is reaching us at a maximum, because it is arriving directly from both stars
2 and 4: reduction in brightness as the stars are eclipsing each other.

E.2.11 Identify the general regions of star types on a Hertzsprung-Russell (HR) diagram.


Discovery by Hertzsprung and Russell in 1910: For most stars, there is a relationship between surface temperature and luminosity. 

Dots on diagram below represent stars, scales are not linear.

Temperature scale: Runs backwards, high temperatures on the left.
Absolute magnitude: The apparent magnitude it would have if it were observed from a distance of 10 parsecs. Absolute magnitudes are much more negative than the apparent magnitudes of the stars.

• 90% of stars fall into the diagonal band known as the main sequence. It can be shown using the Stefan-Boltzmann Law that stars increase in size as we move up the main sequence.
• Lower right: The coolest stars, reddish in colour.
• In the middle: (further towards the left than lower right) hotter, more luminous stars that are yellow and white.
• Lower left: more luminous blue stars.

Mass of star increases moving up the main sequence so the gravitational pressure increases with mass. Therefore, to maintain equilibrium, fusion reactions in the core must generate a greater radiation pressure. The star has to burn at a higher temperature, giving it a greater luminosity.


9% of stars = red giants and supergiants. From Stefan-Boltzmann Law we can see that their high luminosity and low temperature means that they must have a very large area - they are therefore giants. 


WHITE DWARFS are very hot but not luminous, therefore they are much smaller than their counterparts on the main sequence.

The cepheids, congregate in a great band of instability that appears between the main sequence and the red giants.

Images and diagrams from: Heinemenn HL Physics Course Companion, IB Physics study guide by Tim Kirk

E2 Stellar Radiation

E.2.1 State that fusion is the main energy source for stars.

Fusion is the main energy source for stars.

E.2.2. Explain that in a stable star (for example, the Sun), there is an equilibrium between radiation pressure and gravitational pressure.

A stable star is a star in which there is an equilibrium between the radiation pressure and the gravitational pressure. The reason why the powerful reactions in the Sun have not forced away the outer layers of the Sun is because of this balance between the outward pressure and inward gravitational force.

E.2.3. Define the luminosity of a star.

Luminosity is the total power radiated by a star, it is measured in Watts (W). It depends on both the surface temperature of the star and its radius or surface area. If the radius of the two stars is the same, the one with the higher temperature will have the greater luminosity. If the temeperature of the stars is the same, the one with the larger radius will have the great luminosity.

E.2.4 Define apparent brightness and state how it's measured.

Apparent brightness: The power received per unit area. The SI units are Wm^-2.

E.2.5 Apply the Stefan-Boltzmann Law to compare the luminosities of different stars

The radiation from a perfect emitter is known as black body radiation. The graph below shows a spectrum of radiation from black-body emitters at different temperatures. A hot object emits radiation across a broad range and there is a peak in intensity at a particular wavelength. For a hotter body, the peak is at a higher intensity and shorter wavelength.

The peak wavelength (at which the maximum amount of energy is radiated) is related to the surface temperature by Wien's displacement law.

E.2.6 State Wien's (displacement) law and apply it to explain the connection between the colour and temperature of stars.

Questions 5 & 6

5.