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Stars (Distances (Parallax (The apparent movement of stationary objects…
Stars
Distances
Parallax
The apparent movement of stationary objects relative to each other, due to their differing distances away from us and the movement of the observer relative to them both
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As the Earth moves around the sun, the star will appear to move relative to much more distance stars
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The distance of a star from the sun can be found by:\[d=\frac{1}{\theta}\]Where \(\theta\) is the angle of parallax subtended by the star in radians.
Using this method, \(d\) will be in \(AU\)
1 Astronomical Unit
Equals the average radius of the Earth's orbit over one complete rotation around the sun
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1 Light Year
The distance that light travels in a year, in a vacuum
The radius, \(r\), of an object, the distance, \(d\) of the object from us and the angle subtended by the object are related by:\[\theta=\frac{r}{d}\] where \(\theta\) is in radians
Magnitude
Apparent Magnitude m
How bright an object appears, taking no account of it's distance from us
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\[\frac{I_{1}}{I_{2}}=2.51^{m_{2}-m_{1}}\]
Where \(I_{n}\) is the intensity of the star with apparent magnitude \(m_{n}\)
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Absolute Magnitude M
How bright a star would appear if it were \(10\,Pc\) from us
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Intensity I
The total amount of energy reaching each \(m^{2}\) of the Earth's surface, per second, from a star, across all parts of the EM spectrum
\[I=\frac{P}{4\,\pi\,r^{2}}\]
Where \(r\) is the distance of the star from us
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HR Diagram
Graph of absolute magnitude (decreasing upwards) against temperature (log scale decreasing to right)
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50,000K to 2,500K on x-axis labelled with spectral classes
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Temperature
A Black Body
A perfect absorber and emitter of all radiation; a black body absorbs all wavelengths incident onto it and emits all wavelengths of EM radiation
A star behaves approximately as a black body of temperature equal to the surface temperature of the star
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Total power output: \[P=\sigma AT^{4}\] where \(A\) is the surface area of the star and \(T\) is the surface temperature of the star
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Spectra
Spectral Classes
O
50,000K - 25,000K
Blue
He+ lines and He neutral and weak Balmer lines mainly at lower temperatures
B
25,000K-11,000K
Blue
Strong He neutral and Balmer lines
A
11,000K-7,500K
Blue-White
Strongest Balmer lines and metal ions
F
7,500K-6,000K
White
Metal ions
G
6,000K-5,000K
White-Yellow
Metal Ion and metal neutral lines
K
5,000K-3,500K
Orange
Metal Neutral lines
M
< 3,500K
Red
Metal neutral lines and molecular TiO
Balmer Lines
Absorption lines caused by hydrogen electrons being excited from the \(n=2\) level to the \(n=9\) level
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At lower temperatures most hydrogen electrons will be in the \(n=1\) level meaning that few electrons will be able to be excited to higher energy levels from the \(n=2\) level
As the temperature of a gas increases hydrogen atoms gain more energy from more frequent and more energetic collisions with other particles of the gas
Electrons in hydrogen atoms therefore are more likely to be in the \(n=2\) level at any given time, and so more hydrogen electrons are available to absorb Balmer photons and the intensity of the Balmer lines will increase
As the temperature increases even further, the electrons start to gain enough energy, from collisions of hydrogen atoms, for electrons to become excited into \(n=3\) and \(n=4\) levels regularly
This increases the average number of electrons in the higher levels, and decreases the average number of electrons in the \(n=2\) level at a given point in time
This decreases the number of electrons that can absorb Balmer photons and so the intensity of the Balmer lines will decrease
This makes the intensity of the Balmer lines sensitive to temperature and so they can be used to measure temperature
Intensity of Balmer lines is strongest in A type stars (at around 11,000K)
Absorption Lines
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When radiation, of all wavelength, moves outwards towards the surface of the star, photons of energy that correspond to potential electron transitions in atoms and ions, are absorbed by electrons in the outer layers.
When these electrons de-excite they re-emit these photons in many different directions, potentially back into the star
The light may also be re-emit as different energy photons as the electrons cascade through energy levels
This means a lower proportion of this energy photon (and this wavelength of light) of light makes it out of the star, and to the Earth, and so there is a band of lower intensity light in the stars spectrum at this wavelength
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Stellar Evolution
Star starts out as mass of gas, falling inwards to form a spherical mass, under the force of gravity. As the gas is pulled inwards, it's gravitational potential energy decreases and so to conserve total energy, it's kinetic energy must increase. This causes the gas to heat, and the Protostar becomes very hot
Eventually the core of the protostar becomes hot enough for hydrogen to fuse to helium in the core. This is the Core Hydrogen Burning Phase and during this phase the star is in it's Main Sequence
In very small stars, after the main sequence fusion stops and the star fades away
In most stars, once hydrogen runs out in the core, the radiation pressure from within the core is removed and the star collapses once more. The gas inside the star heats once more, and eventually a shell of matter around the core becomes hot enough for hydrogen to fuse to helium. This stage is called the Shell Hydrogen Burning Phase.
The core of the star will continue to collapse, and eventually becomes hot enough for helium to fuse to carbon and oxygen in the core. This starts the Core Helium Burning Phase
Eventually helium runs out in the core and so the core starts to collapse again. Eventually the shell around the core becomes hoe enough for helium to fuse into carbon and oxygen, and another layer around this takes the place of fusing hydrogen into helium. This is called the Shell Helium Burning Phase
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This increases the outwards radiation pressure, and heats the hydrogen shell, increasing the rate of fusion there too. The outwards radiation pressure increases and the outer layers of the star are pushed out further. The star also generates more electromagnetic radiation due to the increased fusion rates. The star become larger, redder and brighter again
The outwards radiation pressure from within the shell will hold up the outer layers of the star under the gravitational pressure, however there is nothing happening in the core to prevent core collapse
The core continues to collapse, and so the core heats, heating the shell in turn. The rate of fusion in the shell increases and so the outwards radiation pressure from the fusion increases, pushing the outer layers of the star outwards.
The causes the outer layers of the star to become less dense and to cool. The rate of energy generation in the star also increases due to the increased fusion rate. As a result the star becomes larger, redder and brighter. This forms a Red Giant
The fusion of hydrogen to helium releases a large amount of energy, which causes the star to emit electromagnetic radiation as a black body
Fusion in the star exerts an outwards radiation pressure which counters the inwards pressure of gravity, causing the star to remain stable, with no further collapse during the main sequence
At this stage the inside of the star is made of a plasma, as (apart from in outer layers) the star is too hot for electrons to remain bound to nuclei; the gain energy through collisions to become ionised almost immediately.
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Black Hole
A concentration of matter surrounded by an event horizon, past which the escape velocity to escape the black hole is greater than the speed of light
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Defining Characteristic of a supernova
A large, brief and rapid decrease in absolute magnitude
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Neutron Stars
Very dense spheres around 30km in diameter comprised entirely of neutrons, meaning that they are at nuclear densities.
In order to conserve angular momentum, when a core collapses into a neutron star, it's rotational speed will increase
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If a neutron star is aligned with us, such that at least once per cycle it's jets pass through our line of sight, then we observe the neutron star as a regular, periodic radio signal, called a pulsar
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