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Cosmology (Quasars (Initially observed as very intense radio sources.…
Cosmology
Quasars
Initially observed as very intense radio sources. Thought to be within own galaxy. However, the emission spectra of the sources were observed to have Balmer lines, red shifted into the radio part of the spectrum.
The high redshift suggested that the objects were very far away (by Hubble's law) and so they must have a very high absolute magnitude to have the high apparent magnitude that they do.
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Once CCD's were invented, high resolution images showed that these objects lay at the centres of large galaxies, at what was believed to be a black hole.
Formed at the centres of galaxies, where a supermassive black hole accretes matter
An accretion disk forms, in which matter rotates around the black hole, and becomes denser as it moves inwards. The matter is heated to very high temperatures and emits very high intensity electromagnetic radiation.
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A very strong magnetic field is generated around the black hole which causes matter and radiation to be ejected in jets along the poles of the magnetic field.
Quasars only occur in active galaxies, around active galactic nuclei, where matter is being taken in by a supermassive black hole.
The Doppler Effect
When a source of waves is moving relative to the observer, the wavelength of the waves will appear different to the observer, than that with which they were produced from the source.
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If a source is moving with speed \(v\) relative to an observer, where \(v<< c\), then cosmological redshift will obey:
\[\frac{\Delta\lambda}{\lambda}=\frac{\Delta\,f}{f}=\pm\frac{v}{c}\]
Red shift, \(z\) is defined by:
\[z=\pm\frac{v}{c}\]
Where \(z\) is greater than zero for a redshift and less than zero for a blueshift
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Hubble's Law
Hubble found the distances to a number of stars by using the period-luminosity relationship of Cepheid variable stars
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Hubble used these values to find the average velocities and distances of the galaxies that contained the stars
Hubble found that the recessional velocity is directly proportional to the distance of the galaxy from us, suggesting that the universe is expanding.
\[v=Hd\]
The age of the universe can be calculated by taking the inverse of the Hubble constant (once in SI units)
\(H\) is Hubble's constant, and is usually in units of \(km\,s^{-1}\,Mpc^{-1}\)
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In actual fact, the expansion of the universe has been shown to be accelerating
If the universe had been expanding at a constant rate then at the big bang, all the galaxies we see would have been on top of us. Using \(s=vt\) these galaxies would have moved to the distance they are away from us, in the time since the big bang, with speed equal to their recessional velocity.
\(T=\frac{s}{v}=\frac{d}{v}\)
Where \(v\) is their recessional velocity and \(d\) is their observed distance from us.
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Binary Stars
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In a spectroscopic binary system we are not looking at the system from the top down. This means that as the stars orbit one another we will observe the absorption spectra of the two stars oscillate between maximum and minimum redshifts
The time period, the linear velocity, the rotational velocity and the radius of the orbits can be found. The relative masses of the two stars can then be found
Eclipsing binaries occur when our line of sight lies approximately in the plane of the orbit of the two stars. When one star eclipses the other there will be an apparent increase in magnitude of the system.
When the brighter star eclipses the dimmer star there will be a lower increase than when the dimmer star eclipses the brighter star. From this the relative brightnesses of the two stars can be found
The transition time for a peak and the total time of a peak will give the diameter of the smaller star and the diameter of the bigger star
If the relative brightness and size of the stars is known then the relative temperature can also be deduced. If the total absolute brightness is known then these values can be made absolute.
Exoplanets
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Radial Velocity Method
Can be used to find the size of the planet relative to the star, period of rotation
When a planet orbits a star it causes a slight wobble in the star, causing the spectrum of the star to oscillate between redshift and blueshift
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When an exoplanet eclipses it's star there will be an apparent increase in magnitude. Transition time gives diameter of planet and transition time plus total increase time gives star diameter
The Big Bang Theory
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Evidence
Hubble's Law
Galaxies further from us appear to be receding faster than closer ones. In order to obey homogeneity all galaxies must observe this, and so it must be the space in between galaxies that is expanding, leading to further galaxies receding faster, as there is more space between us and those galaxies to expand.
Cosmic Microwave Background
The CMB is made up from photons that were present in the hot early universe, shortly after the big bang. The photons have red shifted and are now at microwave frequencies. In order to observe this the universe must have been much hotter, and much denser than it is today, suggesting an expansion.
The CMB is a perfect black body spectrum at a temperature of 2.73K. The CMB is largely isotropic, only containing slight variations in temperature, in agreement with the cosmological principle.
Helium Abundance
The observed abundance of helium in stars (25% by mass) is to high to be attributed only to stellar nucleosynthesis. There must have been a period in the early universe where a large amount of hydrogen (universe wide scale) could have fused into helium. This required a hot early universe, which suggests an expansion and a cooling.
The universe started from an incredibly dense, incredibly hot point, and has been expanding ever since.