Cosmology Flashcards
Describe the Doppler effect
Where the wavelengths of light waves from a star moving towards earth are shorter, and the wavelengths of light from a star moving away from earth are longer, than they would be if the star was stationary.
Explain red shift
Waves are emitted and detected in the opposite direction to the motion of the source. The waves detected are more spaced out so have a longer wavelength so the absorption lines in the star’s spectrum are shifted towards the red end where wavelength is larger.
Explain blue shift
Waves are emitted and detected in the same direction to the motion of the source. The waves detected are less spaced out so have a shorter wavelength so the absorption lines in the star’s spectrum are shifted towards the blue end where wavelength is shorter.
What is Doppler shift (z) and which direction is the star moving in the formula booklet?
z > 0 is defined as the Doppler shift for objects that are redshifted, so moving away from us (receding)
z = Δλ/λ (where λ = emitted wavelength if it was stationary and Δλ = λ_observed - λ )
z = -Δf/f (where f = emitted frequency if it was stationary and Δf = f_observed - f )
z = -v/c (where v = velocity relative to Earth and c = speed of light )
What is a star’s radial speed?
The component of its velocity parallel to the line between earth and the star.
When are the maximum and minimum observed wavelengths for the spectrum from a star in a binary system?
Only works if orbiting in the same plane as the line from earth to the star. Maximum wavelength when star is moving away from earth (λ+Δλ). Minimum when star is moving towards earth (λ-Δλ).
What are two stars that can’t be resolved called?
A spectroscopic binary.
How do spectroscopic binary stars work?
Each spectral line splits into two after the stars cross the line of sight, then merge back into a single spectral line when they move towards the line of sight. The stars orbit a common centre of mass. They have the same period. The heavier star has a smaller orbit and moves slower and has a lower change in wavelength.
How to calculate the age of the universe
The value of Hubble’s constant, H = 68 km s^-1 Mpc^-1. Age of universe is 1/H. Standardising the units, by x1000 to get it to m s^-1 Mpc^-1, then / 3.1 x 10^22 to get it into s^-1. H = 2.2 x 10^-18 s^-1. Then to calculate the age of the universe, 1/H = 4.6 x 10^17 seconds.
How was the speed of recession of distant galaxies calculated?
Using the red shift of light from the galaxy.
Evidence for Big Bang: CMBR
The Big Bang Theory predicted that radiation was created in the form of gamma photons in the Big Bang and has been travelling through the universe ever since. As the universe has expanded, its mean temperature has decreased and is now about 2.7K. The spectrum of radiation from space has a peak in the microwave region and matches the theoretical spectrum of thermal radiation from an object of 2.7K from using Wein’s Displacement Law. It can be interpreted as the radiation left over from the Big Bang. The photons have been stretched to longer wavelengths and lower energies. Because the radiation was detected from all directions in the universe and varies little in intensity it must be universal as it abides by the cosmological principle.
Evidence for Big Bang: relative abundance of H and He
The mass of other elements is negligible. Stars and galaxies contain about 3 times as much H as He. Therefore protons:neutrons = 7:1. This is because rest energy of neutrons are slightly more than protons so when universe cooled enough to allow quarks in 3s to form baryons, protons formed more readily. Precise calculations using the exact difference in rest energies also yield a ratio of 7:1. Big Bang theory predicted fusion of H occured when universe young to form He. The fusion stopped as the universe expanded and cooled.
Evidence for Big Bang: red shift of distant galaxies and Hubbles Constant
The Big Bang theory suggests that the universe is expanding since galaxies are moving away relative to the Earth. This results in a redshift of distant galaxies moving away from the Earth. From this, a relationship between the recessional velocity of galaxies and the distance away from Earth was made - Hubble’s Law. The proportionaly constant is defined as Hubbles Constant.
How did the theory of dark energy arise?
Use different techniques to measure distances to very distant type 1a supernovae. One used red shift and Hubble’s law, other used apparent and known absolute magnitude. The magnitude method gave a distance further than its red shift suggested. To reach this distance, the supernova must have been accelerating so the expansion of the universe has been accelerating. No known force could cause this so a previously unknown force must be releasing energy called dark energy.
Properties of quasars
Has very powerful light output (comparable to galaxies). Relatively small in size (not much bigger than a solar system). Large red shift indicating it is 5k and 10k ly away.
What is an eclipsing binary star system?
This is where two stars that are orbiting each other partially eclipse each other as one passes in front of the other, if the plane of the stars orbits is in the same plane as our line of sight.
Why does the absorption line spectra of an eclipsing binary star system split and then recombine?
FIrstly, the moment when one star eclipses the other, each star will be moving perpendicular to our line of sight - as seen from Earth. When the stars are in this position, the absorption line is one common wavelength. However, when the stars are moving parallel to our line of sight, the absorption line is split into two. This is because one star is moving away from us, so the wavelength of its light increases and its absorption line is red shifted. Whereas the other star is moving towards us, so the wavelength of its light decreases and its absorption line is blue shifted.
What is the value for the maximum Δλ for an eclipsing binary star system?
This is the difference between the single central absorption line, and one of the split lines, so the difference between the two split absorption lines is 2λ.
What is the equation for determining the orbital speed of the stars of an eclipsing binary star system?
where v is the orbital speed of the stars, λ is the observed wavelength of the single absorption line and Δλ is the change in wavelength between the single central absorption line and one of the split lines.
