9.3 cosmology

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Cards (18)

The Doppler effect
The apparent change in wavelength of a wave as the source moves relative to an observer
Compression or spreading out of waves emitted or reflected by a moving source
Wavelengths in front are compressed and wavelengths behind are spread out
For a source moving away the wavelength increases
Red shift
For a source moving towards the wavelength decreases
Blue shift
Red shift
Evidence for expanding universe
All galaxies are red-shifting
The further away the galaxy the greater the red shift
Therefore the universe is expanding
$z=$ $\frac{v}{c}=$ $\frac{\Delta f}{f}=$ $-\frac{\Delta\lambda}{\lambda}$
v = objects receding velocity
The wavelength ratio is negative as the wavelength is inversely proportional to the frequency
Redshift $z=$ $-\frac{v}{c}\ \ if\ \ v<<c$
z is positive if moving away (red-shift) and negative for blue-shift
v is positive if moving towards
Ignores relativistic effects
Applied to optical and radio frequencies
Binary stars
Identified using the Doppler effect
Two stars orbiting a common centre of mass
Spectroscopic binaries = binary star systems where stars are too close to be resolved by a telescope
Only way to identify is by using the Doppler shift of each star
As the stars eclipse each other they are travelling perpendicular to the line of sight from the observer
No Doppler shift in emitted radiation
When one star is travelling away from the observer the other is travelling towards
This causes each spectral line to split in two
One is blue-shifted and the other is red-shifted
Eclipsing binaries = when the plane of the orbit of the stars is in line of sight from Earth to the system
Stars cross in front of each other as they orbit
Can be identified from characteristic light curves
Light curves
No eclipse - brightness is maximum
A larger star in front - blocks all light; the primary minimum
No eclipse - brightness is maximum
Smaller star in front - blocks some light; secondary minimum
Quasars
very large red shifts
Very far away
The power output must be around that of an entire galaxy
Proven with inverse square law
Hubble’s law
Spectra from galaxies all show a red shift
The amount of red shift gives the recessional velocity
The plot of recessional velocity against distance shows they are proportional
Suggests universe is expanding
$v=$ $Hd$
v = recessional velocity in kms-1
d = distance in Mpc
H = Hubble's constant in kms-1Mpc-1
Distance is difficult to measure so astronomers disagreed on the value of H
Ranging from 50 to 100
Now accepted H lies between 65 and 80
Most agree it is in the mid to low 70s
SI unit for H is s-1
Need v in ms-1 and d in m (1 Mpc = $3.08\times10^{22}m$ )
Expansion of the universe
Cosmological principle = universe is homogenous and isotropic
Homogenous = every part is the same
Isotropic = everything looks the same in every direction
The universe doesn't have a centre
Until 1930s, cosmologists believed universe was infinite in space, time and static
The only way it could be stable using Newton’s law of gravitation
Einstein modified the theory of general relativity to be consistent with the steady-state universe
Expanding and cooling down because it is a closed system
Must have been smaller and hotter
Evidence for Big Bang
Accelerating expansion
All the mass in the universe is attracted together by gravity
Slows down the rate of expansion
Thought the expansion was decelerating until 5 billion years ago
In the late 90s, astronomers found evidence that expansion is now accelerating
Explained using dark energy - a type of energy that fills the whole of space
Age of the universe
H=1t
If the universe has been expanding at the same rate
$H=$ $75kms^{-1}Mpc^{-1}$
$t=$ $\frac{1}{2.4\times10^{-18}s}\ =$ $\ 4.1\times10^{17}s\ \ =$ $\ 13$ billion years
Absolute size is unknown but there is a limit on the size of the observable universe
A sphere with a radius equal to the maximum distance that light can travel during its age
If H = 75, the sphere’s radius = 13 billion light years
Taking into account the expansion of the universe, the radius of the observable universe is thought to be 46-47 billion light years
Evidence for Big Bang
Assumed universe began from one point
A singularity infinitely small and hot
Suggests universe began with a huge explosion from this point
Thought there was high energy radiation everywhere
As the universe expanded and cooled radiation would lose energy and be red-shifted
CMBR = cosmological microwave background radiation
Remains of radiation
Microwave radiation detected from all directions in space
relative abundance
During the early stages of the Big Bang nuclear fusion converts hydrogen nuclei into helium nuclei
The universe cooled too much and fusion stopped
Approximately ¼ of all existing hydrogen nuclei were fused into helium
Relative abundance ratio H:He = 3:1
Relative abundance by mass of different elements
73% hydrogen
25% helium
2% everything else
Quasars
Discovered in the late 1950s and are thought to be stars in our galaxy
Spectra unlike normal stars
Sometimes shot out jets of material
Many were very active radio sources
Produced a continuous spectrum unlike the black body radiation curve
Had emission lines of elements unseen before instead of absorption
In 1963, Maarten Schmidt realised they were the blamer series of hydrogen but enormously red shifted
An active galactic nucleus
Supermassive black hole surrounded by a disc of matter
As matter falls into the black hole jets of radiation are emitted from the poles
quasars
Characterised by:
Extremely large optical red-shifts
Very powerful light output
Their size is not much bigger than a star
Thought to be some of the most distant measurable objects
Can estimate power output using inverse square law for intensity
Use the amount of Doppler shift experienced by quasars to find their distance from earth
Shows quasars are extremely powerful and can have the same energy output as several galaxies
quasars
The first quasar to be discovered was 3C 273
Thought to be a dim star
Had much greater radio emissions than expected
Later found to be 26 billion light years away and 1000 times more luminous than the Milky Way
Exoplanets = planets that are not within our solar system
Orbit other stars
Can be difficult to detect directly
Tend to be obscured by the light of their host stars
Radial velocity method
Similar to detecting spectroscopic binaries
Star and planet orbit a common centre of mass
Causes the star to wobble
Causes Doppler shift in the light received from the star
The effect most noticeable with high-mass planets
Have greater gravitational pull on the star
The line spectrum of the star is blue-shifted when it moves towards the Earth and red-shifted when it moves away
There is something else near the star exerting a gravitational force on it - the exoplanet
The time period of the planet's orbit is equal to the period of the Doppler shift
Transit method
Observing intensity of light output of a star
Inclined = don't pass in front of star when observed from earth
Transit = when a planet crosses in front of a star
Intensity dips slightly
If intensity dips regularly it could be a sign that there is an exoplanet orbiting it
If there are variations in the regularity of the dips there may be several planets orbiting the same star
Have a gravitational effect on the transiting planet
The size and orbital period of the planet can be determined from the amount that the intensity falls by and the duration of the dip respectively
disadvantage of the transit method
limited as it only works if the line of sight to the star is in the plane of the planet’s orbit
More likely for planets with small orbits
Most orbits are inclined and smaller orbits mean parts of the planet are more likely to cross in front of the star and block some of its light