Cosmology

The astronomical unit (AU) is defined as:

The mean distance from the centre of the Earth to the centre of the Sun

Why is the value a mean?

the Earth’s orbit around the Sun is elliptical it will be slightly closer to the Sun in January (1.471 × 10¹¹ m) than it is in July (1.521 × 10¹¹ m)

What is one AU?

• 1.496 × 10¹¹ m ≈ 1.5 × 10¹¹ m

A light-year is defined as:

distance travelled by light in one year

parsec is defined as:

• A unit of distance that gives a parallax angle of 1 second of an arc (of a degree), using the radius of the Earth’s orbit (1 AU) as the baseline of a right–angled triangle

Angles smaller than 1 degree can be measured in arcminutes or arcseconds

• 1 degree = 60 arcminutes

• 1 arcminute = 60 arcseconds

• Therefore, 1 degree = 60 x 60 = 3600 arcseconds

• 1 arcsecond = 1/3600 degree

Given that 1 AU = 1.496 × 10¹¹ m, trigonometry can be used to express 1 parsec in metres:

1 AU =

1.496 × 10¹¹ m

Stellar Parallax is defined as:

The apparent shifting in position of a nearby star against a background of distant stars when viewed from different positions of the Earth, during the Earth’s orbit about the Sun

(It involves observing how the position of a nearby star changes over a period of time against a fixed background of distant stars. To an observer the position of distant stars does not change with time)

If a nearby star is viewed from the Earth in _____ and again in ____, when the Earth is at a different position in its orbit around the Sun, the star will appear in different positions against a backdrop of distant stars which will appear to not have moved

January

July

What is this apparent movement of nearby stars called?

stellar parallax

Applying trigonometry to the parallax equation: (not given)

• 1 AU = radius of Earths orbit around the sun

• p = parallax angle from earth to the nearby star

• d = distance to the nearby star

• So, tan(p) = 1 AU/d

• small angles, expressed in radians, tan(p) ≈ p, therefore: p = 1 AU/d

If the distance to the nearby star is to be measured in parsec, then it can be shown that the relationship between the distance to a star from Earth and the angle of stellar parallax is given by:

p = 1/d

• p = parallax (")

• d = the distance to the nearby star (pc)

What is this equation accurate up till and why?

distances of up to 100 pc

• For distances larger than 100 pc the angles involved are so small they are hard to measure accurately

1 arcminute is denoted by __

1'

1 arcsecond is denoted by __

1" 

The cosmological principle states that:

The universe is isotropic, homogenous and the laws of physics are universal

What is isotropic?

means that the universe is the same in all directions to every observer

• Although specific regions of space may be completely empty and other regions may contain galaxies or clusters of galaxies which clump together, over the entire volume of space the distribution of matter appears to be uniform

What does homogenous mean?

means that matter is uniformly distributed, the universe has a uniform density

• Although specific regions of space may contain more matter and other regions may contain less matter, over the entire volume of space the density appears uniform

What does at every point in the universe the laws of physics are universal?

means that the same laws and models apply as here on Earth

The Cosmological Principle is demonstrated using the three models of the universe:

• Model A shows a universe that is isotropic, but not homogenous

  • The universe is the same in all directions to every observer

  • However, there is not a uniform distribution of matter (uniform density) in all regions

• Model B shows a universe that is homogenous, but not isotropic

  • The universe has a uniform distribution of matter (uniform density) in all regions

  • However, the universe is not the same in all directions to every observer due to the orientation of the bricks

• Model C illustrates the Cosmological Principle, it is both isotropic and homogenous

  • The universe is the same in all directions to every observer

  • The universe has a uniform distribution of matter (uniform density) in all regions

What is the doppler effect?

• If a wave source is stationary, the wavefronts spread out symmetrically

• If the wave source is moving, the waves can become squashed together or stretched out

• If the wave source is moving towards an observer the wavefronts will appear _____

• If the wavefront is moving away from an observer the wavefronts will appear ______

• squashed

• stretched out

What observed qualities does this therefore change?

frequency and wavelength

A moving object will cause the wavelength, λ, (and frequency) of the waves to change:

• The wavelength of the waves in front of the source decreases (λ – Δλ) and the frequency increases

• The wavelength behind the source increases (λ + Δλ) and the frequency decreases

However:

• The actual wavelength emitted by the source remains the same

• It is only the wavelength that is received by the observer that appears to have changed

Doppler effect is defined as:

The apparent shift in wavelength occurring when the source of the waves is moving

Doppler effect, or Doppler shift, can be observed using any form of _______

EM rad

Why can the doppler effect be observed by comparing the light spectrum produced from a close object, such as our Sun, with that of a distant galaxy?

• The light from the distant galaxy is shifted towards the red end of the spectrum (There are more spectral lines in the red end)

• This provides evidence that the universe is expanding

Doppler shift (Doppler effect) describes how the wavelength (or frequency) of waves change when ______

the source of the waves and observer are moving relative to each other

If the relative speed between the source of the waves and the observer, ∆v, is small compared to the speed at which the wave is travelling, c, then the Doppler wavelength shift, ∆λ, and frequency shift, ∆f, is given by (given):

• Δv = relative speed between source and observer (m s^–1)

• c = speed of the wave (m s^–1)

• Δf = observed change in frequency between moving source and stationary source of wave (Hz)

• f = unshifted frequency of the wave emitted (Hz)

• Δλ = observed change in wavelength between moving source and stationary source of wave (m)

• λ = unshifted wavelength of the wave emitted (m)

relative speed between source and observer along the line joining them is give by (learn):

∆v = vs – vo

• v_s = velocity of electromagnetic waves source

• v_o = velocity of observer

• Usually, we are calculating the speed of the source of electromagnetic waves relative to an observer which we assume to be stationary

  • Therefore v_o = 0, hence ∆v = v_s = v

  • Where v is the velocity at which the source of the electromagnetic waves is moving from the observer

• Hence, the Doppler shift equation can therefore be written as:

red light has the _____ wavelength and the ______ frequency

longest

smallest

What is the type of light with shorter wavelength and higher frequency?

blue light

How did astronomer Edwin Hubble (1929) show the universe was expanding?

• He did this by observing that the absorption line spectra produced from the light of distant galaxies was shifted towards the red end of the spectrum

• This doppler shift in the wavelength of the light is evidence that distant galaxies are moving away from the Earth

What did light from more distant galaxies being shifted further towards the red end of the spectrum compared to closer galaxies show?

concluded: galaxies or stars further away from the Earth are moving faster than galaxies which are closer

Hubble’s law states:

The recessional velocity, v, of a galaxy is proportional to its distance from Earth

v ≈ H₀d (given)

v ≈ H₀d units

• v = recessional velocity of an object, the velocity of an object moving away from an observer (km s^-1)

• H₀ = Hubble constant, this will be provided in your examination along with the correct units (km s^-1 Mpc^-1)

• d = distance between the object and the Earth (Mpc) 

This Hubble’s law shows:

• The further away a star is from the Earth, the faster it is moving away from us

• The closer a star is to the Earth, the slower it is moving away from us

Why is it difficult to be certain about just how accurate the values for the Hubble constant are?

random and systematic errors involved when calculating the distance to a galaxy or star

Astronomers have concluded from hubble that:

• All galaxies are moving away from the Earth

• Galaxies are moving away from each other

• Distant galaxies are receding faster than closer galaxies

What does this diagram show:

• Light coming to the Earth from a close object, such as the Sun,

• Light coming to the Earth from a supernovae in a distant galaxy

Why when Red-shift is observed when the spectral lines from the distant galaxy move closer to the red end of the spectrum?

• This is because light waves are stretched by the expansion of the universe so the wavelength increases (or frequency decreases)

• This indicates that the galaxies are receding (moving away) from us

The fact the galaxies are moving further apart is what we would expect after an ______

explosion

• Matter is first _______ and as it explodes it moves out in all directions getting further and further from the source of the explosion

• Some matter will be lighter and travel at a ____ speed, further from the source of the explosion

• Some matter will be heavier and travel at a _____ speed, closer to the source of the explosion

densely packed

greater

slower

Around _____ years ago the universe was created from a _________ which was infinitely dense, hot and small

13.7 billion

hot singularity (a single point)

• There was a giant explosion, which is known as the _____

  • ______ were created at this instant

big bang

space and time

caused the universe to _______ from a single point, to form the universe today

expand and cool

Each point ________ from the others

expands away

There are 2 key pieces of evidence to support the Big Bang theory:

• Hubble’s Law shows the universe is expanding, through the red shift of light from distant galaxies

• Microwave background radiation provides evidence that the universe has expanded from a single point and cooled significantly during the time it has been expanding

Why were astronomers unable to detect these microwaves before the development of space flight?

microwaves are absorbed by the atmosphere

The microwave radiation detected came from ____ and at a generally uniform temperature of 2.73 K

all directions

Where has this radiation come from?

• remnant from the early stages of the Universe

• According to the Big Bang theory, the early Universe was an extremely hot and dense environment. As a result of this, it must have emitted thermal radiation.

• This radiation has expanded with the expansion of the universe and is now in the microwave region of the EM spectrum

How has microwave rad been made from thermal rad?

• Initially, this would have been high energy radiation, towards the gamma end of the spectrum

• This is because over the past 13.7 billion years the radiation initially from the Big Bang has become redshifted as the Universe has expanded

• As the Universe expanded, the wavelength of the radiation increased

• It has increased so much that it is now in the microwave region of the spectrum

• Microwave background radiation is uniform and has the exact profile expected to be emitted from a hot body that has cooled down over a very long time

  • This phenomenon is something that other theories (such as the Steady State Theory) cannot explain

What does this diagram show?

• Microwave background radiation is represented by a map of the universe

• This is the closest image that exists to a map of the Universe

• The different colours represent different temperatures

  • The red/orange/brown regions represent warmer temperatures indicating a higher density of galaxies

  • The blue regions represent cooler temperatures indicating a lower density of galaxies

• The temperature of the microwave background radiation is mostly uniform

  • It has a value of 2.7 ± 0.00001 K

  • This implies that all objects in the Universe are uniformly spread out

• The discovery of the microwave background radiation led to the Big Bang theory becoming the currently accepted model

  • If the universe had not started in a Big Bang then there would be no microwave background radiation

  • If the universe was younger than 13.7 billion years then the temperature would be higher than 2.7 K

What does general relativity state?

space and time are connected by a property known as space–time

• Space–time connects the three dimensions of space (the x, y and z–axis) to a fourth dimension, which is time

The evidence suggests that the Big Bang gave rise to the expansion of space–time about ___ billion years ago

13.7

The balloon represents space and the points represent galaxies:

• When the balloon is deflated, all the points are close together and an equal distance apart

• As the balloon expands, all the points become further apart by the same amount

• This is because the space between the galaxies has expanded

• The galaxies are not actually moving through space but being carried along as space itself expands

this therefore agrees with what principle?

cosmological principle which states that the Universe is

• Homogeneous (i.e. matter is uniformly distributed)

• Isotropic (i.e. the Universe is the same in all directions to every observer)

What can be used the estimate the age of the universe?

Hubble’s law

v = H₀d

what assumption is made in this equation?

recessional speed of a galaxy is constant over the history of the universe

• We must assume that all points in the universe were initially together

• If we know how far away a galaxy is from Earth and its recessional speed

• We can calculate the time taken to get to reach that distance from the Earth

what is the equation used?

time = distance/ speed

H₀ = v/d

• Therefore:

time = 1/H0

If we say that all matter was at the same point at the very start of the Big Bang (t = 0), then the time taken for the galaxy to move to its current position will be equal to the age of the universe

In 2020, the best estimate for the Hubble constant, H₀ was 67.4 km s⁻¹ Mpc⁻¹.  Use this value to calculate the age of the universe.

As the time from the Big Bang increases the temperature of the universe _____

decreases

key stages of evolution are:

• Stage 0: The Big Bang

• Stage 1: Big Bang → 10^–35 s after the Big Bang

• Stage 2: 10^–35 s after the Big Bang → 10^–6 s after the Big Bang

• Stage 3: 10^–6 s after the Big Bang → 225 s after the Big Bang

• Stage 4: 225 s after the Big Bang → 1000 years after the Big Bang

• Stage 5: 1000 years after the Big Bang → 3000 years after the Big Bang

• Stage 6: 3000 years after the Big Bang → 300 000 years after the Big Bang

• Stage 7: 300 000 years after the Big Bang → Present

Stage 0 

• This is when the Big Bang occured

• At this point, time and space are created

• The universe is infinitely dense, hot and small, a hot singularity

Stage 1

• Just after the Big Bang → 10^–35 s after the Big Bang

• The universe expands rapidly

  • This is known as inflation

• There is no matter, only high energy gamma photons and electromagnetic radiation

Stage 2

• This is from 10^–35 s after the Big Bang → 10^–6 s after the Big Bang

• Building block particles come into existence (quarks, leptons, photons, and their antiparticles)

• These particles cannot form heavier particles (protons and neutrons) because of the high temperatures present

• There is slightly more matter than antimatter

  • As matter and antimatter annihilate, they leave a matter-dominated universe made from particles and not antiparticles

Stage 3

• This is from 10^–6 s after the Big Bang → 225 s after the Big Bang

• As the universe cools protons and neutrons begin to form from quarks

• Matter and antimatter continue to collide and annihilate

  • Producing enormous quantities of high-energy photons

  • These are continually absorbed and re-emitted as they interact with charged particles

Stage 4

• This is from 225 s after the Big Bang → 1000 years after the Big Bang

• As the universe continues to cool it behaves in the same way as the core of a star

• Nuclear fusion begins

  • Protons and neutrons fuse to form light nuclei like deuterium, helium and lithium

• Matter is in plasma form

  • A state in which protons and electrons are not bound to one another because of high temperatures

• Rapid expansion of the universe continues until 25% of matter is helium nuclei

Stage 5

• This is from 1000 years after the Big Bang → 3000 years after the Big Bang

• At this time, nuclear fusion ends

• Electrons are formed

Stage 6

• This is from 3000 years after the Big Bang → 300 000 years after the Big Bang

• The universe continues to cool and electrons combine with nuclei to form hydrogen and helium atoms

• In decoupling more electrons become attached to protons

  • Radiation and matter separate from each other

  • Photons travel freely through space

  • The universe becomes transparent

  • Photons now become the microwave background radiation that we detect today

Stage 7

• This is from 300 000 years after the Big Bang → Present

• After about 30 million years, the first stars form

• Galaxies begin to form from tiny density fluctuations because of gravitational forces pulling together clouds of hydrogen and existing stars

• Billions of years later, heavy elements form from the gravitational collapse of stars

• After approximately 9 billion years the solar system forms from a supernova nebula

  • Our Sun is formed at the centre of the nebula

  • Earth is formed almost 1 billion years later

• Approximately 11 billion years after the Big Bang, primitive life begins on Earth

• 13.7 billion years after the Big Bang, the first modern humans evolve

Scientists know that the universe is ________ as it expands

accelerating

______ is a hypothetical form of ____ which is used to try and explain the accelerating expansion

dark energy

energy

Dark energy is defined as:

A type of energy that permeates the whole universe and opposes the attractive gravitation force between galaxies via the exertion of a negative pressure

Dark energy cannot be _______

detected directly

It should make up ___ of the total energy in the universe

68%

Astronomers expect to observe the velocity of an object within a galaxy _____ as it moves away from the galaxy’s centre + why did they expect this?

decrease

because of weakening gravitational field strength further from the centre

• This is observed in smaller mass systems, such as the in the solar system, where planets orbiting ____ from the Sun have the slowest orbital velocity

  • This is not the case in larger mass systems, such as entire galaxies

furthest

How is mass spread out in galaxies?

spread out

not concentrated in its centre

However…

all the observable mass of a galaxy is observed to concentrate in the centre of galaxies

what does this therefore mean?

there must be another type of matter that can't be observed- Dark Matter

Dark matter is defined as:

Matter which cannot be seen and that does not emit or absorb electromagnetic radiation

Dark matter cannot be detected directly through ______

telescopes

dark matter is estimated to make up __% of the mass in the universe

27

how is it detected?

based on its gravitational effects relating to either the rotation of galaxies or by the gravitational lensing of starlight