ASTROPHYSICS
SUMMARY
• Star is a massive body of plasma/gas held together by gravity, with fusion going
on at its center, giving off electromagnetic radiation. There is an
equilibrium between radiation/gas pressure and gravitational pressure called
hydrostatic equilibrium.
This equilibrium is gained through nuclear fusion which provides the energy
the star needs to keep it hot so that the star's radiation pressure
This applies to all layers of a star.
is high enough to oppose gravitational contraction.
Gravity pulls outer layers in, gas and
radiation pressure pushes them out.
The fusing of hydrogen into helium takes up the majority of a star’s lifetime and is the reason
why there are far more main sequence stars than those in other phases of their life-cycle.
Stars initially form when gravity causes the gas in a nebula to condense.
As the atoms move towards one another, they lose gravitational PE that is converted into KE.
This raises the temperature of the atoms which then form a protostar.
When the mass of the protostar is large enough, the temperature and pressure at the centre will be
sufficient for hydrogen to fuse into helium, with the release of very large amounts of energy.
As the hydrogen is used up the star will eventually undergo changes that will move it from the
main sequence. During these changes the colour of the star alters as its surface temperature
rises or falls and it will change size accordingly. The original mass of material in the star
determines how the star will change during its lifetime.
Solar System
Asteroid belt situated between Mars and Jupiter, contains millions of asteroids.
Kuiper belt, beyond Neptune, much larger;
In addition to asteroids it is the source of short-period comets and contains dwarf planets
About 4.5 billion years ago, the
Earth’s moon is believed to have
been formed from material ejected
when a collision occurred between
a Mars-size object and the Earth.
Jupiter is the biggest planet in
terms of mass and volume.
Mercury is the smallest.
Asteroids and comets are both celestial bodies orbiting our Sun, and they both can have unusual
orbits, sometimes straying close to Earth or the other planets. They are both “leftovers” — made
from materials from the formation of our Solar System 4.5 billion years ago
Asteroids consist of metals and
rocky material. Those of size less
than 300 km have irregular shape
because their gravity is too weak
to compress them into spheres.
Comets are irregular objects a few kilometres across comprising
frozen gases (ice), and dust that orbit the Sun in sharply elliptical
orbits with periods ranging from a few years to thousands of years.
As they draw near to the Sun the gases in the comet are vaporized,
forming the comet tail always pointing away from the Sun.
Groups of stars
• Binary star is a stellar system consisting of two stars/objects orbiting
around their common center of mass.
The ONLY way to find mass of the stars is when they are the part of binary stars.
Knowing the period of the binary and the separation of the stars the total mass of
the binary system can be calculated.
• Clusters: Gravitationally bound system of galaxies/stars.
• Stellar cluster is a group of stars held together by gravitation in same region of space,
created roughly at the same time from the same nebula.
Open clusters consist of up to several hundred younger stars;
contain some gas and dust;
within our galaxy, and so lie within a single plane.
Globular clusters contain many more older stars;
contain very little gas and dust;
spherically shaped
just outside the Milky Way in its galactic halo
galactic halo is an extended, spherical component of a galaxy
extends beyond the main, visible component.
the galactic spheroid (stars)
the galactic corona (hot gas, i.e. a plasma)
the dark matter halo.
• Constellation is a group of stars that form a pattern as seen from the Earth,
but not bound by gravitation
• Galaxy is a huge group of stars, dust, and gas held together by gravity,
often containing billions of stars, measuring many light years across.
Some in isolation majority come in clusters
Milky Way is part of a cluster “Local Group”
Regular clusters consist of a concentrated core and are spherical in shape.
Irregular clusters have no apparent shape and a lower concentration of galaxies within them.
Hubble Space Telescope: superclusters
In between the clusters there are voids that are apparently empty of galaxies.
Spiral galaxies the most common class of galaxies (both The Milky Way and Andromeda).
a flat rotating disc-shape with spiral arms spreading out from a central galactic
bulge that contains the greatest density of stars.
Belief: at the centre of the galactic bulge, there is a black hole.
The spiral arms contain many young blue stars and a great deal of dust and gas.
Other galaxies are elliptical in shape, being ovoid or
spherical – these contain much less gas and dust than
spiral galaxies; they are thought to have been formed
from collisions between spiral galaxies.
Irregular galaxies are shapeless and may have been
stretched by the presence of other massive galaxies –
the Milky Way appears to be having this effect on
some nearby dwarf galaxies.
Astronomical distances
Resulting from the huge distances involved in astronomical measurements, some unique,
non-SI units have been developed. This avoids using large powers of ten and allows
astrophysicists to gain a feel for relative sizes and distances.
1 light-second = (3.0 × 10 m/s)(1.0 s) = 3.0 × 108 m = 3.0 × 105 km
1 light-minute = 18 × 106 km
1 light-year (ly) 1 ly = 9.46 × 1015 m ≈ l013 km.
The Earth—Moon distance is 384,000 km = 1.28 light-seconds.
The Earth—Sun distance is 150,000,000 km = 8.3 light-minutes.
The astronomical unit (AU): the average distance between the Sun and the Earth. It
is really only useful when dealing with the distances of planets from the Sun.
1 AU= 1.50 × 10 11 m ≈ 8 light minutes
1 parsec (pc): This is the most commonly used unit of distance in astrophysics.
1 pc= 3.26 ly = 3.09 × 10 16 m
Distances between nearby stars are measured in pc, while distances between distant
stars within a galaxy will be in kiloparsecs (kpc), and those between galaxies in
megaparsecs (Mpc) or gigaparsecs (Gpc).
Parallax Method relies on the apparent movement of the nearby star against
the background of further stars as the earth orbits the sun.
• It is the most direct measure of distance.
• two apparent positions of a close star with respect to position
of distant stars as seen by an observer in both January and July
are compared and recorded to find angle p
• tan 𝑝 =
𝑆𝑢𝑛 − 𝐸𝑎𝑟𝑡ℎ 𝑑𝑖𝑠𝑡𝑎𝑛𝑐𝑒 1𝐴𝑈
=
𝑆𝑢𝑛 − 𝑠𝑡𝑎𝑟 𝑑𝑖𝑠𝑡𝑎𝑛𝑐𝑒
𝑑
For small angles: sin p  tan p  p
1𝐴𝑈
𝑑=
𝑝
when talking about stars, parallax is very, very small number.
Parallaxes are expressed in seconds.
p  rad 


180  60  60 p  sec 
d  m 
1
648000 1
→ p rad  
p  sec 
 
1 149597870691 648000  3.08 1016 m

p  sec 
p  sec 
d  pc  
1
p  sec 
1 AU = 149597870691 m
1 pc = 3.09 X 1016 m
“Parsec” is short for
parallax arcsecond
‘One parsec is a distance corresponding to a parallax of one arc second'
There is a limit to the distance that can be measured using stellar parallax – parallax
angles of less than 0.01 arcsecond are difficult to measure from the surface of the Earth
because of the absorption and scattering of light by the atmosphere. Turbulence in the
atmosphere also limits the resolution because it causes stars to “twinkle”.
1
Using the parallax equation, gives a maximum range of 𝑑 = 0.01 = 100 pc
In 1989, the satellite Hipparcos (an acronym for High Precision Parallax Collecting Satellite)
was launched by the European Space Agency (ESA). Being outside the atmosphere,
Hipparcos was able to measure the parallaxes of 118 000 stars with an accuracy of 0.001
arcsecsond (to distances 1000 pc); its mission was completed in 1993.
Gaia, Hipparcos’s successor, was launched in 2013 and is charged with the task of
producing an accurate three-dimensional map showing the positions of about a
billion stars in the Milky Way. This is about one per cent of the total number of stars
in the galaxy! Gaia is able to resolve a parallax angle of 10 microarcsecond
measuring stars at a distance of 100 000 pc.
limits because of small parallaxes:
d ≤ 100 pc from Earth
d ≤ 1000 pc from Hipparcos
d ≤ 100 000 pc from Gaia
A black body is a theoretical object that absorbs 100% of the radiation that is incident upon it.
Because there is no reflection or transmission it appears perfectly black.
Such bodies would also behave as perfect emitters of radiation, emitting the maximum
amount of radiation possible at their temperature.
• Black bodies in thermal equilibrium emit energy to balance the energy they absorb
and remain at a constant temperature.
• Black body emits energy according to Planck’s and Wien’s law
Blackbody radiation
Planck's Law
▪ predicts the radiation of a blackbody at different temperatures.
▪ gives intensity of radiation as a function of wavelength.
▪ it depends only upon the temperature of the black body.
• The hotter the blackbody the more energy
emitted per unite area at all wavelengths.
Wien’s law: Wavelength at which the intensity
of the radiation is a maximum, λmax,is:
2.9×10-3
max (m) 
T(K)
The peak shifts with T.
Shorter λ as the T increases.
Stars’ and planets’ radiation spectrum is approximately the same as black-body radiation.
Except for their surfaces, stars behave as blackbodies.
Surface is responsible for absorption spectrum.
Luminosity of a star is the total power radiated by a star.
(total energy per second)
If we regard stars as black body, then luminosity is
L = A σT4 (W)
Stefan-Boltzmann’s law
A is surface area of the star, T surface temperature (K), σ is Stefan-Boltzmann constant.
When we assume that a star is spherical we can use this equation in the form:
L = 4πR2σT4
(W)
R is the radius of the star
(Apparent) brightness (b) is the power from the star received per
square meter of the Earth’s surface
L
b = 4π𝑑2
(W/m2)
L is luminosity of the star; d its distance from the Earth
Can be measured, for example, by using a telescope and a charge-coupled device ? IB
Photometer!!! Internet
SPECTRA
1. A hot solid, liquid or gas at high pressure produces a continuous spectrum – all λ.
2. A hot, low-density / low pressure gas produces an emission-line spectrum – energy only at specific λ.
3. A continuous spectrum source viewed through a cool, low-density gas
produces an absorption-line spectrum – missing λ – dark lines.
Thus when we see a spectrum we can
tell what type of source we are seeing.
Stars’ spectra:
directly from the surface of the Sun
( spectrum produced by blackbody
radiation – continuous spectrum)
minus lines that have been absorbed after
it has passed through the Sun's
"atmosphere.
● Each element (atom/ion) produces a specific set of absorption (and emission) lines.
We call this the "spectral signature" or “fingerprints” of an atom/ion.
Explain how atomic spectra may be used to deduce chemical and physical data for stars.
•surface temperature of a star is determined by measuring the wavelength
at which most of the radiation is emitted.
2.9×10-3
max (m) 
T(K)
•Most stars essentially have the same chemical composition, yet show
different absorption spectra as they have different temperatures.
• Absorption spectra gives information about the temperature of the star
and its chemical composition.
• Doppler shift information of speed relative to earth (red shift → longer
wavelength, blue shift → shorter wavelength)
Cepheid variables are stars with regular variation in luminosity (rapid brightening, gradual
dimming) which is caused by periodic expansion and contraction of outer surface (brighter as it
expands). This is to do with the balance between the nuclear and gravitational forces within the star.
In most stars these forces are balanced over long periods but in Cepheid variables they seem to take
turns, a bit like a mass bouncing up and down on a spring. The period of these stars varies between
twelve hours and a hundred days. Because they are so luminous it means that very distant Cepheids
can be observed from the Earth.
period-luminosity relationship:
Cepheids with longer periods are
intrinsically more luminous than
those with shorter periods.
Cepheid variable stars are known as “standard candles” because they allow us to measure the
distances to the galaxies containing Cepheid variable stars.
So, to find out how far away Cepheid is:
•
•
•
•
The apparent brightness is measured using a telescope and CCD to get period
Use graph period-luminosity relationship to find luminosity L
Calculate d from b = L/4πd2
Distances to galaxies are then known if the Cepheid can be ascertained to be within a specific galaxy.
Cepheid stars are stars that have completed the hydrogen burning phase and moved off
the main sequence (see later for an explanation of this). The variation in luminosity
occurs because the outer layers within the star expand and contract periodically. This is
shown diagrammatically as:
(1) a layer loses hydrostatic equilibrium and is pulled
inwards by gravity
(2) the layer becomes compressed and less transparent to
radiation
(3) temperature inside the layer increases, building up the
internal pressure
(4) causing the layer to be pushed outwards
(5) During expansion the layer cools, becoming less dense
(6) and more transparent, allowing radiation to escape
and letting the pressure inside fall
(1) Subsequently the layer falls inwards under gravity
and the cycle repeats causing the pulsation of
the radiation emitted by the star.
Stellar Spectra classification system
Class
Temperature
Colour
O
30 000 - 60 000
Blue
B
10 000 - 30 000
Blue-white
A
7 500 - 10 000
White
F
6000 - 7500
Yellow-white
G
5000 - 6000
Yellow
K
3500 - 5000
Orange
M
2000 - 3500
Red
The Hertzsprung–Russell (H – R) diagram is a scattergram of stars showing the relationship between the
stars' luminosities versus their surface temperature. It shows stars of different ages and in different
stages, all at the same time.
Vertical axis: luminosity/ luminosity of the Sun (L⊙= 3.839 × 1026 W). Axis is logarithmic and has no unit.
The temperature axis is also logarithmic and doubles with every division from right (low) to left (high).
main sequence stars: nearly 90% of all stars
▪ fusing hydrogen into helium, the difference between
them is in mass
▪ during the lifetime of a star its position will move on the
diagram as its temperature and luminosity changes
▪ left upper corner more massive than right lower corner
▪ cooler red stars relatively low luminosity;
▪ hotter blue stars: high luminosity.
Red giants are cooler than the Sun
• emit less energy/m2 of surface.
• higher luminosity means they have a much greater surface area.
• a much larger diameter than the Sun – “giant” stars.
White dwarfs
• remnants of old stars
• constitute about 9%of all stars
• energy not produced by nuclear fusion
• very hot when they stopped producing energy,
• they have a relatively low luminosity
• a small surface area.
• very small, hot, very dense stars
• take billions of years to cool down.
Supergiant stars are gigantic and very bright.
• A supergiant has 100 000 times the power and
at the same temperature of the Sun must have
a surface area 100 000 times larger: a diameter that
is over 300 times the diameter of the Sun.
• Only about 1%of stars are giants and supergiants.
• Relationship between the luminosity and the mass:
L ∝ M3.5 (Observations of thousands of main sequence stars)
L is the luminosity in W (or multiples of the Sun’s luminosity, L⊙ )
M is the mass in kg (or multiples of the Sun’s mass, M ⊙ ).
• Even a slight difference in the masses of stars results in a large difference in their luminosities.
• For a star to be stable it needs to be in hydrostatic equilibrium:
the pressure due to the gravitational attraction of inner shells = the thermal and radiation
pressure acting outwards.
For a stable star of higher mass there will be greater gravitational compression and so the core
temperature will be higher. Higher temperatures make the fusion between nuclei in the core
more probable giving a greater rate of nuclear reaction and emission of more energy;
thus increasing the luminosity.
• The mass of a star is fundamental to the star’s lifetime – High mass stars have shorter lifetimes.
Formation of a star
▪ Gravitational attraction of hydrogen nuclei.
▪ Loss of PE leads to gain in KE and an increase in the gas temperature.
▪ The gas becomes denser and, when the protostar has sufficient mass, the temperature becomes high
enough for nuclear fusion to commence.
▪ The star moves onto the main sequence where it remains for as long as its hydrogen is being fused into
helium – this time occupies most of a star’s life.
▪ Eventually when most the hydrogen in the core has fused into helium the star moves off the main
sequence.
The fate of stars
▪ Star collapses when most of the hydrogen nuclei have fused into helium.
▪ Gravity now outweighs the radiation pressure and the star shrinks in size and heats up.
▪ The hydrogen in the layer surrounding the shrunken core is now able to fuse, raising the
temperature of the outer layers which makes them expand, forming a giant star.
▪ Fusion of the hydrogen adds more helium to the core which continues to shrink and heat up,
forming heavier elements including carbon and oxygen.
▪ The very massive stars will continue to undergo fusion until iron and nickel (the most stable
elements) are formed.
▪ What happens at this stage depends on the mass of the star.
A. Sun-like stars
▪ For stars up to about 4 solar masses the core temperature will not be high enough to allow
the fusion of carbon. This means that, when the helium is used up, the core will continue
to shrink while still emitting radiation.
▪ This “blows away” outer layers forming a planetary nebula around the star. When the
remnant of the core has shrunk to about the size of the Earth it consists of carbon and
oxygen ions surrounded by free electrons.
▪ It is prevented from further shrinking by an electron degeneracy pressure. Pauli’s exclusion principle
prevents two electrons from being in the same quantum state and this means that the electrons
provide a repulsive force that prevents gravity from further collapsing the star.
The star is left to cool over billions of years as a white dwarf.
Such stars are of very high density of about 109 kg m–3 .
The probable future for the
Sun is shown as the purple line
on the HR diagram.
B. Larger stars
▪ For the star much bigger than the Sun when in the red giant phase, the core is so large that
the resulting high temperature causes the fusion of nuclei to create elements heavier than carbon.
▪ The giant phase ends with the star having layers of elements with proton numbers that
decrease from the core to the outside (much like layers in an onion).
▪ The dense core causes gravitational contraction which, as for lighter stars, is opposed by electron
degeneracy pressure. Even with this pressure, massive stars cannot stabilize.
▪ The Chandrasekhar limit is the maximum mass of a stable white dwarf: 1.4 times the mass of the Sun.
▪ When the mass of the core reaches this value the electrons combine with protons to form neutrons,
emitting neutrinos in the process. The star collapses with neutrons coming as
close to each other as in a nucleus.
▪ The outer layers of the star rush in towards the core but bounce off it in a huge explosion – a supernova.
▪ Although this process lasts just a few hours it results in the heavy elements being formed.
▪ This blows off the outer layers and leaves the remnant core as a neutron star.
▪ Now neutrons provide a neutron degeneracy pressure that resists further gravitational collapse.
▪ The Oppenheimer–Volkoff limit places an upper value on a neutron star for which neutron degeneracy
is able to resist further collapse into a black hole.
This value is currently estimated at between 1.5 and 3 solar masses.
Black holes
It is not possible to form a neutron star having a mass greater than the Oppenheimer–Volkoff limit
instead the remnant of a supernova forms a black hole. Nothing can escape from a black hole –
including the fastest known particles, photons. For this reason it is impossible to see a black hole
directly but their existence can be strongly inferred by the following.
● The X-rays emitted by matter spiralling towards the edge of a black hole and heating up.
X-ray space telescopes, such as NASA’s Chandra, have observed such characteristic radiation.
● Giant jets of matter have been observed to be emitted by the cores of some galaxies.
It is suggested that only spinning black holes are sufficiently powerful to produce such jets.
● The unimaginably strong gravitational fields have been seen to influence stars in the vicinity,
causing them to effectively spiral. A black hole has been detected in the centre of the Milky Way
and it has been suggested that there is a black hole at the centre of every galaxy.
Techniques for determining stellar distances:
• stellar parallax,
• spectroscopic parallax
• Cepheid variables.
The distances used in astronomy are truly enormous, and this has meant
that a variety of indirect methods have been developed for their
measurement. The method used to measure the distance of an
astronomical object from the Earth is dependent on its proximity.
Spectroscopic parallax: no parallax at all!!!! (a lot of uncertainty in calculations)
• light from star analyzed (relative amplitudes of the absorption spectrum lines) to
give indication of stellar class/temperature
• HR diagram used to estimate the luminosity
• distance away calculated from apparent brightness
• limit: d ≤ 10 Mpc
Spectroscopic parallax is only accurate enough to measure stellar distances of up to
about 10 Mpc. This is because a star has to be sufficiently bright to be able to measure
the spectrum, which can be obscured by matter between the star and the observer.
Even once the spectrum is measured and the star is classified according to its spectral
type there can still be uncertainty in determining its luminosity, and this uncertainty
increases as the stellar distance increases. This is because one spectral type can
correspond to different types of stars and these will have different luminosities.
D3. COSMOLOGY
COSMOLOGY The Universe – what is its age and origin
Newton’s model of the universe assumed that the universe was:
▪ infinite (in space and time)
▪ uniform
▪ static
In 1823, the German astronomer, Heinrich Olbers, suggested that Newton’s
view of an infinite universe conflicted with observation
Olber’s paradox: Why in the world is the sky dark???
According to these assumptions the sky should not be dark
When we look up into the night sky we see darkness but, in an infinite
universe, we should be able to see a star in every direction and, therefore,
the night sky should be uniformly bright on a cloudless night. SHOULD BE.
But it is not.
Olber's Paradox can be reconciled through
1. expansion of the Universe and
2. the finite age and
- both of which are consequences of the Big Bang.
1. Universe is expanding
1a. Doppler’s redshift
Hubble: that stars further away from us have a higher recession velocity.
Consequently, these stars are more red shifted than those closer to us, so we could
perhaps not even see the electromagnetic waves the most distant stars emit, since they
don’t appear in the visible spectrum (dark regions of the night sky).
1b. Cosmological redshift
Which is not a Doppler effect.
Space itself is being stretched by expansion, so electromagnetic waves are also
stretched and therefore redshifted.
Expansion of space can cause the energy of emitted light from
the Big Bang to be reduced via redshift to microwave
wavelengths (1100 times longer than its original wavelength),
and thus form the cosmic microwave background radiation.
2. Universe has a finite age
If the universe is approximately 14 billion years old, we can see light that is less than 14
billion ly away.
And, so…
if we receive light from a finite # of stars, the night sky would be dark
Doppler effect and z-parameter
In the 1920's, Edwin Hubble realized that almost all
galaxies have a positive redshift.
λ of EM waves coming from stars are greater than those obtained in the
laboratory emitted from same elements (He, H).
The shift in a spectral line from a galaxy emission spectrum is given by:
∆λ = λ– λ0
λ0 is the wavelength emitted by the source
λ is the wavelength measured on Earth
The measured red shifts are usually stated in terms of a z parameter.
𝑧=
∆λ 𝑣
≈
λ0 𝑐
v is recession speed of the source
c is the speed of light in vacuum
𝑣≪𝑐
Goal: the speed of the galaxy
Hubble’s Law
He also noticed the farther the galaxy is, the greater the
redshift, therefore the greater the recessional velocity.
Recessional speed of the distant galaxies is
proportional to their distance form Earth.
𝑣 = 𝐻0 𝑑
H0 is the Hubble constant.
(Doppler-shift-measured velocity)
v is usually being measured in km s−1 and d in Mpc,
H0 is usually measured in km s −1 Mpc −1 .
How the Hubble constant may be determined.
• Measuring the distance to distant galaxies
• Measuring their recessional speed using Doppler effect
• Plotting a graph of v against distance.
• Hubble’s constant is equal to the gradient of the graph
Average value of Hubble’s constant is
72 km s-1 Mpc-1
This means that for every megaparsec to a
galaxy, the galaxy's speed away from us will
increase by 72 kilometers/second.
•
There are uncertainties in the distances measured precisely because it is quite
difficult to measure distances to remote galaxies accurately.
EX: This question is about the Hubble constant.
(a) The value of the Hubble constant H0 is accepted by some astronomers to be
in the range 60 km s–1 Mpc–1 to 90 km s–1 Mpc–1.
(i) State and explain why it is difficult to determine a precise value of H0
(2)
(i) The Hubble constant is the constant of proportionality between the recessional velocity of galaxies and
their distance from Earth. The further galaxies are away (from Earth) the more difficult it is to accurately
determine how far away they are. This is because of the difficulty of both locating a standard candle, such
as finding a Cepheid variable within the galaxy, and the difficulties of accurately measuring its luminosity.
(ii) State one reason why it would be desirable to have a precise value of H0.
(1)
(ii) Having a precise value of H0 would allow us to gain an accurate value of
the rate of expansion of the universe and to determine an accurate value to
distant galaxies. It would also allow us to determine a more reliable value for the age of the universe.
b) The line spectrum of the light from the quasar 3C 273 contains a spectral line
of wavelength 750 nm. The wavelength of the same line, measured in the
laboratory, is 660 nm.
Using a value of H0 equal to 70 km s–1 Mpc–1, estimate the distance of the
quasar from Earth.
−9
∆𝜆 = 90 × 10 𝑚
𝑣 = 𝐻0 𝑑
𝑧=
∆λ 𝑣
≈
λ0 𝑐
→ 𝑣 = 4.1 × 107 𝑚𝑠 −1
4.1 × 104 𝑚𝑠 −1
𝑑=
= 590 𝑀𝑝𝑐
70
Why is Doppler effect so important?
1. red-shift of light from galaxies indicates that the universe is expanding.
The universe is moving apart and expanding in all directions.
The farther away they are, the faster they move. This is Hubble's Law.
2. So, if galaxies are moving away from each other then it they may have been much closer in the past.
Matter was concentrated in one point and some “explosion” may have thrown the matter apart.
When did Big Bang happen?
𝑑
𝑑
𝑡= =
𝑣 𝐻0 𝑑
The time since the Big Bang is
𝑇=
1
𝐻0
This is called the Hubble time. Gives how
long it took for the galaxies to reach their
current separation.
It is the same for all of the galaxies!!
•
This is only an upper band as the Universe expanded faster at the beginning (this would imply a
younger Universe). The Universe cannot be older than this.
•
H0 = 70 km s-1 Mpc-1
𝑇=
1
= 4.29 × 1017 𝑠 = 13.6 × 109 𝑦𝑟
3
−1
−1
72 × 10 𝑚𝑠 (𝑀𝑝𝑐)
Big Band – the theory that won
Until the 1960s there were two competing theories of the origin of the universe.
Steady State Theory (Hermann Bondi, Thomas Gold, and Fred Hoyle 1948)
The density of matter in the expanding universe remains unchanged due to a
continuous creation of matter, thus adhering to the
perfect cosmological principle, a principle that asserts
that observable universe is basically the same at any time
as well as at any place.
Big Bang theory: One aspect of the Big Bang theory is that it suggested a very high
temperature early universe that cooled as the universe expanded.
In 1948, Gamow, Alpher, and Herman predicted that the
universe should show the spectrum of a black-body emitter
Density of galaxies falls
as universe expands
at a temperature of about 3 K. In the Big Bang model,
at approximately 4 × 105 years after the formation of the universe,
the temperature had cooled to about 3000 K and the charged ion matter was
able to attract electrons to form neutral atoms. This meant that space had
become transparent to electromagnetic radiation, allowing radiation to escape
in all directions (previously, when matter was ionic, it had been opaque to
radiation).
Background radiation
In 1960 two physicists, Dicke and Peebles, realising that there was more He than it
could be produced by stars, proposed that in the beginning of the Universe it was at a
sufficiently high temperature to produce He by fusion.
In this process a great amount of highly energetic radiation was produced.
However, as the Universe expanded and cooled, the energy of that radiation
decreased as wavelength increased. They predicted that the actual photons would
have an maximum λ (around 7 cm) corresponding to a black body spectrum of 3K.
So, they started to look for microwave radiation.
Shortly after this prediction, Penzias and Wilson
were working with a microwave aerial and found
that no matter in what direction they pointed
the aerial it picked up a steady, continuous
annoying background radiation.
Smoking gun for Big
Bang theory was found.
Background radiation
In every direction, there is a very low energy and very uniform radiation that we
see filling the Universe. This is called the 3 Degree Kelvin Background Radiation, or the
Cosmic Background Radiation, or the Microwave Background.
These names come about because
this radiation is essentially a black
body with temperature slightly less
than 3 degrees Kelvin (about 2.76 K),
which peaks in the microwave portion
of the spectrum.
Why is the background radiation an evidence for the Big Bang?
The CMB in the sky looks essentially the same in all directions (it is “isotropic”) and
does not vary with the time of day; this provides compelling support for the Big Bang
model. With the discovery of CMB, the advocates of the steady state theory were
forced to concede to the strength of evidence.
Big Bang
It postulates that 12 to 14 billion years ago, the singular point at which space, time,
matter and energy were created. It has since expanded from this hot dense state into
the vast and much cooler cosmos we currently inhabit.
We can see remnants of this hot dense matter as the now very cold cosmic
microwave background radiation which still pervades the universe and is visible to
microwave detectors as a uniform glow across the entire sky.
Main evidence:
Expansion of the Universe – the Universe is expanding (redshift)  it was once smaller
 it must have started expanding sometime  “explosion”
Background radiation  evidence of an hot Universe that cooled as it expanded
He abundance  He produced by stars is little  there is no other explanation for the
abundance of He in the Universe than the Big Bang model.
Fate of the Universe should depend on the mass (or not?)
So, how do we measure the density of the Universe?
If we take in account all the mass (stars) that we can see then the total mass
would not be enough to keep the galaxies orbiting about a cluster centre
So, there must be some matter that can not be seen – dark matter.
Dark Matter is matter that emits minimal or no light, BUT does have
gravitational influence. Evidence for dark matter appears to be present in
•
•
•
•
the motion of stars in galaxies.
the orbits of galaxies in galaxy clusters
the temperature of intracluster in galaxy clusters
the gravitational lensing of distant galaxies
Some possible types of dark matter include:
• MACHOS (Massive compact halo objects) – brown and black dwarfs and Jupiter-sized planets that
exist in halos of galaxies. Or similar cold objects and even black holes.
• WIMPS (Weakly interacting massive particles) – These are subatomic particles that have
extremely small masses, but exist in great quantities. Neutrinos are an example of a such particle.
The redshift equation and the cosmic scale factor
Although the cause of the redshift is the stretching of space rather than a constantly
moving source, the electromagnetic Doppler equation holds true and can be used in
astrophysics where the redshift ratio
∆𝜆
𝜆0
is denoted by the symbol z, giving
∆𝜆 𝑣
𝑧=
≈
𝜆0 𝑐
Because CMB suggests that the universe is essentially isotropic and homogeneous at any point in
space at a chosen (proper) time after the Big Bang, it is essentially true that the destiny of matter
should be the same throughout the universe. Soon after the Big Bang the density would have
been greater and at later smaller. The expansion of the universe can be considered to be a
rescaling of it. As the universe expands, all distances are streched with the cosmic scale factor R.
In other words, if the radiation had wavelength λ0 when it was emitted but λ when it was
detected, the cosmic scale factor would have changed from R0 to R. This means that space has
stretched by an amount ∆R in the time that the wavelength has stretched by the amount ∆λ.
Hubble’s law holds because, rather than galaxies receding from one another, space is expanding;
this results in the redshift being a Hubble redshift as opposed to a Doppler redshift.
∆𝜆 𝑣
≈
𝜆0 𝑐
and
𝑧=
∆𝜆 ∆𝑅 𝑅 − 𝑅0
𝑅
=
=
=
−1
𝜆0
𝑅0
𝑅0
𝑅0
Type Ia supernovae and the accelerating universe
In the late 1990s, Type Ia supernovae were found to offer key evidence
regarding the expansion of the universe. By using Type Ia supernovae as
standard candles to estimate galactic distances up to around 1000 Mpc and
measuring their redshifts, strong evidence was obtained suggesting the
universe might currently be undergoing an accelerated expansion. The
universe is known to contain a significant amount of ordinary matter that has a
tendency to slow down its expansion. Acceleration, therefore, would require
some sort of invisible energy source and, although none has been directly
observed, it has been named “dark energy”.
What is DARK ENERGY?
• It is the term used for a possible unseen influence that may be causing
the universal expansion to accelerate. As same as dark matter, dark
energy has been one of the most mysterious issues it exists in science.
• Dark energy is hypotetical form of energy that permeates all of space
and produces a negative pressure, resulting in repulsive gravitational
force. Dark energy may account for accelerating expansion of the
universe, as will as most of its mass. Recent obseravtions of
supernovae have produced a value for an acceleration that implies a
universe that is about 70% dark energy.
It can not be seen with today
technologies, as dark matter.
It might be that once again we are wrong about
gravitation, so
● there was Newton
● then there was Einstein
● And there might be ???????
Precision Cosmology
“…as we know, there are known knowns;
there are things we know we know.
We also know there are known unknowns;
that is to say we know there are some
things we do not know.
But there are also unknown unknowns -the ones we don't know we don't know.”