Download What is Dark Matter?

Centre: 51519
Candidate Number: 3096
G496 - Research Briefing
Sherman Ip
G496 Researching Physics: Research Briefing
What is Dark Matter?
Sherman Ip
1
Centre: 51519
Candidate Number: 3096
G496 - Research Briefing
Sherman Ip
Newton's Laws
The solar system runs like a giant clockwork, there are many planets orbiting the sun and many moons orbiting
planets, going around in circular motion. The force holding these planets and moons together is gravity and this
depends on the mass of the object; the more mass an object has the more gravitational force it has. This explains why
the sun is in the centre of the solar system because the mass of the sun is massive compared to the mass of the
planets so the sun has a lot of gravitational force to hold the planets in orbit.
Isaac Newton derived equations for gravitational force
F=
F =−
GMm
and centripetal force in circular motion
2
r
mv 2
. He combined these two equations to find out the expected orbit speed of a planet if a mass is
r
concentrated in the middle of the orbit, like the sun. The equation for the orbit speed is worked out as
v=

GM
r
Orbit speed (v)
, this is derived as shown in the appendix Fig 1. This equation is very important to find out how fast planets are
expected to orbit but also it is used to work out how fast satellites should orbit when launched into space. Below
shows how the speed of the orbit changes as the distance from the concentrated mass becomes bigger.
Distance from mass (r)
From this, it is expected that objects orbiting further away from the mass should orbit slower. This is true as this is
shown in the solar system; Mercury, the closest planet to the sun, takes about 88 Earth days to orbit the sun while
Neptune, the furthest planet in the Solar System, takes 165 Earth years to orbit the sun!
Newton's laws on gravitational force and circular motion has made it possible to predict orbit speeds for planets and
even the mass of the sun by rearranging his equation.
The problem
As planets orbits around the sun, the sun orbits around a super massive black hole (Sagittarius A*) in a galaxy called
the Milky Way.[9] Other objects and stars also orbits the black hole in the Milky Way with the sun, also like a giant
clockwork, and this can be seen using observatories because stars emit electromagnetic waves.
Using mathematical methods and precise measurements, it is possible to find out the orbital speed of stars in the
Milky Way galaxy by working out how much these electromagnetic waves have been stretched due to Doppler shift.
Using Newton's law, it is predicted that stars will orbit slower when further away from the black hole assuming the
black hole's mass is concentrated in the middle.
Unfortunately this predication is wrong, stars in the Milky Way seems to be orbiting at a constant speed and the
distance from the black hole has no effect on it.[1]
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Centre: 51519
Candidate Number: 3096
G496 - Research Briefing
Sherman Ip
Perhaps this was just the Milky Way galaxy being odd but in fact, astronomer Fritz Zwicky found that stars, hot gases
and cluster of galaxies are also moving faster than predicted. For example, for galaxy NGC 3198 he plotted the radius of
the star orbit against the orbital speed to see the correlation as shown below. [1][4]
The top graph shows the brightness of the centre
of the galaxy is as distance increase. It is brighter at
the centre of the galaxy which suggest a lot of
mass is concentrated at the centre and stars should
orbit it according to Newton's laws.[1][2]
This graph shows the orbital speed of stars against
the radius of its orbit. The solid line shows the
prediction of the orbital speed of stars using
Newton's laws. However actual results, shown as
uncertainty bars, show that the orbital speed
increases linearly at first but becomes almost
constant afterwards, even though there is no
visible mass away from the centre of the galaxy.[1][2]
This has confused a lot of astronomers and physicists, Newton's laws works for the solar system so why not for
galaxies?
Dark Matter appears
One suggestion is that dark matter is affecting the stars' orbits due to the dark matter's gravitational field. The matter
is described as 'dark' because it cannot be seen as it does not emit light or any electromagnetic waves making it
literally invisible and dark. It has mass so it has a gravitational field which will effect objects around it like stars. [1][2][3][4][6]
How the dark matter is distributed in galaxies is worked out by using observational data made by Zwicky that stars
orbital speeds are constant. It was thought that dark matter was distributed evenly throughout the galaxies; by
assuming the density of dark matter is constant, the orbit speed of stars should increase linearly as the radius of the
orbit increases, as shown in appendix Fig 2.[1] In fact if it behaves like a gas shell surrounding the galaxies, much like a
halo. The orbital speed of stars would be constant, as shown in appendix Fig 3. [1]
For this theory to work, the mass of dark matter must be 10 times heavier than normal matter therefore 90% of
galaxies would be made up of dark matter.[4]
Dark matter cannot be seen even using the most powerful telescopes so it is difficult to find out what dark matter
actually is. At the moment, there are two theories or types of dark matter: MACHO and WIMP. [1][2][4]
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Centre: 51519
Candidate Number: 3096
G496 - Research Briefing
Sherman Ip
MACHO
MACHO, massive compact halo objects, suggest that dark matter are *baryonic* matter. They are 'normal' matter
made out of 'normal' *baryonic* fundamental particles; protons, neutrons and electrons; [2][7] but they are compressed
and compacted so much that they are 'invisible', this means they have a lot of gravitational force per unit volume as a
result of being more denser and so have a massive effect on nearby stars. This means they should be detectable. [4]
Astronomers are able to detect MACHO, if they exist, by analysing the gravitational lensing effect they should produce.
Gravitational lensing, predicted by Einstein's theory of general relativity, is when the path of light or photons are
affected by nearby gravitational fields or 'bends' so astronomers will see a distorted or brighter image of galaxies. By
analysing where parts of the image is brighten by gravitational lensing it is possible to work out if dark matter is there
and is made out of normal particles. [4]
*Baryonic* is used to describe 'normal' matter and particles in astronomy, NOT to be confused with particle physics
where baryons are heavy particles which are affected by the strong nuclear interaction force.
WIMP
WIMP, weakly interacting massive particles, are heavy undiscovered particles, 10 to 10,000 times the mass of a proton,
but do not interact with baryonic matter hence the term 'weakly interacting'. [3] They are thought to be lots of neutrino,
particles which are almost massless, invisible and directly undetectable, to make the gravitational field on the outskirts
of galaxies. These neutrinos do not interact with 'normal' particles and at this very moment thousands of neutrinos are
travelling through your body.[2][4]
However neutrinos are very light so they cannot be dark matter as WIMP are up to 10,000 times the mass of a proton
to have a strong gravitational force. In general, there are no particles in the standard model of particle physics which
fits in the description of WIMP.[8]
As a result WIMP are very hard to detect because they only interact with gravitational forces. Many physicist are trying
to detect WIMP to this day.[1][4]
It adds up
How much dark matter there is in the universe is quite important to work out the shape of the universe. The critical
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density, 0 =3H 0 /8G , is the density required for the universe to be flat so it will carry on expanding to a limit
and stop.[5]
To the left shows the geometry of a flat universe. [4][10]
An universe with density less than the critical density would make
the universe negatively curved, as shown to the left, making it
curve outward. It will carry on expanding forever.[4][5][10]
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Centre: 51519
Candidate Number: 3096
G496 - Research Briefing
Sherman Ip
An universe with density more than the critical density would make the
universe positively curved, as shown to the left. The shape of the
universe bends back on itself and could even create a sphere because
the effect of gravity is so strong. The universe will collapse after
expanding due its own huge amount of gravitational force. [4][5][10]
Estimates of the current density of the universe suggest that the universe is negatively curved as the density of the
universe is less than the critical density. However this is an underestimate because there is a lot of dark matter
unaccounted for in the universe and if they add up it could suggest that the density of the universe is greater than the
critical density, making it positively curved, and hence predicts the Big Crunch, where the universe collapses under its
own gravitational force.[5]
Or is it something else?
Dark matter is still a theory because MACHO and WIMP haven't been confirmed yet. It could be that the Newtonian
laws does not work at large scales and the foundation for this problem needs to change. Perhaps it could be explained
by another theory called 'dark energy' where the universe is filled with this 'dark energy' which helps it expands and
speeds up orbits of stars.[1]
Many more theories will be proposed to explain why stars orbit faster than predicted by Newton's laws until dark
matter is discovered.
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Centre: 51519
Candidate Number: 3096
G496 - Research Briefing
Sherman Ip
Appendix
Fig 1. Assuming concentrated mass in the centre of orbit
F =−
GMm
mv 2
=−
2
r
r
GM
=v 2
r
⇒ v=

∴v∝
GM
r
1
⇒ Orbital speed decreases as orbital radius increases
r
Fig 2. Assuming uniform density
GM
2
=v
r
M=
v2 r
=V
G
2
v r 4 3
4
M=
=  r ⇐ volume of sphere=  r 3
G 3
3
v2 r 3
∴M =
∝r ⇒ Most of the mass is away from the centre
G
v2 r 4
3
= r 
G 3
v2 4
=  r2 
G 3
4
2
2
v = Gr 
3
v=

4
G  r2 
3
⇒ v=r

4
G 
3
∴ v ∝r ⇒ Orbital speed of stars is directly proportional to their orbital radius
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Centre: 51519
Candidate Number: 3096
G496 - Research Briefing
Sherman Ip
Fig 3. Assuming dark mater is concentrated into a shell at a distance r
=
M
V
=
M
⇐ volume of shell of sphere with thickness dr =4  r 2 dr
2
4 r dr
M =4  r 2 dr
2
∴ M ∝r ⇒ Most of the mass is away from the centre
v=r

⇒ v=
v=

4
G
3

4 G  r2 M
M
⇐ =
2
3×4 r dr
4  r 2 dr
GM
3 dr
∴ v=constant ⇒Orbital speeds are the same
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Centre: 51519
Candidate Number: 3096
G496 - Research Briefing
Sherman Ip
Bibliography
1.
Jon Ogborn and Rick Marshall
2008 - IOP Publishing
Advancing Physics A2
General detailed information of dark matter including suggestions on how dark matter is distributed and
Zwicky's graph of orbital stars on the galaxy NGC 3198.
2.
Stephen Hawking
2001 - Bantam Press
The Universe in a Nutshell
Zwicky's graph of orbital stars on the galaxy NGC 3198 and information on dark matter.
3.
Leif J. Robinson
2002 - Philip's
Astronomy Encyclopedia
Used to look up astronomical terms.
4.
Heather Couper and Nigel Henbest
1999 - DK
Space Encyclopedia
Information on gravitational lensing, dark matter and the shape of the universe.
5.
Chris Mee, Mike Crundell, Brian Arnold, Wendy Brown
2009 - Hodder Education
OCR Physics for A2
Information on the shape of the universe based on the critical density.
6.
Wikipedia - Dark Matter
http://en.wikipedia.org/wiki/Dark_matter
Used to cross reference on information of dark matter.
7.
Wikipedia - Massive compact halo object
http://en.wikipedia.org/wiki/Massive_compact_halo_object
Used to cross reference on MACHO.
8.
Wikipedia - Weakly interacting massive particles
http://en.wikipedia.org/wiki/Weakly_interacting_massive_particles
Comparison of WIMP with particles in the standard model of particle physics.
9.
Wikipedia – Sagittarius A*
http://en.wikipedia.org/wiki/Sagittarius_A*
Used to confirm if a black hole is in the centre of the Milky Way.
10. Wikipedia – Shape of the Universe
http://en.wikipedia.org/wiki/Shape_of_the_Universe
Pictures of the geometry of the different types of universes.
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