# 34.4 Dark matter and closure  (Page 4/16)

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Neutrino oscillations may also explain the low number of observed solar neutrinos. Detectors for observing solar neutrinos are specifically designed to detect electron neutrinos ${\nu }_{e}$ produced in huge numbers by fusion in the Sun. A large fraction of electron neutrinos ${\nu }_{e}$ may be changing flavor to muon neutrinos ${v}_{\mu }$ on their way out of the Sun, possibly enhanced by specific interactions, reducing the flux of electron neutrinos to observed levels. There is also a discrepancy in observations of neutrinos produced in cosmic ray showers. While these showers of radiation produced by extremely energetic cosmic rays should contain twice as many ${v}_{\mu }$ s as ${\nu }_{e}$ s, their numbers are nearly equal. This may be explained by neutrino oscillations from muon flavor to electron flavor. Massive neutrinos are a particularly appealing possibility for explaining dark matter, since their existence is consistent with a large body of known information and explains more than dark matter. The question is not settled at this writing.

The most radical proposal to explain dark matter is that it consists of previously unknown leptons (sometimes obtusely referred to as non-baryonic matter). These are called weakly interacting massive particles , or WIMPs    , and would also be chargeless, thus interacting negligibly with normal matter, except through gravitation. One proposed group of WIMPs would have masses several orders of magnitude greater than nucleons and are sometimes called neutralinos    . Others are called axions     and would have masses about ${\text{10}}^{-\text{10}}$ that of an electron mass. Both neutralinos and axions would be gravitationally attached to galaxies, but because they are chargeless and only feel the weak force, they would be in a halo rather than interact and coalesce into spirals, and so on, like normal matter (see [link] ).

Some particle theorists have built WIMPs into their unified force theories and into the inflationary scenario of the evolution of the universe so popular today. These particles would have been produced in just the correct numbers to make the universe flat, shortly after the Big Bang. The proposal is radical in the sense that it invokes entirely new forms of matter, in fact two entirely new forms, in order to explain dark matter and other phenomena. WIMPs have the extra burden of automatically being very difficult to observe directly. This is somewhat analogous to quark confinement, which guarantees that quarks are there, but they can never be seen directly. One of the primary goals of the LHC at CERN, however, is to produce and detect WIMPs. At any rate, before WIMPs are accepted as the best explanation, all other possibilities utilizing known phenomena will have to be shown inferior. Should that occur, we will be in the unanticipated position of admitting that, to date, all we know is only 10% of what exists. A far cry from the days when people firmly believed themselves to be not only the center of the universe, but also the reason for its existence.

## Section summary

• Dark matter is non-luminous matter detected in and around galaxies and galactic clusters.
• It may be 10 times the mass of the luminous matter in the universe, and its amount may determine whether the universe is open or closed (expands forever or eventually stops).
• The determining factor is the critical density of the universe and the cosmological constant, a theoretical construct intimately related to the expansion and closure of the universe.
• The critical density ρ c is the density needed to just halt universal expansion. It is estimated to be approximately 10 –26 kg/m 3 .
• An open universe is negatively curved, a closed universe is positively curved, whereas a universe with exactly the critical density is flat.
• Dark matter’s composition is a major mystery, but it may be due to the suspected mass of neutrinos or a completely unknown type of leptonic matter.
• If neutrinos have mass, they will change families, a process known as neutrino oscillations, for which there is growing evidence.

## Conceptual questions

Discuss the possibility that star velocities at the edges of galaxies being greater than expected is due to unknown properties of gravity rather than to the existence of dark matter. Would this mean, for example, that gravity is greater or smaller than expected at large distances? Are there other tests that could be made of gravity at large distances, such as observing the motions of neighboring galaxies?

How does relativistic time dilation prohibit neutrino oscillations if they are massless?

If neutrino oscillations do occur, will they violate conservation of the various lepton family numbers ( ${L}_{e}$ , ${L}_{\mu }$ , and ${L}_{\tau }$ )? Will neutrino oscillations violate conservation of the total number of leptons?

Lacking direct evidence of WIMPs as dark matter, why must we eliminate all other possible explanations based on the known forms of matter before we invoke their existence?

## Problems exercises

If the dark matter in the Milky Way were composed entirely of MACHOs (evidence shows it is not), approximately how many would there have to be? Assume the average mass of a MACHO is 1/1000 that of the Sun, and that dark matter has a mass 10 times that of the luminous Milky Way galaxy with its ${\text{10}}^{\text{11}}$ stars of average mass 1.5 times the Sun’s mass.

$1\text{.}5×{\text{10}}^{\text{15}}$

The critical mass density needed to just halt the expansion of the universe is approximately ${\text{10}}^{-\text{26}}\phantom{\rule{0.25em}{0ex}}\text{kg}/{\text{m}}^{3}$ .

(a) Convert this to $\text{eV}/{c}^{2}\cdot {\text{m}}^{3}$ .

(b) Find the number of neutrinos per cubic meter needed to close the universe if their average mass is $7\phantom{\rule{0.25em}{0ex}}\text{eV}/{c}^{2}$ and they have negligible kinetic energies.

Assume the average density of the universe is 0.1 of the critical density needed for closure. What is the average number of protons per cubic meter, assuming the universe is composed mostly of hydrogen?

$0\text{.}6{m}^{-3}$

To get an idea of how empty deep space is on the average, perform the following calculations:

(a) Find the volume our Sun would occupy if it had an average density equal to the critical density of ${\text{10}}^{-\text{26}}\phantom{\rule{0.25em}{0ex}}\text{kg}/{\text{m}}^{3}$ thought necessary to halt the expansion of the universe.

(b) Find the radius of a sphere of this volume in light years.

(c) What would this radius be if the density were that of luminous matter, which is approximately $5%\text{}$ that of the critical density?

(d) Compare the radius found in part (c) with the 4-ly average separation of stars in the arms of the Milky Way.

How submarines floats one water the same time sink in water
A submarine has the ability to float and sink. The ability to control buoyancy comes from the submarine'strim or ballast tanks which can be filled with either water or air, depending on whether the submarine needs to floator sink. When the submarine floats it means its trim tanks are filled with air
Arif
what is work
Force times distance
Karanja
product of force and distance...
Arif
Is physics a natural science?
what is the difference between a jet engine and a rocket engine.
explain the relationship between momentum and force
A moment is equivalent multiplied by the length passing through the point of reaction and that is perpendicular to the force
Karanja
How to find Squirrel frontal area from it's surface area?
how do we arrange the electronic configuration of elements
hi guys i am an elementary student
hi
Dancan
hello
are you an elementary student too?
benedict
no bro
yes
Che
hi
Miranwa
yes
Miranwa
welcome
Miranwa
what is the four equation of motion
Miranwa
what is strain?
SAMUEL
Change in dimension per unit dimension is called strain. Ex - Change in length per unit length l/L.
ABHIJIT
strain is the ratio of extension to length..=e/l...it has no unit because both are in meters and they cancel each other
How is it possible for one to drink a cold drink from a straw?
most possible as it is for you to drink your wine from your straw
Selina
state the law of conservation of energy
energy can neither be destroy or created,but can be change from one form to another
dare
yeah
Toheeb
it can neither be created nor destroyed
Toheeb
its so sample question dude
Muhsin
what is the difference between a principle and a law?
where are from you wendy .?
ghulam
philippines
Mary
why?
Mary
you are beautiful
ghulam
are you physics student
ghulam
laws are ment to be broken
Ge
hehe ghulam where r u from?
Muhsin
yes
dare
principle are meant to be followed
dare
south Africa
dare
here Nigeria
Toheeb
principle is a rule or law of nature, or the basic idea on how the laws of nature are applied.
Ayoka
Rules are meant to be broken while principals to be followed
Karanja
principle is a rule or law of nature, or the basic idea on how the laws of nature are applied.
tathir
what is momentum?
is the mass times velocity of an object
True
it is the product of mass and velocity of an object.
The momentum possessed by a body is generally defined as the product of its mass and velocity m×v
Usman
momentum is the product of the mass of a body of its velocity
Ugbesia
what about kg it is changing or not
no mass is the quantity or amount of body so it remains constant everywhere
Ahsan
yes
Siyanbola
remains constant
taha
mass of an object is always constant. and that is universally applied.
Shii
mass of a body never changes but the weight can change due to variance of gravity at different points of the world
Saheed
what is hookes law
Joshua
mass of an object does not change
SAMUEL
Is weight a scalar quantity
weight is actually a force of gravity with which earth attracts us downwards so it is a vector quantity. and it has both direction and magnitude
Ahsan
ty
Denise
weight is the earth pull of the body
Ugbesia
why does weight change but not mass?
Theo
Theo, the mass of an object can change but it depends on how you define that object. First, you need to know that mass is the amount of matter an object has, and weight is mass*gravity (the "force" that attracts object A to the object B mass).
Nicolas
So if you face object A with object B, you will get a different result than facing object A with object C, so the weight of object A changes but not its mass.
Nicolas
Now, if you have an object and you take a part away from it, you are changing it mass. Lets use the human body and fat loss process as an example.
Nicolas
When you lose weight by doing exercise, you are being attracted by the same object before and after losing weight so the change of weight is related to a change of mass not a change of gravity.
Nicolas
The explanation of this is simple, we are composed of smaller particles, which are itself objects, so the loose of mass of an object actually is the separation of one object is two different ones.
Nicolas
But if you define an object because of its form and characteristics and not the amount of mass, then the object is the same but you have taken a part of it mass away.
Nicolas
Theo, weight =mass. gravity, here mass is fixed everywhere but gravity change in different places so weight change not mass.
ABHIJIT
yup weight changes and mass does not. That's why we're 1/3 our weight on the moon
clifford
weight is the product of mass × velocity w=m×v = m(v-u) but v=u+1/2at^ weight is a scalar quantity mass of an obj is the amount of particles that obj cont
Usman
mass is fixed always while weight is dynamic
Usman
Why does water wet glass but mercury does not?
Yusuf
thanks guys
Theo
Yusuf Shuaibu, for water the Adhessive force between water molecules and glass is greater than the cohessive force between it's own molecules but for Mercury the cohessive force will be greater in comparison with adhessive force. For this water wet glass but Mercury does not.
ABHIJIT
in electrostatic e bonite rod electron is static. they cannot flow to other. because static. is it correct?
Is weight a scalar quantity
esther
wieght is the vector
ghulam
yes
Mohet
Yes
Karanja