Dark Matter - Fate of Our Universe

Author: Angus 

Is dark matter really a matter in dark? I will say no but nearly.

Matter that doesn’t emit (or emits very little) nor absorb electromagnetic radiation (or absorbs very little) can be considered as dark matter. The term of dark matter is brought up into the world of astronomy by scientists Jan Oort and Fritz Zwicky in early the 20th century to account for the missing part of the total mass in the universe.

Mass-to-light ratio
is used to express the relation between mass and light output of the mass using (of sun) as reference. So mass-to-light ratio of sun is 1. Scientists found out the light emitted from a galaxy multiplying with the average mass-to-light ratio, the mass of the galaxy comes out , followed by division by the volume that the galaxy occupied, we can find out the average density for luminous matter . If we compare the result to the critical density (the density that makes the universe flat, which mentioned in the last part), the density of luminous matter is only 0.5% of critical density. (Iain Nicolson (2007) “Dark Side of the Universe Dark Matter, Dark Energy, and the Fate if the Cosmos” page34)

1. How we discover 

►The figure shows the relationship between angular velocity of stars orbiting the center of the spiral galaxy and the distance of stars away from the center of the spiral galaxy. Line A is the expected Keplerian result which the stars follow Kepler’s laws (square of orbital speed of star is proportional to cube of distance from the semi-major axis, distance between center and the star). Line B is the actual result observed by advanced telescopes. (Picture from Wikipedia) 

►The picture shows how stars distributed in a spiral galaxy

By Newton’s law of universal gravitation 
 and centripetal force , we get the equation . Assuming the disk part is a perfect circle, and the density of matter is even distributed in the disk, we get mass  for disk part. The larger r (distance between center and star) the smaller w (angular speed) we get, but the reality isn’t. What makes the two lines different? The secret lies under dark matter. 

To remain the angular velocity being the same value when distance increases, extra mass must be added, so a large portion of mass without shining also should be taken into account, those are dark matter.

Also, phenomena of gravitational lens can help scientists to find out dark matter. With the assistance of general relativity, mass distorts the nearby spacetime and bends the light when light travels across. The image of background source may be magnified and distorted because of lensing effect. So if unreasonably distorted of images of stars with no shining massive matter stays in front of it may illustrate the presence of dark matter. 

►The image show the lensing effect (Picture from Wikipedia)

2. Types of dark matter

There are two types of dark matter, one is baryonic dark matter and the second is non-baryonic dark matter.

2.1 Baryonic dark matter

Baryonic matter is a matter that made up by three quarks or antiquarks (not to mention any anti-matter in this article), involving into four fundamental force (strong nuclear force, weak nuclear force, electromagnetic force and gravitational force), simply to say, baryon is everything we see, we touch, we lived with.

Baryonic dark matter is talking about the massive astrophysical compact halo object (MACHO), which is present around our galaxy. It can be black holes, neutron stars and dwarfs (white, brown and red one). Black hole with escape speed equaling to speed of light attracts everything nearby, even light (See more detail in previous article by Wayne Chan). But that doesn’t mean black hole wouldn’t emit electromagnetic wave near event horizon. The wave emitted called Hawking Radiation with interesting characteristic, faster emission rate with smaller black hole. Neutron star is a super dense remnant from massive star during a supernova after throwing off most of its surface layer. The materials in the star are supported by the neutron degeneracy pressure (no two neutron can occupy same quantum state). The mass limit is between 1.4 and around 3.2 (the upper limit of neutron star is still not very sure nowadays) solar mass.

White dwarf is the dense remnant of star after the life of main sequence star ends. The material is supported by electron degeneracy pressure, which is similar to the neutron star’s one, with a 1.4 solar mass upper limit according to Chandrasekhar limit. White dwarfs emit its remaining thermal energy stored and no nuclear fusion takes place, with time flies, the white dwarfs will turn into black dwarf after emitting all its remaining light.

Red dwarf is a main sequence star but with upper limit around 0.35 solar mass, it has much less luminosity and the mass isn’t large enough for helium flash. It only fueled by p-p chain, the nuclear fusion with four protons into helium nucleus.

Brown dwarf with an upper limit around 75 Jupiter mass can’t fuse hydrogen into helium, is considered as fail star.

2.2 Non-baryonic dark matter

Non-baryonic matter is a matter not formed from atoms and quarks. The matter only involve in weak nuclear force and gravitation, which is completely different from baryonic matter. But that “ghost” like particle how can we distinguish between the baryonic dark matter and non-baryonic dark matter?

In the first few moments of our early universe, everything is fixed, including the baryon-photon ratio. During the time, the Big Bang nucleo-synthesis took place, of which only atoms like hydrogen, deuterium (heavy hydrogen), helium-3 (light helium), helium and lithium exist. The portion of different types of atoms depends on the baryon-photon ratio, so too many baryon (>8% of total density) on the early universe causes more helium (larger portion in baryon) that we observed today, and too less baryon (<2% of total density) causes much less helium (lower portion in baryon). In the present moment, the baryon mostly composed of 74% of hydrogen and 26% of helium by mass. Then we can conclude that the baryon abundance lie between 2% and 8% of total density required turning our universe into flat (although our universe isn’t flat but nearly) (Adams Laughlin (1999) “The Five Ages Of The Universe” chapter1). So the other ingredients to fill up the universe are around 23% of dark matter and around 70% for dark energy, only 4.6% from atoms.

Non-baryonic dark matter is divided into three types, Hot Dark Matter (speed comparable with speed of light, neutrino is an example), Warm Dark Matter and Cold Dark Matter, in term of their mass and velocity, of which massive matter means lower speed, so mass and velocity are the same things.

3. Fate of our universe

As the previous paragraph mentioned the term “critical density”, but, how critical density relates to our future?

Our universe is under a battle between the gravitation and the force to expand (dark energy). If the mean density of total matter and radiation exactly equal to the critical density, the universe will expand forever but tends to zero when time travels and Euclidean geometry apply (for example, the triangle is 180 degree). If the mean density is below the critical density, the universe is open and the expansion is kept forever but the rate slows down because of gravity. The curvature of the universe would be negative with saddle-shaped surface (triangle is less than 180 degree). If the mean density is above the critical density, the universe is said to be positive curved with spherical surface (triangle is large than 180 degree), of which the universe is limited space but without boundary. The expansion of the universe will be stopped in someday and start shrinking into a “Big Crunch”.

▲Picture from The University of Hong Kong Department of Physics

The situation mentioned above is all about the possible situation without dark energy. Taking account of dark energy makes the situation more complex.

So, scientists certainly find that the mean density of our universe is lie between 0.1 and 10 where 1 equals to critical density. With the Hubble’s law, the redshift (speed of receding) of other galaxies is proportional to the distance between our Earth and galaxies, which shows the universe is expanding.

But no one knows whether the matter is laid in or out of threshold of critical mass and how our universe will evolve into, maybe only time can tell.

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