A&B's Astronomy Lab, Spring 2002, No. 7

Dark Matter and the Fate of the Universe

There exists invisible matter in the universe?!
How do we know there is missing mass
and how it will affect on the fate of the universe?

Galaxy Rotation and Dark Matter

The stars and gas rotate about the center of the Galaxy. The rotation speed varies with distance from the center. From the speed at a given point, we can deduce the mass. The total mass of the galaxy can be computed from Newton's laws. Combining the expression for circular velocity at a given radius with Newton's version of Kepler's third law gives,

Example I
Merry-go-round - the velocity increases (linearly) with increasing distance. This is also called "solid body rotation".
* Note that to one direction, every point have the same angular velocity but the circular velocity increases as one goes further from the center (have you observed a rotating Compact Disk while you are listening to music?).

Example II
Solar system - the velocity decreases (as 1/square-root(r)) with increasing distance. The rotation curve follows Kepler's law. * Note that the whole solar system is not a solid body (a planet do not move like one spot on your music CDs), each planet goes around the Sun following Kepler's law.

Then what about a rotation curve of our Galaxy?
The rotation curve of a galaxy shows how the orbital velocities of the stars change with distance from the center. If the galaxy rotated as a solid disk, the velocity would increase linearly with distance. If most of the mass were concentrated at the the center, as in our solar system, the velocities of the stars would decrease with the square root of the distance. But, that is not what is observed. The rotation curve for the Milky Way is relatively flat.

It is more like the merry-go-round than that of the solar system Thus there is no dominant central mass. Meanwhile, far past the point where no mass is visible, the rotation curves are flat! Mass of the Galaxy Using Newton's form of Kepler's third law we can deduce the mass of the Milky Way at different distances from the center. And the flat rotation curve of the Milky Way means that the mass is still increasing as we move outward, even though we can't see anything! The galaxy must extend much farther out than the luminous matter indicates. For example, the Sun is rotating around the Galactic center with v = 220 km/sec at a radius of 8.5 kpc. It indicates that the mass of the Milky Way within 8.5 kpc is almost 10¹¹ M_sun, which is at least 10 times more mass than we can see! Calculations suggest that this dark matter is likely to be in an extensive halo of "dark matter" which is not detectable. It is sometimes called missing mass because starlight cannot trace it but we know its existence.

Dark Matter and the Ultimate Fate of the Universe

The evolution of the universe is determined by a struggle between the momentum of expansion and the pull (or push!) of gravity. The current rate of expansion is measured by the Hubble Constant, while the strength of gravity depends on the density and pressure of the matter in the universe.

If the pressure of the matter is low, as is the case with most forms of matter we know of, then the fate of the universe is governed by the density. If the density of the universe is less than the critical density (The present average density required to close the universe) which is proportional to the square of the Hubble constant, then the universe will expand forever. If the density of the universe is greater than the critical density, then gravity will eventually win and the universe will collapse back on itself, the so called "Big Crunch".

However, recent observations of distant supernova have suggested that the expansion of the universe is actually accelerating or speeding up, like the unbound curve above, which implies the existence of a form of matter with a strong negative pressure. This strange form of matter is also sometimes referred to as the "dark energy". If dark energy in fact plays a significant role in the evolution of the universe, then in all likelihood the universe will continue to expand forever. There is a growing consensus among cosmologists that the total density of matter is equal to the critical density, so that the universe is spatially flat. Approximately 3/10 of this is in the form of a low pressure matter, most of which is thought to be "non-baryonic" dark matter, while the remaining 7/10 is thought to be in the form of a negative pressure "dark energy", like the cosmological constant. If this is true, then the universe will continue in a runaway expansion, as depicted in the unbound curve above.

Galaxy Rotation and Dark Matter
The stars and gas rotate about the center of the Galaxy. The rotation speed varies with distance from the center. From the speed at a given point, we can deduce the mass. The total mass of the galaxy can be computed from Newton's laws. Combining the expression for circular velocity at a given radius with Newton's version of Kepler's third law gives,
Example I Merry-go-round - the velocity increases (linearly) with increasing distance. This is also called "solid body rotation". * Note that to one direction, every point have the same angular velocity but the circular velocity increases as one goes further from the center (have you observed a rotating Compact Disk while you are listening to music?).
Example II Solar system - the velocity decreases (as 1/square-root(r)) with increasing distance. The rotation curve follows Kepler's law. * Note that the whole solar system is not a solid body (a planet do not move like one spot on your music CDs), each planet goes around the Sun following Kepler's law.
Then what about a rotation curve of our Galaxy? The rotation curve of a galaxy shows how the orbital velocities of the stars change with distance from the center. If the galaxy rotated as a solid disk, the velocity would increase linearly with distance. If most of the mass were concentrated at the the center, as in our solar system, the velocities of the stars would decrease with the square root of the distance. But, that is not what is observed. The rotation curve for the Milky Way is relatively flat. It is more like the merry-go-round than that of the solar system Thus there is no dominant central mass. Meanwhile, far past the point where no mass is visible, the rotation curves are flat! Mass of the Galaxy Using Newton's form of Kepler's third law we can deduce the mass of the Milky Way at different distances from the center. And the flat rotation curve of the Milky Way means that the mass is still increasing as we move outward, even though we can't see anything! The galaxy must extend much farther out than the luminous matter indicates. For example, the Sun is rotating around the Galactic center with v = 220 km/sec at a radius of 8.5 kpc. It indicates that the mass of the Milky Way within 8.5 kpc is almost 10¹¹ M_sun, which is at least 10 times more mass than we can see! Calculations suggest that this dark matter is likely to be in an extensive halo of "dark matter" which is not detectable. It is sometimes called missing mass because starlight cannot trace it but we know its existence.

Dark Matter and the Ultimate Fate of the Universe
The evolution of the universe is determined by a struggle between the momentum of expansion and the pull (or push!) of gravity. The current rate of expansion is measured by the Hubble Constant, while the strength of gravity depends on the density and pressure of the matter in the universe.
	If the pressure of the matter is low, as is the case with most forms of matter we know of, then the fate of the universe is governed by the density. If the density of the universe is less than the critical density (The present average density required to close the universe) which is proportional to the square of the Hubble constant, then the universe will expand forever. If the density of the universe is greater than the critical density, then gravity will eventually win and the universe will collapse back on itself, the so called "Big Crunch".
However, recent observations of distant supernova have suggested that the expansion of the universe is actually accelerating or speeding up, like the unbound curve above, which implies the existence of a form of matter with a strong negative pressure. This strange form of matter is also sometimes referred to as the "dark energy". If dark energy in fact plays a significant role in the evolution of the universe, then in all likelihood the universe will continue to expand forever. There is a growing consensus among cosmologists that the total density of matter is equal to the critical density, so that the universe is spatially flat. Approximately 3/10 of this is in the form of a low pressure matter, most of which is thought to be "non-baryonic" dark matter, while the remaining 7/10 is thought to be in the form of a negative pressure "dark energy", like the cosmological constant. If this is true, then the universe will continue in a runaway expansion, as depicted in the unbound curve above.