In the absence of dark energy, the critical density is defined to be the density that defines the boundary between the density of a universe with enough matter to someday stop expanding (and begin to collapse) and the density of a universe with too little matter for its expansion ever to halt.
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The density of a critical universe is exactly this critical density, so the ratio of actual density to critical density of a critical universe is one. A recollapsing universe has a higher density — meaning a ratio of actual density to critical density that is greater than one— means enough gravity so that it will eventually stop expanding and begin to contract.
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A coasting universe continues to expand and grow in size forever, which means it must have a density lower than the critical density, or a ratio of actual density to critical density that is less than one. That is why the ranking order from smallest ratio to largest ratio is coasting, critical, recollapsing.
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The average distance between galaxies at any future time depends on the rate of expansion: The faster the expansion, the larger this distance will be.
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The recollapsing universe therefore has the smallest average distance between galaxies, because by definition its expansion rate is slowing enough so that the expansion will someday stop altogether.
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The critical universe has the next-lowest rate of expansion, followed by the coasting universe.
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The expansion rate gets larger with time in an accelerating universe, which is why this model predicts the largest distance between galaxies in the future.
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The current age of the universe depends on how long it has taken since the Big Bang for galaxies to reach their current average separations.
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This time is shorter if the past expansion rate has been faster.
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Because the recollapsing universe has its rate of expansion decreasing most rapidly of the four models, its past rate of expansion must be highest, implying the youngest age for the universe.
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The accelerating universe had the lowest past expansion rate, because its rate increases with time, and therefore implies the oldest age for the universe.
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Similarly, the critical universe is slowing more than the coasting universe, and therefore implies a younger age for the universe.
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Which of the following best explains why a higher-mass cluster of galaxies causes light from a distant galaxy to bend more than a lower-mass cluster of galaxies?
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The stronger gravity of a larger cluster curves space itself by a greater amount, and light follows the curvature of space.
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According to Einstein’s general theory of relativity, the gravity of a massive object curves space itself (or, more generally, gravity curves spacetime).
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Because light always follows the straightest possible path, the light must follow the curve caused by gravity.
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A larger cluster means greater curvature of space, which therefore means greater bending in the path the light follows on its way to Earth.
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Consider a distant galaxy located directly behind a cluster of galaxies as shown in this interactive figure. Knowing the distance to the cluster of galaxies and the angular separation of the lensed images of the distant galaxy, astronomers can estimate:
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the total amount of matter in the cluster of galaxies, including both dark matter and matter in stars
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All forms of mass curve spacetime in the same way, regardless of their composition.
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Therefore, measurements of gravitational lensing tell astronomers the total mass of the objects causing the lensing, but do not distinguish between different types of matter.
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The rotation curve for a merry-go-round is a straight line, because a merry-go-round rotates as a rigid body.
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Every point on the merry-go-round circles the center in the same amount of time, but the circles are bigger for points farther from the center, which means these points must move faster to complete their circles in the same time.
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Therefore, the orbital speed of any point is directly proportional to its distance from the center.
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The key point is that for planets orbiting the Sun, speed becomes slower with increasing distance.
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Gravity holds planets in their orbits.
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Because the Sun contains most of the solar system's mass, the major source of gravity in the solar system is concentrated at the Sun's location.
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The force of gravity gets weaker with distance, so planets farther from the Sun feel a weaker force and therefore orbit more slowly.
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Why does the rotation curve for the solar system show speeds that become slower with increasing distance from the Sun?
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Because the Sun contains most of the mass of the solar system
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The net force from mass beyond the star's orbit is nearly zero, because the gravitational pulls from masses on opposite sides of the galaxy nearly cancel one another.
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Therefore, only mass within the star's orbit affects the star's orbital speed.
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According to the law of gravity as we understand it today, the only explanation for these this flatness is that __________.
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substantial amounts of mass must reside at great distances from the galactic center
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This mass is what we call dark matter. To summarize the evidence for dark matter we have examined in this tutorial:
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1. From Part E, we know that the orbital speed of a star (or other object) around the center of the galaxy depends only on the amount of mass contained within that object's orbit. 2. The flat rotation curve in Part D therefore indicates that objects at greater distances must have more mass within their orbits than objects closer in, which means there must be significant mass at great distances from the galactic center. 3. Because we don't see this mass that must be out there, we call it dark matter.
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As noted in the Introduction, some scientists have proposed that dark matter does not really exist. According to this view, all matter is ordinary (baryonic), but at large distances from matter, gravity does not precisely obey either Newton's or Einstein's theories of gravity. Is this alternative view of gravity consistent with what we observe in the Bullet Cluster? Why or why not?
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No. If all matter was ordinary, then the blue region representing the location of most of the matter would line up with the red region representing the hot gas.
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In summary, there are two key observational facts:
The blue region in the composite image represents the distribution of matter of any kind (dark or ordinary) inferred from observations of gravitational lensing.
The red region represents the location of hot, X-ray-emitting gas, which represents most of the ordinary (baryonic) matter.
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Therefore, the location of most of the total matter (blue) is not the same as the location of most of the ordinary matter (red), which means that most of the matter must not be ordinary.
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The two main candidates for making up the majority of dark matter are WIMPs (weakly interacting massive particles) and MACHOs (massive compact halo objects). WIMPs are subatomic particles that are not baryons, and hence they are a type of nonbaryonic matter. MACHOs are made of ordinary (baryonic) matter and may include objects including planet-size bodies, brown dwarfs, and small dim stars; they are dark matter only because they are so far away that we cannot detect them. Evidence suggests that while some dark matter is present in MACHOs, the majority of dark matter must be nonbaryonic, which is why most astronomers suspect that most dark matter consists of WIMPs.
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The rotation curve for a merry-go-round is a straight line, because a merry-go-round rotates as a rigid body. Every point on the merry-go-round circles the center in the same amount of time, but the circles are bigger for points farther from the center, which means these points must move faster to complete their circles in the same time.
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Therefore, the orbital speed of any point is directly proportional to its distance from the center.
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Why does the rotation curve for the solar system show speeds that become slower with increasing distance from the Sun?
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Because the Sun contains most of the mass of the solar system
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Gravity holds planets in their orbits. Because the Sun contains most of the solar system's mass, the major source of gravity in the solar system is concentrated at the Sun's location. The force of gravity gets weaker with distance, so planets farther from the Sun feel a weaker force and therefore orbit more slowly.
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The net force from mass beyond the star's orbit is nearly zero, because the gravitational pulls from masses on opposite sides of the galaxy nearly cancel one another. Therefore, only mass within the star's orbit affects the star's orbital speed.
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This mass is what we call dark matter. To summarize the evidence for dark matter we have examined in this tutorial:
From Part E, we know that the orbital speed of a star (or other object) around the center of the galaxy depends only on the amount of mass contained within that object's orbit.
The flat rotation curve in Part D therefore indicates that objects at greater distances must have more mass within their orbits than objects closer in, which means there must be significant mass at great distances from the galactic center.
Because we don't see this mass that must be out there, we call it dark matter.
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Which of the models predict that galaxies should be getting farther apart now? (Keep in mind that now is located at at [image] on the graph.)
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We observe that the universe is expanding today, meaning that the average distance between galaxies is increasing, so all four models must predict this observed fact. If a model did not agree with these observations, then we would know that the model is not physically realistic.
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Which of the models predict that galaxies will eventually get closer together in the future?
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The fact that the recollapsing curve turns downward in the future (to the right of “now”) means that this model predicts that galaxies will begin to get closer at some time in the future, implying that the universe will eventually stop expanding and start contracting.
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You can see this fact on the graph by looking along an imaginary vertical line corresponding to a time of 6 billion years ago: Notice that the accelerating curve crosses this line highest of the four models, which means that it corresponds to the largest average distance between galaxies.
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What additional data would be most valuable in helping scientists evaluate whether the accelerating model really is the best of the four models?
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These observations would be most useful because the four models have more noticeably different predictions for times farther in the past. Supernovae that can be plotted far in the past—meaning those that we see at great distances—are therefore more useful for distinguishing among the four models.
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matter that we have identified from its gravitational effects but that we cannot see in any wavelength of light
These gravitational effects are easily observed, so either dark matter really exists or there is something wrong with our understanding of how gravity works on large scales.
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It is a name given to whatever is causing the expansion of the universe to accelerate with time.
Observations indicate that the expansion is accelerating, which means something must be causing this acceleration. We don't know what it is, but we call it dark energy.
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dark matter represents much more mass and extends much further from the galactic center than the visible stars of the Milky Way
Observations indicate that dark matter may represent more than 90% of the Milky Way Galaxy's overall mass, and that it extends far beyond the galaxy's visible disk and the visible stars of the halo.
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a graph showing how orbital velocity depends on distance from the center for a spiral galaxy
We plot orbital velocity on the vertical axis and distance from the galactic center on the horizontal axis.
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We construct its rotation curve by measuring Doppler shifts from gas clouds at different distances from the galaxy's center.
More specifically, we generally measure Doppler shifts in the 21-centimeter line that we can detect from atomic hydrogen clouds. These clouds extend beyond the distance at which we see many stars, making them more useful than stars for constructing the rotation curve.
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Gas clouds orbiting far from the galactic center have approximately the same orbital speed as gas clouds located further inward.
Remember that the rotation curve shows velocity on the horizontal axis, so a "flat" curve means the same velocity at different distances.
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Elliptical galaxies probably contain about the same proportion of their mass in the form of dark matter as do spiral galaxies.
Evidence shows that dark matter is indeed dominant in elliptical galaxies as well as spiral galaxies, and we have no reason to think the overall proportion of dark matter is significantly different.
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Elliptical galaxies probably contain about the same proportion of their mass in the form of dark matter as do spiral galaxies.
Evidence shows that dark matter is indeed dominant in elliptical galaxies as well as spiral galaxies, and we have no reason to think the overall proportion of dark matter is significantly different.
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the higher the amount of mass relative to light (higher mass-to-light ratio), the greater the proportion of dark matter
Dark matter has mass but gives off no light that we detect, so it tends to make mass-to-light ratios higher than they would be without the dark matter.
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measuring the temperatures of stars in the halos of the galaxies
Stellar temperatures depend only on the masses and ages of the stars themselves, not on the mass of the galaxy cluster.
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It bends or distorts the light coming from galaxies located behind it.
The amount of the distortion tells us the mass of the cluster causing the lensing. In fact, detailed studies of the distortion even allow us to map out the distribution of mass in the cluster.
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Dark matter is the dominant form of mass in both clusters and in individual galaxies.
In fact, these studies indicate that dark matter outweighs ordinary matter by at least about a factor of 10.
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It consists of atoms or ions with nuclei made from protons and neutrons.
Baryonic matter gets its name because protons and neutrons are both classified as baryons.
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neutrinos
Neutrinos are subatomic particles with very low mass, so they certainly are not "massive compact" objects.
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They respond to the weak force but not to the electromagnetic force, which means they cannot emit light.
Photons are electromagnetic waves and therefore can be emitted only by particles that respond to the electromagnetic force.
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Most dark matter probably consists of weakly interacting particles of a type that we have not yet identified.
Strange as it may seem, the idea that dark matter consists of an as-yet-unknown type of WIMPs is the leading hypothesis for the nature of dark matter.
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the overall arrangement of galaxies, clusters of galaxies, and superclusters in the universe
Studies of this large-scale structure should help us understand how the universe has evolved through time.
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average density the universe would need for gravity to someday halt the current expansion if dark energy did not exist
Note the importance of the caveat "if dark energy did not exist." With dark energy causing the expansion to accelerate, then even the critical density would not by itself be enough to prevent the expansion from continuing indefinitely.
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Observations of white dwarf supernovae.
White dwarf supernovae are good standard candles that allow us to determine distances to far-away galaxies. These data fit an accelerating model better than any other model.
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Dark energy probably exists, but we have little (if any) idea what it is.
Observations of an accelerating cosmos tell us that something must be causing the acceleration, but we really have no good ideas about what it is.
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It emits no radiation that we have been able to detect.
That is, since it doesn't emit light that we can detect, it is "dark" to us.
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There could be something wrong or incomplete with our understanding of how gravity operates on galaxy-size scales.
Evidence to date argues against this idea, since our theory of gravity accounts well for other cosmic phenomena. But we know our theory of gravity is incomplete at the smallest scales --- it may also be incomplete at the largest scales. So unless and until we determine just what the dark matter is, we cannot rule out this alternative possibility.
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The orbital speeds would fall off sharply with increasing distance from the galactic center.
This is what happens to the rotation curve of objects orbiting a centralized mass, such as the planets in our solar system (see the rotation curve for our solar system in Section 22.2).
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Yes, they tell us that dark matter is spread throughout the galaxy, with most located at large distances from the galactic center.
The orbital speed at any distance tells us how much mass is encircled within the orbit. The fact that orbital speeds remain high at great distances from the center means that lots of the matter must be encircled only with orbits far from the center.
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Elliptical galaxies lack the atomic hydrogen gas that we use to determine orbital speeds at great distances from the centers of spiral galaxies.
In spirals, we can measure the mass to distances well beyond the visible stars by detecting the 21 cm radiation from atomic hydrogen gas. Ellipticals have very little atomic hydrogen gas, so we can measure their masses only to the distances where we can see stars.
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We detect this gas with X-ray telescopes.
The hot gas emits X rays, so we can "see" it with X-ray telescopes. Measurements indicate that the total mass in the hot gas exceeds the amount of matter in stars within the galaxies (but it is less than the amount of dark matter).
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The temperature tells us the average speeds of the gas particles, which are held in the cluster by gravity, so we can use these speeds to determine the cluster mass.
Hotter gas means higher particle speeds, which means a greater total mass in the cluster.
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Using Einstein's general theory of relativity, we can calculate the cluster's mass from the precise way in which it distorts the light of galaxies behind it.
In fact, with careful observations, we can also calculate the overall distribution of the mass within the cluster.
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We have detected gravitational lensing of distant objects that appears to be caused by compact but unseen objects in the halo of our galaxy.
However, the frequency of these gravitational lensing events is so small that MACHOs cannot represent more than a small fraction of all dark matter.
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They travel at speeds close to the speed of light.
If they traveled this fast, they would escape from galaxies and clusters instead of being gravitationally bound as the dark matter in galaxies must be. Indeed, it is the high speeds of neutrinos that rule them out as a major component of the dark matter in galaxies. Also, the particles are "massive" (as subatomic particles go) and therefore it would be extremely difficult to accelerate them to relativistic speeds.
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No, because their gravity is strong enough to hold them together even while the universe as a whole expands.
Gravity has overcome expansion in individual galaxies and galaxy clusters, but not for the universe as a whole. That is why the universe continues to expand, but galaxies and galaxy clusters do not.
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Clusters and superclusters appear to be randomly scattered about the universe, like dots sprinkled randomly on a wall.
Clusters and superclusters seem to lie on great chains and sheets, suggesting they fall along a "framework" that was determined in the very early universe.
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the density of dark matter was slightly higher than average when the universe was very young
Dark matter is presumed to dominate the mass of the universe, so its gravity governs the formation of large-scale structure.
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The actual density, even with dark matter included, is less than about a third of the critical density.
That is why, even before the discovery of an accelerating expansion, scientists suspected that the expansion of the universe would never stop.
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We have moderately strong evidence that the acceleration is real, but essentially no idea what is causing it.
We attribute the cause to "dark energy," but that is just a name for something we don't really understand.
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Dark energy does not exist and there is much more dark matter than we are aware of to date.
We'd need the extra dark matter to put the density over the critical density and the lack of dark energy so that the expansion does not accelerate.
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The expansion rate has been increasing with time (an accelerating universe).
An increasing rate of expansion would mean the expansion rate was slower in the past. In that case, it took longer for the universe to reach its current size than it would have at today's rate, so the universe is older than we would predict from today's rate of expansion alone.
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The galaxies in clusters would begin to fly apart.
Dark matter provides most of the gravity that binds galaxies into clusters of galaxies. So without dark matter, the galaxies would fly apart.
