UW-Madison AST 103 - Olber’s Paradox (13 pages)

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Olber’s Paradox



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Olber’s Paradox

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Pages:
13
School:
University of Wisconsin, Madison
Course:
Ast 103 - The Evolving Universe
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Suppose the Universe were not expanding but was in some kind of steady state How should galaxy recession velocities correlate with distance They should a be directly proportional to distance b reverse the trend we see today and correlate inversely with distance c show a scatter plot with most recession velocities positive d show a scatter plot with equal numbers of positive and negative recession velocities Olber s Paradox Over very large distances galaxies in the universe are more or less uniformly distributed homogeneous If there are galaxies in every direction however why do we not have a fully lit sky We should see a star in any direction we look This is called Olber s Paradox If there is an edge to the universe we should be able to see our way out of the woods 1 Olber s Paradox A Solution In a sense there is an edge to the universe an edge in time Light travels at a finite though fast speed The size of the visible universe is defined as the distance light can travel in the age of the universe Galaxies exist at greater distances but light from them has not reached us yet The edge is called the cosmic horizon If we wait long enough the night sky might become bright 2 The Meaning of Redshift As light waves travel through space they are stretched by expansion This increases the wave s wavelength making it appear more red An objects redshift z is z Here is the change in wavelength and is the original wavelength of the photon This is equivalent to z Change in average distance between galaxies Average distance between galaxies The Age of the Universe Thanks to the Hubble Law we can estimate the age of the universe At some point in the distant past matter in the universe must have been densely packed From this point the universe would have expanded at some high speed to become today s universe Assuming a constant expansion over time we find that the age of the universe is around 14 billion years 3 Suppose you ve accepted that the universe is expanding and will always expand You must then accept that a there is no center to the universe b the observable universe is infinite c the distance between stars in the galaxies grows d either the density of the universe always decreases or new matter must be continuously created The Last Scattering Epoch Minutes after the Big Bang the Universe was opaque High temperatures kept all matter ionized Photons could only travel a short distance before being absorbed After 400 000 years the Universe cooled enough for electrons and ions to recombine allowing light to pass Now the Universe was transparent 4 Light from the Early Universe So what should light from 400 000 years after the Big Bang look like It should have a spectrum that corresponds to the temperature of the Universe at that time 3000 K Expansion of space will stretch this light however The Universe has expanded by a factor of 1000 since this time so the wavelength will have stretched by the same amount Spectrum will correspond to a temperature of 3K This light from the early Universe has been found and is called the Cosmic Microwave Background Clumpiness in the CMB 5 Clumpiness in the CMB Clumpiness in the CMB 6 The Curvature of the Universe Remember that mass and energy can curve the space around it As the Universe expands the distances between the galaxies increases like galaxies painted on the surface of an inflating balloon If the universe was like an expanding balloon but with the galaxies distributed in three dimensions travel in any direction would eventually bring you back to your starting place a closed universe No Center No Edge Many galaxies have flat rotation curves Dark matter is not unique to the Milky Way 7 99 percent of the stars in a galaxy are within 20 kpc of the center Gas extends far out into the disk but is not very massive Galaxies are now thought to be embedded in a dark matter halo that surrounds the entire galaxy Unfortunately dark matter cannot be detected directly Dark Matter in Clusters of Galaxies Missing mass is also a problem in clusters of galaxies Not enough visible mass to hold the clusters together by gravitation and to keep hot gas in their vicinity Cluster mass must be 100 times greater than the visible mass Once again dark matter seems to be the solution 8 Gravitational Lenses Dark matter warps space just like ordinary matter does The path of light rays bends in the presence of mass A galaxy or other massive object can bend and distort the light from objects located behind it producing multiple images This is called gravitational lensing Figure 78 06 9 Other Possible Curvatures of Space In addition to a closed or positive curvature of space there are two other options Space could be flat or have zero curvature Space could be curved away from itself or have negative curvature Geometry behaves differently with each curvature Expansion Forever Or Collapse The fate of the universe is ultimately controlled by its total amount of energy Energy of expansion positive Gravitational energy that can slow the expansion negative Binding energy If the total energy is positive or zero the expansion continues forever If the total energy is negative the expansion will halt and the universe will contract and eventually collapse 10 Density of the Universe If we can measure the density of the universe we can predict how much gravitational energy the universe has and therefore whether it will collapse or keep expanding The critical density of the universe C is the density at which the total energy of the universe is zero 3H 2 C 8 G M C where is the measured density of the universe If M 1 the universe will recollapse If M 1 the universe will expand forever If M 1 the universe is exactly at the critical density If the Big Bang theory is correct and there is not enough mass to close the universe then a more Big Bangs will occur b there is no dark matter c the universe will eventually be entirely cold d the expansion will slow to a halt 11 Supernova Type Ia Findings We also need to know how the universe is expanding this can help us determine the value of M We can measure the recession velocity of distant galaxies using Type Ia supernovae as standard candles It appears that the expansion rate at a time when the universe was half its current size z 1 was slower than it is today This shows that the expansion rate is increasing with time Very puzzling Dark Energy Dark energy may provide the solution to the mystery Dark energy remains constant everywhere regardless of the


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