SACE Stage 1 Physics John McCarthy
Issues Investigation:
Redshifting of Light
John McCarthy
In approximately 1670, Isaac Newton showed for the first time strong evidence of the wave-like nature of light. In his famous prism experiment, Newton showed how, as white light travels through a medium, due to the phenomenon of diffraction, the ray of light separates into individual colours. From this point on, light has been shown to exhibit many other wave-like properties. One of these properties, common to other waves such as sound waves or waves in the ocean, is the Doppler Effect. The Doppler Effect occurs when the observed wavelength of a wave changes due to the source of the wave moving relative to the observer. On cosmological scales, this Doppler Effect, caused by the motion relative to earth of distance luminous objects, such as stars or galaxies, causes the wavelength of light to lengthen or shorten relative to the observer, us. When these distant light sources are moving away from us, the wavelength of light increases, shifting it towards the lower end of the spectrum, making it appear redder. This phenomenon is known as redshifting, and it has many uses in astrophysics and cosmology, allowing scientists to understand the expansion of the universe, determine whether distant stars have planets orbiting them or
The redshifting of light can help us understand the expansion of the universe. In 1929, Edwin Hubble made a shocking discovery, that the light coming from each and every galaxy he analyzed had been redshifted to some degree. This finding, suggesting that all stars and galaxies are moving away from the Earth, contradicted strongly with the notion of a static universe common at the time, where the distribution of redshifted and blueshifted light from distant galaxies would have been roughly equal. Through further observation, Hubble was able to determine that not only were these stars and galaxies all moving away from earth, but also from each other, suggesting a universe that is expanding in all directions at all points. Hubble further went on, using Standard Candles, stars with known distances, to estimate quite accurately the distance of a large number of these distant galaxies and stars, and found that when the velocity with which the stars were receding, calculated by the equation v≅zc where c is the speed of light and z is the redshift, was plotted against the distance, the resultant plot was linear. Hubble hence formulated the law connecting these two quantities, v=H0D where H0 is some constant. Using this law, Hubble’s Law, Hubble then used Standard Candles, stars with known distances and velocities, to determine this constant, which he found to equal approximately 500 km/s/MPc where a MPc is a mega parsec, approximately equal to 3 million light years. This value, later found to be grossly overestimated due to incorrect distance measurements of these standard candles, represents the rate of expansion of the universe; that is, every second, two points 1 mega parsec apart become 500km further apart. This expansion of the universe not only changed the way physicists studied cosmology, but the way they view the beginning and end of the universe.
The redshifting of light allows us to determine that the rate of expansion of the universe is accelerating, and by extension how the universe may end. In 2011, three physicists, Saul Perlmutter, Brian P. Schmidt and Adam G. Riess, were awarded the Nobel Prize in Physics for a paper they published together in 1998. In this paper, entitled Discovery of a Supernova Explosion at Half the Age of the Universe and its Cosmological Implications documented the discovery that over time the rate of expansion of the universe has been increasing. To do this, these physicists used high powered telescopes to look at very distant Supernovae, explosions of stars. These supernovae, of Type 1A, occur during the collapse of White Dwarf stars at a mass of 1.4 solar masses. This knowledge allowed scientists to accurately estimate the luminosity of the star, which could then be compared to the apparent luminosity from earth to determine the distance to the star. When observing the distance to these distant supernovae and their redshifts, unlike Hubble, who measured stars of a reasonably close distance to earth relative to the size of the universe, these scientists found that the relationship between the two values was not linear. Instead they found that these supernovae that were deep into the universe, which hence existed during the early universe, had lower redshifts than expected. These lower redshifts, corresponding with overall lower velocities, suggested that instead of the rate of expansion of the universe being linear, such as it was assumed according to Hubble, the rate of expansion was increasing through time. Not only did this discovery lend itself to more and more accurate estimates of the age of the universe, which depend on the rate of expansion, but it also lent itself to understanding how the universe will end. In the early 20th century, prominent physicists were in the process of discovering what would result from the universe having different energy densities. It was shown by Albert Einstein that the energy density of the universe was what caused the curvature of spacetime that his theory of relativity described, and that the net energy density of the universe, Ω, could hence be used to describe the shape of our universe geometrically. This relates to the accelerating expansion of the universe, as, if the universe is above a critical density Ω0, the total gravity of the universe would counteract the expansion caused by dark energy, and result in a Big Crunch, a cosmological event that would provide remarkably similar conditions to the Big Bang, perhaps suggesting an oscillating universe that creates and destroys itself. It was also found that if the density of the universe was equal to or less than the critical density, Ω0≤1, then the acceleration of the universe would be more powerful than the net gravity and hence spacetime would expand forever, leading eventually to the heat death of the universe, where time ceases, or a Big Rip, where the fabric of spacetime is ripped apart by the expansion of the universe. Scientists, in an attempt to find this ultimate fate, use conventional methods of analyzing the energy density of the universe, such as observing galaxies through the universe, as well as analyzing the redshifting of galaxies throughout the history of the universe and backtracking their motion to understand how the universe’s expansion operated under energy densities in the past. The redshifting of light provides us with important information about the expansion and eventual death of the universe, but can also be used for smaller tasks such as finding planets around stars.
The redshifting of light provides us with a means of determining whether planets exist around a distant star. In Cosmology, Doppler Spectroscopy is the method of determining the chemical composition of distant stars or galaxies by observing their spectral lines and accounting for the redshifting of light that occurs due to these distant stars and galaxies moving away from us. When a star has a planet however, the rate at which it recedes from Earth changes periodically, as the planet orbiting the star exerts a small gravitational pull on the star, causing it to orbit a center of gravity not at its core. This small vibration in its distance to Earth is reflected in the shift in the wavelength of light coming from the star. With extremely high accuracy detectors, over long time periods, scientists are able to analyze this change in redshift and hence determine the radial velocity of the star, its speed in a circular motion, and further calculate the period of its orbit around the common center of gravity. Because this period is hence equal to the period of the planet around the star, and according to Kepler’s Third law of Planetary Motion, the distance from a star of a planet is directly proportional to its orbital period, Doppler Spectroscopy can hence be used not only to detect whether a star has a planet, but also to detect how far from the star the planet is. Whilst this method has currently only been used to determine whether stars relatively close to the Earth have planets, because Doppler Spectroscopy depends only on the amount of light received from a distant star, this same process could be used to detect planets around stars millions or even billions of light years away, permitting enough light from the star reaches Earth.
There are many possible uses in cosmology and astrophysics for the redshifting of light. Scientists have been able to use this interesting property of waves, the Doppler Effect, observed first in the pitch of whistles as trains travelled past an observer, to determine information about distant planets, stars, galaxies, and even the universe itself. The redshifting of light, existing as the most miniscule of particles, is a prime example in physics of the important relationship between the very small and the very large.
Bibliography:
J. Lochner, 2010, Universe is Expanding, Last accessed 20th Oct 2012. <http://cosmictimes.gsfc.nasa.gov/online_edition/1929Cosmic/expanding.html>
Leibundgut and Sollerman, 2001, A cosmological surprise: the universe accelerates, Last accessed 20th Oct 2012. <http://www.eso.org/~bleibund/papers/EPN/epn.html
M. Wall, 2012, Discovery! Earth-Size Alien Planet at Alpha Centauri Is Closest Ever Seen, Last accessed 22nd Oct 2012, <http://www.space.com/18089-earth-size-alien-planet-alpha-centauri.html
NASA, 2011, Foundations of Big Bang Cosmology, Last accessed 21st Oct 2012, <http://map.gsfc.nasa.gov/universe/bb_concepts.html
R. Vanderbei, 2011, Nobel Prize in Physics 2011 – The Accelerating Universe, Last accessed 21st Oct 2012, <http://newswatch.nationalgeographic.com/2011/10/12/nobel-prize-in-physics-2011/
S. Perlmutter, 1998, Discovery of supernova explosion at half the age of the Universe, Last accessed 21st Oct 2012, <https://www.cfa.harvard.edu/~rkirshner/whowhatwhen/SCPNature.pdf
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