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and Cosmic Acceleration |
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Super novae are exploding stars that, at their brightest, are as luminous as an entire galaxy - that is, about 1010 times as luminous as our Sun. Thus they can be seen at great distances, and hence high red shifts.
Astronomers classify two basic categories of supernovae: Type I and Type II, based on their spectra. Type II show strong hydrogen lines in their spectra, and come from blue giant stars of O and B class, that explode at the end of their lives, leaving neutron stars or possibly black holes. Type I do not show strong hydrogen lines in their spectra, and come from a binary system of a white dwarf in orbit around a larger star. The denser white dwarf draws mass off its larger companion, and may periodically "nova" and blow off excess mass. If its mass grows to around 1.4 solar masses (the Chandrashekar limit), it is likely to become unstable and blow up into a Type I supernova.
Type I supernovae are further classified into Ia and Ib; Ia show strong silicon absorption lines at 615 nm (6150 Angstroms), while Ib do not. Type Ia supernovae make good "standard candles" for determining cosmic distances for three main reasons:
(1) They are very bright, so can be seen at large distances.
(2) We know their theoretical mass limit - right around 1.4 solar masses. Smaller than this, they are not likely to blow up; larger than this, theory tells us they are not stable. So, knowing their mass, we can calculate their intrinsic luminosity from the well-studied mass/luminosity relationship from stellar evolution.
(3) We can identify them from their spectra, both by the presence of the Si 6150 line, and also the way their spectra change over time. As the supernova fades from peak luminosity, there is a characteristic light curve, with secondary features that are due to the decay of radioactive isotopes that are produced in the supernova explosion itself. So we can identify them relative to other bright, distant, and possibly time-varying sources by their characteristic spectra, shape of their light curves, and change of elements present in their spectra over time.
The coolest aspect, however, of using Type Ia supernovae is that they extend our ability to measure cosmic distances out into the "Hubble flow" - at high redshifts, where we can actually begin to measure the expansion history of the universe. The following article by Saul Perlmutter, of the Lawrence Berkeley Lab Supernova Cosmology Project team gives a good history of High Z Sne (z = redshift, Sne = short for "supernovae.")
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Supernovae, Dark Energy, and the Accelerating Universe |
After reading Saul Perlmutter's article from Physics Today, you should have a pretty good idea of the promises and also the problems inherent in measuring the magnitudes and distances to high redshift, Type Ia supernovae (hereafter referred to as "High-z Sne").
On the "bright side:"
(1) We can independently measure their redshifts from their known spectral lines, and check the measurements by measuring the redshift of their host galaxies;
(2) We can independently infer their absolute magnitudes (or intrinsic luminosities) from their theoretically maximum possible mass and the known mass-luminosity function from stellar evolution theory;
(3) Since their light curves are so well known, if we miss them at peak magnitude, with a few observations we can get enough data points to calculate a light curve, and thus get a good idea of their maximum apparent magnitude.
On the "dark side:"
(1) Since they are redshifted, we must take this fact into account in measuring their peak light output. Normally, their spectra peak in the blue-violet region of the spectrum, in their own restframe. So we observe them in a red-infrared filter, because the blue-violet light is redshifted. If we observe them in blue-violet filters, we won't measure their peak light output, in our rest frame.
(2) They are not predictable! So people have to comb the skies looking for them - and then go back and get a second look on the HST or other large telescope from the ground.
(3) One has to correct for dust from the host galaxy.
(4) One has to be prepared to defend against skeptics.
Never the less, after about a decade of searching and refining, the Supernova Cosmology Project from Berkeley and the High Redshift Supernova Search Team from Harvard have demonstrated, beyond a reasonable doubt that:
*** The luminosities of these High-z Sne appear too faint for their redshifts, for the "Standard Cosmological Model" of the 20th Century. This provides independent evidence for the cosmological consant!
*** The best fitting model indicates that there was an increase in the expansion rate of the universe at a redshift close to z=0.5, corresponding to approximately 5 billion years ago, in the history of the Universe.
In this exercise you will:
1) Input 187 values of the distance modulus and red shift from Reiss, et al. 2004 for their corrected, best observations;
2) Try to fit a simple curve for a uniformly expanding universe to the data;
3) Try another model that takes into account
a "q0" parameter for a change in the expansion rate (cosmic deceleration parameter - assumed positive in the last century!);
4) Try fitting a model that includes "lambda" (the dark energy) and "w" (the equation of state parameter)of the Universe. {Note: this option requires you to install the Xnumber library on your computer, and select it as an "Add In"
when you run Excel.)
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Download the High Z Sne Modeling Activity Now |
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Some Good References: |
Introduction to Cosmology |
Globular Clusters and the Age of the Universe |
Modeling the Power Spectrum of the CMB |