Computing Across the Physics Curriculum
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Stellar Astrophysics
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These modules were designed/constructed based on the text:
An Introduction to Modern Astrophysics, by Carroll and Ostlie.
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Planck Function Homework Activity: Blackbody radiation is a reasonable zeroth approximation for the radiation emitted from a star. The brightness can be described by the Planck function, which is a function of emitted wavelength (or frequency) and surface temperature. An appreciation of how this function varies with temperature will help students understand why stars of different surface temperatures have vastly different colors.
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Rayleigh-Jeans Law Homework Activity: Blackbody radiation is a reasonable approximation to radiation emitted from a star. The brightness can be described by the Planck function, which is a function of emitted wavelength (or frequency) and surface temperature. For long wavelengths, the Planck function can be approximated by the Rayleigh-Jeans function. This works reasonably well for wavelengths longer than the peak wavelength, with increasing accuracy for increasing wavelengths. Shorter than the peak wavelength, the Rayleigh-Jeans approximation fails. Astronomers often speak of the Rayleigh-Jeans tail of the spectral energy distribution.
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Wien's Law Classroom Demonstration: Blackbody radiation is a reasonable zeroth approximation for the radiation emitted from a star. The brightness can be described by the Planck function, which is a function of emitted wavelength (or frequency) and surface temperature. For a given temperature, both Bλ and Bν peak, but the wavelength at which Bλ peaks is not the wavelength equivalent to the frequency νmax at which Bν peaks. This is not immediately intuitive, and a demonstration with calculated values will help to convince the students.
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Calculation of Blackbody Colors: In stellar astrophysics, students are told that stars can be approximated as a blackbody with an effective temperature, Teff. This is not quite true as absorption lines affect the magnitudes (and hence the colors) of stars, causing significant deviation from the locus of points for pure blackbodies.
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Blackbody Colors Vs. Real Stars: In stellar astrophysics, students are told that stars can be approximated as a blackbody with an effective temperature, Teff. This is not quite true as absorption can affect the magnitudes (and hence the color) of stars, causing significant deviation from the blackbody curve. This absorption is dependent on the wavelength of the light as well as the temperature of the star.
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Boltzman Distribution: The velocity of particles such as hydrogen atoms, in a gas obey Fermi-Dirac statistics. When the density is low enough and the temperature is high enough, quantum effects are negligible, and the particles can be described by a Maxwell-Boltzmann distribution.
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Saha Equation Homework Activity: The Saha equation is essential for stellar astrophysics, but is very difficult for introductory students to manipulate. The equation describes the ratio of the number of atoms in the ionization state i to the number of atoms in ionization state i+1 as a function of gas temperature and electron pressure, and can also involve the calculation of the partition function if it is not provided.
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Combining the Boltzmann and Saha Equations Homework Activity: Using both the Saha and Boltzmann equations allows one to calculate the ratio of the number of atoms in a particular energy and ionization state to the total number of atoms present. The easiest case is to calculate the ratio of N2/ Ntotal for a pure hydrogen gas. Plotting this ratio as a function of temperature explains the relative strength of the Balmer lines across the spectral sequence.
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Partial Ionization Zone Homework Activity: The Saha equation is essential for stellar astrophysics, but is very difficult for introductory students to manipulate. The equation describes the ratio of the number of atoms in the ionization state i to the number of atoms in ionization state i+1 as a function of gas temperature and electron pressure, and can also involve the calculation of the partition function if it is not provided.
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Lines of Constant Radius on the H-R Diagram Homework Activity: Blackbody radiation is a reasonable zeroth approximation to the radiation emitted from a star. In this exercise students are asked to use the Stefan-Boltzmann law to calculate the luminosity of a blackbody of a given radius and temperature, and then create lines of constant radius on a theoretical Hertzsprung-Russell diagram of bolometric luminosity versus effective temperature. In this way the students can develop a feel for the relative sizes of stars on the main sequence as well as those of giants, supergiants, and white dwarfs.
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Stellar Evolution Animation Demonstration: When students are introduced to stellar evolution, they are told the relative main sequence lifetimes for stars of different masses, but those timescales vary by so many orders of magnitude that it is difficult to visualize those differences. For low mass stars, typical lifetimes are tens of billions of years or longer while the highest mass stars last only a few million years. Students are also taught that, as a rule of thumb, the main sequence phase of a star is about 90% of its full lifetime. However, most students do not remember this useful factoid until they watch the movie.
