(a) Calculate the Eddington Luminosity for the Sun. Assume = 0.001 m2 kg1. Compa
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(a) Calculate the Eddington Luminosity for the Sun. Assume = 0.001 m2 kg1. Compare this to the Sun’s Luminosity. Is the radiation pressure likely to be significant for the Sun? (b) Calculate the Eddingont Luminosity for a 120 M star with hydrogen mass fraction X = 0.7. In this case assume the opacity is due to electron scattering (because all the hydrogen in the star is ionized). Compare your answer with the star’s luminosity, L = 1.8 × 106 L . Is the radiation pressure likely to be significant for this star ? (c) As stars enter the AGB phase, the drive large mass losses as a wind, which eventually strips off the entire atmosphere of the star leaving the core as a (pre-)white-dwarf star. This wind is thought to be driven by the radiation pressure of the star and the opacity of “dust” in the atmosphere, where the dust is composed of large (0.5–1 m-sized) silicate and carbon molecules. For an AGB star with M = 5M and luminosity L = 1940 L, and assuming the radiation pressure on the dust drives the outflow, calculate the opacity of the dust that would be required. (For example, the luminosity must exceed the Eddington Limit for the wind to blow off the atmosphere of the star).
(a) Calculate the Eddington Luminosity for the Sun. Assume = 0.001 m2 kg1. Compare this to the Sun’s Luminosity. Is the radiation pressure likely to be significant for the Sun? (b) Calculate the Eddingont Luminosity for a 120 M star with hydrogen mass fraction X = 0.7. In this case assume the opacity is due to electron scattering (because all the hydrogen in the star is ionized). Compare your answer with the star’s luminosity, L = 1.8 × 106 L . Is the radiation pressure likely to be significant for this star ? (c) As stars enter the AGB phase, the drive large mass losses as a wind, which eventually strips off the entire atmosphere of the star leaving the core as a (pre-)white-dwarf star. This wind is thought to be driven by the radiation pressure of the star and the opacity of “dust” in the atmosphere, where the dust is composed of large (0.5–1 m-sized) silicate and carbon molecules. For an AGB star with M = 5M and luminosity L = 1940 L, and assuming the radiation pressure on the dust drives the outflow, calculate the opacity of the dust that would be required. (For example, the luminosity must exceed the Eddington Limit for the wind to blow off the atmosphere of the star).
(a) Calculate the Eddington Luminosity for the Sun. Assume = 0.001 m2 kg1. Compare this to the Sun’s Luminosity. Is the radiation pressure likely to be significant for the Sun? (b) Calculate the Eddingont Luminosity for a 120 M star with hydrogen mass fraction X = 0.7. In this case assume the opacity is due to electron scattering (because all the hydrogen in the star is ionized). Compare your answer with the star’s luminosity, L = 1.8 × 106 L . Is the radiation pressure likely to be significant for this star ? (c) As stars enter the AGB phase, the drive large mass losses as a wind, which eventually strips off the entire atmosphere of the star leaving the core as a (pre-)white-dwarf star. This wind is thought to be driven by the radiation pressure of the star and the opacity of “dust” in the atmosphere, where the dust is composed of large (0.5–1 m-sized) silicate and carbon molecules. For an AGB star with M = 5M and luminosity L = 1940 L, and assuming the radiation pressure on the dust drives the outflow, calculate the opacity of the dust that would be required. (For example, the luminosity must exceed the Eddington Limit for the wind to blow off the atmosphere of the star).
Explanation / Answer
A. (1) When the luminosity exceeds the Eddington limit, which is given by
LEdd = 4GMmpc / T,
the Eddington limit is independent of distance from the compact object.
Numerically, if we express the mass in units of mass of the sum M and the luminosity in units of the luminosity of the sun L, then
LEdd = 30,000 (M / M) L.
(2)the luminosity of the Sun is derived by multiplying the intensity of the sunlight received at the Earth by the amount of sunlight that would reach a sphere the size of the Earth's orbit. Counting all wavelengths, the intensity of the sunlight reaching the Earth is approximately 1.4 * 10^3 watts per square meter. A sphere the size of the Earth's orbit has a surface area of 2.8 * 10^23 square meters. Therefore, the luminosity of the Sun is approximately (1.4 * 10^3) * (2.8 * 10^23), or just under 4 * 10^26 watts.
(3) yes, radiation pressure is significant to sun.
Because grain of dust circling the Sun, the Sun's radiation appears to be coming from a slightly forward direction. Therefore, the absorption of this radiation leads to a force with a component against the direction of movement.The result is a slow spiral of dust grains into the Sun.
B. (1) L star = 3.2*10^4 * 120*. 7
L = 2.6 * 10^ 7 erg/s
(2)"Radiation pressure counterbalances the gravitational forces due to the star’s mass which tend to make it contract. When the star’s energy production ceases and the radiation
pressure is removed, the star will start to collapse. "
Therefore radiation pressure is significant to stars.
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