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Unformatted text preview: Chapter 2 Stellar Atmospheres All that we know about stars other than the Sun comes from collecting pho- tons (unless you count the 19 neutrinos that were detected from Supernova 1987a, a star in the process of collapsing). The problem with photons is that they tell us only what is happening in the photosphere , the relatively thin layer of a star from which the photons escape. When we compute the radius of a star, for instance, we are really computing the radius of the stars pho- tosphere. When astronomers talk about the temperature of a star, they mean the temperature of the stars photosphere, unless they explicitly state otherwise. A word of advice: studying the atmospheres of stars requires understand- ing how light interacts with matter. If you feel a bit rusty in your knowledge, you may want to review Chapter 6 of BA and/or Chapter 8 of Zeilik and Gregory. 2.1 Hydrostatic Equilibrium To understand how a stars spectrum is produced, we must understand the basic physics of stellar atmospheres. In some ways, the atmosphere of a star is like the Earths atmosphere; despite winds and storms, both types of atmosphere are in hydrostatic equilibrium (as described in section 10.1.2 of BA ). In other ways, a stars atmosphere is unlike the Earths. For one thing, the Earths atmosphere rests upon a solid or liquid surface; since stars are completely gaseous, you can think of them as being nothing but atmosphere. Another difference between stellar atmospheres and the Earths 28 2.1. HYDROSTATIC EQUILIBRIUM 29 atmosphere is that the atmospheres of stars are relatively hot, and ionization becomes important. For a spherical star in hydrostatic equilibrium ( BA , equation 10.8), dP dr =- GM r r 2 , (2.1) where r is the distance from the stars center, P is the local pressure, M r is the mass contained within a sphere of radius r , is the local mass density, and G is the Newtonian gravitational constant. In other words, the upward force due to the pressure gradient (the left-hand side of equation 2.1) is exactly balanced by the inward force due to gravity (the right-hand side of equation 2.1). The pressure at any point inside the star is well approximated by the perfect gas law: P = nkT , (2.2) where n is the number density of particles (ions, free electrons, atoms, and molecules), k is the Boltzmann constant, and T is the temperature (in Kelvin). 1 When computing pressure forces, what counts is the total number density of particles, n ; low-mass electrons and high-mass molecules contribute equally to the pressure. The number density n is simply related to the mass density : n = m p , (2.3) where is the mean molecular weight of the particles, measured in atomic mass units. Strictly defined, the atomic mass unit is the mass of a carbon-12 atom divided by 12. For practical purposes, as in equation (2.3), we can set it equal to the mass of a proton, m p = 1 . 67 10- 27 kg....
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This note was uploaded on 07/17/2008 for the course ASTRO 292 taught by Professor Ryden during the Winter '06 term at Ohio State.
- Winter '06