The Model Photosphere The Model Photosphere (Chapter 9) (Chapter 9) • Basic Assumptions • Hydrostatic Equilibrium • Temperature Distributions • Physical Conditions in Stars – the dependence of T(), P g (), and P e () on effective temperature and luminosity
The Model Photosphere (Chapter 9). Basic Assumptions Hydrostatic Equilibrium Temperature Distributions Physical Conditions in Stars – the dependence of T( t ), P g ( t ), and P e ( t ) on effective temperature and luminosity. Basic Assumptions in Stellar Atmospheres. - PowerPoint PPT Presentation
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The Model Photosphere (Chapter The Model Photosphere (Chapter 9)9)
• Basic Assumptions• Hydrostatic Equilibrium• Temperature Distributions• Physical Conditions in Stars – the
dependence of T(), Pg(), and Pe() on effective temperature and luminosity
Basic Assumptions in Stellar AtmospheresBasic Assumptions in Stellar Atmospheres
• Local Thermodynamic Equilibrium– Ionization and excitation correctly described by
the Saha and Boltzman equations, and photon distribution is black body
• Hydrostatic Equilibrium– No dynamically significant mass loss– The photosphere is not undergoing large scale
accelerations comparable to surface gravity– No pulsations or large scale flows
• Plane Parallel Atmosphere– Only one spatial coordinate (depth)– Departure from plane parallel much larger than
photon mean free path– Fine structure is negligible (but see the Sun!)
Hydrostatic EquilibriumHydrostatic Equilibrium• Consider an element of gas
with mass dm, height dx and area dA
• The upward and downward forces on the element must balance:
PdA + gdm = (P+dP)dA• If is the density at location
x, thendm= dx dA dP/dx = g
• Since g is (nearly) constant through the atmosphere, we set
g = GM/R2
P
P+dP
x+dx
x
gdm
dP/dx = g
In Optical DepthIn Optical Depth• Since d=dx
• and dP=gdx
CLASS PROBLEM:• Recall that for a gray atmosphere,
For =0.4, Teff=104, and g=GMSun/RSun
2, compute the pressure, density, and depth at =0, ½, 2/3, 1, and 2. (The density and pressure equal zero at =0 and k =1.38 x 10-16 erg K-1)