Reading:

*Chapter 8-7, 10-2, 13-1* (ZG4)

Notes:

*pages 38 - 42*

Key Question: | How does an atmosphere attenuate a beam of light? | |
---|---|---|

Key Principle: | Radiative Transfer | |

Key Problem: | Construct a Model Photosphere |

- Radiative Transfer II - Opacity and Optical Depth
- How does the absorption depend upon the gas density?
- How does the absorption depend upon the incident intensity?
- How does the absorption depend upon the layer thickness?
- What is the
*opacity*of a gas? - What is the
*optical depth*of an absorbing medium? - How do you solve the
*differential equation*for pure absorption? - Why is the solution to the radiative transfer equation an exponential in the optical depth?
- What are the implications of this for the case of observed photons from the solar photosphere?
- How deep is the tau=1 layer in the solar photosphere?

- The Plane-Parallel Atmosphere
- How does the radiative transfer equation scale with inclination angle?
- What is the
*airmass*? - In what limit can observations through the Earth's atmosphere be approximated as absorption in a plane-parallel medium?
- How can observations at different angles be used to solve for
the
*zenith optical depth*and the*incident intensity*? - Why is this important for observational astronomy?

- Radiative Transfer III - Emission + Absorption
- How does the emission depend upon the density and thickness?
- What is the
*source function*? - What is the
*radiative transfer equation*? - Where in the radiative transfer equation is all the physics contained?
- How does the source function "drag" the intensity toward its value?
- What is the solution to the radiative transfer equation for a uniform intensity medium?
- What is the source function for a medium in
*thermodynamic equilibrium*? - What is the solution for a constant source function?
- How fast is the incident intensity replaced by the thermal emission of the medium?

- Opacity in the Solar Photosphere
- How do we know that the solar photosphere is opaque at optical wavelengths?
- How can the photosphere be opaque at the low densities and temperatures prevalent there?
- What is the primary opacity agent in the solar photosphere?
- What is the
*H- ion*? - What is the
*ionization potential*of H- compared with that of H? - What is meant by a
*bound-free*transition? - What is a
*bound-bound*transition? - What is
*free-free*absorption and emission? - What is electron scattering?
- Upon what things do the opacity and source function in a stellar atmosphere depend?

- Interlude - Iterative Solution of Equations
- How do you find the maximum of the blackbody function (Wien's Law)?
- How do you solve the Saha equation for the temperature at a fixed ionization fraction?
- How can you
*iteratively*solve an equation x=f(x)? - How is this related to
*root-finding*? - What determines whether this procedure
*converges*?

I mentioned in class that a wide range of numerical problems can be solved iteratively, often with just your calculator. These problems are of the type that can be put in the form

and that starting with a guess x_1 you can iterate

to arrive at a stable solution. Note that there are often 2 or more
ways to set up the equation, since by taking the inverse
x = f^{-1}(x) should work also (that isnt an exponent, but a
functional inverse).

Prev Lecture --- Next Lecture --- Astr12 Index --- Astr12 Home

*smyers@nrao.edu*
*Steven T. Myers*