L17 Grey atmospheres#
Week 10, Tuesday
Material covered and references#
Using the results from the large optical depth (\(J \sim 3K\)), we can now solve our system of equations to find the temperature structure.
Because we used the results from the large optical depth approximation, we introduced a correction factor \(q(\tau)\). This factor can be found iteratively based on the mean intensity relation with the source function.
But we will use again results from the large optical depth case to estimate a value of \(q\), with will be \(\sim 2/3\).
In the notebook, we compare our estimated model for the temperature structure with the ‘real’ temperature structure of the sun.
In the textbooks:
Leblanc 4.2.1 (in the text, the two-stream approximation is used instead to estimate \(q\) – the large optical depth case is in a “special topic” box on page 114)
Micro-objective:
[N] I can sketch the temperature in the atmosphere of the sun as a function of optical depth.
[N] I can evaluate the quality of the approximations we made to find an analytical solution.
We also find an expression for the wavelength dependent flux (i.e. the spectrum!) that our estimated model predicts.
We are doing this with a worksheet first for the math, and then in the notebook you will compare this with the real solar flux spectrum.
I can use the analytical solution for the temperature to find the specific flux (as a function of wavelength) (worksheet).
[N and worksheet] I can convert between flux in units of ‘per alpha’ to flux in units of ‘per wavelength’.
[N] I can evaluate the quality of the approximation for the temperature in predicting the specific flux.
[N] I can explain the shape of the specific flux (as a function of wavelenght) for layers of different optical depth.