L09 Mean free path (and start of RT)

L09 Mean free path (and start of RT)#

Week 5, Tuesday (no notebook for today)

Material covered and references#

  • We used the concept of mean free path to evaluate how far a star is from thermodynamic equilibrium. We found that particles don’t travel far compared to the gradient of temperature in e.g. the sun, and they only interact with particles of same thermodynamic properties (= Local thermodynamic equilibrium or LTE). It is also true for photons in the interior of the sun, but this breaks down toward the surface where photon can travel distance of the order of the pressure scale height. This is where the field of stellar physics splits into two distinct treatments: interiors and atmospheres.

  • We calculated the spatial location of this transition for the Sun with the pressure scale height. It is only a slim fraction of the stellar radius.

Micro-objective:

  • I can explain the concept of “mean free path”

  • I can explain the concept of Local Thermodynamic Equilibrium for particles. (i.e. comparing the temperature gradient with the mean free path)

  • I can use the concept of mean free path to explain the separation between the “interior” and the “atmosphere” of a star.

  • I can state the conceptual and mathematical definition of the “pressure scale height”

  • I can derive an equation for and compute an estimate of the pressure scale height of the sun

  • I can list the approximations that we will be able/not able to do when considering the atmosphere and the interior of stars.

In the textbooks:

  • (Here’s a new reference book that I just added to the list, Physics of the Sun, by Dermott Mullan aka The “Mullan”) Mullan 5.1, 5.2

  • We discussed specific intensity, mean intensity (which is an average over all directions) and radiative specific flux (which describe the net power flowing through a surface).

  • (If there is time) We also talked about the differences between intensity and flux in the context of astronomical measurements. If an object can be resolved by a telescope (like for the sun), then we are measuring intensity. If propagating in empty space, the intensity does change with distance. If the light from an object is all gathered inside a single resolution element of the telescope, the object is unresolved, and we are measuring flux. Even in empty space, flux decreases with the square of the distance.

  • The goal of radiative transfer is to figure out what happens to the specific intensity as a ray of light goes through matter.

Micro-objectives

  • I can state the conceptual definition and characteristics of a ray of light (i.e. specific intensity)

  • I can mathematically state and sketch the physical definition of specific intensity

  • I can mathematically relate the “mean specific intensity” to the specific intensity

  • I can mathematically state and sketch the physical definition of specific flux

In the textbooks:

  • Leblanc 3.3

  • Rybicki 1.2, 1.3

  • Gray Chap 5

  • Mihalas Chap 1 (in the original edition – the new edition has quantum treatement if you are interested)