Review Questions

1. For the purpose of radiative transfer measurements, why do we treat the radiation field a vector field and not as a scalar field?  When considering the setup of the geometry between the source and the location of the observer, the origin of the coordinate system is always placed where?

2. What is the definition of the solid angle? For an observer positioned a distance D from the source along a given sightline, how does the observed solid angle depend  on the direction of the sightline relative to the object surface and the distance of the observer?

3. In your own words, describe/define the specific intensity. Is it a vector?  In your own words, describe/define the mean intensity. Is it a vector?

4. Explain why flux is a vector and why the observed flux is simply one of its components?

5. In words, what is the astrophysical flux? What is the relationship between the astrophysical flux of an object and the observed flux of that object?

6. In words, what is the extinction coefficient? Say you have a specific intensity incident on an area element. Given the extinction coefficient, what is the relationship between the incident specific intensity, I,  and the decrement in the specific intensity, dI, after it has traveled over a line of sight distance element ds?  At a given frequency, what is the relationship between the extinction coefficient and the photon mean free path?

7. In terms of the extinction coefficient, how is the absorptivity of the gas defined?  In words, how is the optical depth defined?  Optical depth is a unitless number.  In terms of the relationship between the mean free path and the total pathlength through an absorbing gas cloud, what is this number telling you?

8. In words, what is the emission coefficient? Say you have emission at a point in the gas, what is the increment in the specific intensity, dI, a distance ds from the point of origin?

9. In words, what is the source function and what are its units?  Under what conditions is the source function identical to the Planck blackbody radiation curve?

10. For absorption in a cosmologically distant gas structure, what are some of the simplifying assumptions that are virtually unspoken yet built into our radiative transfer formalism and our simple solution for pure absorption? 

11. What is partial covering? What are the signatures in our absorption line data that indicate partial covering is occurring? What type of astrophysical scenarios do we often see the signatures of partial covering? Explain what the effective optical depth is in the context of partial covering.

12. What is column density and how is it defined? Given that the absorption coefficient is the product of the number density of the absorbing ion and the cross section per absorbing ion, what is the simplified relationship between optical depth and column density?

Problems

1. You observed that the relative flux in the core of an absorption line is I/I(0) = e-3 = 0.05. This mean that 5% of the incident photons with wavelengths at the line core survived passing through the cloud (were transmitted).  What is the number of mean free paths that these photons had to travel through the cloud to make it to the observer?  If the cloud has a line-of-sight thickness 30 pc, how many parsecs is the mean free path of these photons?