Review Questions

1. Compare Equations 28.1 and 28.2. What is the summation in Equation 28.1 accounting for and why is it typically appropriate that we can remove that summation, as we have done for Equation 28.2?

2. What is a wavelength redistribution function and why do we need such functions?  What do the free parameters in the wavelength redistribution functions represent?  

3. What mathematical operation is required in order to incorporate wavelength redistribution functions and the natural line broadening cross section in order to obtain the total absorption cross section?

4. For thermal broadening, the free parameter of the wavelength redistribution function is the Doppler width. What is the definition of the Doppler width?  Why do we often parameterize this as a Doppler velocity width?  Finally, what is the Doppler b parameter, and why do we scientists converse using this parameter? 

5. The Doppler width depends on both the gas temperature and the absorbing ion mass.  (i) Describe what panels (a,c) of Figure 28.3 are showing and the general behavior of the redistribution functions?  (ii) Describe what panels (b,d) of Figure 28.3 are showing and the general behavior of the redistribution functions?  

6. What is a Voigt function or Voigt profile? When written as a Voigt profile, what parameters does the optical depth profile depend on?  (HINT: three define the cross section for the atomic transition and two define the thermal wavelength redistribution function).

7. Consider Figure 28.4. (i) Very briefly, describe what (mathematical)  process is being shown here from left to right on the diagram. (ii) What important points are being presented from the top row to the bottom row of the diagram?  (iii) Why does the shape of the optical depth Voigt function in the bottom row appear different than the other optical depth Voigt functions in column (c) even though their shapes are actually identical and they differ only in their amplitudes?  (iv) Explain what is being illustrated by the thick portions of the optical depth curves and the thick portions of the absorption line profiles. (v) Explain the origin of the "damping wings" in the absorption line profile on the bottom row.

8. Explain the interpretation of multi-component absorption profiles seen in high-resolution quasar spectra. Include a discussion of Equation 28.21 and the relationship between observed wavelengths of the multi-component profiles and the rest-frame velocities. 

9. What physical quantities and relationship are described by "the curve of growth" and what are the three parts of the curve growth each called?  

10. Consider the parts of the curve of growth. (i) How does equivalent width depend on column density on the linear part (write the proportionality expression)?  On the logarithmic part (sometimes called the "flat" part)? On the square-root part (sometimes called the damping part)? (ii) Which part(s) are independent of the Doppler b parameter? Which parts have dependence on the Doppler b parameter? 

11. Starting with the definition of the equivalent width (Equation 28.22), what assumptions or approximations are applied to derive the expression for the linear part of the curve of growth? For the flat part? For the square-root part?

12. What is a doublet ratio and how is it defined? For a fine-structure doublet like MgII 2796,2803, what is the range of the doublet ratio values? What value does the ratio approach for small column densities when the equivalent width is on the linear part of the curve of growth? What value does the ratio approach on the flat part of the curve of growth?

13. Explain how the "inverted" curve of growth method is applied for estimating the column density and Doppler b parameter of a doublet or multiplet.

14. Consider apparent optical depth (AOD) methods. When converting the relative flux in a pixel to the optical depth in that pixel, why is it referred to as the "apparent" optical depth? Why is the conversion not an accurate measure of the true optical depth in that pixel? 

15. When integrating under the AOD column density profile, why is it that even with perfect (infinite) resolving power the total integrated apparent column density can be significantly underestimated compared to the true column densities?

16. What is unresolved saturation? In the context of AOD column density profiles, how is unresolved saturation identified?

17. Describe how the covering factor "profile" for resolved doublets can be determined. Describe how the measured profile of the covering factor is affected by the resolution of the spectrum. In cases where the covering factor profile is accurately measured, how does one estimate the column density in the partially covered gas (consider Equation 28.61)?

18. Describe what an ionization break is.  What is a Lyman-limit break? Consider Figure 28.15. Describe how the measured flux at the Lyman-limit break decreases as the HI column density increases: give a few examples, for instance log(NHI ) = 16, 17, 18. What is the central take-away point panel (d) of Figure 28.15?

Problems

1. Derive Equation 28.60 from Equation 28.59.

2. Work in progress