Review Questions

1. Consider Equation 32.1. State, in your own words, what these two population density functions quantify. Consider Equation 32.2. How do these two population density functions differ from the ones expressed in Equation 32.1? Which set of population density functions do you expect to be a constant for all redshift if the population of absorber does not evolve?

2. Describe the mathematical relationship between the population density function (Equation 32.1) and the equivalent width (or column density) distribution functions averaged over a fixed redshift interval. Do the same for the mathematical relationship between the population density function and the redshift path density for a fixed equivalent width (or column density) interval.

3. In practice, one often bins the data to construct the population density function, equivalent width (or column density) distribution function, and/or redshift path density. Say you had completed your survey of an absorber population and had estimated the observed average completeness for arbitrary absorber subspaces. Examining Equation 32.9, describe the process by which you would build binned functions (this is also known as the "direct counting method").

4. Compare and contrast how one implements the "direct counting method" and the "uncorrected-weighted method" for measuring the redshift path density of a given absorber population. Compare and contrast the systematic differences of these methods (consider Figure 32.2).

5. With regard to parameterizing evolution in the redshift path density of an absorber population, two approaches have been discussed.  Compare and contrast these two functional parametrizations and describe why the second functional form was later introduced.

6. With regard to parameterizing the equivalent width (or column density) distribution functions in a given absorber subspace, three functions are typically explored: an exponential, a power-law, and a Schechter function.  Provide a brief description of the defining characteristics of each of these functions.  If the distributions of objects in the Universe are believed to always follow a Schechter function, explain why sometimes our observed data are fitted only by an exponential or only by a power law.

7. When estimating the fitted parameters to the exponential, power-law, and/or Schechter functions, we can use maximum likelihood estimators or binned absorber counts. What is the danger of applying these methods if we do not account for the observed average completeness (consider Figure 32.6)? Describe how, in principle, the maximum likelihood methods derived in Section 32.3.4 properly account for the observed average completeness while providing the most robust estimates of the fitted parameters.

8. How is the absorber cross section related to the co-moving redshift path density of an absorber population?  For our treatment, to what physical structure does the cross section apply? Describe the key assumptions from which the expression for R*, the radius of the CGM of an L* galaxy, is derived (Equation 32.108). In order to obtain a robust estimate of R*, what six quantities need to be independently measured or estimated and comment on the sensitivity of R* to each? 

9. Once you have an estimate for R*, how would you naively estimate the radius of the CGM of a sub-L* galaxy, or a super-L* galaxy? Do you think it is safe to assume that all six quantities on which R* depends also apply for sub-L* or super-L* galaxies?  For example, do you think the covering fraction is the same across the full range of galaxy luminosities?

10. In your own words, state the definition of the mass density, Ω. Why is Ωion the most direct and therefore robust mass density measurement, as opposed to Ωgas? What additional factors are required to estimate Ωgas from Ωion?  

11. Estimating Ω from the data requires estimating the mean column density per absorber in our survey. Describe the two methods we can use to make this estimate and compare and contrast the advantages and disadvantages of each.

Problems

1. Under construction