Review Questions

1. Consider the rates for the creation and destruction of neutral and ionized hydrogen, as written in Equation 35.1. (i) In your own words, describe each creation term for neutral hydrogen. (ii) Describe each destruction term for neutral hydrogen. (iii) Explain why, in the case of hydrogen, the creation/destruction rate for the hydrogen ion is the negative of the rate for the creation/destruction of neutral hydrogen.

2. For this question, some review of material in Chapter 34 my help. Consider Equations 35.2, and 35.3. (i) In your own words, describe how each neutral hydrogen creation reaction rate is computed. Include in your answer whether, for example, interpolation of a parameterized functions are required and which terms have energy and/or temperature dependence. (ii) Repeat part (i) for each destruction rate for neutral hydrogen; don't forget to include the photoionization rate!

3. Describe the timescale conditions by which we determine whether a gas is in ionization equilibrium.  If a given ion is in photoionization and collision ionization equilibrium, is it possible that other ionization stages of this same element or that ions of other elements in the gas are not in photoionization or collision ionization equilibrium?  Explain.

4. What is Cloudy?!  (i) For modeling the gas clouds for absorption line studies, what are the minimum four input quantities required to specify and solve a Cloudy model of an absorber? (ii) What are some of the simplifying assumptions that are often invoked when building Cloudy models? 

5. A very key parameter of a Cloudy model is the ionization parameter. In your own words, define the ionization parameter. Note that, in Figure 35.1, the hydrogen number density of the cloud model is not explicitly specified as an input to the model! How is the number density of the cloud model determined?    

6. Explain why, for cloud models with large HI column density, the shape of the incident ionizing spectrum changes as it penetrates further into the cloud model?  Is the ionizing spectrum getting progressively harder or softer with depth?  How does this phenomenon result in ionization structure in cloud models? What is the common name for this phenomenon?

7. One strategy of exploring ionization models is to create grids of model clouds.  These grids are typically specified to have a minimum of three dimensions (or independent physical quantities).  What three cloud properties are these? (HINT: consider the answer to Problem 4(i)). For each of the three independent cloud properties, what are some recommended ranges (min and max values) and grid step sizes in order to sample the known range astrophysical gas structures effectively?  

8.  Consider Figure 35.5, which is based on a Cloudy grid for a cosmic UVB at z=1 and cloud metallicities of 0.1 solar. In real-world observations, the minimum detection threshold for absorption lines typically corresponds to ion column densities of  log(Nkj) ≥ 12. (i) For the cloud models with log(NHI) = 16.0, which ions do the models predict you should be able to detect? For each of these detectable ions, what is the approximate range of predicted hydrogen number densities of the clouds in which they would be detected? What is the approximate range of predicted ionization parameter of the clouds in which they would be detected? Present your findings in a three column table with columns (1) ion, (2) density range, (iii) ionization parameter range. (ii) Repeat (i) for the cloud model with  log(NHI) = 17.5.

9. Explain why metallicity scaling of the predicted ion column densities can be applied to all cloud models, whereas their scaling with HI column density is valid only for optically thin models with log(NHI) ≤ 16.

10. What is the definition of the ionization correction (IC)? Explain what role it is playing when estimating [X/H] from a measured ion column density (see Equation 35.40).  Examining Figure 35.6, why do we become concerned when ionization corrections, such as those for CIV and OVI are large (i.e., greater than 2 or less then -2)?

11. Consider Figure 35.7. (i) For which ions and metallicity ranges do we become concerned that non-equilibrium collisional ionization may be important when modeling cloud chemical-ionization conditions?  (ii) How might the application/adoption of non-equilibrium ionization change what we infer about an absorbing gas cloud for which we have measured the column densities of one or more of these senstivie ions? (iii) Explain why non-equilibrium collisional ionization effects are sensitive to (change with) metallicity?

12. Briefly summarize how the shape of the ionizing spectrum (cosmic UVB) can affect the ion column densities predicted by model clouds.  Also summarize how our inferences of the absorbing cloud metallicities can be skewed, including a quantitative estimate of how much our estimates can be skewed.

13. Consider the resulting cloud size (pathlength L through a model cloud).  If the hydrogen ionization fraction in the cloud was increased by a factor of 10, by what factor would the cloud size need to change so that the neutral hydrogen column density of the cloud model is preserved//unchanged.  

14. Consider the estimated cloud mass, M, of a model cloud. If the hydrogen ionization fraction in the cloud was increased by a factor of 10, by what factor would the cloud mass need to change so that the neutral hydrogen column density of the cloud model is preserved/unchanged.  

15. In your own words, what is the Jean's length and what physical principles govern its estimated size. In your own words, what is the Jean's mass.  Of all the macro variables that the Jean's mass is dependent upon, to which two is its fractional change most sensitive ?

Problems

1. Chemical-ionization modeling requires that the number densities of all ionization stages of all elements and the number density of the free electrons in a gas are determined. Consider a pure hydrogen and helium gas,. The number density of H and He are balanced by Equations 35.1 through 35.10. Using these equations, derive the number density ratios given in Equations 35.20 and 35.21.  

2. Given the solutions for the number density ratios in Equations 35.20 and 35.21, and the expressions for the ionization fractions in Equations 35.17, 35.18, and 35.19, apply particle density conservation to derive the full expressions for the number densities of all H and He ions. [A review of Sections 33.2 and 33.3 may be helpful]

3. Repeat Review Question 8 for both model clouds but scale the cloud model metallicities upward by 0.5 dex. Comparing your tabulated results, summarize the difference in what you can detect in the higher metallicity cloud in terms of ions and hydrogen number density ranges. 

4. Repeat Review Question 8, but only for the log(NHI) = 16.0 model cloud; scale the HI column density of the model downward by 0.5 dex while simultaneously scaling the metallicity upward by 0.5 dex. Comparing your tabulated results, summarize the difference (or lack of) in what you can detect in the lower HI, higher metallicity cloud in terms of ions and hydrogen number density ranges. 

5. Under construction