Fitting Models of Halo Emission to Real Date

Written Report

This is the third and final project that you will do as a group. Your group will hand in a single report that describes your results from all three group assignment in a coherent fashion. All group members must contribute and be listed as authors. The report should read as a single, complete study on the full problem of making observations of oxygen line emission from the halo, modeling the halo, fitting the models to the halo, and then interpreting the results. The report should be similar to a scientific paper with sections for Introduction and statement of the problem (a few sentences each), description of the models and code (turn in the code separately, do not include it in the body of the report), results/predictions from the models for given parameters, and a discussion of the results. It should address all the questions asked in the assignment description.
Also, your group should prepare a presentation on the whole project. The presentations will be made on the last day of class. If desired, we can schedule a day to practice the presentations in advance of the final presentation. All group members must contribute to the final project write up and the project presentation.

The local bubble model

Re-read the paper "Constraining the Milky Way's Hot Gas Halo with O VII and O VIII Emission Lines" by Matthew Miller and Joel Bregman at http://adsabs.harvard.edu/abs/2015ApJ...800...14M.
Miller and Bregman use a relatively involved local bubble model, but, according to private communication with Matthew Miller, it does not have a large effect on their fitting. We will parametrize the local bubble as an optically thin, constant density, and constant temperature sphere centered on the Earth with a radius of 150 pc. How many effective parameters are needed to characterize the observed oxygen line intensity from this model? How is(are) the parameter(s) related to the physical properties of the model?
Write Python code to implement your local bubble model. Think carefully about the previous step as the correct answer may greatly simplify your code.
Combine your local bubble model with your spherically symmetric model from the previous project.

Fitting the real data

You will now write code to find the set of model parameters that best fit the real data.
Use your code from the previous assignment to read in the list of (l, b) values, line intensities, and uncertainties from H&S. Unlike in the previous assignment, we will keep the actual measured line intensities this time.
Re-read both H&S and M&B and decide on data selection criteria. Note that you do not need to use the selection criteria from either paper. However, in your write up you must explain your criteria, the motivation for your criteria, and report some statistics about your remaining data sample (such as the number of point and their latitude and longitude distributions).
Modify your fitting code to simultaneously fit for the parameters of the spherically symmetric halo and the local bubble. Based on your evaluation of brute force fitting and a more refined technique in the previous assignment, choose which technique to use for here.
Find the parameters that minimize $\chi ^{2}$ and how much the parameters can vary and keep the increase in $\chi ^{2}$ to less than 2.71. If feasible, contour plots of $\chi ^{2}$ versus pairs of parameter values. Do fits for the OVII and OVIII data separately. Discuss the quality of your fits and the consistency of the two data sets with your model and with each other in your report.
In your report, discuss any resulting thoughts that you have regarding this work.