Week 5 (Oct 31, Nov 2 ) In-Class Problems

For problem 2 (Wednesday this week) - you are going to need a computer that can run python!! 

It will help if it already has numpy, scipy, astropy, matplotlib, etc. installed. We will be using linetools, available here: 

https://linetools.readthedocs.io/en/latest/install.html Links to an external site.

NOTE: Problem 2 is NOT DUE on Friday - it has been moved to next week's problems. Only hand in Problem 1 this week Friday. 

Problem 1: 

In this problem, we will consider the SII (singly-ionized Sulfur) ion, and transitions between its various energy levels in the ground state. When applicable, we will assume we are observing it in an HII region with electron or kinetic temperature, $T_e\:=T_{kin}\:=\:10,000\:K$. Note this temperature is not (necessarily) equivalent to the excitation temperature, $T_{ex}$ . Recall the Boltzmann constant, $k\:=\:1.38\times10^{-16}\:erg\:K^{-1}$.  

You will find the following two tables of constants and relative level populations for the SII ion essential to complete this problem: SIIUsefulNumbers.pdf Download SIIUsefulNumbers.pdf

a. How many electrons does SII have, and what is its electronic configuration in the ground state? 

b. The spectroscopic terms of SII in the ground state are (all have odd parity, but I am not writing that out, and it's not really going to come into play here at all): $^2P\:_{\frac{3}{2}},^2D\:_{\frac{3}{2}},^4S\:_{\frac{3}{2}}\:^2P\:_{\frac{1}{2}},^2D\:_{\frac{5}{2}}$. Note, I have not put these in order from lowest to highest. You need to do that! Make note of the values for the spin, angular momentum, and total momentum. 

Draw and label an energy level diagram for SII (noting specifically n = 1, 2, and 3 and the wavelengths of these transitions). 

c. Consider only transitions within the first three levels, and you can ignore the fine structure IR line (why?).  Calculate the total cooling rate per SII ion at the 3 values of the electron density in the table, $n_{e} = 10, 10^{3} , 10^{5} [cm^{-3} ]$.  Assume the luminosity due to cooling (i.e. total cooling rate) is just the sum of the line intensities under consideration and keep things in cgs units.

d. Calculate the excitation temperatures for the $^{2}D_{3/2} \longrightarrow ^{4}S_{3/2}$ transition for each of the same three electron densities in the given table. Remember, the degeneracies of each level are 2J + 1. 

e. Discuss in a couple sentences the behavior of the excitation temperature and the cooling rate at high and low electron densities. (e.g. where is the cooling rate lower, and why?). 

f. Would the emission line intensity ratio between the $^{2}D_{5/2} \longrightarrow ^{4}S_{3/2}$ and $^{2}D_{3/2} \longrightarrow ^{4}S_{3/2}$transitions be used as a temperature or a density diagnostic for an HII region? (e.g. is the ratio of line luminosities more strongly dependent on density or on temperature)? Explain your answer in a sentence or two. 

g. What would you measure for the intensity ratio of the line referenced above (e.g. [SII] 6716/[SII] 6731) in the low density limit? 

h. What would you measure for the intensity ratio of the line referenced above (e.g. [SII] 6716/[SII] 6731) in the high density limit? 

Problem 2:  Measuring Emission Lines! (to be continued next week). 

For this problem, we are going to be working with ACTUAL spectra and measuring some emission lines to determine classic emission-line diagnostics for real galaxies. You will want to make sure you have the python package linetools installed. For instructions, see: https://linetools.readthedocs.io/en/latest/install.html Links to an external site.

For those of you not terribly familiar with linetools, I will show an example of how to use the GUI to measure lines. 

You are going to want to download the following three fits files: 

This is an SDSS optical spectrum: 

J0929+4644_172_157_spec.fits Download J0929+4644_172_157_spec.fits

This is from Keck/LRIS so it is split between blue and red sides. 

J0943+0531_106_34_bluespec.fits Download J0943+0531_106_34_bluespec.fits  and J0943+0531_106_34_redspec.fits Download J0943+0531_106_34_redspec.fits 

First, read in the SDSS spectrum of the galaxy J0929+4644 172_157 using the xspecgui that is part of the python package linetools.

For those of you not familiar with linetools or GUIs in python, here's an example of what I am able to start by running a simple ipython session: 

from linetools.spectra.xspectrum1d import XSpectrum1D

from linetools.guis import xspecgui as ltxsg

fname = 'J0929+4644_172_157_spec.fits'

sp = XSpectrum1D.from_file(fname)

ltxsg.main(sp)

That should give you a GUI. Typing "?" will list the possible commands. This link Links to an external site. is helpful. Play around with the GUI a bit! It is fun! 

Also, for book-keeping purposes here, it will be helpful if you make a table of your line measurements. Not a requirement, but it helps to start out being organized. You'll be measuring 6 emission lines per spectrum. And taking various ratios. 

a) Using the emission lines present in the spectrum, find the redshift of the galaxy J0929+4644 172_157. Hint: you can toggle to the "galaxy" line list, and adjust the redshift until you find a good fit. I always find that identifying [OIII] 5007 and Hbeta 4861 is the easiest way to get a redshift with these optical emission line spectra. If you click on a line that you think is the right line, you can select it from a pop up list by right-clicking...

b) For the galaxy  J0929+4644 172_157 measure the emission line ratio [SII] 6716/[SII] 6731. Hint: Use the 'G" key to fit a gaussian to the emission line and measure a line flux! Note this is the cooling luminosity!! Are we looking primarily at the high density or low density limit? 

c) For the galaxy  J0929+4644 172_157 measure the emission line ratio [OIII] 5007 / H$\beta$ . For H$\beta$ , it may be in an absorption trough, and you'll want to measure the line flux from the very bottom to make sure to get all the line flux. We'll call this ratio O3HB. 

d). For the galaxy  J0929+4644 172_157 measure the emission line ratio [NII] 6583/ H$\alpha$. We'll call this N2. 

e). Pettini and Pagel (2004) developed a nice abundance formula, using Cloudy, that uses O3HB and N2 to determine the average oxygen abundance of the HII regions that dominate the emission line fluxes in a galaxy. So, let's use their formulae to determine the oxygen abundance of J0929+4644 172_157. 

First, note that the Log (O3HB/N2) will be called O3N2 in the below equation. 

Pettini and Pagel's equations are as follows: