The Spectra of Supernova Remnants

june 22, 2004
revised for GEARS June 2010
goals:
1) to identify emission lines in the x-ray spectra os a supernova remnant
2) to determine the temperature of the remnant from the spectrum
3) to make a 3-color image
4) to determine the age of your remnant

choosing a supernova remnant for analysis

Choose a supernova remnant (SNR) for analysis from the Chandra catalog. 
Brighter SNR images are more likely to give much better results. 
Look at the SNR flux and the observation time to make a good choice. 
You might also want to choose a historical supernova (i.e., one which people actually saw and recorded).
Write down the Chandra ObsId number (so that you can open your image in the ds9 image processor) of each of your choices.

IMPORTANT: in the following directions to this lab, I have used the supernova remnant Cas A as an example of how to do various things.  You will do the same things for YOUR supernova, not Cas A!  (therefore you cannot choose Cas A for one of your three choices!)
obtaining the spectrum of the supernova remnant

1) open ds9
2) under  Analysis, select  Virtual Observatory
3) in the pop-up Virtual Obsevatory window, click in the Chandra-Ed Archive Server box
4) the Chandra-Ed box should turn green, and a third ds9 window opens with Chandra-Ed images
5) locate the ObsId number for your SNR and double-click on the image title
(there will be an authentication message and an acknowledgement that the image successfully loaded in the original ds9 window;
however, if you wish to load a different image from the Chandra-Ed list at a later time, return to this third ds9 window,
and click on the left-pointing blue arrow at the upper left)
6) the image of your SNR should have opened in the original ds9 window
7) use the Color and Scale options to enhance the appearance of your image
8) ds9 will use the entire image unless you select a specic region to analyze;
a specific region can be created by clicking and dragging
9) under Analysis, select Chandra-Ed Analysis Tools, Quick Energy Spectrum Plot
10) the spectrum should be returned in a new window
11) in the spectrum window, explore different option  under Graph
identifying spectral lines

1) you can use a table of the typical strong x-ray lines in SNRs or search the ATOMDB database for lines in a given energy range
2) you can zoom in on a region of the spectrum window by left-clicking-and-dragging followed by a left click;
     a right-click reverse the process; multiple zoom-ins are allowed
3) ds9 does not make it easy to print or save useful spectra files;
     you can save the plot in .plt form (a unix extension) by selecting File, Save Configuration;
     the plot can be reopened in a plot window only
     you can save the data (ordered pairs) in .dat form that can then be opened in a spreadsheet
4) the best way to print an image of the plot is to use  Print Screen;
     if you have software that can print the screen (or active window) to an image file, use that
5) identify as many strong lines as you can; during identification, make use of the last column in the identification table;
    your strong lines will likely have a high value of the relative intensity number

here is an example of SNR (Cas A) with lines identified




determining the temperature of your SNR


method 1: using the emission lines

The temperature of the SNR also determines the ionization state of the various elements in the ejecta.

Ionization energies are available in a table here. 
The left-most value in a given row of the table is the energy required to remove the first (the outermost)) electron.
The next entry in the table is the energy required to remove the second electron.  And so on.

Therefore, to find the total energy required to remove, for example,  9 electrons from a neon atom, 
the first 9 ionization energies in the neon row must be added.
In other words, to produce Ne X (which is a neon atom with nine electrons removed, or, equivalently,
a neon nucleus surrounded by only one electron) requires 21.6 ev (to remove the first electron)
+ 41.0 ev (to remove just the second electron) +  ...  + 1196 ev (to remove the 9th electron) = 2150 ev. 

In addition, it requires 1500 ev to excite the 10th electron to the excited level in which it is initially resides before it emits the x-ray photon by dropping to the ground state.   (We know this because the emitted photon carries this much energy, and therefore the electron must be initially excited in the Ne X ion by at least that much energy)
Therefore, the total energy required to produce a Ne X electron in the excited state is approximately 3700 ev.

Convert this excitation/ionization energy to temperature in the usual way.
For the case of the Ne X line, a temperature of 3.7 million degrees Kelvin is therefore required to produce the excitation/ionization energy = 3700 ev.

How do you know which lines in your SNR spectrum to use for the temperature calculation? 
Pick at least 3 of the strongest lines and do a temperature calculation for each.

method 2: using the continuous spectrum  (optional)

In most SNR spectra, bremsstrahlung is the dominant contributor to the continuous spectrum. 
Bremsstrahlung (braking radiation) occurs when a free electron decelerates (in the presence of other charges) by emitting a photon. 
The bremsstrahlung spectrum has a flux dependence on energy E has the form  flux a   (kT)-1/2 e-E/kT
where k is Boltzmann's constant and T is the temperature of the plasma.
This means that a log flux vs energy plot should be linear with a negative slope proportional to (kT)-1.
As you can see from the above spectrum, the flux does vary linearly (with negative slope) with the energy from about 1000 ev to approximately 8000 ev,
if one ignores the emission lines.  The largest spectral region devoid of emission lines is from 4000 ev to 6000 ev.

To determine the slope of the linear portion of the spectrum:
1) under Analysis, select Chandra-Ed Analysis Tools, CIAO/Sherpa Spectral Fit
2) in the sherpa_par  box that opens, click on the button at the top (which probably says "power law"), and select bremsstrahlung
3) in the sherpa energies slot, type in :4,6:  which indicates that you want to select the region from 4 kev to 6 kev (the region where the continuous spectrum dominates and that is devoid of emission lines)
4) in the CIAO/Sherpa Spectral Fit pop-up box appears (this should be the 5th), the inverse of the slope is returned in units of kev
5) convert the ambient energy present to explain the continuous spectrum to temperature in the usual way

now compare the temperatures obtained from the two methods (continuous spectrum and lines).

how to make a 3-color image

1) Open Cas A via Virtual Observatory in the ds9 image processor.  (Once again, remember that YOU are not doing Cas A; you are doing this for YOUR supernova remnant..... also, shouldn't -- necessarily -- do the same set of spectral lines & ionization states that I did for Cas A; you have to look at which lines are strong in YOUR supernova remnant spectrum!)

Do a Quick Energy Cut (under  Analysis, Chandra Ed Analysis Tools) for the energy range 6.4 - 6.8 kev which is where a strong line of Fe XXV resides.  
The image returned shows only photons in this particular range of  energy. 
Change the color to, say, green, and then save this image as a separately-named jpg image. 
However, be sure to delete the frame with the original Cas A image, or else that will also be saved as part of the jpg image. 
Here's how my  Fe XXV energy cut looked.


2) Delete this frame, go back to ds9 Virtual Observatory, and reload the original Cas A image.  Do another Quick Energy Cut, this time for the range of energy  1.65 - 1.95 kev, where a strong line of Si XIII exists.  Color this image blue, and save as another jpg image.
(Again, be sure to delete the original Cas A image frame before saving.) 
Here's how my Si XIII energy cut looked.  Adjust your color intensity to make the image vivid.


3) Finally, delete this frame, go back again to ds9 Virtual Observatory, and reload the original Cas A image. 
Do a third Quick Energy Cut, this time for the energy range 2.3 - 2.5 kev, where a strong line of S XV exists. 
Color this image red, and save as another jpg image.  (Again, delete the original Cas A image frame before saving.) 
Here's how the final S XV energy cut looked.


4) Now we combine the images. 
Open the Makali'i/Subaru image processor (or some other photoshop-like program that can process JPG images),
and then open all three of the previously saved jpg images. 
Under Image, select Batch Processing. 
Make sure that the only the three jpg images you want are in the list.  I used Add under
Composite Method.  You can change the contrast and brightness in the usual ways (max, min, log, etc.)
Because you obtained each jpg for the same Cas A image, there is no need to align the images. 
Here's how my final result looked.


5) Notes.  The Si and the S seem to overlap in position, but the Fe seems to be missing from the blowout region at the upper left, at least compared to the Si and S.

6) Suggestions.  Another thing to try is use three images all from the same element, but in 3 different ionization stages; for example, do energy cuts at the energies corresponding to lines of Si XII, Si XIII, and Si XIV.



more about your supernova remnant: finding the size and age

1) Determine the angular radius of your supernova. 
The scale of the Chandra images is 0.5"/Physical pixel.

2) Check with the Chandra catalog to make sure that you are in the right ballpark for your measured angular size.

3) Use the distance given in the Chandra catalog to determine the radius of your SNR in pc.

4) A typical expansion speed of a young SNR is 10,000 km/s. 
Find an approximate age for your SNR. 
Compare your calculated age to an accepted age, if known.

5) Is a pulsar apparent in your SNR?  How can you be sure that the object you identify as the pulsar really is a pulsar?

6) Check the latest Chandra observations for your SNR to see if there is anything new.

and even more extensions

1) Some of the SNRs have multiple Chandra observations.  Can you detect /measure an expansion?
here is what a high school found found for Cas A in 2004;
here is what Chandra scientists found in 2008

2) How does the temperature of the ejecta depend on distance from the center of the remnant? 
(to do this, create annular regions to study this)

3) Once the class's results are collected, is there any evidence that the temperature of a SNR is related to it age?