Education Activities To Accompany Chandra Data Analysis Software M31 & Coma
Big, Bigger, Biggest
Activity 4: The size and temperature of the x-ray gas
A) In the same way as we did for 3C273, we can find the distance to Coma.Since the cluster is far closer, the change in the wavelengths of the spectral lines is much smaller, however.In this case, Dl/l = 0.02, instead of 0.13.Show that this implies a distance to the cluster of about 120 Mpc.
B) Now, estimate the size (in physical pixels) of the "long" dimension of the diffuse emission, and show that the extent of the x-ray gas is about 500 kpc in size. (Note that your estimates for this will differ because of different estimates for the diameter of the region on the image). This is roughly the same order of magnitude as the entire distance to M31 from our own galaxy. Also remember that this is merely the central, brightest portion of the cluster that extends for a far greater distance into space. This central region is called the core radius of the cluster.
C) To find out the temperature of the gas, we can fit the emission with a spectral model (thermal bremsstrahlung). This model attempts to quantify the way rarified, hot gas would behave in an environment similar to that of the Coma cluster. First, select an elliptical region by going to Edit > pointer, then Region > shape > ellipse. Then, estimate where the "center" of the elliptical (red appearing) x-ray emission is, and click once to place the ellipse on the cluster. You can then click again to select the region, and drag the corners to the proper shape and size of the cluster. You may want to try this several times to get a better fitting region from which to do the analysis. (Remember, if you want to delete a region and start over, just select the region by clicking once within it, and with the cursor anywhere inside the region, hit the "delete" key on your keyboard). Now, if we were really trying to get some accurate numbers, we would select a background region to subtract from our source region estimates, but since the Coma cluster is so bright, and we are just interested in reasonable estimates, we will omit this step. So, after your region is selected, go to: Analysis > CIAO/Sherpa Spectral Fit. Then, when the dialog box pops up, select "bremsstrahlung" for the Model type, and hit OK. After a few moments you will see the data displayed, as well as the model fit to the data. From the text file display, you will find a line that gives you the temperature for the final fitted model. This should have a value of about 7 to 9 keV. This corresponds to a temperature of about 100 million degrees (on the absolute scale)!
