In the Cas-A data we are studying, there are a lot of interesting features. The whole image looks like a ring of x-ray photons with some relatively empty spots inside the ring. Which part of the data is brightest, i.e., which part has the greatest concentration of x-ray photons in each pixel? We can get some idea of this simply by moving the mouse around while looking at the DS9 Value display. In this way we can see that the region around physical X,Y of 4158,4398 appears to have fairly large values in each nearby pixel. To check this quantitatively, we might want to know the average number of x-ray photons per pixel in that area compared to other areas in the data set.
Thus, we need to identify some regions of interest in which we can do analysis and we need to run some programs to give us some quantitative results. First, let's learn how to define regions of interest, known more colloquially to astronomers simply as regions.
DS9 allows you to define differently shaped regions interactively, with full control over position, size, rotation, etc. The options for working with regions are found in the Region menu in the top menu bar of the program. However, the most oft-used region, a simple circle, is already defined in DS9 and you can create a circular region directly without use of the Region menu. Simply move the mouse to the place on the image where you want to place the region and press the left mouse button. (Remember, the right mouse button controls the color contrast.) For example, click the left button near the point physical X,Y equal to 4158,4398. Don't worry if you are not exactly on that point. Notice that a green circle is drawn on the screen. (By default, the radius of this circle is 20 pixels). This is a region marker and we will use it to perform analysis on the data within that region of the image.
Did you not place the region marker exactly where you want it? No problem! Simply move the mouse into the region and press the left mouse button. Then, while keeping the left button pressed, move the mouse: the region marker will start to move as well. You now can line up the mouse with X,Y of 4158,4398 by watching DS9's X,Y position display. For even more control, simply click the mouse once inside the region. The region will become selected and will display 4 square handles at its corners. When selected, you can use the arrow keys to fine-tune the region position. When you have it placed exactly where you want it, click again in the region to de-select.
We would like to determine how many x-ray photons are in the bright area around X,Y 4158,4398 without processing the pixels surrounding it. The size of the region we created is a bit too large for this purpose, but we can easily change the size. Once again, select the region by clicking once inside the region. Now move the mouse over one of the four handles (so that the cursor changes from its usual arrow) and press down. You can now resize the region by moving the mouse around while the left mouse button is pressed: see how the size of the circle gets larger and smaller. When you have the size you want, stop pressing the left button.
You can make regions of different shapes, including circles, ellipses, boxes, polygons. Generally, astronomers use circles or annuli (multiple concentric cirles). They sometimes will choose a different shape in order to cover an area of interest completely with minimal inclusion of unwanted area. Sometimes a region can be well-covered, for example, by a rotated ellipse. Sometimes nothing but a carefully constructed multi-sided polygon will do. But in general, circles are most often used. (Regions also can be defined to exclude an area from a region of interest, for example, exclude an elliptical region within a polygon.)
The Funtools analysis routines you just loaded are used by astronomers around the world. In our setup, the analysis actually will be performed remotely at Smithsonian Astrophysical Observatory on the Chandra data we also loaded from SAO. In this way, the programs can be run on powerful computers at SAO with the results displayed on your computer.
The analysis we want to run now is called Counts in Regions, which actually runs a Funtools program called funcnts to sum up the x-ray photons in the region(s) specified. To run this program, pull down the Analysis menu and select the Counts in Regions menu option. In a few seconds, a window will display your analysis results. The net_counts value is the number of x-ray events inside the region, while the surf_bri (surface brightness) value is a measure of the average number of x-ray photons in a unit area.
Now move the region around to different places on the Cas-A image and run Counts in Regions in different locations. Doing this will give you a quantitative idea of how strong the x-ray emission is in various parts of the image.
To get a better idea of the shape of x-ray emission from interesting parts of Cas-A, we can run another program on our regions of interest called a Radial Profile Plot. This program will display a graphical plot of the brightness of the x-ray emission (average number of photons per unit area) in concentric annuli around a central point. If the x-ray emission in our annular region is coming from a very strong central source, the shape of the plot will fall off steeply. If the x-ray emission is less strong (but still coming from a central source), the plot will have a more gradual downward slope. If the x-ray emission comes from a diffuse source, the plot might not even have a recognizable shape.
The Radial Profile Plot only runs on a circular annuli and therefore we must create an annulus region instead of using a circle. To do this, first delete the previous circular region by pulling down the Region menu and selecting the Delete All menu option. (Alternatively, you can put the mouse inside the region and press the Delete key.) Now again pull down the Region menu, select the Shape sub-menu, and then choose its Annulus sub-menu option. Create an annular region by moving the mouse to the location on the Cas-A image where you want to place the region and then pressing the left mouse button. For example, we can do this once again at position physical X,Y = 4158,4398. An annulus region with 2 annuli will be displayed. You can make more annuli by double clicking inside the region to bring up the Annulus dialog box. Change the value of 2 in the Annuli input area to, say, 10. Press the Generate button and then the Apply button. You now will see that the annulus region consists of 10 concentric annuli. (Note that you can also change other annulus parameters. For example, change the size of the annulus by changing the Outer Radius value.) Press the Close button in the Annulus dialog box.
Having created an annulus region, we now can run Radial Profile Plot. Simply pull down the Analysis menu and select the Radial Profile Plot menu option. In a few seconds, a plot window will display your analysis results. Try running this analysis program on annuli in different places on the Cas-A image by moving the annulus. For example, move it to near Physical X,Y = 4506,4576 (in the "empty" part of the image). See how the resulting radial profile is much different from that of the bright spot at X,Y = 4158,4398.
The first step in spectral analysis is to extract the energy information in the form of a spectrum, i.e., a one dimensional histogram of the number of x-ray photons falling into each of the discrete energy ranges (or bins) that ACIS can identify. We usually do this within a circular region of interest, just as we did for spatial analysis with the Counts in Regions task. Therefore, we will need to delete all previous regions (using the Delete All menu option of the Region menu) and then create a circular region (using the Shape sub-menu of the Region menu). Once you have created a circular region, run the Energy Spectrum Plot analysis task in the Analysis menu. Try this at different places on the Cas-A image, and notice how the spectrum changes.
A similar analysis can be made of the timing information associated with each x-ray photon. Once again, we perform the analysis in circular regions of interest. This time, however, we extract timing information from the data in the form of a light curve, that is, a one-dimensional histogram of the number of x-ray photons that fall into discrete time bins. The ACIS detector records rough timing information with each x-ray photon, so we can practice extracting light curves from x-ray timing data with Cas-A. To do this, simply select a circular region and run the Light Curve Plot in the Analysis menu. When you run this task, a dialog box will pop up asking you to enter the number of bins to use. Specifying the number of bins is necessary because the timing information recorded by ACIS and HRC is not continuous, but has values that get read out by the satellite in discrete intervals. For example, this ACIS observation has a binning time of 3.2401 seconds. Any photon that is detected within that interval will be assigned the same arrival time. We therefore must decide how to divide up our data. We can choose to do this in a number of ways. The most informative is to choose a bin width that has a reasonable number of photons in it, and to normalize it as a function of time, so that we can see the count rate, i.e. the number of counts each second that the satellite detects. For now, you can use 32.401 seconds as the value to enter in the top line of the dialog box, and check both boxes in the two subsequent lines. Once you have created a circular region, run the Light Curve Plot analysis task in the Analysis menu at different places on the Cas-A image, and notice if the light curve changes.
Remember, these are the basic techniques of x-ray analysis: