The objective of this tutorial is to provide a straightforward method for obtaining magnitudes and fluxes of photon sources in SEO observations and data files.

Requirements

1. A .FITS file viewer; such as SAOImageDS9, or the stars.uchicago web-viewer.
2. SEO observation data; .FITS images.

 

1. Loading your data into DS9

Note: If you are using the stars.uchicago web-viewer, and you have your FITS image open, you may skip to section 2.1.

First and foremost, we will need to pass our data into a .FITS viewer software, so that we may be able to visualize and analyze the information captured by the telescope directly. This is the critical function of DS9 (and other FITS viewer softwares).

• 1.1: [file → open → data .FITS]. Upon startup of DS9, an empty canvas at the bottom of the screen and an empty table at the top are separated by a menu of buttons {file, edit, view, frame, … , help}. Click on file, revealing the subdirectory of options, of which open we wish to click on next. A file viewer window will appear, allowing you to find and select the desired .FITS file stored locally on your device.
• 1.2: [scale → 99.5%]. The SEO image should now be visible on the canvas, and the above table should populate with positional data as you move your cursor over the image. If the image appears uniformly black, try adjusting the scale with the scale menu options. I suggest changing the bounds from min max to 99.5% to mitigate the effects of outliers. 

You should now be able to see the photon sources in your .FITS image, stars surrounding a central interstellar object perhaps. Decide on which star/source you wish to calculate a magnitude for, and then we may begin analysis.

 

2. Regions and Image Statistics

Note: If you are using DS9, skip to section 2.2.

With your desired photon source selected, you’ll want to zoom in onto the object [use mouse scroll or trackpad] to reveal its circular shape and isolate it from surrounding objects. Next we wish to extract statistical values for the object – most important are the FWHM radius, the pixel sum, and the background. To get these values, we will use DS9’s regions to extract information from the .FITS file.

2.1: Stars Web-Viewer Statistics – See picture above.

• 2.1.1: [Analysis Tools → Stats | Box → check]. Make sure you have selected the stats tool in the upper right corner of the screen. Also confirm that Box is checked, so that you may have a square to delimit the source area.
• 2.1.2: Drag the corners and edges of the box to reshape and reposition the box so that it is only encasing the image source you want to calculate magnitude for.
• 2.2.1: Take note of the Sum: value in the upper right, this value encodes the amount of photons received from the source. Also note the Npix value, this is the pixel size of the region in the image.
• 2.2.3: Move the square box to a region of the image with no apparent photon sources, empty sky. Here, take note of the new Sum: value, this decreased number will be our background flux, bkg. Make sure that Npix reads the same number as before.

2.2: DS9 Circular Regions and Pixel Sums – See picture below.

• 2.2.1: [Region → Shape → Circle]. Change region shape to circle. Then draw a circle, whose center is the center of the photon source, onto the image canvas with your mouse or trackpad.
• 2.2.2: [double click → Analysis → Statistics]. Double click on the region to reveal its menu, here one can change the radius of their region if they calculated the FWHM (see 2.1). Notice the new menu items at the top of the screen, {File, Edit, Color, Width, … , Analysis}. We wish to expand the Analysis menu and select Statistics.
• 2.2.3: A new window with a table of values pertaining to the circle region should appear. We want to take note of the sum value and the npix value. The former represents all of the pixel counts within the region, and the latter denotes the size of the region.
• 2.2.4: Simply drag the circle region away from the desired source, and over a seemingly empty region of the image. Again take note of the sum value – this will be our background value, bkg. Make sure the size of the region, npix, is the same for background value extraction.

 

 

3. Calculating Magnitude from Image Statistics

Now that we have gathered the relevant statistics from the image, we may calculate the apparent magnitude of the desired source. The following equation demonstrates the relationship between the pixel sum in the .FITS image, and the apparent magnitude scale:

The sum variable is the number we got from the circle region statistics when the circle was placed over the photon source in DS9. The bkg variable is the same sum but when the region was over the empty sky in the image. The PHOTO ZP variable is the photometric zero point for our detector. It is the magnitude required of a source to produce one count per second on the detector. The photometric zero point for SEO can be found in the FITS header – but it is {8.9} in case you do not wish to look.

If you wish to better understand the meaning of the magnitude statistic you just calculated, or the method by which we obtained the value, you can check out the following wikipedia pages covering relevant material:

• Zero Point (Photometry)
• Apparent Magnitude
• Point Spread Function

 

Appendix

A. – Point Spread Function and FWHM in DS9 (optional)

• A.a: [Region → Shape → Projection | Edit → Region | mouse draw across source]. First we want a measure for how much the point source is being spread out on the CCD (PSF). Hover over the Region menu at the top of your screen, then navigate to Shape, and finally select Projection. This will allow us to draw a line region across the source and observe how the light intensity changes with position.
• A.b: [double click on region line | (Projection) fk5 → Physical → Apply]. Make sure to convert the projection graph x-axis to physical coordinates of the image (the default is WCS coordinates).
• A.c: Zoom in on the projection graph to find the coordinates where the pixel intensity (y-axis, Jy / pixel average) is at ½ of the maximum value. Use the distance formula to calculate the physical distance between these half-max points. We will then double this value and use it as the radius for circular regions.