Determine Stellar Magnitude from a CCD Image
(Differential Photometry)

Overview

Photometry is the process of measuring light collected from an astronomical object and then assigning a magnitude. Assigning magnitudes to stars across multiple images is complex since many corrections must be applied. A simpler approach is to determine the magnitude of a star by comparing the brightness of the star with a reference star in the same image. In this case most correction factors can be ignored without significant inaccuracy. This is differential photometry.

Measuring Light from a Star

CCD pixels collect light linearly up to a maximum value. The light collected from a star is called flux and a star’s flux is measured directly from a CCD image by summing all the light within a circle and then subtracting the flux due to the nearby background sky. In this example, the Aperture Photometry Tool (APT) software package will be used to measure stellar flux.


The strategy is to lookup the magnitude of a reference star using Aladin or any other sky atlas software. Measure the light collected on a CCD from the reference star and the target star. Then use these three values to calculate the magnitude of the target star. The target star can be any point like object – star, asteroid, variable star, quasar, etc.


By selecting the dimmest star in the image as the target star, it is possible to measure the image's limiting stellar magnitude.

Procedure

  1. Load the FITS image into Aladin Sky Atlas and load the SIMBAD catalog data for the image. The FITS image must not be stretched or post processed.

  2. Select a reference star and retrieve the V-band magnitude of the reference star. The reference star must not be a variable star. Choose a star that is bright, not overexposed and not overlapping any other stars. Identify candidate reference stars using the Aladin filter:

    ${otype} ="Star" && ${V} <17 { draw red circle (30) }


  3. Load the image into APT. In More Settings, Select Model B (Sky-annulus median subtraction). Select the reference star by double clicking. Use the Alter button to adjust the size of the aperture circle. Adjust the inner red circle to surround the star. The outer circles should not touch any other stars. Press "Recompute Photometry". APT displays the star's flux in the field "Source intensity (sky subtracted)".



  4. Similarly, use APT to determine the flux of the target star.

  5. Calculate the magnitude of the target star:

    mag target = mag reference – 2.512 * log (flux target / flux reference)

    log is log base 10

Worked Example

In this image of NGC 1365, a reference star was identified to determine the unknown magnitude of a dimmer target star.

  1. Reference star V-band mag = 12.747

  2. Reference star, using major radius = 8, inner sky radius = 13, outer sky radius = 18
    then Source Intensity = 5.023e+6

  3. Target star, using major radius = 3, inner sky radius = 7, outer sky radius = 11
    then Source Intensity = 195560

Target star calculated mag = 16.3




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