Example: Extracting the surface brightness profile and total magnitude from a galaxy image

In this example, we show you how we extract the surface brightness profile SB(r), the ellipticity and the total magnitude from a galaxy image.

 Here is an image of the galaxy. In order to fit the isophotes (contours of equal brightness), we must artificially mask the foreground stars in the image. The contour fitting routine then interpolates over the masked stars, so that we do include any of their light in making the measurement of the galaxy's light. For example, the large white-appearing square to the right of the galaxy is a masked region. The righthand image shows the contours superimposed on the raw image.

We then use the intensity, ellipticity (eps) and position angle of the major axis (theta) of each ellipse to derive the profile, the inclination of the galaxy and its regularity. The total magnitude is the sum of the intensities within all the ellipses out to the outermost measurement point, and then extrapolated to infinity assuming that the light follows an exponential distribution:

S.B.(r) = S.B.(0) exp (-r / rd)

where rd is the disk scale length.

 To the right, we plot the radial variations (in arcseconds) along the major axis of the surface brightness (surfmag), the ellipticity (eps), the position angle (theta) and the magnitude (totmag). The measurement of the ellipticity given here is the ratio of the minor and major axes of the isophotal ellipses. Notice that the ellipticity becomes rounder in the central, bulge dominated regions. The linear fit to the exponential portion of the surface brightness profile is shown in the bottom panel. The fit is performed between the two vertial dashed lines. The levels of the mean disk ellipticity and the mean position angle, averaged over the disk portion are indicated by solid horizontal lines in the eps and theta plots. The final total magnitude, indicated by the dashed horizontal line in the top panel, has been obtained by extrapolating analytically the fitted disk, beyond the last measured point to infinity.