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Galaxy surface photometry

ELLIPROF measures the intensity I0 of each isophote in the image's own units per pixel, after the sky is subtracted. To compare galaxies, or to compare with models, you convert this to surface brightness in magnitudes per square arcsecond. ELLIPROF does not do that conversion for you.

From I0 to mag/arcsec²

You need:

  1. the pixel scale \(s\), in arcseconds per pixel;
  2. a photometric zeropoint: the magnitude \(m_1\) of one unit of image flux (for example, of 1 electron, or of 1 electron per second if the image is in e/s).

Then

\[ \mu = m_1 - 2.5\log_{10}\!\left(\frac{I_0}{s^2}\right) \quad [\text{mag arcsec}^{-2}] \]

Dividing by \(s^2\) converts "per pixel" into "per square arcsecond".

Check the image units

The zeropoint must match the units of the pixel values. If the image is in electrons per second, use the zeropoint for 1 e/s. If it is in total electrons, add \(2.5\log_{10}(t_\mathrm{exp})\) to that zeropoint.

For publication-quality photometry you would also correct for Galactic extinction and, for distant galaxies, apply a K-correction and the \((1+z)^4\) cosmological surface-brightness dimming.

The UGC 12517 example

On this site, the UGC 12517 profile is shown in the image's own units: I0 per pixel, exactly as ELLIPROF reports it. To express it in mag/arcsec², use the formula above with the zeropoint for the image's units and \(s\) = 0.128″/pixel.

The outer isophotes

The outskirts of galaxies carry information about their assembly: haloes, shells, tidal debris. They are also where isophote fitting is least reliable.

  • The sky dominates. A small sky error changes the outer profile strongly; see Why the sky matters.
  • Few good pixels. Large ellipses cross many masked sources and the image edges, and the fit then has fewer samples.
  • The image edge. An isophote that runs off the image is sampled only on one side. Its centre and shape then become unreliable.
  • Noise per sample is large, so centres, ellipticities and angles scatter more. Watch for sudden jumps in the outer profile.

How far out can I trust the profile?

A practical rule: trust the outer profile only while the galaxy is clearly brighter than the uncertainty of the sky, and while the ellipse stays inside the image with most of its samples unmasked. Repeat the fit with the sky changed by its uncertainty. Where the profiles disagree by more than you can accept, stop.

Other derived quantities

From the profile you can compute, for example:

  • total magnitudes and half-light radii, by integrating the intensity over the area of the elliptical annuli (the area of an ellipse is \(\pi a^2 (1-\epsilon)\));
  • Sérsic or de Vaucouleurs fits to \(\mu(a)\);
  • colour profiles, by comparing two filters at matched semi-major axes (the same R0, R1, NR, RLAW and centre). Fit each filter, check that the geometries agree, and difference the surface brightnesses. (elliprof, as of 0.1.4, cannot impose the geometry of one fit on another. FIXCTR=1 fixes the centre, and ELLIP= fixes one ellipticity for all isophotes.)

With --verbose, ELLIPROF also prints its own de Vaucouleurs fit at the end of a run (a line starting Re =, in pixels and image units). It uses the separate SKY= keyword and is intended as a quick look.