Kron Photometry

Tom Jarrett, IPAC
Feb 01, 2001
revised: Feb 5, 2001

Kron's clever technique (see ApJS, 43, 305) uses the intensity-weighted 1st moment radius to scale the aperture that captures the total flux of a galaxy. Kron notes that the first moment radius is aproximately equal to the half-light radius (depending on the morphology and radial light distribution). As such, Kron scaled this radius by a factor of two to measure the total flux. Others (e.g., Bertin & Arnouts 1996, A&AS, 117, 393) use a scaling of 2.5 for their "Kron" aperture. 2MASS has adopted this scaling for consistency, among others, with the DENIS survey.

The tricky part about this operation is the first-moment determination. How far should the integral be carried out? An integration radius that is too small will bias the Kron apertures (see more below), while a radius that is too large will suffer from stellar contamination (and hence will bias the Kron aperture toward the high side).

For the incremental releases, 2MASS carried out the integration to aproximately the one-sigma isophote level. This integration radius turns out to be too small, which biases the Kron apertures toward the isophotal aperture. This effect is demonstrated in the repeatability plot:

The end result is that the Kron photometry underestimates the total photometry by ~20%.

Final Reprocessing Modifications
To improve the Kron aperture determination, the first-moment integration radius is expanded to better match the radial light profile of the galaxy. The key is to employ the modified exponential function to trace the radial light distribution,

More details are given here. Assuming we can calculate the disk (or spheroidal) scale length, alpha (and beta), an effective integration radius corresponds to ~four scale lengths. In practice, the 2MASS PSF completely dominates the radial surface profile for small radii (<4"), so the exponential function is fit to the profile for r>4". Hence, the integration radius is The Kron aperture is now more closely matched to the radial profile (although, on the down side, is much more prone to stellar contamination). Some examples are given here, including images (before/after star subtraction) and radial profiles and the Kron apertures. The biases seen in the incremental photometry are now eliminated: The end result is that the Kron photometry now underestimates the total photometry by only ~8%.

Caveats & Final Notes

Although the Kron aperture is now better matched to the physical extent of the galaxy being measured, it is also more susceptible to contaminating stars. The repeatability RMS is correspondingly larger: A potentially more robust "total" flux measure comes from the extrapolation of the radial surface brightness profile. See Extrapolated Photometry.