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magnitude, PetrosianStored as petroMag. For galaxy photometry, measuring flux is more difficult than for stars, because galaxies do not all have the same radial surface brightness profile, and have no sharp edges. In order to avoid biases, we wish to measure a constant fraction of the total light, independent of the position and distance of the object. To satisfy these requirements, the SDSS has adopted a modified form of the Petrosian (1976) system, measuring galaxy fluxes within a circular aperture whose radius is defined by the shape of the azimuthally averaged light profile.
profileAn azimuthally-averaged radial surface brightness profile. In the catalogs, it is given as the average surface brightness in a series of annuli. This quantity is in units of maggies per square arcsec. The number of annuli for which there is a measurable signal is listed as nprof, the mean surface brightness is listed as profMean, and the error is listed as profErr. This error includes both photon noise, and the small-scale "bumpiness" in the counts as a function of azimuthal angle.
When converting the profMean values to a local surface brightness, it is not the best approach to assign the mean surface brightness to some radius within the annulus and then linearly interpolate between radial bins. Do not use smoothing splines, as they will not go through the points in the cumulative profile and thus (obviously) will not conserve flux. What frames pipeline does, e.g., in determining the Petrosian ratio, is to fit a taut spline to the cumulative profile and then differentiate that spline fit, after transforming both the radii and cumulative profiles with asinh functions. We recommend doing the same here.
surface brightnessThe frames pipeline also reports the radii containing 50% and 90% of the Petrosian flux for each band, petroR50 and petroR90 respectively. The usual characterization of surface-brightness in the target selection pipeline of the SDSS is the mean surface brightness within petroR50.
It turns out that the ratio of petroR50 to petroR90, the so-called "inverse concentration index", is correlated with morphology (Shimasaku et al. 2001, Strateva et al. 2001). Galaxies with a de Vaucouleurs profile have an inverse concentration index of around 0.3; exponential galaxies have an inverse concentration index of around 0.43. Thus, this parameter can be used as a simple morphological classifier.
An important caveat when using these quantities is that they are not corrected for seeing. This causes the surface brightness to be underestimated, and the inverse concentration index to be overestimated, for objects of size comparable to the PSF. The amplitudes of these effects, however, are not yet well characterized.