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The Petrosian magnitude |
Stored 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.
We define the "Petrosian ratio" RP at a radius
r from
the center of an object to be the ratio of the local surface
brightness in an annulus at r to the mean surface brightness within
r, as described by Blanton et al. 2001a, Yasuda et al. 2001: where I(r) is the azimuthally averaged surface brightness profile.
The Petrosian radius rP is defined as the radius
at which
RP(rP) equals some specified value
RP,lim, set to 0.2 in our case. The
Petrosian flux in any band is then defined as the flux within a
certain number NP (equal to 2.0 in our case) of
r Petrosian radii:  In the SDSS five-band photometry, the aperture in all bands is set by the profile of the galaxy in the r band alone. This procedure ensures that the color measured by comparing the Petrosian flux FP in different bands is measured through a consistent aperture. The aperture 2rP is large enough to contain nearly all of the flux for typical galaxy profiles, but small enough that the sky noise in FP is small. Thus, even substantial errors in rP cause only small errors in the Petrosian flux (typical statistical errors near the spectroscopic flux limit of r ~17.7 are < 5%), although these errors are correlated. The Petrosian radius in each band is the parameter petroRad, and the Petrosian magnitude in each band (calculated, remember, using only petroRad for the r band) is the parameter petroMag.
In practice, there are a number of complications associated with this
definition, because noise, substructure, and the finite size of
objects can cause objects to have no Petrosian radius, or more than
one. Those with more than one are flagged
How well does the Petrosian magnitude perform as a reliable and
complete measure of galaxy flux? Theoretically, the Petrosian
magnitudes defined here should recover essentially all of the flux of
an exponential galaxy profile and about 80% of the flux for a de
Vaucouleurs profile. As shown by Blanton et al. (2001a), this fraction is
fairly constant with axis ratio, while as galaxies become smaller (due
to worse seeing or greater distance) the fraction of light recovered
becomes closer to that fraction measured for a typical PSF, about 95%
in the case of the SDSS. This implies that the fraction of flux
measured for exponential profiles decreases while the fraction of flux
measured for deVaucouleurs profiles increases as a function of
distance. However, for galaxies in the spectroscopic sample
(r<17.7), these effects are small;
the Petrosian radius measured by frames |
