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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
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
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 as MANYPETRO; the largest one is used. Those with none have NOPETRO set. Most commonly, these objects are faint (r > 20.5 or so); the Petrosian ratio becomes unmeasurable before dropping to the limiting value of 0.2; these have PETROFAINT set and have their "Petrosian radii" set to the default value of the larger of 3" or the outermost measured point in the radial profile. Finally, a galaxy with a bright stellar nucleus, such as a Seyfert galaxy, can have a Petrosian radius set by the nucleus alone; in this case, the Petrosian flux misses most of the extended light of the object. This happens quite rarely, but one dramatic example in the EDR data is the Seyfert galaxy NGC 7603 = Arp 092, at RA(2000) = 23:18:56.6, Dec(2000) = +00:14:38.
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 is extraordinarily constant in physical size as a function of redshift.