## Surface Brightness Profiles

The radial surface brightness is carried out for each band per object. The assumptions are as follows: (1) center of object is given by the J-band centroid of the nucleus; (2) the shape of the object is symmetric and remains so throughout; (3) the shape of the object is elliptical and parameterized using the 3-sigma isophote (i.e., elliptical fit to the 3-sigma isophote; see below); for small objects (not particularly relevant to the LGA), the axis ratio is circularized due to the influence of the PSF (see Axis Ratio and Small Radii); (4) mean surface brightness is represented by the median in the pixel distribution found within the elliptical annulus.

Begin with a set of nested elliptical annuli, each of whose width is roughly of size 5%*radius, giving an elliptical annulus width ranging from 1 pixel (small radii) to 100 pixels (large radii). The pixel distribution within each annulus is statistically characterized, including the median, mean and RMS. The median surface brightness (per annulus) is computed, with the radial profile terminated at the point at which the S/N drops below 1*sigma. Two flavors of profiles are computed (per band per object): with and without disk inclination correction. The inclination correction is based on the axis ratio computed from the "super" (J+H+K) 3-sigma isophote.

The radial surface brightness is fit using a modified exponential function (aka Sersic Function). The fit is carried out starting at a point beyond the nucleus and influence of the point-spread-function, and extending down to 2*sigma in the annular S/N statistics. The shape of the radial profile (parameterized using the Sersic Function) is used to determine the "total" size of the object (defined to be four disk scale-lengths in radius).

See also the Photometry and Basic Measurements and Improved Ellipse Fitting and Isophotal Photometry in Crowded Fields.

The LGA includes traditional surface brightness measurements:
mag per arcsec^{2} vs. elliptical radius, and the corresponding
J-K color distribution. An example of a resultant plot is given for
M82.
The upper panel shows the surface brightness profile for each band.
Demarked are the sky noise limits, half-light, isophotal and total
light radii. The lower panel shows the corresponding J-Ks color
distribution, with the radius normalized by the J-band half-light
radius.

The LGA includes the radial profile showing the Sersic fit to the profile. An example of a resultant plot is given for M82. The upper panel shows J band and the lower Ks band. The skynoise, half-light, isophotal, Kron and total light radii are demarked.