IV. 2MASS Data Processing

The standard 2MASS aperture is the ellipse fit to the K_s = 20 mag arcsec^-2 isophote, corresponding to roughly 1- of the typical background noise in the K_s images. This aperture is determined using the axis ratio (b/a) and position angle () of the fit to the 3- isophote, allowing the semi-major axis (r₂₀) to vary, so that the mean surface brightness along the ellipse is 20 mag arcsec^-2. The integrated fluxes within this ellipse in the background-subtracted J, H and K_s mosaic images are then calculated.

Large apertures are used to capture the lower surface brightness galaxy flux. We employ two techniques: (1) Kron apertures, and, (2) curve of growth, or extrapolation of the surface brightness profile. A well-behaved radial surface brightness profile provides a means for recovering the flux lost in the background noise. Fortunately in the near-infrared, galaxies are, for the most part, smooth and axisymmetric (cf. Jarrett 2000). Deducing the "total" flux, with robust repeatability, is therefore possible using large apertures (e.g., Kron) and curve-of-growth techniques.

The Kron (1980) aperture corresponds to a scaling of the intensity-weighted first moment radius. It was designed to robustly measure the integrated flux of a galaxy. In an attempt to recover most of the underlying flux of the galaxy, we define the Kron radius to be 2.5 times the first moment radius, consistent with the scaling used by the 2MASS and DENIS projects (see also Bertin & Arnouts 1996). The first-moment itself is computed from an area that is large enough to incorporate the total flux of the galaxy. This "total" aperture is determined from the radial light distribution, which is constructed from the median surface brightness computed within elliptical annuli centered on the galaxy (see Jarrett et al. 2000 for more details). We define the "total" aperture radius, r_tot, to be the point at which the surface brightness extends down to about four disk scale lengths, detailed below.

We employ what is effectively a Sersic (1968) modified exponential function to trace the elliptical radial light distribution,

f = f₀ * [exp (-r / )^{1 /} ],

where r is the radius (semi-major axis), f₀ is the central surface brightness, and and are the scale length parameters. In practice, the 2MASS PSF completely dominates the radial surface profile for small radii (r < 5´´), so the exponential function is only fit to those points beyond the PSF and nuclear influence. The fit extends from r >> 5´´ to the point at which the SNR > 2. The best fit is weighted by the SNR, as we solve for the scale length parameters and central surface brightness. The number of degrees of freedom in the fit is n/(2-3), where n is the number of points in the radial distribution, the "2" comes from the correlated pixels (frame-to-coadd conversion) and the "3" is the number of parameters. The final reduced ² represents the goodness-of-fit, or alternatively, the deviation from the assumed Sersic model.

For the first moment calculation, we adopt an effective integration radius of the total aperture, r_tot, that corresponds to about four scale lengths. For a pure exponential disk, = 1, thus fixing f/f₀ = 55. It then follows that the total integration radius is

r_tot = r' + [ * ln (55)]

where r' is the starting point radius (typically > 5-10´´). For robustness, the total aperture radius is not allowed to exceed five times the isophotal radius, r₂₀. The intensity-weighted first moment radius, r₁, is computed from the aperture delimited by r_tot. The Kron radius, r_Kron, is then 2.5 * r₁. In this way, the Kron aperture is closely tied to the measured radial light distribution and, thus, represents an integrated flux metric. On the downside, the relatively large Kron aperture, compared to the isophotal aperture is much more sensitive to stellar contamination and other deleterious effects of the background.

For the curve-of-growth technique, the approach is to integrate the radial surface brightness profile, with the lower radial boundary given by the 20 mag arcsec^-2 isophotal radius and the upper boundary delimited by the shape of the profile. As noted above, we adopt about four disk scale lengths as the delimiting boundary, r_tot, representing the full diameter of a "normal" galaxy. This integration, or extrapolation of the profile to low SNR extents, recovers the underlying flux of the galaxy, which in combination with the isophotal photometry, leads to the "total" flux of the galaxy. Hence, we will refer to this photometry as the "total" aperture photometry (not to be confused with the Kron aperture photometry). For consistency across bands, we adopt the J-band integration limit, r_tot (see above), for all three bands, since the J-band images are the most sensitive to the low surface brightness galaxy signal (J = 21.4 mag at 1 ) and consequently lead to the most precise radial surface brightness profile. The only exception to this rule is for the heavily obscured, reddened galaxies seen behind the Milky Way (e.g., Maffei 2 and the Circinus galaxy), where we instead use the K_s-band surface brightness to deduce the r_tot extent of the galaxy.

To summarize, for the curve-of-growth technique, we quote one integration radius, r_tot, common to all three bands, and radial surface brightness solutions for each band, reduced ² fit for each band, and the integrated magnitude for each band. For the estimated uncertainty in the magnitudes, we root-square-sum the formal errors associated with the background removal, the isophotal photometry uncertainty, the ellipse fit to the 3- isophote, and the fit to the radial surface brightness distribution (details given in appendices of Jarrett et al. 2000).

The de Vaucouleurs "effective" aperture measures the galaxy half-light, as computed from the "total" flux. For the total flux, we adopt the surface brightness profile extrapolation method. Using the elliptical shape of the galaxy, we integrate in small annular steps starting from the center (r > 5´´), until we reach the integrated half-light point. We then interpolate across the surface brightness profile to arrive at a more precise half-light radius. We report the half-light radius for each band, and the corresponding half-light mean surface brightness (in units of mag arcsec^-2). We do not correct for PSF effects: For small galaxies, the half-light radius is susceptible to circularizing effects from the PSF, although this is generally not a concern for the Large Galaxy Atlas.

The concentration index characterizes the nuclear-to-bulge concentration of the galaxy. The index corresponds to the ratio of the three-quarter light-radius to the one-quarter light-radius (the de Vaucouleurs convention). These radial points are derived in a similar fashion as to the half-light radius.