The Peculiar Motions of Early-type Galaxies in Two Distant Regions. IV. The Photometric Fitting Procedure

The EFAR project is a study of 736 candidate early-type galaxies in 84 clusters lying in two regions toward Hercules-Corona Borealis and Perseus-Cetus at distances cz ≈ 6000-15,000 km s-1. In this paper we describe a new method of galaxy photometry adopted to derive the photometric parameters of the EFAR galaxies. The algorithm fits the circularized surface brightness profiles as the sum of two seeing-convolved components, an R1/4 and an exponential law. This approach allows us to fit the large variety of luminosity profiles displayed by the EFAR galaxies homogeneously and to derive (for at least a subset of these) bulge and disk parameters. Multiple exposures of the same objects are optimally combined and an optional sky-fitting procedure has been developed to correct for sky-subtraction errors. Extensive Monte Carlo simulations are analyzed to test the performance of the algorithm and estimate the size of random and systematic errors. Random errors are small, provided that the global signal-to-noise ratio of the fitted profiles is larger than ≈ 300. Systematic errors can result from (1) errors in the sky subtraction, (2) the limited radial extent of the fitted profiles, (3) the lack of resolution due to seeing convolution and pixel sampling, (4) the use of circularized profiles for very flattened objects seen edge-on, and (5) a poor match of the fitting functions to the object profiles. Large systematic errors are generated by the widely used simple R1/4 law to fit luminosity profiles when a disk component, as small as 20% of the total light, is present. The size of the systematic errors cannot be determined from the shape of the χ2 function near its minimum because extrapolation is involved. Rather, we must estimate them by a set of quality parameters, calibrated against our simulations, which take into account the amount of extrapolation involved to derive the total magnitudes, the size of the sky correction, the average surface brightness of the galaxy relative to the sky, the radial extent of the profile, its signal-to-noise ratio, the seeing value, and the reduced χ2 of the fit. We formulate a combined quality parameter Q, which indicates the expected precision of the fits. Errors in total magnitudes MTOT less than 0.05 mag and in half-luminosity radii Re less than 10% are expected if Q = 1, and less than 0.15 mag and 25% if Q = 2; 89% of the EFAR galaxies have fits with Q = 1 or Q = 2. The errors on the combined fundamental plane quantity FP = log Re-0.3⟨SBe⟩, where ⟨SBe⟩ is the average effective surface brightness, are smaller than 0.03 even if Q = 3. Thus, systematic errors on MTOT and Re only have a marginal effect on the distance estimates that involve FP. We show that the sequence of R1/n profiles, recently used to fit the luminosity profiles of elliptical galaxies, is equivalent (for n ≤ 8) to a subsample of R1/4 and exponential profiles, with appropriate scale lengths and disk-to-bulge ratios. This suggests that the variety of luminosity profiles shown by early-type galaxies may be due to the presence of a disk component.