THE PECULIAR MOTIONS OF EARLY-TYPE GALAXIES IN 2 DISTANT REGIONS .4. 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 Per seus-Cetus at distances cz approximate to 6000-15,000 km s(-1). In thi s paper we describe a new method of galaxy photometry adopted to deriv e the photometric parameters of the EFAR galaxies. The algorithm fits the circularized surface brightness profiles as the sum of two seeing- convolved components, an R(1/4) 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 ob jects 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 algorit hm and estimate the size of random and systematic errors. Random error s are small, provided that the global signal-to-noise ratio of the fit ted profiles is larger than approximate to 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 seei ng convolution and pixel sampling, (4) the use of circularized profile s 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 R(1/4) law to fit luminosity prof iles when a disk component, as small as 20% of the total light, is pre sent. The size of the systematic errors cannot be determined from the shape of the chi(2) 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 amou nt of extrapolation involved to derive the total magnitudes, the size of the sky correction, the average surface brightness of the galaxy re lative to the sky, the radial extent of the profile, its signal-to-noi se ratio, the seeing value, and the reduced chi(2) Of the st. We formu late a combined quality parameter Q, which indicates the expected prec ision of the fits. Errors in total magnitudes M(TOT) less than 0.05 ma g and in half-luminosity radii R(e) less than 10% are expected if Q = 1, and less than 0.15 mag and 25% if e = 2; 89% of the EFAR galaxies h ave fits with e = 1 or e = 2. The errors on the combined fundamental p lane quantity FP = log R(e) -0.3[SBe], where [SBe] is the average effe ctive surface brightness, are smaller than 0.03 even if Q = 3. Thus, s ystematic errors on M(TOT) and R(e) only have a marginal effect on the distance estimates that involve FP. We show that the sequence of R(1/ n) profiles, recently used to ht the luminosity profiles of elliptical galaxies, is equivalent (for n less than or equal to 8) to a subsampl e of R(1/4) and exponential profiles, with appropriate scale lengths a nd 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.