Simulations

The galaxy models that have been extensively tested include an exponential law, meant to represent a disk galaxy, and an law, representing ellipticals. Both are fully described by six adjustable parameters: total magnitude, half-light radius, axis ratio, position angle, and the coordinates of the center. When both fits are performed on a simulated image of either kind, the value of the likelihood function is very effective in choosing the ``right'' model down to typical magnitudes of or with a single-orbit WFPC exposure, and about one magnitude fainter with the expected parameters for WFPC 2 observations (see Table 1). (Six orbits are required to reach one magnitude fainter with either camera.)

Fits can be successfully performed for fainter galaxies, but at one magnitude fainter than the value in Table 1, the ability to discriminate between models is substantially impaired, and therefore the fitted half-light radius may be biased by the model adopted. Not surprisingly, the bias is smaller than the error in the estimated parameters.

In order to fit more complex models successfully, better signal-to-noise ratio is required. Typically, we estimate that the image must be one magnitude brighter for each additional parameter to be fitted. An additional complication arises for combined models consisting of an exponential (disk) and an law (bulge) together. We find that the magnitude difference between the disk and the bulge correlates strongly with the ratio of their sizes, even for bright simulated images. This indicates that an image fit has poor leverage to determine the parameters of the two components independently.

We note also that stellar images can be easily fitted about two magnitudes fainter than the limits in the table, thanks to the smaller number of free parameters. However, we have not investigated the effects of errors in the PSF, which may have a greater impact on stellar than on galaxy images. Such issues have been discussed extensively for stellar photometry packages that use the fitting approach, such as DAOPHOT.